%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP181-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n019.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 10:37:33 EDT 2022

% Result   : Unsatisfiable 41.82s 42.05s
% Output   : CNFRefutation 42.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   98
%            Number of leaves      :  593
% Syntax   : Number of clauses     : 2827 (1440 unt;   0 nHn;1635 RR)
%            Number of literals    : 4821 (4820 equ;1996 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   : 4439 (  93 sgn)

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

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

cnf(associativity,axiom,
    multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).

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(idempotence_of_gld,axiom,
    greatest_lower_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(monotony_glb2,axiom,
    multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).

cnf(p12_1,hypothesis,
    inverse(identity) = identity ).

cnf(p12_2,hypothesis,
    inverse(inverse(X)) = X ).

cnf(p12_3,hypothesis,
    inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ).

cnf(p12_4,hypothesis,
    greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ).

cnf(p12_5,hypothesis,
    least_upper_bound(a,c) = least_upper_bound(b,c) ).

cnf(prove_p12,negated_conjecture,
    a != b ).

cnf(refute_0_0,plain,
    inverse(multiply(inverse(X_83),multiply(X_83,X_84))) = multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))),
    inference(subst,[],[p12_3:[bind(X,$fot(inverse(X_83))),bind(Y,$fot(multiply(X_83,X_84)))]]) ).

cnf(refute_0_1,plain,
    multiply(multiply(inverse(X_81),X_81),X_82) = multiply(inverse(X_81),multiply(X_81,X_82)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_81))),bind(Y,$fot(X_81)),bind(Z,$fot(X_82))]]) ).

cnf(refute_0_2,plain,
    multiply(inverse(X_81),X_81) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_81))]]) ).

cnf(refute_0_3,plain,
    ( multiply(multiply(inverse(X_81),X_81),X_82) != multiply(inverse(X_81),multiply(X_81,X_82))
    | multiply(inverse(X_81),X_81) != identity
    | multiply(identity,X_82) = multiply(inverse(X_81),multiply(X_81,X_82)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_81),X_81),X_82),multiply(inverse(X_81),multiply(X_81,X_82))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_4,plain,
    ( multiply(multiply(inverse(X_81),X_81),X_82) != multiply(inverse(X_81),multiply(X_81,X_82))
    | multiply(identity,X_82) = multiply(inverse(X_81),multiply(X_81,X_82)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_81),X_81),identity) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    multiply(identity,X_82) = multiply(inverse(X_81),multiply(X_81,X_82)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_81),X_81),X_82),multiply(inverse(X_81),multiply(X_81,X_82))) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    multiply(identity,X_82) = X_82,
    inference(subst,[],[left_identity:[bind(X,$fot(X_82))]]) ).

cnf(refute_0_7,plain,
    ( multiply(identity,X_82) != X_82
    | multiply(identity,X_82) != multiply(inverse(X_81),multiply(X_81,X_82))
    | X_82 = multiply(inverse(X_81),multiply(X_81,X_82)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_82),multiply(inverse(X_81),multiply(X_81,X_82))) ),[0],$fot(X_82)]]) ).

cnf(refute_0_8,plain,
    ( multiply(identity,X_82) != multiply(inverse(X_81),multiply(X_81,X_82))
    | X_82 = multiply(inverse(X_81),multiply(X_81,X_82)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_82),X_82) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    X_82 = multiply(inverse(X_81),multiply(X_81,X_82)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_82),multiply(inverse(X_81),multiply(X_81,X_82))) )],[refute_0_5,refute_0_8]) ).

cnf(refute_0_10,plain,
    X_84 = multiply(inverse(X_83),multiply(X_83,X_84)),
    inference(subst,[],[refute_0_9:[bind(X_81,$fot(X_83)),bind(X_82,$fot(X_84))]]) ).

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

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

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

cnf(refute_0_14,plain,
    ( X_84 != multiply(inverse(X_83),multiply(X_83,X_84))
    | multiply(inverse(X_83),multiply(X_83,X_84)) = X_84 ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(X_84)),bind(Y0,$fot(multiply(inverse(X_83),multiply(X_83,X_84))))]]) ).

cnf(refute_0_15,plain,
    multiply(inverse(X_83),multiply(X_83,X_84)) = X_84,
    inference(resolve,[$cnf( $equal(X_84,multiply(inverse(X_83),multiply(X_83,X_84))) )],[refute_0_10,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( multiply(inverse(X_83),multiply(X_83,X_84)) != X_84
    | inverse(multiply(inverse(X_83),multiply(X_83,X_84))) != multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83)))
    | inverse(X_84) = multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_83),multiply(X_83,X_84))),multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83)))) ),[0,0],$fot(X_84)]]) ).

cnf(refute_0_17,plain,
    ( inverse(multiply(inverse(X_83),multiply(X_83,X_84))) != multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83)))
    | inverse(X_84) = multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_83),multiply(X_83,X_84)),X_84) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    inverse(X_84) = multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_83),multiply(X_83,X_84))),multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83)))) )],[refute_0_0,refute_0_17]) ).

cnf(refute_0_19,plain,
    inverse(multiply(inverse(X),X_18)) = multiply(inverse(X_18),inverse(inverse(X))),
    inference(subst,[],[p12_3:[bind(X,$fot(inverse(X))),bind(Y,$fot(X_18))]]) ).

cnf(refute_0_20,plain,
    ( inverse(multiply(inverse(X),X_18)) != multiply(inverse(X_18),inverse(inverse(X)))
    | inverse(inverse(X)) != X
    | inverse(multiply(inverse(X),X_18)) = multiply(inverse(X_18),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),X_18)),multiply(inverse(X_18),inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).

cnf(refute_0_21,plain,
    ( inverse(multiply(inverse(X),X_18)) != multiply(inverse(X_18),inverse(inverse(X)))
    | inverse(multiply(inverse(X),X_18)) = multiply(inverse(X_18),X) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p12_2,refute_0_20]) ).

cnf(refute_0_22,plain,
    inverse(multiply(inverse(X),X_18)) = multiply(inverse(X_18),X),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),X_18)),multiply(inverse(X_18),inverse(inverse(X)))) )],[refute_0_19,refute_0_21]) ).

cnf(refute_0_23,plain,
    inverse(multiply(inverse(X_83),multiply(X_83,X_84))) = multiply(inverse(multiply(X_83,X_84)),X_83),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_83)),bind(X_18,$fot(multiply(X_83,X_84)))]]) ).

cnf(refute_0_24,plain,
    ( inverse(multiply(X,Y)) != multiply(inverse(Y),inverse(X))
    | multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(inverse(Y),inverse(X))))]]) ).

cnf(refute_0_25,plain,
    multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))) )],[p12_3,refute_0_24]) ).

cnf(refute_0_26,plain,
    multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))) = inverse(multiply(inverse(X_83),multiply(X_83,X_84))),
    inference(subst,[],[refute_0_25:[bind(X,$fot(inverse(X_83))),bind(Y,$fot(multiply(X_83,X_84)))]]) ).

cnf(refute_0_27,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_28,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_13,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))) != inverse(multiply(inverse(X_83),multiply(X_83,X_84)))
    | inverse(multiply(inverse(X_83),multiply(X_83,X_84))) != multiply(inverse(multiply(X_83,X_84)),X_83)
    | multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))) = multiply(inverse(multiply(X_83,X_84)),X_83) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))))),bind(Y0,$fot(inverse(multiply(inverse(X_83),multiply(X_83,X_84))))),bind(Z0,$fot(multiply(inverse(multiply(X_83,X_84)),X_83)))]]) ).

cnf(refute_0_30,plain,
    ( inverse(multiply(inverse(X_83),multiply(X_83,X_84))) != multiply(inverse(multiply(X_83,X_84)),X_83)
    | multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))) = multiply(inverse(multiply(X_83,X_84)),X_83) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))),inverse(multiply(inverse(X_83),multiply(X_83,X_84)))) )],[refute_0_26,refute_0_29]) ).

cnf(refute_0_31,plain,
    multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))) = multiply(inverse(multiply(X_83,X_84)),X_83),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_83),multiply(X_83,X_84))),multiply(inverse(multiply(X_83,X_84)),X_83)) )],[refute_0_23,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))) != multiply(inverse(multiply(X_83,X_84)),X_83)
    | inverse(X_84) != multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83)))
    | inverse(X_84) = multiply(inverse(multiply(X_83,X_84)),X_83) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(X_84),multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83)))) ),[1],$fot(multiply(inverse(multiply(X_83,X_84)),X_83))]]) ).

cnf(refute_0_33,plain,
    ( inverse(X_84) != multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83)))
    | inverse(X_84) = multiply(inverse(multiply(X_83,X_84)),X_83) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83))),multiply(inverse(multiply(X_83,X_84)),X_83)) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    inverse(X_84) = multiply(inverse(multiply(X_83,X_84)),X_83),
    inference(resolve,[$cnf( $equal(inverse(X_84),multiply(inverse(multiply(X_83,X_84)),inverse(inverse(X_83)))) )],[refute_0_18,refute_0_33]) ).

cnf(refute_0_35,plain,
    inverse(greatest_lower_bound(X_107,inverse(X_83))) = multiply(inverse(multiply(X_83,greatest_lower_bound(X_107,inverse(X_83)))),X_83),
    inference(subst,[],[refute_0_34:[bind(X_84,$fot(greatest_lower_bound(X_107,inverse(X_83))))]]) ).

cnf(refute_0_36,plain,
    multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))) = greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,inverse(X_103))),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_103)),bind(Y,$fot(X_104)),bind(Z,$fot(inverse(X_103)))]]) ).

cnf(refute_0_37,plain,
    multiply(inverse(inverse(X)),inverse(X)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X)))]]) ).

cnf(refute_0_38,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_39,plain,
    ( multiply(inverse(inverse(X)),inverse(X)) != identity
    | multiply(X,inverse(X)) = identity ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p12_2,refute_0_38]) ).

cnf(refute_0_40,plain,
    multiply(X,inverse(X)) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X)),inverse(X)),identity) )],[refute_0_37,refute_0_39]) ).

cnf(refute_0_41,plain,
    multiply(X_103,inverse(X_103)) = identity,
    inference(subst,[],[refute_0_40:[bind(X,$fot(X_103))]]) ).

cnf(refute_0_42,plain,
    ( multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))) != greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,inverse(X_103)))
    | multiply(X_103,inverse(X_103)) != identity
    | multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))) = greatest_lower_bound(multiply(X_103,X_104),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))),greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,inverse(X_103)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_43,plain,
    ( multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))) != greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,inverse(X_103)))
    | multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))) = greatest_lower_bound(multiply(X_103,X_104),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_103,inverse(X_103)),identity) )],[refute_0_41,refute_0_42]) ).

cnf(refute_0_44,plain,
    multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))) = greatest_lower_bound(multiply(X_103,X_104),identity),
    inference(resolve,[$cnf( $equal(multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))),greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,inverse(X_103)))) )],[refute_0_36,refute_0_43]) ).

cnf(refute_0_45,plain,
    ( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
    | greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).

cnf(refute_0_46,plain,
    greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_45]) ).

cnf(refute_0_47,plain,
    greatest_lower_bound(multiply(X_103,X_104),identity) = greatest_lower_bound(identity,multiply(X_103,X_104)),
    inference(subst,[],[refute_0_46:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_103,X_104)))]]) ).

cnf(refute_0_48,plain,
    ( multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))) != greatest_lower_bound(multiply(X_103,X_104),identity)
    | greatest_lower_bound(multiply(X_103,X_104),identity) != greatest_lower_bound(identity,multiply(X_103,X_104))
    | multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))) = greatest_lower_bound(identity,multiply(X_103,X_104)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))),greatest_lower_bound(identity,multiply(X_103,X_104))) ),[0],$fot(greatest_lower_bound(multiply(X_103,X_104),identity))]]) ).

cnf(refute_0_49,plain,
    ( multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))) != greatest_lower_bound(multiply(X_103,X_104),identity)
    | multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))) = greatest_lower_bound(identity,multiply(X_103,X_104)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_103,X_104),identity),greatest_lower_bound(identity,multiply(X_103,X_104))) )],[refute_0_47,refute_0_48]) ).

cnf(refute_0_50,plain,
    multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))) = greatest_lower_bound(identity,multiply(X_103,X_104)),
    inference(resolve,[$cnf( $equal(multiply(X_103,greatest_lower_bound(X_104,inverse(X_103))),greatest_lower_bound(multiply(X_103,X_104),identity)) )],[refute_0_44,refute_0_49]) ).

cnf(refute_0_51,plain,
    multiply(X_83,greatest_lower_bound(X_107,inverse(X_83))) = greatest_lower_bound(identity,multiply(X_83,X_107)),
    inference(subst,[],[refute_0_50:[bind(X_103,$fot(X_83)),bind(X_104,$fot(X_107))]]) ).

cnf(refute_0_52,plain,
    ( multiply(X_83,greatest_lower_bound(X_107,inverse(X_83))) != greatest_lower_bound(identity,multiply(X_83,X_107))
    | inverse(greatest_lower_bound(X_107,inverse(X_83))) != multiply(inverse(multiply(X_83,greatest_lower_bound(X_107,inverse(X_83)))),X_83)
    | inverse(greatest_lower_bound(X_107,inverse(X_83))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_83,X_107))),X_83) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_107,inverse(X_83))),multiply(inverse(multiply(X_83,greatest_lower_bound(X_107,inverse(X_83)))),X_83)) ),[1,0,0],$fot(greatest_lower_bound(identity,multiply(X_83,X_107)))]]) ).

cnf(refute_0_53,plain,
    ( inverse(greatest_lower_bound(X_107,inverse(X_83))) != multiply(inverse(multiply(X_83,greatest_lower_bound(X_107,inverse(X_83)))),X_83)
    | inverse(greatest_lower_bound(X_107,inverse(X_83))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_83,X_107))),X_83) ),
    inference(resolve,[$cnf( $equal(multiply(X_83,greatest_lower_bound(X_107,inverse(X_83))),greatest_lower_bound(identity,multiply(X_83,X_107))) )],[refute_0_51,refute_0_52]) ).

cnf(refute_0_54,plain,
    inverse(greatest_lower_bound(X_107,inverse(X_83))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_83,X_107))),X_83),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_107,inverse(X_83))),multiply(inverse(multiply(X_83,greatest_lower_bound(X_107,inverse(X_83)))),X_83)) )],[refute_0_35,refute_0_53]) ).

cnf(refute_0_55,plain,
    inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))) = multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(a,b),inverse(b)))),greatest_lower_bound(a,b)),
    inference(subst,[],[refute_0_54:[bind(X_107,$fot(inverse(b))),bind(X_83,$fot(greatest_lower_bound(a,b)))]]) ).

cnf(refute_0_56,plain,
    multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) = greatest_lower_bound(multiply(X_134,inverse(X_135)),multiply(X_135,inverse(X_135))),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_135))),bind(Y,$fot(X_134)),bind(Z,$fot(X_135))]]) ).

cnf(refute_0_57,plain,
    multiply(X_135,inverse(X_135)) = identity,
    inference(subst,[],[refute_0_40:[bind(X,$fot(X_135))]]) ).

cnf(refute_0_58,plain,
    ( multiply(X_135,inverse(X_135)) != identity
    | multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) != greatest_lower_bound(multiply(X_134,inverse(X_135)),multiply(X_135,inverse(X_135)))
    | multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) = greatest_lower_bound(multiply(X_134,inverse(X_135)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)),greatest_lower_bound(multiply(X_134,inverse(X_135)),multiply(X_135,inverse(X_135)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_59,plain,
    ( multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) != greatest_lower_bound(multiply(X_134,inverse(X_135)),multiply(X_135,inverse(X_135)))
    | multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) = greatest_lower_bound(multiply(X_134,inverse(X_135)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_135,inverse(X_135)),identity) )],[refute_0_57,refute_0_58]) ).

cnf(refute_0_60,plain,
    multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) = greatest_lower_bound(multiply(X_134,inverse(X_135)),identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)),greatest_lower_bound(multiply(X_134,inverse(X_135)),multiply(X_135,inverse(X_135)))) )],[refute_0_56,refute_0_59]) ).

cnf(refute_0_61,plain,
    greatest_lower_bound(multiply(X_134,inverse(X_135)),identity) = greatest_lower_bound(identity,multiply(X_134,inverse(X_135))),
    inference(subst,[],[refute_0_46:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_134,inverse(X_135))))]]) ).

cnf(refute_0_62,plain,
    ( multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) != greatest_lower_bound(multiply(X_134,inverse(X_135)),identity)
    | greatest_lower_bound(multiply(X_134,inverse(X_135)),identity) != greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))
    | multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) = greatest_lower_bound(identity,multiply(X_134,inverse(X_135))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)),greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) ),[0],$fot(greatest_lower_bound(multiply(X_134,inverse(X_135)),identity))]]) ).

cnf(refute_0_63,plain,
    ( multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) != greatest_lower_bound(multiply(X_134,inverse(X_135)),identity)
    | multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) = greatest_lower_bound(identity,multiply(X_134,inverse(X_135))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_134,inverse(X_135)),identity),greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) )],[refute_0_61,refute_0_62]) ).

cnf(refute_0_64,plain,
    multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) = greatest_lower_bound(identity,multiply(X_134,inverse(X_135))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)),greatest_lower_bound(multiply(X_134,inverse(X_135)),identity)) )],[refute_0_60,refute_0_63]) ).

cnf(refute_0_65,plain,
    multiply(greatest_lower_bound(X_140,greatest_lower_bound(Y,X_140)),inverse(greatest_lower_bound(Y,X_140))) = greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140)))),
    inference(subst,[],[refute_0_64:[bind(X_134,$fot(X_140)),bind(X_135,$fot(greatest_lower_bound(Y,X_140)))]]) ).

cnf(refute_0_66,plain,
    greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) = X_12,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).

cnf(refute_0_67,plain,
    least_upper_bound(X_13,X_12) = least_upper_bound(X_12,X_13),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).

cnf(refute_0_68,plain,
    ( least_upper_bound(X_13,X_12) != least_upper_bound(X_12,X_13)
    | least_upper_bound(X_12,X_13) = least_upper_bound(X_13,X_12) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_13,X_12))),bind(Y0,$fot(least_upper_bound(X_12,X_13)))]]) ).

cnf(refute_0_69,plain,
    least_upper_bound(X_12,X_13) = least_upper_bound(X_13,X_12),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_13,X_12),least_upper_bound(X_12,X_13)) )],[refute_0_67,refute_0_68]) ).

cnf(refute_0_70,plain,
    ( greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) != X_12
    | least_upper_bound(X_12,X_13) != least_upper_bound(X_13,X_12)
    | greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12 ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)),X_12) ),[0,1],$fot(least_upper_bound(X_13,X_12))]]) ).

cnf(refute_0_71,plain,
    ( greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) != X_12
    | greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12 ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_12,X_13),least_upper_bound(X_13,X_12)) )],[refute_0_69,refute_0_70]) ).

cnf(refute_0_72,plain,
    greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)),X_12) )],[refute_0_66,refute_0_71]) ).

cnf(refute_0_73,plain,
    greatest_lower_bound(greatest_lower_bound(X_30,Y),least_upper_bound(X_30,greatest_lower_bound(X_30,Y))) = greatest_lower_bound(X_30,Y),
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(greatest_lower_bound(X_30,Y))),bind(X_13,$fot(X_30))]]) ).

cnf(refute_0_74,plain,
    least_upper_bound(X_30,greatest_lower_bound(X_30,Y)) = X_30,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_30))]]) ).

cnf(refute_0_75,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_30,Y),least_upper_bound(X_30,greatest_lower_bound(X_30,Y))) != greatest_lower_bound(X_30,Y)
    | least_upper_bound(X_30,greatest_lower_bound(X_30,Y)) != X_30
    | greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) = greatest_lower_bound(X_30,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,Y),least_upper_bound(X_30,greatest_lower_bound(X_30,Y))),greatest_lower_bound(X_30,Y)) ),[0,1],$fot(X_30)]]) ).

cnf(refute_0_76,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_30,Y),least_upper_bound(X_30,greatest_lower_bound(X_30,Y))) != greatest_lower_bound(X_30,Y)
    | greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) = greatest_lower_bound(X_30,Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_30,greatest_lower_bound(X_30,Y)),X_30) )],[refute_0_74,refute_0_75]) ).

cnf(refute_0_77,plain,
    greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) = greatest_lower_bound(X_30,Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,Y),least_upper_bound(X_30,greatest_lower_bound(X_30,Y))),greatest_lower_bound(X_30,Y)) )],[refute_0_73,refute_0_76]) ).

cnf(refute_0_78,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_13:[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_79,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_78]) ).

cnf(refute_0_80,plain,
    greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) = greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_30)),bind(Z,$fot(X_30))]]) ).

cnf(refute_0_81,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) != greatest_lower_bound(X_30,Y)
    | greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) != greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30))
    | greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30)) = greatest_lower_bound(X_30,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30),greatest_lower_bound(X_30,Y)) ),[0],$fot(greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30)))]]) ).

cnf(refute_0_82,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30) != greatest_lower_bound(X_30,Y)
    | greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30)) = greatest_lower_bound(X_30,Y) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30),greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30))) )],[refute_0_80,refute_0_81]) ).

cnf(refute_0_83,plain,
    greatest_lower_bound(X_30,greatest_lower_bound(Y,X_30)) = greatest_lower_bound(X_30,Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_30,Y),X_30),greatest_lower_bound(X_30,Y)) )],[refute_0_77,refute_0_82]) ).

cnf(refute_0_84,plain,
    greatest_lower_bound(X_140,greatest_lower_bound(Y,X_140)) = greatest_lower_bound(X_140,Y),
    inference(subst,[],[refute_0_83:[bind(X_30,$fot(X_140))]]) ).

cnf(refute_0_85,plain,
    ( multiply(greatest_lower_bound(X_140,greatest_lower_bound(Y,X_140)),inverse(greatest_lower_bound(Y,X_140))) != greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140))))
    | greatest_lower_bound(X_140,greatest_lower_bound(Y,X_140)) != greatest_lower_bound(X_140,Y)
    | multiply(greatest_lower_bound(X_140,Y),inverse(greatest_lower_bound(Y,X_140))) = greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_140,greatest_lower_bound(Y,X_140)),inverse(greatest_lower_bound(Y,X_140))),greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140))))) ),[0,0],$fot(greatest_lower_bound(X_140,Y))]]) ).

cnf(refute_0_86,plain,
    ( multiply(greatest_lower_bound(X_140,greatest_lower_bound(Y,X_140)),inverse(greatest_lower_bound(Y,X_140))) != greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140))))
    | multiply(greatest_lower_bound(X_140,Y),inverse(greatest_lower_bound(Y,X_140))) = greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_140,greatest_lower_bound(Y,X_140)),greatest_lower_bound(X_140,Y)) )],[refute_0_84,refute_0_85]) ).

cnf(refute_0_87,plain,
    multiply(greatest_lower_bound(X_140,Y),inverse(greatest_lower_bound(Y,X_140))) = greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_140,greatest_lower_bound(Y,X_140)),inverse(greatest_lower_bound(Y,X_140))),greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140))))) )],[refute_0_65,refute_0_86]) ).

cnf(refute_0_88,plain,
    multiply(greatest_lower_bound(X_115,X_116),inverse(greatest_lower_bound(X_115,X_116))) = identity,
    inference(subst,[],[refute_0_40:[bind(X,$fot(greatest_lower_bound(X_115,X_116)))]]) ).

cnf(refute_0_89,plain,
    inverse(greatest_lower_bound(X_112,X_113)) = multiply(inverse(multiply(inverse(X_112),greatest_lower_bound(X_112,X_113))),inverse(X_112)),
    inference(subst,[],[refute_0_34:[bind(X_83,$fot(inverse(X_112))),bind(X_84,$fot(greatest_lower_bound(X_112,X_113)))]]) ).

cnf(refute_0_90,plain,
    multiply(inverse(X_104),greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(multiply(inverse(X_104),X_104),multiply(inverse(X_104),X_105)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_104))),bind(Y,$fot(X_104)),bind(Z,$fot(X_105))]]) ).

cnf(refute_0_91,plain,
    multiply(inverse(X_104),X_104) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_104))]]) ).

cnf(refute_0_92,plain,
    ( multiply(inverse(X_104),X_104) != identity
    | multiply(inverse(X_104),greatest_lower_bound(X_104,X_105)) != greatest_lower_bound(multiply(inverse(X_104),X_104),multiply(inverse(X_104),X_105))
    | multiply(inverse(X_104),greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(identity,multiply(inverse(X_104),X_105)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_104),greatest_lower_bound(X_104,X_105)),greatest_lower_bound(multiply(inverse(X_104),X_104),multiply(inverse(X_104),X_105))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_93,plain,
    ( multiply(inverse(X_104),greatest_lower_bound(X_104,X_105)) != greatest_lower_bound(multiply(inverse(X_104),X_104),multiply(inverse(X_104),X_105))
    | multiply(inverse(X_104),greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(identity,multiply(inverse(X_104),X_105)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_104),X_104),identity) )],[refute_0_91,refute_0_92]) ).

cnf(refute_0_94,plain,
    multiply(inverse(X_104),greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(identity,multiply(inverse(X_104),X_105)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_104),greatest_lower_bound(X_104,X_105)),greatest_lower_bound(multiply(inverse(X_104),X_104),multiply(inverse(X_104),X_105))) )],[refute_0_90,refute_0_93]) ).

cnf(refute_0_95,plain,
    multiply(inverse(X_112),greatest_lower_bound(X_112,X_113)) = greatest_lower_bound(identity,multiply(inverse(X_112),X_113)),
    inference(subst,[],[refute_0_94:[bind(X_104,$fot(X_112)),bind(X_105,$fot(X_113))]]) ).

cnf(refute_0_96,plain,
    ( multiply(inverse(X_112),greatest_lower_bound(X_112,X_113)) != greatest_lower_bound(identity,multiply(inverse(X_112),X_113))
    | inverse(greatest_lower_bound(X_112,X_113)) != multiply(inverse(multiply(inverse(X_112),greatest_lower_bound(X_112,X_113))),inverse(X_112))
    | inverse(greatest_lower_bound(X_112,X_113)) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_112,X_113)),multiply(inverse(multiply(inverse(X_112),greatest_lower_bound(X_112,X_113))),inverse(X_112))) ),[1,0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_112),X_113)))]]) ).

cnf(refute_0_97,plain,
    ( inverse(greatest_lower_bound(X_112,X_113)) != multiply(inverse(multiply(inverse(X_112),greatest_lower_bound(X_112,X_113))),inverse(X_112))
    | inverse(greatest_lower_bound(X_112,X_113)) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_112),greatest_lower_bound(X_112,X_113)),greatest_lower_bound(identity,multiply(inverse(X_112),X_113))) )],[refute_0_95,refute_0_96]) ).

cnf(refute_0_98,plain,
    inverse(greatest_lower_bound(X_112,X_113)) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_112,X_113)),multiply(inverse(multiply(inverse(X_112),greatest_lower_bound(X_112,X_113))),inverse(X_112))) )],[refute_0_89,refute_0_97]) ).

cnf(refute_0_99,plain,
    inverse(inverse(X_112)) = X_112,
    inference(subst,[],[p12_2:[bind(X,$fot(X_112))]]) ).

cnf(refute_0_100,plain,
    greatest_lower_bound(X_113,inverse(inverse(X_112))) = greatest_lower_bound(X_113,inverse(inverse(X_112))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_113,inverse(inverse(X_112))))]]) ).

cnf(refute_0_101,plain,
    ( greatest_lower_bound(X_113,inverse(inverse(X_112))) != greatest_lower_bound(X_113,inverse(inverse(X_112)))
    | inverse(inverse(X_112)) != X_112
    | greatest_lower_bound(X_113,inverse(inverse(X_112))) = greatest_lower_bound(X_113,X_112) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_113,inverse(inverse(X_112))),greatest_lower_bound(X_113,inverse(inverse(X_112)))) ),[1,1],$fot(X_112)]]) ).

cnf(refute_0_102,plain,
    ( inverse(inverse(X_112)) != X_112
    | greatest_lower_bound(X_113,inverse(inverse(X_112))) = greatest_lower_bound(X_113,X_112) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_113,inverse(inverse(X_112))),greatest_lower_bound(X_113,inverse(inverse(X_112)))) )],[refute_0_100,refute_0_101]) ).

cnf(refute_0_103,plain,
    greatest_lower_bound(X_113,inverse(inverse(X_112))) = greatest_lower_bound(X_113,X_112),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_112)),X_112) )],[refute_0_99,refute_0_102]) ).

cnf(refute_0_104,plain,
    inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))) = inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))))]]) ).

cnf(refute_0_105,plain,
    ( greatest_lower_bound(X_113,inverse(inverse(X_112))) != greatest_lower_bound(X_113,X_112)
    | inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))) != inverse(greatest_lower_bound(X_113,inverse(inverse(X_112))))
    | inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))) = inverse(greatest_lower_bound(X_113,X_112)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))),inverse(greatest_lower_bound(X_113,inverse(inverse(X_112))))) ),[1,0],$fot(greatest_lower_bound(X_113,X_112))]]) ).

cnf(refute_0_106,plain,
    ( greatest_lower_bound(X_113,inverse(inverse(X_112))) != greatest_lower_bound(X_113,X_112)
    | inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))) = inverse(greatest_lower_bound(X_113,X_112)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))),inverse(greatest_lower_bound(X_113,inverse(inverse(X_112))))) )],[refute_0_104,refute_0_105]) ).

cnf(refute_0_107,plain,
    inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))) = inverse(greatest_lower_bound(X_113,X_112)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_113,inverse(inverse(X_112))),greatest_lower_bound(X_113,X_112)) )],[refute_0_103,refute_0_106]) ).

cnf(refute_0_108,plain,
    ( inverse(greatest_lower_bound(X_107,inverse(X_83))) != multiply(inverse(greatest_lower_bound(identity,multiply(X_83,X_107))),X_83)
    | multiply(inverse(greatest_lower_bound(identity,multiply(X_83,X_107))),X_83) = inverse(greatest_lower_bound(X_107,inverse(X_83))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(X_107,inverse(X_83))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,multiply(X_83,X_107))),X_83)))]]) ).

cnf(refute_0_109,plain,
    multiply(inverse(greatest_lower_bound(identity,multiply(X_83,X_107))),X_83) = inverse(greatest_lower_bound(X_107,inverse(X_83))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_107,inverse(X_83))),multiply(inverse(greatest_lower_bound(identity,multiply(X_83,X_107))),X_83)) )],[refute_0_54,refute_0_108]) ).

cnf(refute_0_110,plain,
    multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)) = inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))),
    inference(subst,[],[refute_0_109:[bind(X_107,$fot(X_113)),bind(X_83,$fot(inverse(X_112)))]]) ).

cnf(refute_0_111,plain,
    ( multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)) != inverse(greatest_lower_bound(X_113,inverse(inverse(X_112))))
    | inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))) != inverse(greatest_lower_bound(X_113,X_112))
    | multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)) = inverse(greatest_lower_bound(X_113,X_112)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_113,X_112))))]]) ).

cnf(refute_0_112,plain,
    ( inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))) != inverse(greatest_lower_bound(X_113,X_112))
    | multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)) = inverse(greatest_lower_bound(X_113,X_112)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)),inverse(greatest_lower_bound(X_113,inverse(inverse(X_112))))) )],[refute_0_110,refute_0_111]) ).

cnf(refute_0_113,plain,
    multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)) = inverse(greatest_lower_bound(X_113,X_112)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_113,inverse(inverse(X_112)))),inverse(greatest_lower_bound(X_113,X_112))) )],[refute_0_107,refute_0_112]) ).

cnf(refute_0_114,plain,
    ( multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)) != inverse(greatest_lower_bound(X_113,X_112))
    | inverse(greatest_lower_bound(X_112,X_113)) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112))
    | inverse(greatest_lower_bound(X_112,X_113)) = inverse(greatest_lower_bound(X_113,X_112)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_112,X_113)),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112))) ),[1],$fot(inverse(greatest_lower_bound(X_113,X_112)))]]) ).

cnf(refute_0_115,plain,
    ( inverse(greatest_lower_bound(X_112,X_113)) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112))
    | inverse(greatest_lower_bound(X_112,X_113)) = inverse(greatest_lower_bound(X_113,X_112)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112)),inverse(greatest_lower_bound(X_113,X_112))) )],[refute_0_113,refute_0_114]) ).

cnf(refute_0_116,plain,
    inverse(greatest_lower_bound(X_112,X_113)) = inverse(greatest_lower_bound(X_113,X_112)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_112,X_113)),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_112),X_113))),inverse(X_112))) )],[refute_0_98,refute_0_115]) ).

cnf(refute_0_117,plain,
    inverse(greatest_lower_bound(X_115,X_116)) = inverse(greatest_lower_bound(X_116,X_115)),
    inference(subst,[],[refute_0_116:[bind(X_112,$fot(X_115)),bind(X_113,$fot(X_116))]]) ).

cnf(refute_0_118,plain,
    ( multiply(greatest_lower_bound(X_115,X_116),inverse(greatest_lower_bound(X_115,X_116))) != identity
    | inverse(greatest_lower_bound(X_115,X_116)) != inverse(greatest_lower_bound(X_116,X_115))
    | multiply(greatest_lower_bound(X_115,X_116),inverse(greatest_lower_bound(X_116,X_115))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_115,X_116),inverse(greatest_lower_bound(X_115,X_116))),identity) ),[0,1],$fot(inverse(greatest_lower_bound(X_116,X_115)))]]) ).

cnf(refute_0_119,plain,
    ( multiply(greatest_lower_bound(X_115,X_116),inverse(greatest_lower_bound(X_115,X_116))) != identity
    | multiply(greatest_lower_bound(X_115,X_116),inverse(greatest_lower_bound(X_116,X_115))) = identity ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_115,X_116)),inverse(greatest_lower_bound(X_116,X_115))) )],[refute_0_117,refute_0_118]) ).

cnf(refute_0_120,plain,
    multiply(greatest_lower_bound(X_115,X_116),inverse(greatest_lower_bound(X_116,X_115))) = identity,
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_115,X_116),inverse(greatest_lower_bound(X_115,X_116))),identity) )],[refute_0_88,refute_0_119]) ).

cnf(refute_0_121,plain,
    multiply(greatest_lower_bound(X_140,Y),inverse(greatest_lower_bound(Y,X_140))) = identity,
    inference(subst,[],[refute_0_120:[bind(X_115,$fot(X_140)),bind(X_116,$fot(Y))]]) ).

cnf(refute_0_122,plain,
    ( multiply(greatest_lower_bound(X_140,Y),inverse(greatest_lower_bound(Y,X_140))) != greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140))))
    | multiply(greatest_lower_bound(X_140,Y),inverse(greatest_lower_bound(Y,X_140))) != identity
    | identity = greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_140,Y),inverse(greatest_lower_bound(Y,X_140))),greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140))))) ),[0],$fot(identity)]]) ).

cnf(refute_0_123,plain,
    ( multiply(greatest_lower_bound(X_140,Y),inverse(greatest_lower_bound(Y,X_140))) != greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140))))
    | identity = greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_140,Y),inverse(greatest_lower_bound(Y,X_140))),identity) )],[refute_0_121,refute_0_122]) ).

cnf(refute_0_124,plain,
    identity = greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_140,Y),inverse(greatest_lower_bound(Y,X_140))),greatest_lower_bound(identity,multiply(X_140,inverse(greatest_lower_bound(Y,X_140))))) )],[refute_0_87,refute_0_123]) ).

cnf(refute_0_125,plain,
    identity = greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c))))))),
    inference(subst,[],[refute_0_124:[bind(Y,$fot(identity)),bind(X_140,$fot(multiply(a,greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_126,plain,
    multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(multiply(inverse(X_105),X_104),multiply(inverse(X_105),X_105)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_105))),bind(Y,$fot(X_104)),bind(Z,$fot(X_105))]]) ).

cnf(refute_0_127,plain,
    multiply(inverse(X_105),X_105) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_105))]]) ).

cnf(refute_0_128,plain,
    ( multiply(inverse(X_105),X_105) != identity
    | multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) != greatest_lower_bound(multiply(inverse(X_105),X_104),multiply(inverse(X_105),X_105))
    | multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(multiply(inverse(X_105),X_104),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)),greatest_lower_bound(multiply(inverse(X_105),X_104),multiply(inverse(X_105),X_105))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_129,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) != greatest_lower_bound(multiply(inverse(X_105),X_104),multiply(inverse(X_105),X_105))
    | multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(multiply(inverse(X_105),X_104),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),X_105),identity) )],[refute_0_127,refute_0_128]) ).

cnf(refute_0_130,plain,
    multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(multiply(inverse(X_105),X_104),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)),greatest_lower_bound(multiply(inverse(X_105),X_104),multiply(inverse(X_105),X_105))) )],[refute_0_126,refute_0_129]) ).

cnf(refute_0_131,plain,
    greatest_lower_bound(multiply(inverse(X_105),X_104),identity) = greatest_lower_bound(identity,multiply(inverse(X_105),X_104)),
    inference(subst,[],[refute_0_46:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_105),X_104)))]]) ).

cnf(refute_0_132,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) != greatest_lower_bound(multiply(inverse(X_105),X_104),identity)
    | greatest_lower_bound(multiply(inverse(X_105),X_104),identity) != greatest_lower_bound(identity,multiply(inverse(X_105),X_104))
    | multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(identity,multiply(inverse(X_105),X_104)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)),greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))]]) ).

cnf(refute_0_133,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) != greatest_lower_bound(multiply(inverse(X_105),X_104),identity)
    | multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(identity,multiply(inverse(X_105),X_104)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_105),X_104),identity),greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) )],[refute_0_131,refute_0_132]) ).

cnf(refute_0_134,plain,
    multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(identity,multiply(inverse(X_105),X_104)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)),greatest_lower_bound(multiply(inverse(X_105),X_104),identity)) )],[refute_0_130,refute_0_133]) ).

cnf(refute_0_135,plain,
    multiply(inverse(X_105),greatest_lower_bound(X_105,X_104)) = greatest_lower_bound(identity,multiply(inverse(X_105),X_104)),
    inference(subst,[],[refute_0_94:[bind(X_104,$fot(X_105)),bind(X_105,$fot(X_104))]]) ).

cnf(refute_0_136,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_105,X_104)) != greatest_lower_bound(identity,multiply(inverse(X_105),X_104))
    | greatest_lower_bound(identity,multiply(inverse(X_105),X_104)) = multiply(inverse(X_105),greatest_lower_bound(X_105,X_104)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(inverse(X_105),greatest_lower_bound(X_105,X_104)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))))]]) ).

cnf(refute_0_137,plain,
    greatest_lower_bound(identity,multiply(inverse(X_105),X_104)) = multiply(inverse(X_105),greatest_lower_bound(X_105,X_104)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_105,X_104)),greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) )],[refute_0_135,refute_0_136]) ).

cnf(refute_0_138,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) != greatest_lower_bound(identity,multiply(inverse(X_105),X_104))
    | greatest_lower_bound(identity,multiply(inverse(X_105),X_104)) != multiply(inverse(X_105),greatest_lower_bound(X_105,X_104))
    | multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) = multiply(inverse(X_105),greatest_lower_bound(X_105,X_104)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)),multiply(inverse(X_105),greatest_lower_bound(X_105,X_104))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)))]]) ).

cnf(refute_0_139,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) != greatest_lower_bound(identity,multiply(inverse(X_105),X_104))
    | multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) = multiply(inverse(X_105),greatest_lower_bound(X_105,X_104)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)),multiply(inverse(X_105),greatest_lower_bound(X_105,X_104))) )],[refute_0_137,refute_0_138]) ).

cnf(refute_0_140,plain,
    multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) = multiply(inverse(X_105),greatest_lower_bound(X_105,X_104)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)),greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) )],[refute_0_134,refute_0_139]) ).

cnf(refute_0_141,plain,
    multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) = multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))),
    inference(subst,[],[refute_0_140:[bind(X_104,$fot(greatest_lower_bound(inverse(b),inverse(c)))),bind(X_105,$fot(inverse(a)))]]) ).

cnf(refute_0_142,plain,
    inverse(inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))),
    inference(subst,[],[p12_2:[bind(X,$fot(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_143,plain,
    inverse(multiply(X_17,inverse(X))) = multiply(inverse(inverse(X)),inverse(X_17)),
    inference(subst,[],[p12_3:[bind(X,$fot(X_17)),bind(Y,$fot(inverse(X)))]]) ).

cnf(refute_0_144,plain,
    ( inverse(multiply(X_17,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_17))
    | inverse(inverse(X)) != X
    | inverse(multiply(X_17,inverse(X))) = multiply(X,inverse(X_17)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_17,inverse(X))),multiply(inverse(inverse(X)),inverse(X_17))) ),[1,0],$fot(X)]]) ).

cnf(refute_0_145,plain,
    ( inverse(multiply(X_17,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_17))
    | inverse(multiply(X_17,inverse(X))) = multiply(X,inverse(X_17)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p12_2,refute_0_144]) ).

cnf(refute_0_146,plain,
    inverse(multiply(X_17,inverse(X))) = multiply(X,inverse(X_17)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_17,inverse(X))),multiply(inverse(inverse(X)),inverse(X_17))) )],[refute_0_143,refute_0_145]) ).

cnf(refute_0_147,plain,
    inverse(multiply(X_17,inverse(multiply(X_37,inverse(X_36))))) = multiply(multiply(X_37,inverse(X_36)),inverse(X_17)),
    inference(subst,[],[refute_0_146:[bind(X,$fot(multiply(X_37,inverse(X_36))))]]) ).

cnf(refute_0_148,plain,
    inverse(multiply(X_37,inverse(X_36))) = multiply(X_36,inverse(X_37)),
    inference(subst,[],[refute_0_146:[bind(X,$fot(X_36)),bind(X_17,$fot(X_37))]]) ).

cnf(refute_0_149,plain,
    ( inverse(multiply(X_17,inverse(multiply(X_37,inverse(X_36))))) != multiply(multiply(X_37,inverse(X_36)),inverse(X_17))
    | inverse(multiply(X_37,inverse(X_36))) != multiply(X_36,inverse(X_37))
    | inverse(multiply(X_17,multiply(X_36,inverse(X_37)))) = multiply(multiply(X_37,inverse(X_36)),inverse(X_17)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_17,inverse(multiply(X_37,inverse(X_36))))),multiply(multiply(X_37,inverse(X_36)),inverse(X_17))) ),[0,0,1],$fot(multiply(X_36,inverse(X_37)))]]) ).

cnf(refute_0_150,plain,
    ( inverse(multiply(X_17,inverse(multiply(X_37,inverse(X_36))))) != multiply(multiply(X_37,inverse(X_36)),inverse(X_17))
    | inverse(multiply(X_17,multiply(X_36,inverse(X_37)))) = multiply(multiply(X_37,inverse(X_36)),inverse(X_17)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_37,inverse(X_36))),multiply(X_36,inverse(X_37))) )],[refute_0_148,refute_0_149]) ).

cnf(refute_0_151,plain,
    inverse(multiply(X_17,multiply(X_36,inverse(X_37)))) = multiply(multiply(X_37,inverse(X_36)),inverse(X_17)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_17,inverse(multiply(X_37,inverse(X_36))))),multiply(multiply(X_37,inverse(X_36)),inverse(X_17))) )],[refute_0_147,refute_0_150]) ).

cnf(refute_0_152,plain,
    multiply(inverse(X_36),inverse(X_17)) = inverse(multiply(X_17,X_36)),
    inference(subst,[],[refute_0_25:[bind(X,$fot(X_17)),bind(Y,$fot(X_36))]]) ).

cnf(refute_0_153,plain,
    multiply(X_37,multiply(inverse(X_36),inverse(X_17))) = multiply(X_37,multiply(inverse(X_36),inverse(X_17))),
    introduced(tautology,[refl,[$fot(multiply(X_37,multiply(inverse(X_36),inverse(X_17))))]]) ).

cnf(refute_0_154,plain,
    ( multiply(X_37,multiply(inverse(X_36),inverse(X_17))) != multiply(X_37,multiply(inverse(X_36),inverse(X_17)))
    | multiply(inverse(X_36),inverse(X_17)) != inverse(multiply(X_17,X_36))
    | multiply(X_37,multiply(inverse(X_36),inverse(X_17))) = multiply(X_37,inverse(multiply(X_17,X_36))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,multiply(inverse(X_36),inverse(X_17))),multiply(X_37,multiply(inverse(X_36),inverse(X_17)))) ),[1,1],$fot(inverse(multiply(X_17,X_36)))]]) ).

cnf(refute_0_155,plain,
    ( multiply(inverse(X_36),inverse(X_17)) != inverse(multiply(X_17,X_36))
    | multiply(X_37,multiply(inverse(X_36),inverse(X_17))) = multiply(X_37,inverse(multiply(X_17,X_36))) ),
    inference(resolve,[$cnf( $equal(multiply(X_37,multiply(inverse(X_36),inverse(X_17))),multiply(X_37,multiply(inverse(X_36),inverse(X_17)))) )],[refute_0_153,refute_0_154]) ).

cnf(refute_0_156,plain,
    multiply(X_37,multiply(inverse(X_36),inverse(X_17))) = multiply(X_37,inverse(multiply(X_17,X_36))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_36),inverse(X_17)),inverse(multiply(X_17,X_36))) )],[refute_0_152,refute_0_155]) ).

cnf(refute_0_157,plain,
    multiply(multiply(X_37,inverse(X_36)),inverse(X_17)) = multiply(X_37,multiply(inverse(X_36),inverse(X_17))),
    inference(subst,[],[associativity:[bind(X,$fot(X_37)),bind(Y,$fot(inverse(X_36))),bind(Z,$fot(inverse(X_17)))]]) ).

cnf(refute_0_158,plain,
    ( multiply(X_37,multiply(inverse(X_36),inverse(X_17))) != multiply(X_37,inverse(multiply(X_17,X_36)))
    | multiply(multiply(X_37,inverse(X_36)),inverse(X_17)) != multiply(X_37,multiply(inverse(X_36),inverse(X_17)))
    | multiply(multiply(X_37,inverse(X_36)),inverse(X_17)) = multiply(X_37,inverse(multiply(X_17,X_36))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(multiply(X_37,inverse(X_36)),inverse(X_17)))),bind(Y0,$fot(multiply(X_37,multiply(inverse(X_36),inverse(X_17))))),bind(Z0,$fot(multiply(X_37,inverse(multiply(X_17,X_36)))))]]) ).

cnf(refute_0_159,plain,
    ( multiply(X_37,multiply(inverse(X_36),inverse(X_17))) != multiply(X_37,inverse(multiply(X_17,X_36)))
    | multiply(multiply(X_37,inverse(X_36)),inverse(X_17)) = multiply(X_37,inverse(multiply(X_17,X_36))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_37,inverse(X_36)),inverse(X_17)),multiply(X_37,multiply(inverse(X_36),inverse(X_17)))) )],[refute_0_157,refute_0_158]) ).

cnf(refute_0_160,plain,
    multiply(multiply(X_37,inverse(X_36)),inverse(X_17)) = multiply(X_37,inverse(multiply(X_17,X_36))),
    inference(resolve,[$cnf( $equal(multiply(X_37,multiply(inverse(X_36),inverse(X_17))),multiply(X_37,inverse(multiply(X_17,X_36)))) )],[refute_0_156,refute_0_159]) ).

cnf(refute_0_161,plain,
    ( multiply(multiply(X_37,inverse(X_36)),inverse(X_17)) != multiply(X_37,inverse(multiply(X_17,X_36)))
    | inverse(multiply(X_17,multiply(X_36,inverse(X_37)))) != multiply(multiply(X_37,inverse(X_36)),inverse(X_17))
    | inverse(multiply(X_17,multiply(X_36,inverse(X_37)))) = multiply(X_37,inverse(multiply(X_17,X_36))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_17,multiply(X_36,inverse(X_37)))),multiply(multiply(X_37,inverse(X_36)),inverse(X_17))) ),[1],$fot(multiply(X_37,inverse(multiply(X_17,X_36))))]]) ).

cnf(refute_0_162,plain,
    ( inverse(multiply(X_17,multiply(X_36,inverse(X_37)))) != multiply(multiply(X_37,inverse(X_36)),inverse(X_17))
    | inverse(multiply(X_17,multiply(X_36,inverse(X_37)))) = multiply(X_37,inverse(multiply(X_17,X_36))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_37,inverse(X_36)),inverse(X_17)),multiply(X_37,inverse(multiply(X_17,X_36)))) )],[refute_0_160,refute_0_161]) ).

cnf(refute_0_163,plain,
    inverse(multiply(X_17,multiply(X_36,inverse(X_37)))) = multiply(X_37,inverse(multiply(X_17,X_36))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_17,multiply(X_36,inverse(X_37)))),multiply(multiply(X_37,inverse(X_36)),inverse(X_17))) )],[refute_0_151,refute_0_162]) ).

cnf(refute_0_164,plain,
    inverse(multiply(X_61,multiply(inverse(inverse(X_63)),inverse(X_63)))) = multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))),
    inference(subst,[],[refute_0_163:[bind(X_17,$fot(X_61)),bind(X_36,$fot(inverse(inverse(X_63)))),bind(X_37,$fot(X_63))]]) ).

cnf(refute_0_165,plain,
    multiply(inverse(inverse(X_63)),inverse(X_63)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_63)))]]) ).

cnf(refute_0_166,plain,
    ( multiply(inverse(inverse(X_63)),inverse(X_63)) != identity
    | inverse(multiply(X_61,multiply(inverse(inverse(X_63)),inverse(X_63)))) != multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))
    | inverse(multiply(X_61,identity)) = multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_61,multiply(inverse(inverse(X_63)),inverse(X_63)))),multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))) ),[0,0,1],$fot(identity)]]) ).

cnf(refute_0_167,plain,
    ( inverse(multiply(X_61,multiply(inverse(inverse(X_63)),inverse(X_63)))) != multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))
    | inverse(multiply(X_61,identity)) = multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_63)),inverse(X_63)),identity) )],[refute_0_165,refute_0_166]) ).

cnf(refute_0_168,plain,
    inverse(multiply(X_61,identity)) = multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_61,multiply(inverse(inverse(X_63)),inverse(X_63)))),multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))) )],[refute_0_164,refute_0_167]) ).

cnf(refute_0_169,plain,
    inverse(multiply(identity,X_18)) = multiply(inverse(X_18),inverse(identity)),
    inference(subst,[],[p12_3:[bind(X,$fot(identity)),bind(Y,$fot(X_18))]]) ).

cnf(refute_0_170,plain,
    ( inverse(multiply(identity,X_18)) != multiply(inverse(X_18),inverse(identity))
    | inverse(identity) != identity
    | inverse(multiply(identity,X_18)) = multiply(inverse(X_18),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_18)),multiply(inverse(X_18),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_171,plain,
    ( inverse(multiply(identity,X_18)) != multiply(inverse(X_18),inverse(identity))
    | inverse(multiply(identity,X_18)) = multiply(inverse(X_18),identity) ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p12_1,refute_0_170]) ).

cnf(refute_0_172,plain,
    inverse(multiply(identity,X_18)) = multiply(inverse(X_18),identity),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_18)),multiply(inverse(X_18),inverse(identity))) )],[refute_0_169,refute_0_171]) ).

cnf(refute_0_173,plain,
    multiply(identity,X_18) = X_18,
    inference(subst,[],[left_identity:[bind(X,$fot(X_18))]]) ).

cnf(refute_0_174,plain,
    inverse(multiply(identity,X_18)) = inverse(multiply(identity,X_18)),
    introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_18)))]]) ).

cnf(refute_0_175,plain,
    ( multiply(identity,X_18) != X_18
    | inverse(multiply(identity,X_18)) != inverse(multiply(identity,X_18))
    | inverse(multiply(identity,X_18)) = inverse(X_18) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_18)),inverse(multiply(identity,X_18))) ),[1,0],$fot(X_18)]]) ).

cnf(refute_0_176,plain,
    ( multiply(identity,X_18) != X_18
    | inverse(multiply(identity,X_18)) = inverse(X_18) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_18)),inverse(multiply(identity,X_18))) )],[refute_0_174,refute_0_175]) ).

cnf(refute_0_177,plain,
    inverse(multiply(identity,X_18)) = inverse(X_18),
    inference(resolve,[$cnf( $equal(multiply(identity,X_18),X_18) )],[refute_0_173,refute_0_176]) ).

cnf(refute_0_178,plain,
    ( inverse(multiply(identity,X_18)) != multiply(inverse(X_18),identity)
    | inverse(multiply(identity,X_18)) != inverse(X_18)
    | inverse(X_18) = multiply(inverse(X_18),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_18)),multiply(inverse(X_18),identity)) ),[0],$fot(inverse(X_18))]]) ).

cnf(refute_0_179,plain,
    ( inverse(multiply(identity,X_18)) != multiply(inverse(X_18),identity)
    | inverse(X_18) = multiply(inverse(X_18),identity) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_18)),inverse(X_18)) )],[refute_0_177,refute_0_178]) ).

cnf(refute_0_180,plain,
    inverse(X_18) = multiply(inverse(X_18),identity),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_18)),multiply(inverse(X_18),identity)) )],[refute_0_172,refute_0_179]) ).

cnf(refute_0_181,plain,
    inverse(inverse(X)) = multiply(inverse(inverse(X)),identity),
    inference(subst,[],[refute_0_180:[bind(X_18,$fot(inverse(X)))]]) ).

cnf(refute_0_182,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_183,plain,
    ( inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
    | inverse(inverse(X)) = multiply(X,identity) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p12_2,refute_0_182]) ).

cnf(refute_0_184,plain,
    inverse(inverse(X)) = multiply(X,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) )],[refute_0_181,refute_0_183]) ).

cnf(refute_0_185,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_186,plain,
    ( inverse(inverse(X)) != multiply(X,identity)
    | X = multiply(X,identity) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p12_2,refute_0_185]) ).

cnf(refute_0_187,plain,
    X = multiply(X,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) )],[refute_0_184,refute_0_186]) ).

cnf(refute_0_188,plain,
    ( X != multiply(X,identity)
    | multiply(X,identity) = X ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,identity)))]]) ).

cnf(refute_0_189,plain,
    multiply(X,identity) = X,
    inference(resolve,[$cnf( $equal(X,multiply(X,identity)) )],[refute_0_187,refute_0_188]) ).

cnf(refute_0_190,plain,
    multiply(X_61,identity) = X_61,
    inference(subst,[],[refute_0_189:[bind(X,$fot(X_61))]]) ).

cnf(refute_0_191,plain,
    inverse(multiply(X_61,identity)) = inverse(multiply(X_61,identity)),
    introduced(tautology,[refl,[$fot(inverse(multiply(X_61,identity)))]]) ).

cnf(refute_0_192,plain,
    ( multiply(X_61,identity) != X_61
    | inverse(multiply(X_61,identity)) != inverse(multiply(X_61,identity))
    | inverse(multiply(X_61,identity)) = inverse(X_61) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_61,identity)),inverse(multiply(X_61,identity))) ),[1,0],$fot(X_61)]]) ).

cnf(refute_0_193,plain,
    ( multiply(X_61,identity) != X_61
    | inverse(multiply(X_61,identity)) = inverse(X_61) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_61,identity)),inverse(multiply(X_61,identity))) )],[refute_0_191,refute_0_192]) ).

cnf(refute_0_194,plain,
    inverse(multiply(X_61,identity)) = inverse(X_61),
    inference(resolve,[$cnf( $equal(multiply(X_61,identity),X_61) )],[refute_0_190,refute_0_193]) ).

cnf(refute_0_195,plain,
    ( inverse(multiply(X_61,identity)) != multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))
    | inverse(multiply(X_61,identity)) != inverse(X_61)
    | inverse(X_61) = multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_61,identity)),multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))) ),[0],$fot(inverse(X_61))]]) ).

cnf(refute_0_196,plain,
    ( inverse(multiply(X_61,identity)) != multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))
    | inverse(X_61) = multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_61,identity)),inverse(X_61)) )],[refute_0_194,refute_0_195]) ).

cnf(refute_0_197,plain,
    multiply(inverse(X_63),inverse(X_61)) = inverse(multiply(X_61,X_63)),
    inference(subst,[],[refute_0_25:[bind(X,$fot(X_61)),bind(Y,$fot(X_63))]]) ).

cnf(refute_0_198,plain,
    inverse(multiply(X_61,inverse(inverse(X_63)))) = multiply(inverse(X_63),inverse(X_61)),
    inference(subst,[],[refute_0_146:[bind(X,$fot(inverse(X_63))),bind(X_17,$fot(X_61))]]) ).

cnf(refute_0_199,plain,
    ( multiply(inverse(X_63),inverse(X_61)) != inverse(multiply(X_61,X_63))
    | inverse(multiply(X_61,inverse(inverse(X_63)))) != multiply(inverse(X_63),inverse(X_61))
    | inverse(multiply(X_61,inverse(inverse(X_63)))) = inverse(multiply(X_61,X_63)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(inverse(multiply(X_61,inverse(inverse(X_63)))))),bind(Y0,$fot(multiply(inverse(X_63),inverse(X_61)))),bind(Z0,$fot(inverse(multiply(X_61,X_63))))]]) ).

cnf(refute_0_200,plain,
    ( multiply(inverse(X_63),inverse(X_61)) != inverse(multiply(X_61,X_63))
    | inverse(multiply(X_61,inverse(inverse(X_63)))) = inverse(multiply(X_61,X_63)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_61,inverse(inverse(X_63)))),multiply(inverse(X_63),inverse(X_61))) )],[refute_0_198,refute_0_199]) ).

cnf(refute_0_201,plain,
    inverse(multiply(X_61,inverse(inverse(X_63)))) = inverse(multiply(X_61,X_63)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_63),inverse(X_61)),inverse(multiply(X_61,X_63))) )],[refute_0_197,refute_0_200]) ).

cnf(refute_0_202,plain,
    multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))) = multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))),
    introduced(tautology,[refl,[$fot(multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))))]]) ).

cnf(refute_0_203,plain,
    ( multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))) != multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))
    | inverse(multiply(X_61,inverse(inverse(X_63)))) != inverse(multiply(X_61,X_63))
    | multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))) = multiply(X_63,inverse(multiply(X_61,X_63))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))),multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))) ),[1,1],$fot(inverse(multiply(X_61,X_63)))]]) ).

cnf(refute_0_204,plain,
    ( inverse(multiply(X_61,inverse(inverse(X_63)))) != inverse(multiply(X_61,X_63))
    | multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))) = multiply(X_63,inverse(multiply(X_61,X_63))) ),
    inference(resolve,[$cnf( $equal(multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))),multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))) )],[refute_0_202,refute_0_203]) ).

cnf(refute_0_205,plain,
    multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))) = multiply(X_63,inverse(multiply(X_61,X_63))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_61,inverse(inverse(X_63)))),inverse(multiply(X_61,X_63))) )],[refute_0_201,refute_0_204]) ).

cnf(refute_0_206,plain,
    ( multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))) != multiply(X_63,inverse(multiply(X_61,X_63)))
    | inverse(X_61) != multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))
    | inverse(X_61) = multiply(X_63,inverse(multiply(X_61,X_63))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(X_61),multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))) ),[1],$fot(multiply(X_63,inverse(multiply(X_61,X_63))))]]) ).

cnf(refute_0_207,plain,
    ( inverse(X_61) != multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))
    | inverse(X_61) = multiply(X_63,inverse(multiply(X_61,X_63))) ),
    inference(resolve,[$cnf( $equal(multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63))))),multiply(X_63,inverse(multiply(X_61,X_63)))) )],[refute_0_205,refute_0_206]) ).

cnf(refute_0_208,plain,
    ( inverse(multiply(X_61,identity)) != multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))
    | inverse(X_61) = multiply(X_63,inverse(multiply(X_61,X_63))) ),
    inference(resolve,[$cnf( $equal(inverse(X_61),multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))) )],[refute_0_196,refute_0_207]) ).

cnf(refute_0_209,plain,
    inverse(X_61) = multiply(X_63,inverse(multiply(X_61,X_63))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_61,identity)),multiply(X_63,inverse(multiply(X_61,inverse(inverse(X_63)))))) )],[refute_0_168,refute_0_208]) ).

cnf(refute_0_210,plain,
    inverse(inverse(X_105)) = multiply(greatest_lower_bound(X_104,X_105),inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)))),
    inference(subst,[],[refute_0_209:[bind(X_61,$fot(inverse(X_105))),bind(X_63,$fot(greatest_lower_bound(X_104,X_105)))]]) ).

cnf(refute_0_211,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) != greatest_lower_bound(identity,multiply(inverse(X_105),X_104))
    | inverse(inverse(X_105)) != multiply(greatest_lower_bound(X_104,X_105),inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))))
    | inverse(inverse(X_105)) = multiply(greatest_lower_bound(X_104,X_105),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_105)),multiply(greatest_lower_bound(X_104,X_105),inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))))) ),[1,1,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)))]]) ).

cnf(refute_0_212,plain,
    ( inverse(inverse(X_105)) != multiply(greatest_lower_bound(X_104,X_105),inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))))
    | inverse(inverse(X_105)) = multiply(greatest_lower_bound(X_104,X_105),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)),greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) )],[refute_0_134,refute_0_211]) ).

cnf(refute_0_213,plain,
    inverse(inverse(X_105)) = multiply(greatest_lower_bound(X_104,X_105),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_105)),multiply(greatest_lower_bound(X_104,X_105),inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))))) )],[refute_0_210,refute_0_212]) ).

cnf(refute_0_214,plain,
    inverse(inverse(X_105)) = X_105,
    inference(subst,[],[p12_2:[bind(X,$fot(X_105))]]) ).

cnf(refute_0_215,plain,
    ( inverse(inverse(X_105)) != X_105
    | inverse(inverse(X_105)) != multiply(greatest_lower_bound(X_104,X_105),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))))
    | X_105 = multiply(greatest_lower_bound(X_104,X_105),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_105)),multiply(greatest_lower_bound(X_104,X_105),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))))) ),[0],$fot(X_105)]]) ).

cnf(refute_0_216,plain,
    ( inverse(inverse(X_105)) != multiply(greatest_lower_bound(X_104,X_105),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))))
    | X_105 = multiply(greatest_lower_bound(X_104,X_105),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_105)),X_105) )],[refute_0_214,refute_0_215]) ).

cnf(refute_0_217,plain,
    X_105 = multiply(greatest_lower_bound(X_104,X_105),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_105)),multiply(greatest_lower_bound(X_104,X_105),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))))) )],[refute_0_213,refute_0_216]) ).

cnf(refute_0_218,plain,
    inverse(greatest_lower_bound(inverse(a),inverse(c))) = multiply(greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))),
    inference(subst,[],[refute_0_217:[bind(X_104,$fot(b)),bind(X_105,$fot(inverse(greatest_lower_bound(inverse(a),inverse(c)))))]]) ).

cnf(refute_0_219,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_40)) = greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_40),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(least_upper_bound(a,c))),bind(Z,$fot(X_40))]]) ).

cnf(refute_0_220,plain,
    greatest_lower_bound(b,least_upper_bound(b,c)) = b,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).

cnf(refute_0_221,plain,
    ( least_upper_bound(a,c) != least_upper_bound(b,c)
    | least_upper_bound(b,c) = least_upper_bound(a,c) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(a,c))),bind(Y0,$fot(least_upper_bound(b,c)))]]) ).

cnf(refute_0_222,plain,
    least_upper_bound(b,c) = least_upper_bound(a,c),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,c),least_upper_bound(b,c)) )],[p12_5,refute_0_221]) ).

cnf(refute_0_223,plain,
    ( greatest_lower_bound(b,least_upper_bound(b,c)) != b
    | least_upper_bound(b,c) != least_upper_bound(a,c)
    | greatest_lower_bound(b,least_upper_bound(a,c)) = b ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,c)),b) ),[0,1],$fot(least_upper_bound(a,c))]]) ).

cnf(refute_0_224,plain,
    ( greatest_lower_bound(b,least_upper_bound(b,c)) != b
    | greatest_lower_bound(b,least_upper_bound(a,c)) = b ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,c),least_upper_bound(a,c)) )],[refute_0_222,refute_0_223]) ).

cnf(refute_0_225,plain,
    greatest_lower_bound(b,least_upper_bound(a,c)) = b,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,c)),b) )],[refute_0_220,refute_0_224]) ).

cnf(refute_0_226,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_40)) != greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_40)
    | greatest_lower_bound(b,least_upper_bound(a,c)) != b
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_40)) = greatest_lower_bound(b,X_40) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_40)),greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_40)) ),[1,0],$fot(b)]]) ).

cnf(refute_0_227,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_40)) != greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_40)
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_40)) = greatest_lower_bound(b,X_40) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,c)),b) )],[refute_0_225,refute_0_226]) ).

cnf(refute_0_228,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_40)) = greatest_lower_bound(b,X_40),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_40)),greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_40)) )],[refute_0_219,refute_0_227]) ).

cnf(refute_0_229,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(least_upper_bound(a,c),Y))) = greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)),
    inference(subst,[],[refute_0_228:[bind(X_40,$fot(least_upper_bound(least_upper_bound(a,c),Y)))]]) ).

cnf(refute_0_230,plain,
    greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(least_upper_bound(a,c),Y)) = least_upper_bound(a,c),
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_231,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(least_upper_bound(a,c),Y))) != greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))
    | greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(least_upper_bound(a,c),Y)) != least_upper_bound(a,c)
    | greatest_lower_bound(b,least_upper_bound(a,c)) = greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(least_upper_bound(a,c),Y))),greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))) ),[0,1],$fot(least_upper_bound(a,c))]]) ).

cnf(refute_0_232,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(least_upper_bound(a,c),Y))) != greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))
    | greatest_lower_bound(b,least_upper_bound(a,c)) = greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(least_upper_bound(a,c),Y)),least_upper_bound(a,c)) )],[refute_0_230,refute_0_231]) ).

cnf(refute_0_233,plain,
    greatest_lower_bound(b,least_upper_bound(a,c)) = greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(least_upper_bound(a,c),Y))),greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))) )],[refute_0_229,refute_0_232]) ).

cnf(refute_0_234,plain,
    ( greatest_lower_bound(b,least_upper_bound(a,c)) != b
    | greatest_lower_bound(b,least_upper_bound(a,c)) != greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))
    | b = greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,c)),greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))) ),[0],$fot(b)]]) ).

cnf(refute_0_235,plain,
    ( greatest_lower_bound(b,least_upper_bound(a,c)) != greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))
    | b = greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,c)),b) )],[refute_0_225,refute_0_234]) ).

cnf(refute_0_236,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_13:[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_237,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_236]) ).

cnf(refute_0_238,plain,
    least_upper_bound(least_upper_bound(a,c),Y) = least_upper_bound(a,least_upper_bound(c,Y)),
    inference(subst,[],[refute_0_237:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_239,plain,
    greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)) = greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)))]]) ).

cnf(refute_0_240,plain,
    ( greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)) != greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))
    | least_upper_bound(least_upper_bound(a,c),Y) != least_upper_bound(a,least_upper_bound(c,Y))
    | greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)) = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)),greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))) ),[1,1],$fot(least_upper_bound(a,least_upper_bound(c,Y)))]]) ).

cnf(refute_0_241,plain,
    ( least_upper_bound(least_upper_bound(a,c),Y) != least_upper_bound(a,least_upper_bound(c,Y))
    | greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)) = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)),greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))) )],[refute_0_239,refute_0_240]) ).

cnf(refute_0_242,plain,
    greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)) = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,c),Y),least_upper_bound(a,least_upper_bound(c,Y))) )],[refute_0_238,refute_0_241]) ).

cnf(refute_0_243,plain,
    ( b != greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))
    | greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)) != greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,Y)))
    | b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(b,greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,Y)))) ),[0],$fot(greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)))]]) ).

cnf(refute_0_244,plain,
    ( b != greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))
    | b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y)),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,Y)))) )],[refute_0_242,refute_0_243]) ).

cnf(refute_0_245,plain,
    ( greatest_lower_bound(b,least_upper_bound(a,c)) != greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))
    | b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,Y))) ),
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))) )],[refute_0_235,refute_0_244]) ).

cnf(refute_0_246,plain,
    b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,c)),greatest_lower_bound(b,least_upper_bound(least_upper_bound(a,c),Y))) )],[refute_0_233,refute_0_245]) ).

cnf(refute_0_247,plain,
    b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,multiply(c,X_98)))),
    inference(subst,[],[refute_0_246:[bind(Y,$fot(multiply(c,X_98)))]]) ).

cnf(refute_0_248,plain,
    multiply(X_94,least_upper_bound(X_95,identity)) = least_upper_bound(multiply(X_94,X_95),multiply(X_94,identity)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_94)),bind(Y,$fot(X_95)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_249,plain,
    X_94 = multiply(X_94,identity),
    inference(subst,[],[refute_0_187:[bind(X,$fot(X_94))]]) ).

cnf(refute_0_250,plain,
    ( X_94 != multiply(X_94,identity)
    | multiply(X_94,identity) = X_94 ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(X_94)),bind(Y0,$fot(multiply(X_94,identity)))]]) ).

cnf(refute_0_251,plain,
    multiply(X_94,identity) = X_94,
    inference(resolve,[$cnf( $equal(X_94,multiply(X_94,identity)) )],[refute_0_249,refute_0_250]) ).

cnf(refute_0_252,plain,
    ( multiply(X_94,identity) != X_94
    | multiply(X_94,least_upper_bound(X_95,identity)) != least_upper_bound(multiply(X_94,X_95),multiply(X_94,identity))
    | multiply(X_94,least_upper_bound(X_95,identity)) = least_upper_bound(multiply(X_94,X_95),X_94) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_94,least_upper_bound(X_95,identity)),least_upper_bound(multiply(X_94,X_95),multiply(X_94,identity))) ),[1,1],$fot(X_94)]]) ).

cnf(refute_0_253,plain,
    ( multiply(X_94,least_upper_bound(X_95,identity)) != least_upper_bound(multiply(X_94,X_95),multiply(X_94,identity))
    | multiply(X_94,least_upper_bound(X_95,identity)) = least_upper_bound(multiply(X_94,X_95),X_94) ),
    inference(resolve,[$cnf( $equal(multiply(X_94,identity),X_94) )],[refute_0_251,refute_0_252]) ).

cnf(refute_0_254,plain,
    multiply(X_94,least_upper_bound(X_95,identity)) = least_upper_bound(multiply(X_94,X_95),X_94),
    inference(resolve,[$cnf( $equal(multiply(X_94,least_upper_bound(X_95,identity)),least_upper_bound(multiply(X_94,X_95),multiply(X_94,identity))) )],[refute_0_248,refute_0_253]) ).

cnf(refute_0_255,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_13:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).

cnf(refute_0_256,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_255]) ).

cnf(refute_0_257,plain,
    least_upper_bound(multiply(X_94,X_95),X_94) = least_upper_bound(X_94,multiply(X_94,X_95)),
    inference(subst,[],[refute_0_256:[bind(X,$fot(X_94)),bind(Y,$fot(multiply(X_94,X_95)))]]) ).

cnf(refute_0_258,plain,
    ( multiply(X_94,least_upper_bound(X_95,identity)) != least_upper_bound(multiply(X_94,X_95),X_94)
    | least_upper_bound(multiply(X_94,X_95),X_94) != least_upper_bound(X_94,multiply(X_94,X_95))
    | multiply(X_94,least_upper_bound(X_95,identity)) = least_upper_bound(X_94,multiply(X_94,X_95)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_94,least_upper_bound(X_95,identity)),least_upper_bound(X_94,multiply(X_94,X_95))) ),[0],$fot(least_upper_bound(multiply(X_94,X_95),X_94))]]) ).

cnf(refute_0_259,plain,
    ( multiply(X_94,least_upper_bound(X_95,identity)) != least_upper_bound(multiply(X_94,X_95),X_94)
    | multiply(X_94,least_upper_bound(X_95,identity)) = least_upper_bound(X_94,multiply(X_94,X_95)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),X_94),least_upper_bound(X_94,multiply(X_94,X_95))) )],[refute_0_257,refute_0_258]) ).

cnf(refute_0_260,plain,
    multiply(X_94,least_upper_bound(X_95,identity)) = least_upper_bound(X_94,multiply(X_94,X_95)),
    inference(resolve,[$cnf( $equal(multiply(X_94,least_upper_bound(X_95,identity)),least_upper_bound(multiply(X_94,X_95),X_94)) )],[refute_0_254,refute_0_259]) ).

cnf(refute_0_261,plain,
    multiply(c,least_upper_bound(X_98,identity)) = least_upper_bound(c,multiply(c,X_98)),
    inference(subst,[],[refute_0_260:[bind(X_94,$fot(c)),bind(X_95,$fot(X_98))]]) ).

cnf(refute_0_262,plain,
    ( multiply(c,least_upper_bound(X_98,identity)) != least_upper_bound(c,multiply(c,X_98))
    | least_upper_bound(c,multiply(c,X_98)) = multiply(c,least_upper_bound(X_98,identity)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(c,least_upper_bound(X_98,identity)))),bind(Y0,$fot(least_upper_bound(c,multiply(c,X_98))))]]) ).

cnf(refute_0_263,plain,
    least_upper_bound(c,multiply(c,X_98)) = multiply(c,least_upper_bound(X_98,identity)),
    inference(resolve,[$cnf( $equal(multiply(c,least_upper_bound(X_98,identity)),least_upper_bound(c,multiply(c,X_98))) )],[refute_0_261,refute_0_262]) ).

cnf(refute_0_264,plain,
    ( b != greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,multiply(c,X_98))))
    | least_upper_bound(c,multiply(c,X_98)) != multiply(c,least_upper_bound(X_98,identity))
    | b = greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(X_98,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,multiply(c,X_98))))) ),[1,1,1],$fot(multiply(c,least_upper_bound(X_98,identity)))]]) ).

cnf(refute_0_265,plain,
    ( b != greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,multiply(c,X_98))))
    | b = greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(X_98,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(c,multiply(c,X_98)),multiply(c,least_upper_bound(X_98,identity))) )],[refute_0_263,refute_0_264]) ).

cnf(refute_0_266,plain,
    b = greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(X_98,identity)))),
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,multiply(c,X_98))))) )],[refute_0_247,refute_0_265]) ).

cnf(refute_0_267,plain,
    b = greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(X_165,identity)))),
    inference(subst,[],[refute_0_266:[bind(X_98,$fot(X_165))]]) ).

cnf(refute_0_268,plain,
    least_upper_bound(identity,X_165) = least_upper_bound(X_165,identity),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_165))]]) ).

cnf(refute_0_269,plain,
    ( least_upper_bound(identity,X_165) != least_upper_bound(X_165,identity)
    | least_upper_bound(X_165,identity) = least_upper_bound(identity,X_165) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(identity,X_165))),bind(Y0,$fot(least_upper_bound(X_165,identity)))]]) ).

cnf(refute_0_270,plain,
    least_upper_bound(X_165,identity) = least_upper_bound(identity,X_165),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_165),least_upper_bound(X_165,identity)) )],[refute_0_268,refute_0_269]) ).

cnf(refute_0_271,plain,
    ( b != greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(X_165,identity))))
    | least_upper_bound(X_165,identity) != least_upper_bound(identity,X_165)
    | b = greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(identity,X_165)))) ),
    introduced(tautology,[equality,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(X_165,identity))))) ),[1,1,1,1],$fot(least_upper_bound(identity,X_165))]]) ).

cnf(refute_0_272,plain,
    ( b != greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(X_165,identity))))
    | b = greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(identity,X_165)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_165,identity),least_upper_bound(identity,X_165)) )],[refute_0_270,refute_0_271]) ).

cnf(refute_0_273,plain,
    b = greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(identity,X_165)))),
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(X_165,identity))))) )],[refute_0_267,refute_0_272]) ).

cnf(refute_0_274,plain,
    b = greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))),
    inference(subst,[],[refute_0_273:[bind(X_165,$fot(multiply(inverse(greatest_lower_bound(a,c)),a)))]]) ).

cnf(refute_0_275,plain,
    least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) = X_8,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).

cnf(refute_0_276,plain,
    greatest_lower_bound(X_9,X_8) = greatest_lower_bound(X_8,X_9),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).

cnf(refute_0_277,plain,
    ( greatest_lower_bound(X_9,X_8) != greatest_lower_bound(X_8,X_9)
    | greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_9,X_8))),bind(Y0,$fot(greatest_lower_bound(X_8,X_9)))]]) ).

cnf(refute_0_278,plain,
    greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,X_8),greatest_lower_bound(X_8,X_9)) )],[refute_0_276,refute_0_277]) ).

cnf(refute_0_279,plain,
    ( greatest_lower_bound(X_8,X_9) != greatest_lower_bound(X_9,X_8)
    | least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
    | least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) ),[0,1],$fot(greatest_lower_bound(X_9,X_8))]]) ).

cnf(refute_0_280,plain,
    ( least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
    | least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,X_9),greatest_lower_bound(X_9,X_8)) )],[refute_0_278,refute_0_279]) ).

cnf(refute_0_281,plain,
    least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8,
    inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) )],[refute_0_275,refute_0_280]) ).

cnf(refute_0_282,plain,
    least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) = multiply(inverse(greatest_lower_bound(a,c)),a),
    inference(subst,[],[refute_0_281:[bind(X_8,$fot(multiply(inverse(greatest_lower_bound(a,c)),a))),bind(X_9,$fot(identity))]]) ).

cnf(refute_0_283,plain,
    multiply(greatest_lower_bound(identity,X_141),inverse(X_141)) = greatest_lower_bound(identity,multiply(identity,inverse(X_141))),
    inference(subst,[],[refute_0_64:[bind(X_134,$fot(identity)),bind(X_135,$fot(X_141))]]) ).

cnf(refute_0_284,plain,
    multiply(identity,inverse(X_141)) = inverse(X_141),
    inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_141)))]]) ).

cnf(refute_0_285,plain,
    ( multiply(greatest_lower_bound(identity,X_141),inverse(X_141)) != greatest_lower_bound(identity,multiply(identity,inverse(X_141)))
    | multiply(identity,inverse(X_141)) != inverse(X_141)
    | multiply(greatest_lower_bound(identity,X_141),inverse(X_141)) = greatest_lower_bound(identity,inverse(X_141)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_141),inverse(X_141)),greatest_lower_bound(identity,multiply(identity,inverse(X_141)))) ),[1,1],$fot(inverse(X_141))]]) ).

cnf(refute_0_286,plain,
    ( multiply(greatest_lower_bound(identity,X_141),inverse(X_141)) != greatest_lower_bound(identity,multiply(identity,inverse(X_141)))
    | multiply(greatest_lower_bound(identity,X_141),inverse(X_141)) = greatest_lower_bound(identity,inverse(X_141)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_141)),inverse(X_141)) )],[refute_0_284,refute_0_285]) ).

cnf(refute_0_287,plain,
    multiply(greatest_lower_bound(identity,X_141),inverse(X_141)) = greatest_lower_bound(identity,inverse(X_141)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_141),inverse(X_141)),greatest_lower_bound(identity,multiply(identity,inverse(X_141)))) )],[refute_0_283,refute_0_286]) ).

cnf(refute_0_288,plain,
    multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))),
    inference(subst,[],[refute_0_287:[bind(X_141,$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))]]) ).

cnf(refute_0_289,plain,
    multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(X_144,greatest_lower_bound(a,c))) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(greatest_lower_bound(X_144,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_290,plain,
    multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66))),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_103)),bind(Y,$fot(a)),bind(Z,$fot(greatest_lower_bound(c,X_66)))]]) ).

cnf(refute_0_291,plain,
    greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,greatest_lower_bound(X_66,c))) = greatest_lower_bound(greatest_lower_bound(X_66,c),b),
    inference(subst,[],[refute_0_83:[bind(Y,$fot(b)),bind(X_30,$fot(greatest_lower_bound(X_66,c)))]]) ).

cnf(refute_0_292,plain,
    greatest_lower_bound(b,greatest_lower_bound(c,X_40)) = greatest_lower_bound(greatest_lower_bound(b,c),X_40),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(c)),bind(Z,$fot(X_40))]]) ).

cnf(refute_0_293,plain,
    ( greatest_lower_bound(a,c) != greatest_lower_bound(b,c)
    | greatest_lower_bound(b,c) = greatest_lower_bound(a,c) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(a,c))),bind(Y0,$fot(greatest_lower_bound(b,c)))]]) ).

cnf(refute_0_294,plain,
    greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),greatest_lower_bound(b,c)) )],[p12_4,refute_0_293]) ).

cnf(refute_0_295,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | greatest_lower_bound(b,greatest_lower_bound(c,X_40)) != greatest_lower_bound(greatest_lower_bound(b,c),X_40)
    | greatest_lower_bound(b,greatest_lower_bound(c,X_40)) = greatest_lower_bound(greatest_lower_bound(a,c),X_40) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_40)),greatest_lower_bound(greatest_lower_bound(b,c),X_40)) ),[1,0],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_296,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_40)) != greatest_lower_bound(greatest_lower_bound(b,c),X_40)
    | greatest_lower_bound(b,greatest_lower_bound(c,X_40)) = greatest_lower_bound(greatest_lower_bound(a,c),X_40) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_294,refute_0_295]) ).

cnf(refute_0_297,plain,
    greatest_lower_bound(b,greatest_lower_bound(c,X_40)) = greatest_lower_bound(greatest_lower_bound(a,c),X_40),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_40)),greatest_lower_bound(greatest_lower_bound(b,c),X_40)) )],[refute_0_292,refute_0_296]) ).

cnf(refute_0_298,plain,
    greatest_lower_bound(greatest_lower_bound(a,c),X_40) = greatest_lower_bound(a,greatest_lower_bound(c,X_40)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(X_40))]]) ).

cnf(refute_0_299,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_40)) != greatest_lower_bound(greatest_lower_bound(a,c),X_40)
    | greatest_lower_bound(greatest_lower_bound(a,c),X_40) != greatest_lower_bound(a,greatest_lower_bound(c,X_40))
    | greatest_lower_bound(b,greatest_lower_bound(c,X_40)) = greatest_lower_bound(a,greatest_lower_bound(c,X_40)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_40)),greatest_lower_bound(a,greatest_lower_bound(c,X_40))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(a,c),X_40))]]) ).

cnf(refute_0_300,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_40)) != greatest_lower_bound(greatest_lower_bound(a,c),X_40)
    | greatest_lower_bound(b,greatest_lower_bound(c,X_40)) = greatest_lower_bound(a,greatest_lower_bound(c,X_40)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),X_40),greatest_lower_bound(a,greatest_lower_bound(c,X_40))) )],[refute_0_298,refute_0_299]) ).

cnf(refute_0_301,plain,
    greatest_lower_bound(b,greatest_lower_bound(c,X_40)) = greatest_lower_bound(a,greatest_lower_bound(c,X_40)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_40)),greatest_lower_bound(greatest_lower_bound(a,c),X_40)) )],[refute_0_297,refute_0_300]) ).

cnf(refute_0_302,plain,
    greatest_lower_bound(b,greatest_lower_bound(c,X_65)) = greatest_lower_bound(a,greatest_lower_bound(c,X_65)),
    inference(subst,[],[refute_0_301:[bind(X_40,$fot(X_65))]]) ).

cnf(refute_0_303,plain,
    greatest_lower_bound(X_65,c) = greatest_lower_bound(c,X_65),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_65)),bind(Y,$fot(c))]]) ).

cnf(refute_0_304,plain,
    ( greatest_lower_bound(X_65,c) != greatest_lower_bound(c,X_65)
    | greatest_lower_bound(c,X_65) = greatest_lower_bound(X_65,c) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_65,c))),bind(Y0,$fot(greatest_lower_bound(c,X_65)))]]) ).

cnf(refute_0_305,plain,
    greatest_lower_bound(c,X_65) = greatest_lower_bound(X_65,c),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_65,c),greatest_lower_bound(c,X_65)) )],[refute_0_303,refute_0_304]) ).

cnf(refute_0_306,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_65)) != greatest_lower_bound(a,greatest_lower_bound(c,X_65))
    | greatest_lower_bound(c,X_65) != greatest_lower_bound(X_65,c)
    | greatest_lower_bound(b,greatest_lower_bound(X_65,c)) = greatest_lower_bound(a,greatest_lower_bound(c,X_65)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_65)),greatest_lower_bound(a,greatest_lower_bound(c,X_65))) ),[0,1],$fot(greatest_lower_bound(X_65,c))]]) ).

cnf(refute_0_307,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_65)) != greatest_lower_bound(a,greatest_lower_bound(c,X_65))
    | greatest_lower_bound(b,greatest_lower_bound(X_65,c)) = greatest_lower_bound(a,greatest_lower_bound(c,X_65)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,X_65),greatest_lower_bound(X_65,c)) )],[refute_0_305,refute_0_306]) ).

cnf(refute_0_308,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_65,c)) = greatest_lower_bound(a,greatest_lower_bound(c,X_65)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_65)),greatest_lower_bound(a,greatest_lower_bound(c,X_65))) )],[refute_0_302,refute_0_307]) ).

cnf(refute_0_309,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_66,c)) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)),
    inference(subst,[],[refute_0_308:[bind(X_65,$fot(X_66))]]) ).

cnf(refute_0_310,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_66,c)) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,greatest_lower_bound(X_66,c))) != greatest_lower_bound(greatest_lower_bound(X_66,c),b)
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(greatest_lower_bound(X_66,c),b) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,greatest_lower_bound(X_66,c))),greatest_lower_bound(greatest_lower_bound(X_66,c),b)) ),[0,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_66)))]]) ).

cnf(refute_0_311,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,greatest_lower_bound(X_66,c))) != greatest_lower_bound(greatest_lower_bound(X_66,c),b)
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(greatest_lower_bound(X_66,c),b) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_66,c)),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) )],[refute_0_309,refute_0_310]) ).

cnf(refute_0_312,plain,
    greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(greatest_lower_bound(X_66,c),b),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,greatest_lower_bound(X_66,c))),greatest_lower_bound(greatest_lower_bound(X_66,c),b)) )],[refute_0_291,refute_0_311]) ).

cnf(refute_0_313,plain,
    greatest_lower_bound(X_32,greatest_lower_bound(X_31,X_32)) = greatest_lower_bound(X_32,X_31),
    inference(subst,[],[refute_0_83:[bind(Y,$fot(X_31)),bind(X_30,$fot(X_32))]]) ).

cnf(refute_0_314,plain,
    greatest_lower_bound(X_32,X_31) = greatest_lower_bound(X_31,X_32),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_32)),bind(Y,$fot(X_31))]]) ).

cnf(refute_0_315,plain,
    ( greatest_lower_bound(X_32,X_31) != greatest_lower_bound(X_31,X_32)
    | greatest_lower_bound(X_31,X_32) = greatest_lower_bound(X_32,X_31) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_32,X_31))),bind(Y0,$fot(greatest_lower_bound(X_31,X_32)))]]) ).

cnf(refute_0_316,plain,
    greatest_lower_bound(X_31,X_32) = greatest_lower_bound(X_32,X_31),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,X_31),greatest_lower_bound(X_31,X_32)) )],[refute_0_314,refute_0_315]) ).

cnf(refute_0_317,plain,
    ( greatest_lower_bound(X_31,X_32) != greatest_lower_bound(X_32,X_31)
    | greatest_lower_bound(X_32,greatest_lower_bound(X_31,X_32)) != greatest_lower_bound(X_32,X_31)
    | greatest_lower_bound(X_32,greatest_lower_bound(X_32,X_31)) = greatest_lower_bound(X_32,X_31) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(X_31,X_32)),greatest_lower_bound(X_32,X_31)) ),[0,1],$fot(greatest_lower_bound(X_32,X_31))]]) ).

cnf(refute_0_318,plain,
    ( greatest_lower_bound(X_32,greatest_lower_bound(X_31,X_32)) != greatest_lower_bound(X_32,X_31)
    | greatest_lower_bound(X_32,greatest_lower_bound(X_32,X_31)) = greatest_lower_bound(X_32,X_31) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_31,X_32),greatest_lower_bound(X_32,X_31)) )],[refute_0_316,refute_0_317]) ).

cnf(refute_0_319,plain,
    greatest_lower_bound(X_32,greatest_lower_bound(X_32,X_31)) = greatest_lower_bound(X_32,X_31),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,greatest_lower_bound(X_31,X_32)),greatest_lower_bound(X_32,X_31)) )],[refute_0_313,refute_0_318]) ).

cnf(refute_0_320,plain,
    greatest_lower_bound(c,greatest_lower_bound(c,X_66)) = greatest_lower_bound(c,X_66),
    inference(subst,[],[refute_0_319:[bind(X_31,$fot(X_66)),bind(X_32,$fot(c))]]) ).

cnf(refute_0_321,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))))]]) ).

cnf(refute_0_322,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66)))
    | greatest_lower_bound(c,greatest_lower_bound(c,X_66)) != greatest_lower_bound(c,X_66)
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66)))) ),[1,1],$fot(greatest_lower_bound(c,X_66))]]) ).

cnf(refute_0_323,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(c,X_66)) != greatest_lower_bound(c,X_66)
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66)))) )],[refute_0_321,refute_0_322]) ).

cnf(refute_0_324,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(c,X_66)),greatest_lower_bound(c,X_66)) )],[refute_0_320,refute_0_323]) ).

cnf(refute_0_325,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) = greatest_lower_bound(greatest_lower_bound(X_38,greatest_lower_bound(Y,X_38)),X_40),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_38)),bind(Y,$fot(greatest_lower_bound(Y,X_38))),bind(Z,$fot(X_40))]]) ).

cnf(refute_0_326,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(Y,X_38)) = greatest_lower_bound(X_38,Y),
    inference(subst,[],[refute_0_83:[bind(X_30,$fot(X_38))]]) ).

cnf(refute_0_327,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(Y,X_38)) != greatest_lower_bound(X_38,Y)
    | greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) != greatest_lower_bound(greatest_lower_bound(X_38,greatest_lower_bound(Y,X_38)),X_40)
    | greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) = greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)),greatest_lower_bound(greatest_lower_bound(X_38,greatest_lower_bound(Y,X_38)),X_40)) ),[1,0],$fot(greatest_lower_bound(X_38,Y))]]) ).

cnf(refute_0_328,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) != greatest_lower_bound(greatest_lower_bound(X_38,greatest_lower_bound(Y,X_38)),X_40)
    | greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) = greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(Y,X_38)),greatest_lower_bound(X_38,Y)) )],[refute_0_326,refute_0_327]) ).

cnf(refute_0_329,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) = greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)),greatest_lower_bound(greatest_lower_bound(X_38,greatest_lower_bound(Y,X_38)),X_40)) )],[refute_0_325,refute_0_328]) ).

cnf(refute_0_330,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_39))) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(greatest_lower_bound(Y,X_39)))]]) ).

cnf(refute_0_331,plain,
    greatest_lower_bound(X_39,greatest_lower_bound(Y,X_39)) = greatest_lower_bound(X_39,Y),
    inference(subst,[],[refute_0_83:[bind(X_30,$fot(X_39))]]) ).

cnf(refute_0_332,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_39))) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39))
    | greatest_lower_bound(X_39,greatest_lower_bound(Y,X_39)) != greatest_lower_bound(X_39,Y)
    | greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_39))),greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39))) ),[0,1],$fot(greatest_lower_bound(X_39,Y))]]) ).

cnf(refute_0_333,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_39))) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39))
    | greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(Y,X_39)),greatest_lower_bound(X_39,Y)) )],[refute_0_331,refute_0_332]) ).

cnf(refute_0_334,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_39,greatest_lower_bound(Y,X_39))),greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39))) )],[refute_0_330,refute_0_333]) ).

cnf(refute_0_335,plain,
    greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_336,plain,
    greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)) = greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)))]]) ).

cnf(refute_0_337,plain,
    ( greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)) != greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y))
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y) != greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))
    | greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)) = greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)),greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y))) ),[1,1],$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))]]) ).

cnf(refute_0_338,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y) != greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))
    | greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)) = greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)),greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y))) )],[refute_0_336,refute_0_337]) ).

cnf(refute_0_339,plain,
    greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)) = greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y),greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))) )],[refute_0_335,refute_0_338]) ).

cnf(refute_0_340,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),X),
    inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_38,X_39)))]]) ).

cnf(refute_0_341,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_39,X)) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),X),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(X))]]) ).

cnf(refute_0_342,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_39,X)) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),X)
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),X) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_38,X_39),X)))]]) ).

cnf(refute_0_343,plain,
    greatest_lower_bound(greatest_lower_bound(X_38,X_39),X) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X)),greatest_lower_bound(greatest_lower_bound(X_38,X_39),X)) )],[refute_0_341,refute_0_342]) ).

cnf(refute_0_344,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),X)
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),X) != greatest_lower_bound(X_38,greatest_lower_bound(X_39,X))
    | greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)),greatest_lower_bound(X_38,greatest_lower_bound(X_39,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_38,X_39),X))]]) ).

cnf(refute_0_345,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),X)
    | greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_38,X_39),X),greatest_lower_bound(X_38,greatest_lower_bound(X_39,X))) )],[refute_0_343,refute_0_344]) ).

cnf(refute_0_346,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)),greatest_lower_bound(greatest_lower_bound(X_38,X_39),X)) )],[refute_0_340,refute_0_345]) ).

cnf(refute_0_347,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)) != greatest_lower_bound(X_38,greatest_lower_bound(X_39,X))
    | greatest_lower_bound(X_38,greatest_lower_bound(X_39,X)) = greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)))),bind(Y0,$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X))))]]) ).

cnf(refute_0_348,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_39,X)) = greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_38,X_39)),greatest_lower_bound(X_38,greatest_lower_bound(X_39,X))) )],[refute_0_346,refute_0_347]) ).

cnf(refute_0_349,plain,
    greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)) = greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)),
    inference(subst,[],[refute_0_348:[bind(X,$fot(X_39)),bind(X_38,$fot(greatest_lower_bound(X_38,X_39))),bind(X_39,$fot(Y))]]) ).

cnf(refute_0_350,plain,
    ( greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)) != greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)) != greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y))
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)) = greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)))),bind(Y0,$fot(greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)))),bind(Z0,$fot(greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))))]]) ).

cnf(refute_0_351,plain,
    ( greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)) != greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)) = greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)),greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y))) )],[refute_0_349,refute_0_350]) ).

cnf(refute_0_352,plain,
    greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)) = greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(greatest_lower_bound(X_38,X_39),Y)),greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))) )],[refute_0_339,refute_0_351]) ).

cnf(refute_0_353,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39))
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)) != greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))
    | greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)) = greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)),greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)))]]) ).

cnf(refute_0_354,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39))
    | greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)) = greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39)),greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))) )],[refute_0_352,refute_0_353]) ).

cnf(refute_0_355,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)) = greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)),greatest_lower_bound(greatest_lower_bound(X_38,X_39),greatest_lower_bound(Y,X_39))) )],[refute_0_334,refute_0_354]) ).

cnf(refute_0_356,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)) != greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))
    | greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))),bind(Y0,$fot(greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))))]]) ).

cnf(refute_0_357,plain,
    greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y))) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)),greatest_lower_bound(X_39,greatest_lower_bound(X_38,greatest_lower_bound(X_39,Y)))) )],[refute_0_355,refute_0_356]) ).

cnf(refute_0_358,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))) = greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)),
    inference(subst,[],[refute_0_357:[bind(Y,$fot(X_40)),bind(X_38,$fot(Y)),bind(X_39,$fot(X_38))]]) ).

cnf(refute_0_359,plain,
    greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40) = greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(Y)),bind(Y,$fot(X_38)),bind(Z,$fot(X_40))]]) ).

cnf(refute_0_360,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) = greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)))]]) ).

cnf(refute_0_361,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) != greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40))
    | greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40) != greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))
    | greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) = greatest_lower_bound(X_38,greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)),greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)))]]) ).

cnf(refute_0_362,plain,
    ( greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40) != greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))
    | greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) = greatest_lower_bound(X_38,greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)),greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40))) )],[refute_0_360,refute_0_361]) ).

cnf(refute_0_363,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) = greatest_lower_bound(X_38,greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40),greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))) )],[refute_0_359,refute_0_362]) ).

cnf(refute_0_364,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))) != greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))
    | greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) != greatest_lower_bound(X_38,greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)))
    | greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) = greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)))),bind(Y0,$fot(greatest_lower_bound(X_38,greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))))]]) ).

cnf(refute_0_365,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))) != greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))
    | greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) = greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)),greatest_lower_bound(X_38,greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)))) )],[refute_0_363,refute_0_364]) ).

cnf(refute_0_366,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) = greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))),greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))) )],[refute_0_358,refute_0_365]) ).

cnf(refute_0_367,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) != greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))
    | greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) != greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40)
    | greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) = greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)),greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40)) ),[0],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)))]]) ).

cnf(refute_0_368,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) != greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40)
    | greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) = greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)),greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40))) )],[refute_0_366,refute_0_367]) ).

cnf(refute_0_369,plain,
    greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40) = greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_38)),bind(Z,$fot(X_40))]]) ).

cnf(refute_0_370,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) != greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40)
    | greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40) != greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40))
    | greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) = greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)),greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40))]]) ).

cnf(refute_0_371,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) != greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40)
    | greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) = greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40),greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40))) )],[refute_0_369,refute_0_370]) ).

cnf(refute_0_372,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)) != greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40)
    | greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) = greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)),greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40)) )],[refute_0_368,refute_0_371]) ).

cnf(refute_0_373,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) = greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(greatest_lower_bound(Y,X_38),X_40)),greatest_lower_bound(greatest_lower_bound(X_38,Y),X_40)) )],[refute_0_329,refute_0_372]) ).

cnf(refute_0_374,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) != greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40))
    | greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40)) = greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)))),bind(Y0,$fot(greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40))))]]) ).

cnf(refute_0_375,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40)) = greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_38,X_40)),greatest_lower_bound(X_38,greatest_lower_bound(Y,X_40))) )],[refute_0_373,refute_0_374]) ).

cnf(refute_0_376,plain,
    greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))),
    inference(subst,[],[refute_0_375:[bind(Y,$fot(a)),bind(X_38,$fot(c)),bind(X_40,$fot(greatest_lower_bound(c,X_66)))]]) ).

cnf(refute_0_377,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66)))
    | greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_66))))]]) ).

cnf(refute_0_378,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66)))) )],[refute_0_376,refute_0_377]) ).

cnf(refute_0_379,plain,
    greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,X_66))),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) )],[refute_0_324,refute_0_378]) ).

cnf(refute_0_380,plain,
    greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)) = greatest_lower_bound(X_66,c),
    inference(subst,[],[refute_0_319:[bind(X_31,$fot(c)),bind(X_32,$fot(X_66))]]) ).

cnf(refute_0_381,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) = greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))))]]) ).

cnf(refute_0_382,plain,
    ( greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)) != greatest_lower_bound(X_66,c)
    | greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) != greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)))
    | greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) = greatest_lower_bound(b,greatest_lower_bound(X_66,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))),greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)))) ),[1,1],$fot(greatest_lower_bound(X_66,c))]]) ).

cnf(refute_0_383,plain,
    ( greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)) != greatest_lower_bound(X_66,c)
    | greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) = greatest_lower_bound(b,greatest_lower_bound(X_66,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))),greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)))) )],[refute_0_381,refute_0_382]) ).

cnf(refute_0_384,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) = greatest_lower_bound(b,greatest_lower_bound(X_66,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)),greatest_lower_bound(X_66,c)) )],[refute_0_380,refute_0_383]) ).

cnf(refute_0_385,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_66,c)) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) != greatest_lower_bound(b,greatest_lower_bound(X_66,c))
    | greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_66,c)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_66))))]]) ).

cnf(refute_0_386,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_66,c)) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))),greatest_lower_bound(b,greatest_lower_bound(X_66,c))) )],[refute_0_384,refute_0_385]) ).

cnf(refute_0_387,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_66,c)),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) )],[refute_0_309,refute_0_386]) ).

cnf(refute_0_388,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40)) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(X_40))]]) ).

cnf(refute_0_389,plain,
    greatest_lower_bound(X_40,X_39) = greatest_lower_bound(X_39,X_40),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_40)),bind(Y,$fot(X_39))]]) ).

cnf(refute_0_390,plain,
    ( greatest_lower_bound(X_40,X_39) != greatest_lower_bound(X_39,X_40)
    | greatest_lower_bound(X_39,X_40) = greatest_lower_bound(X_40,X_39) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_40,X_39))),bind(Y0,$fot(greatest_lower_bound(X_39,X_40)))]]) ).

cnf(refute_0_391,plain,
    greatest_lower_bound(X_39,X_40) = greatest_lower_bound(X_40,X_39),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_40,X_39),greatest_lower_bound(X_39,X_40)) )],[refute_0_389,refute_0_390]) ).

cnf(refute_0_392,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40)) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40)
    | greatest_lower_bound(X_39,X_40) != greatest_lower_bound(X_40,X_39)
    | greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40)),greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40)) ),[0,1],$fot(greatest_lower_bound(X_40,X_39))]]) ).

cnf(refute_0_393,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40)) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40)
    | greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,X_40),greatest_lower_bound(X_40,X_39)) )],[refute_0_391,refute_0_392]) ).

cnf(refute_0_394,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40)),greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40)) )],[refute_0_388,refute_0_393]) ).

cnf(refute_0_395,plain,
    greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(X_40))]]) ).

cnf(refute_0_396,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40)
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40) != greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40))
    | greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)),greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40))]]) ).

cnf(refute_0_397,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40)
    | greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40),greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40))) )],[refute_0_395,refute_0_396]) ).

cnf(refute_0_398,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)),greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_40)) )],[refute_0_394,refute_0_397]) ).

cnf(refute_0_399,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)) != greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40))
    | greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40)) = greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)))),bind(Y0,$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40))))]]) ).

cnf(refute_0_400,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40)) = greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_40,X_39)),greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_40))) )],[refute_0_398,refute_0_399]) ).

cnf(refute_0_401,plain,
    greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_66,c),X_66)) = greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))),
    inference(subst,[],[refute_0_400:[bind(X_38,$fot(b)),bind(X_39,$fot(greatest_lower_bound(X_66,c))),bind(X_40,$fot(X_66))]]) ).

cnf(refute_0_402,plain,
    greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)) = greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_66,c),X_66)),
    inference(subst,[],[refute_0_375:[bind(Y,$fot(b)),bind(X_38,$fot(greatest_lower_bound(X_66,c))),bind(X_40,$fot(X_66))]]) ).

cnf(refute_0_403,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_66,c),X_66)) != greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)) != greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_66,c),X_66))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)) = greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_66,c),X_66)))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)))))]]) ).

cnf(refute_0_404,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_66,c),X_66)) != greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)) = greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)),greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_66,c),X_66))) )],[refute_0_402,refute_0_403]) ).

cnf(refute_0_405,plain,
    greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)) = greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_66,c),X_66)),greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)))) )],[refute_0_401,refute_0_404]) ).

cnf(refute_0_406,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)) != greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_66))))]]) ).

cnf(refute_0_407,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)),greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c)))) )],[refute_0_405,refute_0_406]) ).

cnf(refute_0_408,plain,
    greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_66,greatest_lower_bound(X_66,c))),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) )],[refute_0_387,refute_0_407]) ).

cnf(refute_0_409,plain,
    greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))) = greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))))]]) ).

cnf(refute_0_410,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))) != greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))),greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)))) ),[1,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_66)))]]) ).

cnf(refute_0_411,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))),greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)))) )],[refute_0_409,refute_0_410]) ).

cnf(refute_0_412,plain,
    greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) )],[refute_0_408,refute_0_411]) ).

cnf(refute_0_413,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))) != greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66)))
    | greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))))),bind(Y0,$fot(greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_66))))]]) ).

cnf(refute_0_414,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))),greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66)))) )],[refute_0_412,refute_0_413]) ).

cnf(refute_0_415,plain,
    greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,X_66))),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) )],[refute_0_379,refute_0_414]) ).

cnf(refute_0_416,plain,
    greatest_lower_bound(X,greatest_lower_bound(b,greatest_lower_bound(X_66,c))) = greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)),
    inference(subst,[],[associativity_of_glb:[bind(Y,$fot(b)),bind(Z,$fot(greatest_lower_bound(X_66,c)))]]) ).

cnf(refute_0_417,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(b,greatest_lower_bound(X_66,c))) != greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c))
    | greatest_lower_bound(b,greatest_lower_bound(X_66,c)) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(b,greatest_lower_bound(X_66,c))),greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c))) ),[0,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_66)))]]) ).

cnf(refute_0_418,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(b,greatest_lower_bound(X_66,c))) != greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c))
    | greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_66,c)),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) )],[refute_0_309,refute_0_417]) ).

cnf(refute_0_419,plain,
    greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(b,greatest_lower_bound(X_66,c))),greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c))) )],[refute_0_416,refute_0_418]) ).

cnf(refute_0_420,plain,
    greatest_lower_bound(greatest_lower_bound(X,b),X_66) = greatest_lower_bound(X,greatest_lower_bound(b,X_66)),
    inference(subst,[],[refute_0_79:[bind(Y,$fot(b)),bind(Z,$fot(X_66))]]) ).

cnf(refute_0_421,plain,
    greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)) = greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)))]]) ).

cnf(refute_0_422,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)) != greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66))
    | greatest_lower_bound(greatest_lower_bound(X,b),X_66) != greatest_lower_bound(X,greatest_lower_bound(b,X_66))
    | greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)) = greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)),greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66))) ),[1,1],$fot(greatest_lower_bound(X,greatest_lower_bound(b,X_66)))]]) ).

cnf(refute_0_423,plain,
    ( greatest_lower_bound(greatest_lower_bound(X,b),X_66) != greatest_lower_bound(X,greatest_lower_bound(b,X_66))
    | greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)) = greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)),greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66))) )],[refute_0_421,refute_0_422]) ).

cnf(refute_0_424,plain,
    greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)) = greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,b),X_66),greatest_lower_bound(X,greatest_lower_bound(b,X_66))) )],[refute_0_420,refute_0_423]) ).

cnf(refute_0_425,plain,
    greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)) = greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)),
    inference(subst,[],[refute_0_348:[bind(X,$fot(c)),bind(X_38,$fot(greatest_lower_bound(X,b))),bind(X_39,$fot(X_66))]]) ).

cnf(refute_0_426,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)) != greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66)))
    | greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)) != greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66))
    | greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)) = greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)))),bind(Y0,$fot(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)))),bind(Z0,$fot(greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66)))))]]) ).

cnf(refute_0_427,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)) != greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66)))
    | greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)) = greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)),greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66))) )],[refute_0_425,refute_0_426]) ).

cnf(refute_0_428,plain,
    greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)) = greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X,b),X_66)),greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66)))) )],[refute_0_424,refute_0_427]) ).

cnf(refute_0_429,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c))
    | greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)) != greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66)))
    | greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,X_66))),greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)))]]) ).

cnf(refute_0_430,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c))
    | greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c)),greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66)))) )],[refute_0_428,refute_0_429]) ).

cnf(refute_0_431,plain,
    greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(c,greatest_lower_bound(X,greatest_lower_bound(b,X_66))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,X_66))),greatest_lower_bound(greatest_lower_bound(X,b),greatest_lower_bound(X_66,c))) )],[refute_0_419,refute_0_430]) ).

cnf(refute_0_432,plain,
    greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))),
    inference(subst,[],[refute_0_431:[bind(X,$fot(greatest_lower_bound(X_66,c)))]]) ).

cnf(refute_0_433,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))))),bind(Y0,$fot(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_66))))]]) ).

cnf(refute_0_434,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))),greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66)))) )],[refute_0_432,refute_0_433]) ).

cnf(refute_0_435,plain,
    greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) = greatest_lower_bound(a,greatest_lower_bound(c,X_66)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(b,X_66))),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) )],[refute_0_415,refute_0_434]) ).

cnf(refute_0_436,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(a,greatest_lower_bound(c,X_66))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(greatest_lower_bound(X_66,c),b)
    | greatest_lower_bound(a,greatest_lower_bound(c,X_66)) = greatest_lower_bound(greatest_lower_bound(X_66,c),b) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))),greatest_lower_bound(greatest_lower_bound(X_66,c),b)) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_66)))]]) ).

cnf(refute_0_437,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(greatest_lower_bound(X_66,c),b)
    | greatest_lower_bound(a,greatest_lower_bound(c,X_66)) = greatest_lower_bound(greatest_lower_bound(X_66,c),b) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) )],[refute_0_435,refute_0_436]) ).

cnf(refute_0_438,plain,
    greatest_lower_bound(X_66,greatest_lower_bound(b,c)) = greatest_lower_bound(X_66,greatest_lower_bound(b,c)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_66,greatest_lower_bound(b,c)))]]) ).

cnf(refute_0_439,plain,
    ( greatest_lower_bound(X_66,greatest_lower_bound(b,c)) != greatest_lower_bound(X_66,greatest_lower_bound(b,c))
    | greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | greatest_lower_bound(X_66,greatest_lower_bound(b,c)) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_66,greatest_lower_bound(b,c)),greatest_lower_bound(X_66,greatest_lower_bound(b,c))) ),[1,1],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_440,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | greatest_lower_bound(X_66,greatest_lower_bound(b,c)) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_66,greatest_lower_bound(b,c)),greatest_lower_bound(X_66,greatest_lower_bound(b,c))) )],[refute_0_438,refute_0_439]) ).

cnf(refute_0_441,plain,
    greatest_lower_bound(X_66,greatest_lower_bound(b,c)) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_294,refute_0_440]) ).

cnf(refute_0_442,plain,
    greatest_lower_bound(X_66,greatest_lower_bound(c,b)) = greatest_lower_bound(X_66,greatest_lower_bound(b,c)),
    inference(subst,[],[refute_0_400:[bind(X_38,$fot(X_66)),bind(X_39,$fot(c)),bind(X_40,$fot(b))]]) ).

cnf(refute_0_443,plain,
    greatest_lower_bound(greatest_lower_bound(X_66,c),b) = greatest_lower_bound(X_66,greatest_lower_bound(c,b)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_66)),bind(Y,$fot(c)),bind(Z,$fot(b))]]) ).

cnf(refute_0_444,plain,
    ( greatest_lower_bound(X_66,greatest_lower_bound(c,b)) != greatest_lower_bound(X_66,greatest_lower_bound(b,c))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),b) != greatest_lower_bound(X_66,greatest_lower_bound(c,b))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),b) = greatest_lower_bound(X_66,greatest_lower_bound(b,c)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_66,c),b))),bind(Y0,$fot(greatest_lower_bound(X_66,greatest_lower_bound(c,b)))),bind(Z0,$fot(greatest_lower_bound(X_66,greatest_lower_bound(b,c))))]]) ).

cnf(refute_0_445,plain,
    ( greatest_lower_bound(X_66,greatest_lower_bound(c,b)) != greatest_lower_bound(X_66,greatest_lower_bound(b,c))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),b) = greatest_lower_bound(X_66,greatest_lower_bound(b,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),b),greatest_lower_bound(X_66,greatest_lower_bound(c,b))) )],[refute_0_443,refute_0_444]) ).

cnf(refute_0_446,plain,
    greatest_lower_bound(greatest_lower_bound(X_66,c),b) = greatest_lower_bound(X_66,greatest_lower_bound(b,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_66,greatest_lower_bound(c,b)),greatest_lower_bound(X_66,greatest_lower_bound(b,c))) )],[refute_0_442,refute_0_445]) ).

cnf(refute_0_447,plain,
    ( greatest_lower_bound(X_66,greatest_lower_bound(b,c)) != greatest_lower_bound(X_66,greatest_lower_bound(a,c))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),b) != greatest_lower_bound(X_66,greatest_lower_bound(b,c))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),b) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_66,c),b))),bind(Y0,$fot(greatest_lower_bound(X_66,greatest_lower_bound(b,c)))),bind(Z0,$fot(greatest_lower_bound(X_66,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_448,plain,
    ( greatest_lower_bound(X_66,greatest_lower_bound(b,c)) != greatest_lower_bound(X_66,greatest_lower_bound(a,c))
    | greatest_lower_bound(greatest_lower_bound(X_66,c),b) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),b),greatest_lower_bound(X_66,greatest_lower_bound(b,c))) )],[refute_0_446,refute_0_447]) ).

cnf(refute_0_449,plain,
    greatest_lower_bound(greatest_lower_bound(X_66,c),b) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_66,greatest_lower_bound(b,c)),greatest_lower_bound(X_66,greatest_lower_bound(a,c))) )],[refute_0_441,refute_0_448]) ).

cnf(refute_0_450,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,X_66)) != greatest_lower_bound(greatest_lower_bound(X_66,c),b)
    | greatest_lower_bound(greatest_lower_bound(X_66,c),b) != greatest_lower_bound(X_66,greatest_lower_bound(a,c))
    | greatest_lower_bound(a,greatest_lower_bound(c,X_66)) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_66)),greatest_lower_bound(X_66,greatest_lower_bound(a,c))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_66,c),b))]]) ).

cnf(refute_0_451,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,X_66)) != greatest_lower_bound(greatest_lower_bound(X_66,c),b)
    | greatest_lower_bound(a,greatest_lower_bound(c,X_66)) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),b),greatest_lower_bound(X_66,greatest_lower_bound(a,c))) )],[refute_0_449,refute_0_450]) ).

cnf(refute_0_452,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(greatest_lower_bound(X_66,c),b)
    | greatest_lower_bound(a,greatest_lower_bound(c,X_66)) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_66)),greatest_lower_bound(greatest_lower_bound(X_66,c),b)) )],[refute_0_437,refute_0_451]) ).

cnf(refute_0_453,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,X_66)) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_66,c),greatest_lower_bound(a,greatest_lower_bound(c,X_66))),greatest_lower_bound(greatest_lower_bound(X_66,c),b)) )],[refute_0_312,refute_0_452]) ).

cnf(refute_0_454,plain,
    ( multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66)))
    | greatest_lower_bound(a,greatest_lower_bound(c,X_66)) != greatest_lower_bound(X_66,greatest_lower_bound(a,c))
    | multiply(X_103,greatest_lower_bound(X_66,greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66))),greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66)))) ),[0,1],$fot(greatest_lower_bound(X_66,greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_455,plain,
    ( multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) != greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66)))
    | multiply(X_103,greatest_lower_bound(X_66,greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_66)),greatest_lower_bound(X_66,greatest_lower_bound(a,c))) )],[refute_0_453,refute_0_454]) ).

cnf(refute_0_456,plain,
    multiply(X_103,greatest_lower_bound(X_66,greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66))),
    inference(resolve,[$cnf( $equal(multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66))),greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66)))) )],[refute_0_290,refute_0_455]) ).

cnf(refute_0_457,plain,
    ( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
    | greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).

cnf(refute_0_458,plain,
    greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_457]) ).

cnf(refute_0_459,plain,
    greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66))) = multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66))),
    inference(subst,[],[refute_0_458:[bind(X,$fot(X_103)),bind(Y,$fot(a)),bind(Z,$fot(greatest_lower_bound(c,X_66)))]]) ).

cnf(refute_0_460,plain,
    ( multiply(X_103,greatest_lower_bound(X_66,greatest_lower_bound(a,c))) != greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66)))
    | greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66))) != multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66)))
    | multiply(X_103,greatest_lower_bound(X_66,greatest_lower_bound(a,c))) = multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_103,greatest_lower_bound(X_66,greatest_lower_bound(a,c))),multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66)))) ),[0],$fot(greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66))))]]) ).

cnf(refute_0_461,plain,
    ( multiply(X_103,greatest_lower_bound(X_66,greatest_lower_bound(a,c))) != greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66)))
    | multiply(X_103,greatest_lower_bound(X_66,greatest_lower_bound(a,c))) = multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66))),multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66)))) )],[refute_0_459,refute_0_460]) ).

cnf(refute_0_462,plain,
    multiply(X_103,greatest_lower_bound(X_66,greatest_lower_bound(a,c))) = multiply(X_103,greatest_lower_bound(a,greatest_lower_bound(c,X_66))),
    inference(resolve,[$cnf( $equal(multiply(X_103,greatest_lower_bound(X_66,greatest_lower_bound(a,c))),greatest_lower_bound(multiply(X_103,a),multiply(X_103,greatest_lower_bound(c,X_66)))) )],[refute_0_456,refute_0_461]) ).

cnf(refute_0_463,plain,
    multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(X_144,greatest_lower_bound(a,c))) = multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,X_144))),
    inference(subst,[],[refute_0_462:[bind(X_103,$fot(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))))),bind(X_66,$fot(X_144))]]) ).

cnf(refute_0_464,plain,
    ( multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(X_144,greatest_lower_bound(a,c))) != multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,X_144)))
    | multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(X_144,greatest_lower_bound(a,c))) != identity
    | multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,X_144))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(X_144,greatest_lower_bound(a,c))),identity) ),[0],$fot(multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,X_144))))]]) ).

cnf(refute_0_465,plain,
    ( multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(X_144,greatest_lower_bound(a,c))) != identity
    | multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,X_144))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(X_144,greatest_lower_bound(a,c))),multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,X_144)))) )],[refute_0_463,refute_0_464]) ).

cnf(refute_0_466,plain,
    multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,X_144))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_144,greatest_lower_bound(a,c))),greatest_lower_bound(X_144,greatest_lower_bound(a,c))),identity) )],[refute_0_289,refute_0_465]) ).

cnf(refute_0_467,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,a))) = identity,
    inference(subst,[],[refute_0_466:[bind(X_144,$fot(a))]]) ).

cnf(refute_0_468,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,a)) = greatest_lower_bound(a,c),
    inference(subst,[],[refute_0_83:[bind(Y,$fot(c)),bind(X_30,$fot(a))]]) ).

cnf(refute_0_469,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,a))) != identity
    | greatest_lower_bound(a,greatest_lower_bound(c,a)) != greatest_lower_bound(a,c)
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,c)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,a))),identity) ),[0,1],$fot(greatest_lower_bound(a,c))]]) ).

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

cnf(refute_0_471,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,c)) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,a))),identity) )],[refute_0_467,refute_0_470]) ).

cnf(refute_0_472,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) = inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity)),
    inference(subst,[],[refute_0_116:[bind(X_112,$fot(identity)),bind(X_113,$fot(multiply(inverse(X_105),X_104)))]]) ).

cnf(refute_0_473,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) != greatest_lower_bound(identity,multiply(inverse(X_105),X_104))
    | greatest_lower_bound(identity,multiply(inverse(X_105),X_104)) = multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))))]]) ).

cnf(refute_0_474,plain,
    greatest_lower_bound(identity,multiply(inverse(X_105),X_104)) = multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)),greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) )],[refute_0_134,refute_0_473]) ).

cnf(refute_0_475,plain,
    ( greatest_lower_bound(identity,multiply(inverse(X_105),X_104)) != multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) != inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))
    | inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))) = inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))),inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))) ),[0,0],$fot(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105)))]]) ).

cnf(refute_0_476,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) != inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))
    | inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))) = inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)),multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))) )],[refute_0_474,refute_0_475]) ).

cnf(refute_0_477,plain,
    inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))) = inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))),inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))) )],[refute_0_472,refute_0_476]) ).

cnf(refute_0_478,plain,
    inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))) = multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_105)),bind(X_18,$fot(greatest_lower_bound(X_104,X_105)))]]) ).

cnf(refute_0_479,plain,
    ( inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))) != multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105)
    | inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))) != inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))
    | multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105) = inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))),inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))) ),[0],$fot(multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105))]]) ).

cnf(refute_0_480,plain,
    ( inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))) != inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))
    | multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105) = inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))),multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105)) )],[refute_0_478,refute_0_479]) ).

cnf(refute_0_481,plain,
    ( inverse(greatest_lower_bound(X_112,X_113)) != inverse(greatest_lower_bound(X_113,X_112))
    | inverse(greatest_lower_bound(X_113,X_112)) = inverse(greatest_lower_bound(X_112,X_113)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(X_112,X_113)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_113,X_112))))]]) ).

cnf(refute_0_482,plain,
    inverse(greatest_lower_bound(X_113,X_112)) = inverse(greatest_lower_bound(X_112,X_113)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_112,X_113)),inverse(greatest_lower_bound(X_113,X_112))) )],[refute_0_116,refute_0_481]) ).

cnf(refute_0_483,plain,
    inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))),
    inference(subst,[],[refute_0_482:[bind(X_112,$fot(identity)),bind(X_113,$fot(multiply(inverse(X_105),X_104)))]]) ).

cnf(refute_0_484,plain,
    ( multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105) != inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))
    | inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)))
    | multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105) = inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)))) ),[0],$fot(inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity)))]]) ).

cnf(refute_0_485,plain,
    ( multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105) != inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))
    | multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105) = inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity)),inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104)))) )],[refute_0_483,refute_0_484]) ).

cnf(refute_0_486,plain,
    ( inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))) != inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))
    | multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105) = inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105),inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))) )],[refute_0_480,refute_0_485]) ).

cnf(refute_0_487,plain,
    multiply(inverse(greatest_lower_bound(X_104,X_105)),X_105) = inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_104))),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_105),greatest_lower_bound(X_104,X_105))),inverse(greatest_lower_bound(multiply(inverse(X_105),X_104),identity))) )],[refute_0_477,refute_0_486]) ).

cnf(refute_0_488,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,c)) = inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),
    inference(subst,[],[refute_0_487:[bind(X_104,$fot(a)),bind(X_105,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_489,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,c)) != identity
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,c)) != inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))
    | inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,c)),identity) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))]]) ).

cnf(refute_0_490,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,c)) != identity
    | inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,c)),inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) )],[refute_0_488,refute_0_489]) ).

cnf(refute_0_491,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(a,c))),greatest_lower_bound(a,c)),identity) )],[refute_0_471,refute_0_490]) ).

cnf(refute_0_492,plain,
    ( multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))
    | inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) != identity
    | multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_493,plain,
    ( multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))
    | multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) )],[refute_0_491,refute_0_492]) ).

cnf(refute_0_494,plain,
    multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))) )],[refute_0_288,refute_0_493]) ).

cnf(refute_0_495,plain,
    greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)),
    inference(subst,[],[refute_0_319:[bind(X_31,$fot(multiply(inverse(greatest_lower_bound(a,c)),a))),bind(X_32,$fot(identity))]]) ).

cnf(refute_0_496,plain,
    multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),
    inference(subst,[],[refute_0_189:[bind(X,$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))))]]) ).

cnf(refute_0_497,plain,
    ( multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))
    | greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))
    | multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))]]) ).

cnf(refute_0_498,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))
    | multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) )],[refute_0_496,refute_0_497]) ).

cnf(refute_0_499,plain,
    multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) )],[refute_0_495,refute_0_498]) ).

cnf(refute_0_500,plain,
    ( multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))
    | multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))]]) ).

cnf(refute_0_501,plain,
    ( multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) )],[refute_0_499,refute_0_500]) ).

cnf(refute_0_502,plain,
    greatest_lower_bound(identity,identity) = identity,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(identity))]]) ).

cnf(refute_0_503,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))))]]) ).

cnf(refute_0_504,plain,
    ( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))
    | inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) != identity
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) = greatest_lower_bound(identity,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_505,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) != identity
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) = greatest_lower_bound(identity,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))) )],[refute_0_503,refute_0_504]) ).

cnf(refute_0_506,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) = greatest_lower_bound(identity,identity),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) )],[refute_0_491,refute_0_505]) ).

cnf(refute_0_507,plain,
    ( greatest_lower_bound(identity,identity) != identity
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) != greatest_lower_bound(identity,identity)
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) = identity ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))))),bind(Y0,$fot(greatest_lower_bound(identity,identity))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_508,plain,
    ( greatest_lower_bound(identity,identity) != identity
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))),greatest_lower_bound(identity,identity)) )],[refute_0_506,refute_0_507]) ).

cnf(refute_0_509,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) = identity,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,identity),identity) )],[refute_0_502,refute_0_508]) ).

cnf(refute_0_510,plain,
    ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))) != identity
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) = identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)),identity) ),[0],$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))))]]) ).

cnf(refute_0_511,plain,
    ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))),identity) )],[refute_0_509,refute_0_510]) ).

cnf(refute_0_512,plain,
    ( multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))) )],[refute_0_501,refute_0_511]) ).

cnf(refute_0_513,plain,
    greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) = identity,
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),identity),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))))) )],[refute_0_494,refute_0_512]) ).

cnf(refute_0_514,plain,
    ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) != identity
    | least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) != multiply(inverse(greatest_lower_bound(a,c)),a)
    | least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),identity) = multiply(inverse(greatest_lower_bound(a,c)),a) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),multiply(inverse(greatest_lower_bound(a,c)),a)) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_515,plain,
    ( least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) != multiply(inverse(greatest_lower_bound(a,c)),a)
    | least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),identity) = multiply(inverse(greatest_lower_bound(a,c)),a) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)),identity) )],[refute_0_513,refute_0_514]) ).

cnf(refute_0_516,plain,
    least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),identity) = multiply(inverse(greatest_lower_bound(a,c)),a),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))),multiply(inverse(greatest_lower_bound(a,c)),a)) )],[refute_0_282,refute_0_515]) ).

cnf(refute_0_517,plain,
    least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),identity) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)),
    inference(subst,[],[refute_0_256:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(greatest_lower_bound(a,c)),a)))]]) ).

cnf(refute_0_518,plain,
    ( least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),identity) != multiply(inverse(greatest_lower_bound(a,c)),a)
    | least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),identity) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))
    | least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) = multiply(inverse(greatest_lower_bound(a,c)),a) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),identity),multiply(inverse(greatest_lower_bound(a,c)),a)) ),[0],$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))]]) ).

cnf(refute_0_519,plain,
    ( least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),identity) != multiply(inverse(greatest_lower_bound(a,c)),a)
    | least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) = multiply(inverse(greatest_lower_bound(a,c)),a) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),identity),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a))) )],[refute_0_517,refute_0_518]) ).

cnf(refute_0_520,plain,
    least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) = multiply(inverse(greatest_lower_bound(a,c)),a),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(a,c)),a),identity),multiply(inverse(greatest_lower_bound(a,c)),a)) )],[refute_0_516,refute_0_519]) ).

cnf(refute_0_521,plain,
    ( b != greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))))
    | least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)) != multiply(inverse(greatest_lower_bound(a,c)),a)
    | b = greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) ),
    introduced(tautology,[equality,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))))) ),[1,1,1,1],$fot(multiply(inverse(greatest_lower_bound(a,c)),a))]]) ).

cnf(refute_0_522,plain,
    ( b != greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))))
    | b = greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)),multiply(inverse(greatest_lower_bound(a,c)),a)) )],[refute_0_520,refute_0_521]) ).

cnf(refute_0_523,plain,
    b = greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))),
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(a,multiply(c,least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),a)))))) )],[refute_0_274,refute_0_522]) ).

cnf(refute_0_524,plain,
    multiply(multiply(c,inverse(greatest_lower_bound(a,c))),a) = multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)),
    inference(subst,[],[associativity:[bind(X,$fot(c)),bind(Y,$fot(inverse(greatest_lower_bound(a,c)))),bind(Z,$fot(a))]]) ).

cnf(refute_0_525,plain,
    multiply(least_upper_bound(X_119,X_120),inverse(X_120)) = least_upper_bound(multiply(X_119,inverse(X_120)),multiply(X_120,inverse(X_120))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_120))),bind(Y,$fot(X_119)),bind(Z,$fot(X_120))]]) ).

cnf(refute_0_526,plain,
    multiply(X_120,inverse(X_120)) = identity,
    inference(subst,[],[refute_0_40:[bind(X,$fot(X_120))]]) ).

cnf(refute_0_527,plain,
    ( multiply(X_120,inverse(X_120)) != identity
    | multiply(least_upper_bound(X_119,X_120),inverse(X_120)) != least_upper_bound(multiply(X_119,inverse(X_120)),multiply(X_120,inverse(X_120)))
    | multiply(least_upper_bound(X_119,X_120),inverse(X_120)) = least_upper_bound(multiply(X_119,inverse(X_120)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_119,X_120),inverse(X_120)),least_upper_bound(multiply(X_119,inverse(X_120)),multiply(X_120,inverse(X_120)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_528,plain,
    ( multiply(least_upper_bound(X_119,X_120),inverse(X_120)) != least_upper_bound(multiply(X_119,inverse(X_120)),multiply(X_120,inverse(X_120)))
    | multiply(least_upper_bound(X_119,X_120),inverse(X_120)) = least_upper_bound(multiply(X_119,inverse(X_120)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_120,inverse(X_120)),identity) )],[refute_0_526,refute_0_527]) ).

cnf(refute_0_529,plain,
    multiply(least_upper_bound(X_119,X_120),inverse(X_120)) = least_upper_bound(multiply(X_119,inverse(X_120)),identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,X_120),inverse(X_120)),least_upper_bound(multiply(X_119,inverse(X_120)),multiply(X_120,inverse(X_120)))) )],[refute_0_525,refute_0_528]) ).

cnf(refute_0_530,plain,
    least_upper_bound(multiply(X_119,inverse(X_120)),identity) = least_upper_bound(identity,multiply(X_119,inverse(X_120))),
    inference(subst,[],[refute_0_256:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_119,inverse(X_120))))]]) ).

cnf(refute_0_531,plain,
    ( multiply(least_upper_bound(X_119,X_120),inverse(X_120)) != least_upper_bound(multiply(X_119,inverse(X_120)),identity)
    | least_upper_bound(multiply(X_119,inverse(X_120)),identity) != least_upper_bound(identity,multiply(X_119,inverse(X_120)))
    | multiply(least_upper_bound(X_119,X_120),inverse(X_120)) = least_upper_bound(identity,multiply(X_119,inverse(X_120))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_119,X_120),inverse(X_120)),least_upper_bound(identity,multiply(X_119,inverse(X_120)))) ),[0],$fot(least_upper_bound(multiply(X_119,inverse(X_120)),identity))]]) ).

cnf(refute_0_532,plain,
    ( multiply(least_upper_bound(X_119,X_120),inverse(X_120)) != least_upper_bound(multiply(X_119,inverse(X_120)),identity)
    | multiply(least_upper_bound(X_119,X_120),inverse(X_120)) = least_upper_bound(identity,multiply(X_119,inverse(X_120))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,inverse(X_120)),identity),least_upper_bound(identity,multiply(X_119,inverse(X_120)))) )],[refute_0_530,refute_0_531]) ).

cnf(refute_0_533,plain,
    multiply(least_upper_bound(X_119,X_120),inverse(X_120)) = least_upper_bound(identity,multiply(X_119,inverse(X_120))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,X_120),inverse(X_120)),least_upper_bound(multiply(X_119,inverse(X_120)),identity)) )],[refute_0_529,refute_0_532]) ).

cnf(refute_0_534,plain,
    multiply(least_upper_bound(X_128,greatest_lower_bound(X_9,X_128)),inverse(greatest_lower_bound(X_9,X_128))) = least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128)))),
    inference(subst,[],[refute_0_533:[bind(X_119,$fot(X_128)),bind(X_120,$fot(greatest_lower_bound(X_9,X_128)))]]) ).

cnf(refute_0_535,plain,
    least_upper_bound(X_128,greatest_lower_bound(X_9,X_128)) = X_128,
    inference(subst,[],[refute_0_281:[bind(X_8,$fot(X_128))]]) ).

cnf(refute_0_536,plain,
    ( multiply(least_upper_bound(X_128,greatest_lower_bound(X_9,X_128)),inverse(greatest_lower_bound(X_9,X_128))) != least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))))
    | least_upper_bound(X_128,greatest_lower_bound(X_9,X_128)) != X_128
    | multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))) = least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_128,greatest_lower_bound(X_9,X_128)),inverse(greatest_lower_bound(X_9,X_128))),least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))))) ),[0,0],$fot(X_128)]]) ).

cnf(refute_0_537,plain,
    ( multiply(least_upper_bound(X_128,greatest_lower_bound(X_9,X_128)),inverse(greatest_lower_bound(X_9,X_128))) != least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))))
    | multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))) = least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_128,greatest_lower_bound(X_9,X_128)),X_128) )],[refute_0_535,refute_0_536]) ).

cnf(refute_0_538,plain,
    multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))) = least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_128,greatest_lower_bound(X_9,X_128)),inverse(greatest_lower_bound(X_9,X_128))),least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))))) )],[refute_0_534,refute_0_537]) ).

cnf(refute_0_539,plain,
    ( multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))) != least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))))
    | least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128)))) = multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))))))]]) ).

cnf(refute_0_540,plain,
    least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128)))) = multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))),
    inference(resolve,[$cnf( $equal(multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))),least_upper_bound(identity,multiply(X_128,inverse(greatest_lower_bound(X_9,X_128))))) )],[refute_0_538,refute_0_539]) ).

cnf(refute_0_541,plain,
    least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(c,inverse(greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_540:[bind(X_128,$fot(c)),bind(X_9,$fot(a))]]) ).

cnf(refute_0_542,plain,
    multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a) = multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a))]]) ).

cnf(refute_0_543,plain,
    ( multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a) != multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a)
    | least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a) = multiply(multiply(c,inverse(greatest_lower_bound(a,c))),a) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a),multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a)) ),[1,0],$fot(multiply(c,inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_544,plain,
    ( least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a) = multiply(multiply(c,inverse(greatest_lower_bound(a,c))),a) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a),multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a)) )],[refute_0_542,refute_0_543]) ).

cnf(refute_0_545,plain,
    multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a) = multiply(multiply(c,inverse(greatest_lower_bound(a,c))),a),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_541,refute_0_544]) ).

cnf(refute_0_546,plain,
    ( multiply(multiply(c,inverse(greatest_lower_bound(a,c))),a) != multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))
    | multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a) != multiply(multiply(c,inverse(greatest_lower_bound(a,c))),a)
    | multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a) = multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a))),bind(Y0,$fot(multiply(multiply(c,inverse(greatest_lower_bound(a,c))),a))),bind(Z0,$fot(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))))]]) ).

cnf(refute_0_547,plain,
    ( multiply(multiply(c,inverse(greatest_lower_bound(a,c))),a) != multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))
    | multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a) = multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a),multiply(multiply(c,inverse(greatest_lower_bound(a,c))),a)) )],[refute_0_545,refute_0_546]) ).

cnf(refute_0_548,plain,
    multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a) = multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)),
    inference(resolve,[$cnf( $equal(multiply(multiply(c,inverse(greatest_lower_bound(a,c))),a),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) )],[refute_0_524,refute_0_547]) ).

cnf(refute_0_549,plain,
    multiply(least_upper_bound(X_119,identity),X_118) = least_upper_bound(multiply(X_119,X_118),multiply(identity,X_118)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_118)),bind(Y,$fot(X_119)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_550,plain,
    multiply(identity,X_118) = X_118,
    inference(subst,[],[left_identity:[bind(X,$fot(X_118))]]) ).

cnf(refute_0_551,plain,
    ( multiply(identity,X_118) != X_118
    | multiply(least_upper_bound(X_119,identity),X_118) != least_upper_bound(multiply(X_119,X_118),multiply(identity,X_118))
    | multiply(least_upper_bound(X_119,identity),X_118) = least_upper_bound(multiply(X_119,X_118),X_118) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_119,identity),X_118),least_upper_bound(multiply(X_119,X_118),multiply(identity,X_118))) ),[1,1],$fot(X_118)]]) ).

cnf(refute_0_552,plain,
    ( multiply(least_upper_bound(X_119,identity),X_118) != least_upper_bound(multiply(X_119,X_118),multiply(identity,X_118))
    | multiply(least_upper_bound(X_119,identity),X_118) = least_upper_bound(multiply(X_119,X_118),X_118) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_118),X_118) )],[refute_0_550,refute_0_551]) ).

cnf(refute_0_553,plain,
    multiply(least_upper_bound(X_119,identity),X_118) = least_upper_bound(multiply(X_119,X_118),X_118),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,identity),X_118),least_upper_bound(multiply(X_119,X_118),multiply(identity,X_118))) )],[refute_0_549,refute_0_552]) ).

cnf(refute_0_554,plain,
    least_upper_bound(multiply(X_119,X_118),X_118) = least_upper_bound(X_118,multiply(X_119,X_118)),
    inference(subst,[],[refute_0_256:[bind(X,$fot(X_118)),bind(Y,$fot(multiply(X_119,X_118)))]]) ).

cnf(refute_0_555,plain,
    ( multiply(least_upper_bound(X_119,identity),X_118) != least_upper_bound(multiply(X_119,X_118),X_118)
    | least_upper_bound(multiply(X_119,X_118),X_118) != least_upper_bound(X_118,multiply(X_119,X_118))
    | multiply(least_upper_bound(X_119,identity),X_118) = least_upper_bound(X_118,multiply(X_119,X_118)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_119,identity),X_118),least_upper_bound(X_118,multiply(X_119,X_118))) ),[0],$fot(least_upper_bound(multiply(X_119,X_118),X_118))]]) ).

cnf(refute_0_556,plain,
    ( multiply(least_upper_bound(X_119,identity),X_118) != least_upper_bound(multiply(X_119,X_118),X_118)
    | multiply(least_upper_bound(X_119,identity),X_118) = least_upper_bound(X_118,multiply(X_119,X_118)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),X_118),least_upper_bound(X_118,multiply(X_119,X_118))) )],[refute_0_554,refute_0_555]) ).

cnf(refute_0_557,plain,
    multiply(least_upper_bound(X_119,identity),X_118) = least_upper_bound(X_118,multiply(X_119,X_118)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,identity),X_118),least_upper_bound(multiply(X_119,X_118),X_118)) )],[refute_0_553,refute_0_556]) ).

cnf(refute_0_558,plain,
    multiply(least_upper_bound(multiply(X,Y),identity),X_121) = least_upper_bound(X_121,multiply(multiply(X,Y),X_121)),
    inference(subst,[],[refute_0_557:[bind(X_118,$fot(X_121)),bind(X_119,$fot(multiply(X,Y)))]]) ).

cnf(refute_0_559,plain,
    multiply(multiply(X,Y),X_121) = multiply(X,multiply(Y,X_121)),
    inference(subst,[],[associativity:[bind(Z,$fot(X_121))]]) ).

cnf(refute_0_560,plain,
    ( multiply(multiply(X,Y),X_121) != multiply(X,multiply(Y,X_121))
    | multiply(least_upper_bound(multiply(X,Y),identity),X_121) != least_upper_bound(X_121,multiply(multiply(X,Y),X_121))
    | multiply(least_upper_bound(multiply(X,Y),identity),X_121) = least_upper_bound(X_121,multiply(X,multiply(Y,X_121))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(multiply(X,Y),identity),X_121),least_upper_bound(X_121,multiply(multiply(X,Y),X_121))) ),[1,1],$fot(multiply(X,multiply(Y,X_121)))]]) ).

cnf(refute_0_561,plain,
    ( multiply(least_upper_bound(multiply(X,Y),identity),X_121) != least_upper_bound(X_121,multiply(multiply(X,Y),X_121))
    | multiply(least_upper_bound(multiply(X,Y),identity),X_121) = least_upper_bound(X_121,multiply(X,multiply(Y,X_121))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_121),multiply(X,multiply(Y,X_121))) )],[refute_0_559,refute_0_560]) ).

cnf(refute_0_562,plain,
    multiply(least_upper_bound(multiply(X,Y),identity),X_121) = least_upper_bound(X_121,multiply(X,multiply(Y,X_121))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(multiply(X,Y),identity),X_121),least_upper_bound(X_121,multiply(multiply(X,Y),X_121))) )],[refute_0_558,refute_0_561]) ).

cnf(refute_0_563,plain,
    least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) = least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(least_upper_bound(X_15,X_16))),bind(Y,$fot(X_15)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_564,plain,
    least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) = least_upper_bound(X_15,X_16),
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(least_upper_bound(X_15,X_16)))]]) ).

cnf(refute_0_565,plain,
    ( least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) != least_upper_bound(X_15,X_16)
    | least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16)
    | least_upper_bound(X_15,X_16) = least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)),least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16)) ),[0],$fot(least_upper_bound(X_15,X_16))]]) ).

cnf(refute_0_566,plain,
    ( least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16)
    | least_upper_bound(X_15,X_16) = least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)),least_upper_bound(X_15,X_16)) )],[refute_0_564,refute_0_565]) ).

cnf(refute_0_567,plain,
    least_upper_bound(X_15,X_16) = least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)),least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16)) )],[refute_0_563,refute_0_566]) ).

cnf(refute_0_568,plain,
    least_upper_bound(X_14,least_upper_bound(X_15,X_16)) = least_upper_bound(least_upper_bound(X_14,X_15),X_16),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_14)),bind(Y,$fot(X_15)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_569,plain,
    least_upper_bound(X_16,X_15) = least_upper_bound(X_15,X_16),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_16)),bind(Y,$fot(X_15))]]) ).

cnf(refute_0_570,plain,
    ( least_upper_bound(X_16,X_15) != least_upper_bound(X_15,X_16)
    | least_upper_bound(X_15,X_16) = least_upper_bound(X_16,X_15) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_16,X_15))),bind(Y0,$fot(least_upper_bound(X_15,X_16)))]]) ).

cnf(refute_0_571,plain,
    least_upper_bound(X_15,X_16) = least_upper_bound(X_16,X_15),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_16,X_15),least_upper_bound(X_15,X_16)) )],[refute_0_569,refute_0_570]) ).

cnf(refute_0_572,plain,
    ( least_upper_bound(X_14,least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(X_14,X_15),X_16)
    | least_upper_bound(X_15,X_16) != least_upper_bound(X_16,X_15)
    | least_upper_bound(X_14,least_upper_bound(X_16,X_15)) = least_upper_bound(least_upper_bound(X_14,X_15),X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(X_15,X_16)),least_upper_bound(least_upper_bound(X_14,X_15),X_16)) ),[0,1],$fot(least_upper_bound(X_16,X_15))]]) ).

cnf(refute_0_573,plain,
    ( least_upper_bound(X_14,least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(X_14,X_15),X_16)
    | least_upper_bound(X_14,least_upper_bound(X_16,X_15)) = least_upper_bound(least_upper_bound(X_14,X_15),X_16) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,X_16),least_upper_bound(X_16,X_15)) )],[refute_0_571,refute_0_572]) ).

cnf(refute_0_574,plain,
    least_upper_bound(X_14,least_upper_bound(X_16,X_15)) = least_upper_bound(least_upper_bound(X_14,X_15),X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(X_15,X_16)),least_upper_bound(least_upper_bound(X_14,X_15),X_16)) )],[refute_0_568,refute_0_573]) ).

cnf(refute_0_575,plain,
    least_upper_bound(least_upper_bound(X_14,X_15),X_16) = least_upper_bound(X_14,least_upper_bound(X_15,X_16)),
    inference(subst,[],[refute_0_237:[bind(X,$fot(X_14)),bind(Y,$fot(X_15)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_576,plain,
    ( least_upper_bound(X_14,least_upper_bound(X_16,X_15)) != least_upper_bound(least_upper_bound(X_14,X_15),X_16)
    | least_upper_bound(least_upper_bound(X_14,X_15),X_16) != least_upper_bound(X_14,least_upper_bound(X_15,X_16))
    | least_upper_bound(X_14,least_upper_bound(X_16,X_15)) = least_upper_bound(X_14,least_upper_bound(X_15,X_16)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_14,least_upper_bound(X_16,X_15)),least_upper_bound(X_14,least_upper_bound(X_15,X_16))) ),[0],$fot(least_upper_bound(least_upper_bound(X_14,X_15),X_16))]]) ).

cnf(refute_0_577,plain,
    ( least_upper_bound(X_14,least_upper_bound(X_16,X_15)) != least_upper_bound(least_upper_bound(X_14,X_15),X_16)
    | least_upper_bound(X_14,least_upper_bound(X_16,X_15)) = least_upper_bound(X_14,least_upper_bound(X_15,X_16)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_14,X_15),X_16),least_upper_bound(X_14,least_upper_bound(X_15,X_16))) )],[refute_0_575,refute_0_576]) ).

cnf(refute_0_578,plain,
    least_upper_bound(X_14,least_upper_bound(X_16,X_15)) = least_upper_bound(X_14,least_upper_bound(X_15,X_16)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(X_16,X_15)),least_upper_bound(least_upper_bound(X_14,X_15),X_16)) )],[refute_0_574,refute_0_577]) ).

cnf(refute_0_579,plain,
    ( least_upper_bound(X_14,least_upper_bound(X_16,X_15)) != least_upper_bound(X_14,least_upper_bound(X_15,X_16))
    | least_upper_bound(X_14,least_upper_bound(X_15,X_16)) = least_upper_bound(X_14,least_upper_bound(X_16,X_15)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_14,least_upper_bound(X_16,X_15)))),bind(Y0,$fot(least_upper_bound(X_14,least_upper_bound(X_15,X_16))))]]) ).

cnf(refute_0_580,plain,
    least_upper_bound(X_14,least_upper_bound(X_15,X_16)) = least_upper_bound(X_14,least_upper_bound(X_16,X_15)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(X_16,X_15)),least_upper_bound(X_14,least_upper_bound(X_15,X_16))) )],[refute_0_578,refute_0_579]) ).

cnf(refute_0_581,plain,
    least_upper_bound(X_16,least_upper_bound(least_upper_bound(X_15,X_16),X_15)) = least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))),
    inference(subst,[],[refute_0_580:[bind(X_14,$fot(X_16)),bind(X_15,$fot(least_upper_bound(X_15,X_16))),bind(X_16,$fot(X_15))]]) ).

cnf(refute_0_582,plain,
    least_upper_bound(X,least_upper_bound(X_14,X_15)) = least_upper_bound(least_upper_bound(X_14,X_15),X),
    inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_14,X_15)))]]) ).

cnf(refute_0_583,plain,
    least_upper_bound(X_14,least_upper_bound(X_15,X)) = least_upper_bound(least_upper_bound(X_14,X_15),X),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_14)),bind(Y,$fot(X_15)),bind(Z,$fot(X))]]) ).

cnf(refute_0_584,plain,
    ( least_upper_bound(X_14,least_upper_bound(X_15,X)) != least_upper_bound(least_upper_bound(X_14,X_15),X)
    | least_upper_bound(least_upper_bound(X_14,X_15),X) = least_upper_bound(X_14,least_upper_bound(X_15,X)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_14,least_upper_bound(X_15,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_14,X_15),X)))]]) ).

cnf(refute_0_585,plain,
    least_upper_bound(least_upper_bound(X_14,X_15),X) = least_upper_bound(X_14,least_upper_bound(X_15,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(X_15,X)),least_upper_bound(least_upper_bound(X_14,X_15),X)) )],[refute_0_583,refute_0_584]) ).

cnf(refute_0_586,plain,
    ( least_upper_bound(X,least_upper_bound(X_14,X_15)) != least_upper_bound(least_upper_bound(X_14,X_15),X)
    | least_upper_bound(least_upper_bound(X_14,X_15),X) != least_upper_bound(X_14,least_upper_bound(X_15,X))
    | least_upper_bound(X,least_upper_bound(X_14,X_15)) = least_upper_bound(X_14,least_upper_bound(X_15,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_14,X_15)),least_upper_bound(X_14,least_upper_bound(X_15,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_14,X_15),X))]]) ).

cnf(refute_0_587,plain,
    ( least_upper_bound(X,least_upper_bound(X_14,X_15)) != least_upper_bound(least_upper_bound(X_14,X_15),X)
    | least_upper_bound(X,least_upper_bound(X_14,X_15)) = least_upper_bound(X_14,least_upper_bound(X_15,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_14,X_15),X),least_upper_bound(X_14,least_upper_bound(X_15,X))) )],[refute_0_585,refute_0_586]) ).

cnf(refute_0_588,plain,
    least_upper_bound(X,least_upper_bound(X_14,X_15)) = least_upper_bound(X_14,least_upper_bound(X_15,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_14,X_15)),least_upper_bound(least_upper_bound(X_14,X_15),X)) )],[refute_0_582,refute_0_587]) ).

cnf(refute_0_589,plain,
    ( least_upper_bound(X,least_upper_bound(X_14,X_15)) != least_upper_bound(X_14,least_upper_bound(X_15,X))
    | least_upper_bound(X_14,least_upper_bound(X_15,X)) = least_upper_bound(X,least_upper_bound(X_14,X_15)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_14,X_15)))),bind(Y0,$fot(least_upper_bound(X_14,least_upper_bound(X_15,X))))]]) ).

cnf(refute_0_590,plain,
    least_upper_bound(X_14,least_upper_bound(X_15,X)) = least_upper_bound(X,least_upper_bound(X_14,X_15)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_14,X_15)),least_upper_bound(X_14,least_upper_bound(X_15,X))) )],[refute_0_588,refute_0_589]) ).

cnf(refute_0_591,plain,
    least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) = least_upper_bound(X_16,least_upper_bound(least_upper_bound(X_15,X_16),X_15)),
    inference(subst,[],[refute_0_590:[bind(X,$fot(X_16)),bind(X_14,$fot(least_upper_bound(X_15,X_16)))]]) ).

cnf(refute_0_592,plain,
    ( least_upper_bound(X_16,least_upper_bound(least_upper_bound(X_15,X_16),X_15)) != least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))
    | least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) != least_upper_bound(X_16,least_upper_bound(least_upper_bound(X_15,X_16),X_15))
    | least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) = least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)))),bind(Y0,$fot(least_upper_bound(X_16,least_upper_bound(least_upper_bound(X_15,X_16),X_15)))),bind(Z0,$fot(least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))))]]) ).

cnf(refute_0_593,plain,
    ( least_upper_bound(X_16,least_upper_bound(least_upper_bound(X_15,X_16),X_15)) != least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))
    | least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) = least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)),least_upper_bound(X_16,least_upper_bound(least_upper_bound(X_15,X_16),X_15))) )],[refute_0_591,refute_0_592]) ).

cnf(refute_0_594,plain,
    least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) = least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_16,least_upper_bound(least_upper_bound(X_15,X_16),X_15)),least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))) )],[refute_0_581,refute_0_593]) ).

cnf(refute_0_595,plain,
    least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16) = least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)),
    inference(subst,[],[refute_0_237:[bind(X,$fot(least_upper_bound(X_15,X_16))),bind(Y,$fot(X_15)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_596,plain,
    ( least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) != least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))
    | least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16) != least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16))
    | least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16) = least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)))),bind(Z0,$fot(least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))))]]) ).

cnf(refute_0_597,plain,
    ( least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)) != least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))
    | least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16) = least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16),least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16))) )],[refute_0_595,refute_0_596]) ).

cnf(refute_0_598,plain,
    least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16) = least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,X_16),least_upper_bound(X_15,X_16)),least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))) )],[refute_0_594,refute_0_597]) ).

cnf(refute_0_599,plain,
    ( least_upper_bound(X_15,X_16) != least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16)
    | least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16) != least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))
    | least_upper_bound(X_15,X_16) = least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_15,X_16),least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))) ),[0],$fot(least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16))]]) ).

cnf(refute_0_600,plain,
    ( least_upper_bound(X_15,X_16) != least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16)
    | least_upper_bound(X_15,X_16) = least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16),least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))) )],[refute_0_598,refute_0_599]) ).

cnf(refute_0_601,plain,
    least_upper_bound(X_15,X_16) = least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,X_16),least_upper_bound(least_upper_bound(least_upper_bound(X_15,X_16),X_15),X_16)) )],[refute_0_567,refute_0_600]) ).

cnf(refute_0_602,plain,
    least_upper_bound(X_15,least_upper_bound(X_15,X_16)) = least_upper_bound(least_upper_bound(X_15,X_15),X_16),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_15)),bind(Y,$fot(X_15)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_603,plain,
    least_upper_bound(X_15,X_15) = X_15,
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_15))]]) ).

cnf(refute_0_604,plain,
    ( least_upper_bound(X_15,X_15) != X_15
    | least_upper_bound(X_15,least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(X_15,X_15),X_16)
    | least_upper_bound(X_15,least_upper_bound(X_15,X_16)) = least_upper_bound(X_15,X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,X_16)),least_upper_bound(least_upper_bound(X_15,X_15),X_16)) ),[1,0],$fot(X_15)]]) ).

cnf(refute_0_605,plain,
    ( least_upper_bound(X_15,least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(X_15,X_15),X_16)
    | least_upper_bound(X_15,least_upper_bound(X_15,X_16)) = least_upper_bound(X_15,X_16) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,X_15),X_15) )],[refute_0_603,refute_0_604]) ).

cnf(refute_0_606,plain,
    least_upper_bound(X_15,least_upper_bound(X_15,X_16)) = least_upper_bound(X_15,X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,X_16)),least_upper_bound(least_upper_bound(X_15,X_15),X_16)) )],[refute_0_602,refute_0_605]) ).

cnf(refute_0_607,plain,
    least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) = least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))))]]) ).

cnf(refute_0_608,plain,
    ( least_upper_bound(X_15,least_upper_bound(X_15,X_16)) != least_upper_bound(X_15,X_16)
    | least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) != least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))
    | least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) = least_upper_bound(X_16,least_upper_bound(X_15,X_16)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))),least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))) ),[1,1],$fot(least_upper_bound(X_15,X_16))]]) ).

cnf(refute_0_609,plain,
    ( least_upper_bound(X_15,least_upper_bound(X_15,X_16)) != least_upper_bound(X_15,X_16)
    | least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) = least_upper_bound(X_16,least_upper_bound(X_15,X_16)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))),least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))) )],[refute_0_607,refute_0_608]) ).

cnf(refute_0_610,plain,
    least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) = least_upper_bound(X_16,least_upper_bound(X_15,X_16)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,X_16)),least_upper_bound(X_15,X_16)) )],[refute_0_606,refute_0_609]) ).

cnf(refute_0_611,plain,
    ( least_upper_bound(X_15,X_16) != least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))
    | least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))) != least_upper_bound(X_16,least_upper_bound(X_15,X_16))
    | least_upper_bound(X_15,X_16) = least_upper_bound(X_16,least_upper_bound(X_15,X_16)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_15,X_16),least_upper_bound(X_16,least_upper_bound(X_15,X_16))) ),[0],$fot(least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))))]]) ).

cnf(refute_0_612,plain,
    ( least_upper_bound(X_15,X_16) != least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))
    | least_upper_bound(X_15,X_16) = least_upper_bound(X_16,least_upper_bound(X_15,X_16)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16))),least_upper_bound(X_16,least_upper_bound(X_15,X_16))) )],[refute_0_610,refute_0_611]) ).

cnf(refute_0_613,plain,
    least_upper_bound(X_15,X_16) = least_upper_bound(X_16,least_upper_bound(X_15,X_16)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,X_16),least_upper_bound(X_16,least_upper_bound(X_15,least_upper_bound(X_15,X_16)))) )],[refute_0_601,refute_0_612]) ).

cnf(refute_0_614,plain,
    least_upper_bound(X_15,multiply(X_122,X_15)) = least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))),
    inference(subst,[],[refute_0_613:[bind(X_16,$fot(multiply(X_122,X_15)))]]) ).

cnf(refute_0_615,plain,
    multiply(least_upper_bound(X_122,identity),X_15) = least_upper_bound(X_15,multiply(X_122,X_15)),
    inference(subst,[],[refute_0_557:[bind(X_118,$fot(X_15)),bind(X_119,$fot(X_122))]]) ).

cnf(refute_0_616,plain,
    ( multiply(least_upper_bound(X_122,identity),X_15) != least_upper_bound(X_15,multiply(X_122,X_15))
    | least_upper_bound(X_15,multiply(X_122,X_15)) = multiply(least_upper_bound(X_122,identity),X_15) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_122,identity),X_15))),bind(Y0,$fot(least_upper_bound(X_15,multiply(X_122,X_15))))]]) ).

cnf(refute_0_617,plain,
    least_upper_bound(X_15,multiply(X_122,X_15)) = multiply(least_upper_bound(X_122,identity),X_15),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_122,identity),X_15),least_upper_bound(X_15,multiply(X_122,X_15))) )],[refute_0_615,refute_0_616]) ).

cnf(refute_0_618,plain,
    ( least_upper_bound(X_15,multiply(X_122,X_15)) != multiply(least_upper_bound(X_122,identity),X_15)
    | least_upper_bound(X_15,multiply(X_122,X_15)) != least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15)))
    | multiply(least_upper_bound(X_122,identity),X_15) = least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,multiply(X_122,X_15)),least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15)))) ),[0],$fot(multiply(least_upper_bound(X_122,identity),X_15))]]) ).

cnf(refute_0_619,plain,
    ( least_upper_bound(X_15,multiply(X_122,X_15)) != least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15)))
    | multiply(least_upper_bound(X_122,identity),X_15) = least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_122,X_15)),multiply(least_upper_bound(X_122,identity),X_15)) )],[refute_0_617,refute_0_618]) ).

cnf(refute_0_620,plain,
    multiply(least_upper_bound(X_122,identity),X_15) = least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_122,X_15)),least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15)))) )],[refute_0_614,refute_0_619]) ).

cnf(refute_0_621,plain,
    least_upper_bound(X_122,X_122) = X_122,
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_122))]]) ).

cnf(refute_0_622,plain,
    least_upper_bound(identity,least_upper_bound(X_122,X_122)) = least_upper_bound(identity,least_upper_bound(X_122,X_122)),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(X_122,X_122)))]]) ).

cnf(refute_0_623,plain,
    ( least_upper_bound(X_122,X_122) != X_122
    | least_upper_bound(identity,least_upper_bound(X_122,X_122)) != least_upper_bound(identity,least_upper_bound(X_122,X_122))
    | least_upper_bound(identity,least_upper_bound(X_122,X_122)) = least_upper_bound(identity,X_122) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_122,X_122)),least_upper_bound(identity,least_upper_bound(X_122,X_122))) ),[1,1],$fot(X_122)]]) ).

cnf(refute_0_624,plain,
    ( least_upper_bound(X_122,X_122) != X_122
    | least_upper_bound(identity,least_upper_bound(X_122,X_122)) = least_upper_bound(identity,X_122) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_122,X_122)),least_upper_bound(identity,least_upper_bound(X_122,X_122))) )],[refute_0_622,refute_0_623]) ).

cnf(refute_0_625,plain,
    least_upper_bound(identity,least_upper_bound(X_122,X_122)) = least_upper_bound(identity,X_122),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_122,X_122),X_122) )],[refute_0_621,refute_0_624]) ).

cnf(refute_0_626,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15) = multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15))]]) ).

cnf(refute_0_627,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15) != multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)
    | least_upper_bound(identity,least_upper_bound(X_122,X_122)) != least_upper_bound(identity,X_122)
    | multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15) = multiply(least_upper_bound(identity,X_122),X_15) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15),multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)) ),[1,0],$fot(least_upper_bound(identity,X_122))]]) ).

cnf(refute_0_628,plain,
    ( least_upper_bound(identity,least_upper_bound(X_122,X_122)) != least_upper_bound(identity,X_122)
    | multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15) = multiply(least_upper_bound(identity,X_122),X_15) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15),multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)) )],[refute_0_626,refute_0_627]) ).

cnf(refute_0_629,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15) = multiply(least_upper_bound(identity,X_122),X_15),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_122,X_122)),least_upper_bound(identity,X_122)) )],[refute_0_625,refute_0_628]) ).

cnf(refute_0_630,plain,
    least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)),
    inference(subst,[],[refute_0_606:[bind(X_15,$fot(multiply(X_119,X_118))),bind(X_16,$fot(multiply(X_120,X_118)))]]) ).

cnf(refute_0_631,plain,
    multiply(least_upper_bound(X_119,X_120),X_118) = least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_118)),bind(Y,$fot(X_119)),bind(Z,$fot(X_120))]]) ).

cnf(refute_0_632,plain,
    ( multiply(least_upper_bound(X_119,X_120),X_118) != least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))
    | least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)) = multiply(least_upper_bound(X_119,X_120),X_118) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_119,X_120),X_118))),bind(Y0,$fot(least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))))]]) ).

cnf(refute_0_633,plain,
    least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)) = multiply(least_upper_bound(X_119,X_120),X_118),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,X_120),X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) )],[refute_0_631,refute_0_632]) ).

cnf(refute_0_634,plain,
    ( least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)) != multiply(least_upper_bound(X_119,X_120),X_118)
    | least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) != least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))
    | least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = multiply(least_upper_bound(X_119,X_120),X_118) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) ),[1],$fot(multiply(least_upper_bound(X_119,X_120),X_118))]]) ).

cnf(refute_0_635,plain,
    ( least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) != least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))
    | least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = multiply(least_upper_bound(X_119,X_120),X_118) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)),multiply(least_upper_bound(X_119,X_120),X_118)) )],[refute_0_633,refute_0_634]) ).

cnf(refute_0_636,plain,
    least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = multiply(least_upper_bound(X_119,X_120),X_118),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) )],[refute_0_630,refute_0_635]) ).

cnf(refute_0_637,plain,
    least_upper_bound(X_119,X_119) = X_119,
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_119))]]) ).

cnf(refute_0_638,plain,
    least_upper_bound(X_120,least_upper_bound(X_119,X_119)) = least_upper_bound(X_120,least_upper_bound(X_119,X_119)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_120,least_upper_bound(X_119,X_119)))]]) ).

cnf(refute_0_639,plain,
    ( least_upper_bound(X_119,X_119) != X_119
    | least_upper_bound(X_120,least_upper_bound(X_119,X_119)) != least_upper_bound(X_120,least_upper_bound(X_119,X_119))
    | least_upper_bound(X_120,least_upper_bound(X_119,X_119)) = least_upper_bound(X_120,X_119) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),least_upper_bound(X_120,least_upper_bound(X_119,X_119))) ),[1,1],$fot(X_119)]]) ).

cnf(refute_0_640,plain,
    ( least_upper_bound(X_119,X_119) != X_119
    | least_upper_bound(X_120,least_upper_bound(X_119,X_119)) = least_upper_bound(X_120,X_119) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),least_upper_bound(X_120,least_upper_bound(X_119,X_119))) )],[refute_0_638,refute_0_639]) ).

cnf(refute_0_641,plain,
    least_upper_bound(X_120,least_upper_bound(X_119,X_119)) = least_upper_bound(X_120,X_119),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_119,X_119),X_119) )],[refute_0_637,refute_0_640]) ).

cnf(refute_0_642,plain,
    multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118) = multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118))]]) ).

cnf(refute_0_643,plain,
    ( multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118) != multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118)
    | least_upper_bound(X_120,least_upper_bound(X_119,X_119)) != least_upper_bound(X_120,X_119)
    | multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118) = multiply(least_upper_bound(X_120,X_119),X_118) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118),multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118)) ),[1,0],$fot(least_upper_bound(X_120,X_119))]]) ).

cnf(refute_0_644,plain,
    ( least_upper_bound(X_120,least_upper_bound(X_119,X_119)) != least_upper_bound(X_120,X_119)
    | multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118) = multiply(least_upper_bound(X_120,X_119),X_118) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118),multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118)) )],[refute_0_642,refute_0_643]) ).

cnf(refute_0_645,plain,
    multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118) = multiply(least_upper_bound(X_120,X_119),X_118),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),least_upper_bound(X_120,X_119)) )],[refute_0_641,refute_0_644]) ).

cnf(refute_0_646,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_13:[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_647,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_646]) ).

cnf(refute_0_648,plain,
    least_upper_bound(multiply(X_120,X_118),multiply(least_upper_bound(X_119,X_119),X_118)) = multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118),
    inference(subst,[],[refute_0_647:[bind(X,$fot(X_118)),bind(Y,$fot(X_120)),bind(Z,$fot(least_upper_bound(X_119,X_119)))]]) ).

cnf(refute_0_649,plain,
    least_upper_bound(X,least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X)),
    inference(subst,[],[refute_0_588:[bind(X_14,$fot(multiply(X_119,X_118))),bind(X_15,$fot(multiply(X_120,X_118)))]]) ).

cnf(refute_0_650,plain,
    ( least_upper_bound(X,least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) != least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X))
    | least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)) != multiply(least_upper_bound(X_119,X_120),X_118)
    | least_upper_bound(X,multiply(least_upper_bound(X_119,X_120),X_118)) = least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))),least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X))) ),[0,1],$fot(multiply(least_upper_bound(X_119,X_120),X_118))]]) ).

cnf(refute_0_651,plain,
    ( least_upper_bound(X,least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) != least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X))
    | least_upper_bound(X,multiply(least_upper_bound(X_119,X_120),X_118)) = least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)),multiply(least_upper_bound(X_119,X_120),X_118)) )],[refute_0_633,refute_0_650]) ).

cnf(refute_0_652,plain,
    least_upper_bound(X,multiply(least_upper_bound(X_119,X_120),X_118)) = least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))),least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X))) )],[refute_0_649,refute_0_651]) ).

cnf(refute_0_653,plain,
    ( least_upper_bound(X,multiply(least_upper_bound(X_119,X_120),X_118)) != least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X))
    | least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X)) = least_upper_bound(X,multiply(least_upper_bound(X_119,X_120),X_118)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X,multiply(least_upper_bound(X_119,X_120),X_118)))),bind(Y0,$fot(least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X))))]]) ).

cnf(refute_0_654,plain,
    least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X)) = least_upper_bound(X,multiply(least_upper_bound(X_119,X_120),X_118)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(least_upper_bound(X_119,X_120),X_118)),least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_120,X_118),X))) )],[refute_0_652,refute_0_653]) ).

cnf(refute_0_655,plain,
    least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = least_upper_bound(multiply(X_120,X_118),multiply(least_upper_bound(X_119,X_119),X_118)),
    inference(subst,[],[refute_0_654:[bind(X,$fot(multiply(X_120,X_118))),bind(X_120,$fot(X_119))]]) ).

cnf(refute_0_656,plain,
    ( least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) != least_upper_bound(multiply(X_120,X_118),multiply(least_upper_bound(X_119,X_119),X_118))
    | least_upper_bound(multiply(X_120,X_118),multiply(least_upper_bound(X_119,X_119),X_118)) != multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118)
    | least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))))),bind(Y0,$fot(least_upper_bound(multiply(X_120,X_118),multiply(least_upper_bound(X_119,X_119),X_118)))),bind(Z0,$fot(multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118)))]]) ).

cnf(refute_0_657,plain,
    ( least_upper_bound(multiply(X_120,X_118),multiply(least_upper_bound(X_119,X_119),X_118)) != multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118)
    | least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))),least_upper_bound(multiply(X_120,X_118),multiply(least_upper_bound(X_119,X_119),X_118))) )],[refute_0_655,refute_0_656]) ).

cnf(refute_0_658,plain,
    least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_120,X_118),multiply(least_upper_bound(X_119,X_119),X_118)),multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118)) )],[refute_0_648,refute_0_657]) ).

cnf(refute_0_659,plain,
    ( multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118) != multiply(least_upper_bound(X_120,X_119),X_118)
    | least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) != multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118)
    | least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = multiply(least_upper_bound(X_120,X_119),X_118) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))))),bind(Y0,$fot(multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118))),bind(Z0,$fot(multiply(least_upper_bound(X_120,X_119),X_118)))]]) ).

cnf(refute_0_660,plain,
    ( multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118) != multiply(least_upper_bound(X_120,X_119),X_118)
    | least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = multiply(least_upper_bound(X_120,X_119),X_118) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))),multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118)) )],[refute_0_658,refute_0_659]) ).

cnf(refute_0_661,plain,
    least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) = multiply(least_upper_bound(X_120,X_119),X_118),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_120,least_upper_bound(X_119,X_119)),X_118),multiply(least_upper_bound(X_120,X_119),X_118)) )],[refute_0_645,refute_0_660]) ).

cnf(refute_0_662,plain,
    ( least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) != multiply(least_upper_bound(X_119,X_120),X_118)
    | least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) != multiply(least_upper_bound(X_120,X_119),X_118)
    | multiply(least_upper_bound(X_120,X_119),X_118) = multiply(least_upper_bound(X_119,X_120),X_118) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))),multiply(least_upper_bound(X_119,X_120),X_118)) ),[0],$fot(multiply(least_upper_bound(X_120,X_119),X_118))]]) ).

cnf(refute_0_663,plain,
    ( least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))) != multiply(least_upper_bound(X_119,X_120),X_118)
    | multiply(least_upper_bound(X_120,X_119),X_118) = multiply(least_upper_bound(X_119,X_120),X_118) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))),multiply(least_upper_bound(X_120,X_119),X_118)) )],[refute_0_661,refute_0_662]) ).

cnf(refute_0_664,plain,
    multiply(least_upper_bound(X_120,X_119),X_118) = multiply(least_upper_bound(X_119,X_120),X_118),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))),multiply(least_upper_bound(X_119,X_120),X_118)) )],[refute_0_636,refute_0_663]) ).

cnf(refute_0_665,plain,
    ( multiply(least_upper_bound(X_120,X_119),X_118) != multiply(least_upper_bound(X_119,X_120),X_118)
    | multiply(least_upper_bound(X_119,X_120),X_118) = multiply(least_upper_bound(X_120,X_119),X_118) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_120,X_119),X_118))),bind(Y0,$fot(multiply(least_upper_bound(X_119,X_120),X_118)))]]) ).

cnf(refute_0_666,plain,
    multiply(least_upper_bound(X_119,X_120),X_118) = multiply(least_upper_bound(X_120,X_119),X_118),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_120,X_119),X_118),multiply(least_upper_bound(X_119,X_120),X_118)) )],[refute_0_664,refute_0_665]) ).

cnf(refute_0_667,plain,
    multiply(least_upper_bound(least_upper_bound(X_122,X_122),identity),X_15) = multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15),
    inference(subst,[],[refute_0_666:[bind(X_118,$fot(X_15)),bind(X_119,$fot(least_upper_bound(X_122,X_122))),bind(X_120,$fot(identity))]]) ).

cnf(refute_0_668,plain,
    ( multiply(least_upper_bound(X_119,identity),X_118) != least_upper_bound(X_118,multiply(X_119,X_118))
    | least_upper_bound(X_118,multiply(X_119,X_118)) = multiply(least_upper_bound(X_119,identity),X_118) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_119,identity),X_118))),bind(Y0,$fot(least_upper_bound(X_118,multiply(X_119,X_118))))]]) ).

cnf(refute_0_669,plain,
    least_upper_bound(X_118,multiply(X_119,X_118)) = multiply(least_upper_bound(X_119,identity),X_118),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,identity),X_118),least_upper_bound(X_118,multiply(X_119,X_118))) )],[refute_0_557,refute_0_668]) ).

cnf(refute_0_670,plain,
    least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)) = multiply(least_upper_bound(least_upper_bound(X_122,X_122),identity),X_15),
    inference(subst,[],[refute_0_669:[bind(X_118,$fot(X_15)),bind(X_119,$fot(least_upper_bound(X_122,X_122)))]]) ).

cnf(refute_0_671,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_122,X_122),identity),X_15) != multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)
    | least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)) != multiply(least_upper_bound(least_upper_bound(X_122,X_122),identity),X_15)
    | least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)) = multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_122,X_122),identity),X_15))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)))]]) ).

cnf(refute_0_672,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_122,X_122),identity),X_15) != multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)
    | least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)) = multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)),multiply(least_upper_bound(least_upper_bound(X_122,X_122),identity),X_15)) )],[refute_0_670,refute_0_671]) ).

cnf(refute_0_673,plain,
    least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)) = multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_122,X_122),identity),X_15),multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)) )],[refute_0_667,refute_0_672]) ).

cnf(refute_0_674,plain,
    least_upper_bound(multiply(X_120,X_118),least_upper_bound(X_14,multiply(X_119,X_118))) = least_upper_bound(X_14,least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118))),
    inference(subst,[],[refute_0_588:[bind(X,$fot(multiply(X_120,X_118))),bind(X_15,$fot(multiply(X_119,X_118)))]]) ).

cnf(refute_0_675,plain,
    ( least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)) != multiply(least_upper_bound(X_119,X_120),X_118)
    | least_upper_bound(multiply(X_120,X_118),least_upper_bound(X_14,multiply(X_119,X_118))) != least_upper_bound(X_14,least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)))
    | least_upper_bound(multiply(X_120,X_118),least_upper_bound(X_14,multiply(X_119,X_118))) = least_upper_bound(X_14,multiply(least_upper_bound(X_119,X_120),X_118)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_120,X_118),least_upper_bound(X_14,multiply(X_119,X_118))),least_upper_bound(X_14,least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)))) ),[1,1],$fot(multiply(least_upper_bound(X_119,X_120),X_118))]]) ).

cnf(refute_0_676,plain,
    ( least_upper_bound(multiply(X_120,X_118),least_upper_bound(X_14,multiply(X_119,X_118))) != least_upper_bound(X_14,least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)))
    | least_upper_bound(multiply(X_120,X_118),least_upper_bound(X_14,multiply(X_119,X_118))) = least_upper_bound(X_14,multiply(least_upper_bound(X_119,X_120),X_118)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)),multiply(least_upper_bound(X_119,X_120),X_118)) )],[refute_0_633,refute_0_675]) ).

cnf(refute_0_677,plain,
    least_upper_bound(multiply(X_120,X_118),least_upper_bound(X_14,multiply(X_119,X_118))) = least_upper_bound(X_14,multiply(least_upper_bound(X_119,X_120),X_118)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_120,X_118),least_upper_bound(X_14,multiply(X_119,X_118))),least_upper_bound(X_14,least_upper_bound(multiply(X_119,X_118),multiply(X_120,X_118)))) )],[refute_0_674,refute_0_676]) ).

cnf(refute_0_678,plain,
    least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) = least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)),
    inference(subst,[],[refute_0_677:[bind(X_118,$fot(X_15)),bind(X_119,$fot(X_122)),bind(X_120,$fot(X_122)),bind(X_14,$fot(X_15))]]) ).

cnf(refute_0_679,plain,
    ( least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)) != multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)
    | least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) != least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15))
    | least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) = multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))))),bind(Y0,$fot(least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)))]]) ).

cnf(refute_0_680,plain,
    ( least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)) != multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)
    | least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) = multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))),least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15))) )],[refute_0_678,refute_0_679]) ).

cnf(refute_0_681,plain,
    least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) = multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(least_upper_bound(X_122,X_122),X_15)),multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)) )],[refute_0_673,refute_0_680]) ).

cnf(refute_0_682,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15) != multiply(least_upper_bound(identity,X_122),X_15)
    | least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) != multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)
    | least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) = multiply(least_upper_bound(identity,X_122),X_15) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_122),X_15)))]]) ).

cnf(refute_0_683,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15) != multiply(least_upper_bound(identity,X_122),X_15)
    | least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) = multiply(least_upper_bound(identity,X_122),X_15) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))),multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15)) )],[refute_0_681,refute_0_682]) ).

cnf(refute_0_684,plain,
    least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) = multiply(least_upper_bound(identity,X_122),X_15),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_122,X_122)),X_15),multiply(least_upper_bound(identity,X_122),X_15)) )],[refute_0_629,refute_0_683]) ).

cnf(refute_0_685,plain,
    ( multiply(least_upper_bound(X_122,identity),X_15) != least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15)))
    | least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))) != multiply(least_upper_bound(identity,X_122),X_15)
    | multiply(least_upper_bound(X_122,identity),X_15) = multiply(least_upper_bound(identity,X_122),X_15) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_122,identity),X_15),multiply(least_upper_bound(identity,X_122),X_15)) ),[0],$fot(least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))))]]) ).

cnf(refute_0_686,plain,
    ( multiply(least_upper_bound(X_122,identity),X_15) != least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15)))
    | multiply(least_upper_bound(X_122,identity),X_15) = multiply(least_upper_bound(identity,X_122),X_15) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15))),multiply(least_upper_bound(identity,X_122),X_15)) )],[refute_0_684,refute_0_685]) ).

cnf(refute_0_687,plain,
    multiply(least_upper_bound(X_122,identity),X_15) = multiply(least_upper_bound(identity,X_122),X_15),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_122,identity),X_15),least_upper_bound(multiply(X_122,X_15),least_upper_bound(X_15,multiply(X_122,X_15)))) )],[refute_0_620,refute_0_686]) ).

cnf(refute_0_688,plain,
    multiply(least_upper_bound(multiply(X,Y),identity),X_121) = multiply(least_upper_bound(identity,multiply(X,Y)),X_121),
    inference(subst,[],[refute_0_687:[bind(X_122,$fot(multiply(X,Y))),bind(X_15,$fot(X_121))]]) ).

cnf(refute_0_689,plain,
    ( multiply(least_upper_bound(multiply(X,Y),identity),X_121) != multiply(least_upper_bound(identity,multiply(X,Y)),X_121)
    | multiply(least_upper_bound(multiply(X,Y),identity),X_121) != least_upper_bound(X_121,multiply(X,multiply(Y,X_121)))
    | multiply(least_upper_bound(identity,multiply(X,Y)),X_121) = least_upper_bound(X_121,multiply(X,multiply(Y,X_121))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(multiply(X,Y),identity),X_121),least_upper_bound(X_121,multiply(X,multiply(Y,X_121)))) ),[0],$fot(multiply(least_upper_bound(identity,multiply(X,Y)),X_121))]]) ).

cnf(refute_0_690,plain,
    ( multiply(least_upper_bound(multiply(X,Y),identity),X_121) != least_upper_bound(X_121,multiply(X,multiply(Y,X_121)))
    | multiply(least_upper_bound(identity,multiply(X,Y)),X_121) = least_upper_bound(X_121,multiply(X,multiply(Y,X_121))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(multiply(X,Y),identity),X_121),multiply(least_upper_bound(identity,multiply(X,Y)),X_121)) )],[refute_0_688,refute_0_689]) ).

cnf(refute_0_691,plain,
    multiply(least_upper_bound(identity,multiply(X,Y)),X_121) = least_upper_bound(X_121,multiply(X,multiply(Y,X_121))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(multiply(X,Y),identity),X_121),least_upper_bound(X_121,multiply(X,multiply(Y,X_121)))) )],[refute_0_562,refute_0_690]) ).

cnf(refute_0_692,plain,
    ( multiply(least_upper_bound(identity,multiply(X,Y)),X_121) != least_upper_bound(X_121,multiply(X,multiply(Y,X_121)))
    | least_upper_bound(X_121,multiply(X,multiply(Y,X_121))) = multiply(least_upper_bound(identity,multiply(X,Y)),X_121) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(X,Y)),X_121))),bind(Y0,$fot(least_upper_bound(X_121,multiply(X,multiply(Y,X_121)))))]]) ).

cnf(refute_0_693,plain,
    least_upper_bound(X_121,multiply(X,multiply(Y,X_121))) = multiply(least_upper_bound(identity,multiply(X,Y)),X_121),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X,Y)),X_121),least_upper_bound(X_121,multiply(X,multiply(Y,X_121)))) )],[refute_0_691,refute_0_692]) ).

cnf(refute_0_694,plain,
    least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) = multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a),
    inference(subst,[],[refute_0_693:[bind(X,$fot(c)),bind(Y,$fot(inverse(greatest_lower_bound(a,c)))),bind(X_121,$fot(a))]]) ).

cnf(refute_0_695,plain,
    ( multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a) != multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))
    | least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) != multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a)
    | least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) = multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a))),bind(Z0,$fot(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))))]]) ).

cnf(refute_0_696,plain,
    ( multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a) != multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))
    | least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) = multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))),multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a)) )],[refute_0_694,refute_0_695]) ).

cnf(refute_0_697,plain,
    least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) = multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))),a),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) )],[refute_0_548,refute_0_696]) ).

cnf(refute_0_698,plain,
    greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) = greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))))]]) ).

cnf(refute_0_699,plain,
    ( greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) != greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))))
    | least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) != multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))
    | greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) = greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))),greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))))) ),[1,1],$fot(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))]]) ).

cnf(refute_0_700,plain,
    ( least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) != multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))
    | greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) = greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))),greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))))) )],[refute_0_698,refute_0_699]) ).

cnf(refute_0_701,plain,
    greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) = greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) )],[refute_0_697,refute_0_700]) ).

cnf(refute_0_702,plain,
    ( b != greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))))
    | greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) != greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))
    | b = greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(b,greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) ),[0],$fot(greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))))]]) ).

cnf(refute_0_703,plain,
    ( b != greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))))
    | b = greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))),greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) )],[refute_0_701,refute_0_702]) ).

cnf(refute_0_704,plain,
    b = greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))),
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(a,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))))) )],[refute_0_523,refute_0_703]) ).

cnf(refute_0_705,plain,
    inverse(greatest_lower_bound(inverse(c),inverse(a))) = inverse(greatest_lower_bound(inverse(a),inverse(c))),
    inference(subst,[],[refute_0_482:[bind(X_112,$fot(inverse(a))),bind(X_113,$fot(inverse(c)))]]) ).

cnf(refute_0_706,plain,
    inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_350,inverse(X_135)))),X_350),
    inference(subst,[],[refute_0_54:[bind(X_107,$fot(inverse(X_135))),bind(X_83,$fot(X_350))]]) ).

cnf(refute_0_707,plain,
    multiply(greatest_lower_bound(X_350,X_135),inverse(X_135)) = greatest_lower_bound(identity,multiply(X_350,inverse(X_135))),
    inference(subst,[],[refute_0_64:[bind(X_134,$fot(X_350))]]) ).

cnf(refute_0_708,plain,
    ( multiply(greatest_lower_bound(X_350,X_135),inverse(X_135)) != greatest_lower_bound(identity,multiply(X_350,inverse(X_135)))
    | greatest_lower_bound(identity,multiply(X_350,inverse(X_135))) = multiply(greatest_lower_bound(X_350,X_135),inverse(X_135)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_350,inverse(X_135)))))]]) ).

cnf(refute_0_709,plain,
    greatest_lower_bound(identity,multiply(X_350,inverse(X_135))) = multiply(greatest_lower_bound(X_350,X_135),inverse(X_135)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135)),greatest_lower_bound(identity,multiply(X_350,inverse(X_135)))) )],[refute_0_707,refute_0_708]) ).

cnf(refute_0_710,plain,
    ( greatest_lower_bound(identity,multiply(X_350,inverse(X_135))) != multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))
    | inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) != multiply(inverse(greatest_lower_bound(identity,multiply(X_350,inverse(X_135)))),X_350)
    | inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) = multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))),multiply(inverse(greatest_lower_bound(identity,multiply(X_350,inverse(X_135)))),X_350)) ),[1,0,0],$fot(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135)))]]) ).

cnf(refute_0_711,plain,
    ( inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) != multiply(inverse(greatest_lower_bound(identity,multiply(X_350,inverse(X_135)))),X_350)
    | inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) = multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_350,inverse(X_135))),multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))) )],[refute_0_709,refute_0_710]) ).

cnf(refute_0_712,plain,
    inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) = multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))),multiply(inverse(greatest_lower_bound(identity,multiply(X_350,inverse(X_135)))),X_350)) )],[refute_0_706,refute_0_711]) ).

cnf(refute_0_713,plain,
    multiply(multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))),X_350) = multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350)),
    inference(subst,[],[associativity:[bind(X,$fot(X_135)),bind(Y,$fot(inverse(greatest_lower_bound(X_350,X_135)))),bind(Z,$fot(X_350))]]) ).

cnf(refute_0_714,plain,
    inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))) = multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))),
    inference(subst,[],[refute_0_146:[bind(X,$fot(X_135)),bind(X_17,$fot(greatest_lower_bound(X_350,X_135)))]]) ).

cnf(refute_0_715,plain,
    multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) = multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350),
    introduced(tautology,[refl,[$fot(multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350))]]) ).

cnf(refute_0_716,plain,
    ( multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) != multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350)
    | inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))) != multiply(X_135,inverse(greatest_lower_bound(X_350,X_135)))
    | multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) = multiply(multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))),X_350) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350),multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350)) ),[1,0],$fot(multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))))]]) ).

cnf(refute_0_717,plain,
    ( inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))) != multiply(X_135,inverse(greatest_lower_bound(X_350,X_135)))
    | multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) = multiply(multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))),X_350) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350),multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350)) )],[refute_0_715,refute_0_716]) ).

cnf(refute_0_718,plain,
    multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) = multiply(multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))),X_350),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),multiply(X_135,inverse(greatest_lower_bound(X_350,X_135)))) )],[refute_0_714,refute_0_717]) ).

cnf(refute_0_719,plain,
    ( multiply(multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))),X_350) != multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350))
    | multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) != multiply(multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))),X_350)
    | multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) = multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350))),bind(Y0,$fot(multiply(multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))),X_350))),bind(Z0,$fot(multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350))))]]) ).

cnf(refute_0_720,plain,
    ( multiply(multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))),X_350) != multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350))
    | multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) = multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350),multiply(multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))),X_350)) )],[refute_0_718,refute_0_719]) ).

cnf(refute_0_721,plain,
    multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) = multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_135,inverse(greatest_lower_bound(X_350,X_135))),X_350),multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350))) )],[refute_0_713,refute_0_720]) ).

cnf(refute_0_722,plain,
    ( multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350) != multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350))
    | inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) != multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350)
    | inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) = multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))),multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350)) ),[1],$fot(multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350)))]]) ).

cnf(refute_0_723,plain,
    ( inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) != multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350)
    | inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) = multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350),multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350))) )],[refute_0_721,refute_0_722]) ).

cnf(refute_0_724,plain,
    inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) = multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))),multiply(inverse(multiply(greatest_lower_bound(X_350,X_135),inverse(X_135))),X_350)) )],[refute_0_712,refute_0_723]) ).

cnf(refute_0_725,plain,
    ( inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) != multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350))
    | multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350)) = inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))))),bind(Y0,$fot(multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350))))]]) ).

cnf(refute_0_726,plain,
    multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350)) = inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_135),inverse(X_350))),multiply(X_135,multiply(inverse(greatest_lower_bound(X_350,X_135)),X_350))) )],[refute_0_724,refute_0_725]) ).

cnf(refute_0_727,plain,
    multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)) = inverse(greatest_lower_bound(inverse(c),inverse(a))),
    inference(subst,[],[refute_0_726:[bind(X_135,$fot(c)),bind(X_350,$fot(a))]]) ).

cnf(refute_0_728,plain,
    ( multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)) != inverse(greatest_lower_bound(inverse(c),inverse(a)))
    | inverse(greatest_lower_bound(inverse(c),inverse(a))) != inverse(greatest_lower_bound(inverse(a),inverse(c)))
    | multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)) = inverse(greatest_lower_bound(inverse(a),inverse(c))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(c),inverse(a))))),bind(Z0,$fot(inverse(greatest_lower_bound(inverse(a),inverse(c)))))]]) ).

cnf(refute_0_729,plain,
    ( inverse(greatest_lower_bound(inverse(c),inverse(a))) != inverse(greatest_lower_bound(inverse(a),inverse(c)))
    | multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)) = inverse(greatest_lower_bound(inverse(a),inverse(c))) ),
    inference(resolve,[$cnf( $equal(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)),inverse(greatest_lower_bound(inverse(c),inverse(a)))) )],[refute_0_727,refute_0_728]) ).

cnf(refute_0_730,plain,
    multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)) = inverse(greatest_lower_bound(inverse(a),inverse(c))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(c),inverse(a))),inverse(greatest_lower_bound(inverse(a),inverse(c)))) )],[refute_0_705,refute_0_729]) ).

cnf(refute_0_731,plain,
    greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) = greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))))]]) ).

cnf(refute_0_732,plain,
    ( multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)) != inverse(greatest_lower_bound(inverse(a),inverse(c)))
    | greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) != greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))
    | greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) = greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))),greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) ),[1,1],$fot(inverse(greatest_lower_bound(inverse(a),inverse(c))))]]) ).

cnf(refute_0_733,plain,
    ( multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)) != inverse(greatest_lower_bound(inverse(a),inverse(c)))
    | greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) = greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))),greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) )],[refute_0_731,refute_0_732]) ).

cnf(refute_0_734,plain,
    greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) = greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))),
    inference(resolve,[$cnf( $equal(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)),inverse(greatest_lower_bound(inverse(a),inverse(c)))) )],[refute_0_730,refute_0_733]) ).

cnf(refute_0_735,plain,
    ( b != greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))
    | greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))) != greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c))))
    | b = greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(b,greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c))))) ),[0],$fot(greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))))]]) ).

cnf(refute_0_736,plain,
    ( b != greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))
    | b = greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a))),greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c))))) )],[refute_0_734,refute_0_735]) ).

cnf(refute_0_737,plain,
    b = greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))),
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(b,multiply(c,multiply(inverse(greatest_lower_bound(a,c)),a)))) )],[refute_0_704,refute_0_736]) ).

cnf(refute_0_738,plain,
    ( b != greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c))))
    | greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))) = b ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(b)),bind(Y0,$fot(greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c))))))]]) ).

cnf(refute_0_739,plain,
    greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))) = b,
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c))))) )],[refute_0_737,refute_0_738]) ).

cnf(refute_0_740,plain,
    ( greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))) != b
    | inverse(greatest_lower_bound(inverse(a),inverse(c))) != multiply(greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))))
    | inverse(greatest_lower_bound(inverse(a),inverse(c))) = multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(a),inverse(c))),multiply(greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))))) ),[1,0],$fot(b)]]) ).

cnf(refute_0_741,plain,
    ( inverse(greatest_lower_bound(inverse(a),inverse(c))) != multiply(greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))))
    | inverse(greatest_lower_bound(inverse(a),inverse(c))) = multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) )],[refute_0_739,refute_0_740]) ).

cnf(refute_0_742,plain,
    inverse(greatest_lower_bound(inverse(a),inverse(c))) = multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(a),inverse(c))),multiply(greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))))) )],[refute_0_218,refute_0_741]) ).

cnf(refute_0_743,plain,
    greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) = greatest_lower_bound(X_209,greatest_lower_bound(X_210,greatest_lower_bound(Y,X_210))),
    inference(subst,[],[refute_0_346:[bind(X,$fot(greatest_lower_bound(Y,X_210))),bind(X_38,$fot(X_209)),bind(X_39,$fot(X_210))]]) ).

cnf(refute_0_744,plain,
    greatest_lower_bound(X_210,greatest_lower_bound(Y,X_210)) = greatest_lower_bound(X_210,Y),
    inference(subst,[],[refute_0_83:[bind(X_30,$fot(X_210))]]) ).

cnf(refute_0_745,plain,
    ( greatest_lower_bound(X_210,greatest_lower_bound(Y,X_210)) != greatest_lower_bound(X_210,Y)
    | greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) != greatest_lower_bound(X_209,greatest_lower_bound(X_210,greatest_lower_bound(Y,X_210)))
    | greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) = greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)),greatest_lower_bound(X_209,greatest_lower_bound(X_210,greatest_lower_bound(Y,X_210)))) ),[1,1],$fot(greatest_lower_bound(X_210,Y))]]) ).

cnf(refute_0_746,plain,
    ( greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) != greatest_lower_bound(X_209,greatest_lower_bound(X_210,greatest_lower_bound(Y,X_210)))
    | greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) = greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_210,greatest_lower_bound(Y,X_210)),greatest_lower_bound(X_210,Y)) )],[refute_0_744,refute_0_745]) ).

cnf(refute_0_747,plain,
    greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) = greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)),greatest_lower_bound(X_209,greatest_lower_bound(X_210,greatest_lower_bound(Y,X_210)))) )],[refute_0_743,refute_0_746]) ).

cnf(refute_0_748,plain,
    greatest_lower_bound(X_30,greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30)) = greatest_lower_bound(X_30,greatest_lower_bound(X_38,X_39)),
    inference(subst,[],[refute_0_83:[bind(Y,$fot(greatest_lower_bound(X_38,X_39)))]]) ).

cnf(refute_0_749,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30)) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(X_30))]]) ).

cnf(refute_0_750,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30)) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30)
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30)))]]) ).

cnf(refute_0_751,plain,
    greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30)),greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30)) )],[refute_0_749,refute_0_750]) ).

cnf(refute_0_752,plain,
    ( greatest_lower_bound(X_30,greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30)) != greatest_lower_bound(X_30,greatest_lower_bound(X_38,X_39))
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30) != greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30))
    | greatest_lower_bound(X_30,greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30))) = greatest_lower_bound(X_30,greatest_lower_bound(X_38,X_39)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_30,greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30)),greatest_lower_bound(X_30,greatest_lower_bound(X_38,X_39))) ),[0,1],$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30)))]]) ).

cnf(refute_0_753,plain,
    ( greatest_lower_bound(X_30,greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30)) != greatest_lower_bound(X_30,greatest_lower_bound(X_38,X_39))
    | greatest_lower_bound(X_30,greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30))) = greatest_lower_bound(X_30,greatest_lower_bound(X_38,X_39)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30),greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30))) )],[refute_0_751,refute_0_752]) ).

cnf(refute_0_754,plain,
    greatest_lower_bound(X_30,greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_30))) = greatest_lower_bound(X_30,greatest_lower_bound(X_38,X_39)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_30,greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_30)),greatest_lower_bound(X_30,greatest_lower_bound(X_38,X_39))) )],[refute_0_748,refute_0_753]) ).

cnf(refute_0_755,plain,
    greatest_lower_bound(X_210,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_210))) = greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)),
    inference(subst,[],[refute_0_754:[bind(X_30,$fot(X_210)),bind(X_38,$fot(X_209)),bind(X_39,$fot(Y))]]) ).

cnf(refute_0_756,plain,
    greatest_lower_bound(X_208,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_209))) = greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)),
    inference(subst,[],[refute_0_346:[bind(X,$fot(X_208)),bind(X_38,$fot(X_209)),bind(X_39,$fot(greatest_lower_bound(Y,X_209)))]]) ).

cnf(refute_0_757,plain,
    greatest_lower_bound(X_209,greatest_lower_bound(Y,X_209)) = greatest_lower_bound(X_209,Y),
    inference(subst,[],[refute_0_83:[bind(X_30,$fot(X_209))]]) ).

cnf(refute_0_758,plain,
    ( greatest_lower_bound(X_208,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_209))) != greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208))
    | greatest_lower_bound(X_209,greatest_lower_bound(Y,X_209)) != greatest_lower_bound(X_209,Y)
    | greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)) = greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_208,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_209))),greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208))) ),[0,1],$fot(greatest_lower_bound(X_209,Y))]]) ).

cnf(refute_0_759,plain,
    ( greatest_lower_bound(X_208,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_209))) != greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208))
    | greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)) = greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_209,greatest_lower_bound(Y,X_209)),greatest_lower_bound(X_209,Y)) )],[refute_0_757,refute_0_758]) ).

cnf(refute_0_760,plain,
    greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)) = greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_208,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_209))),greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208))) )],[refute_0_756,refute_0_759]) ).

cnf(refute_0_761,plain,
    greatest_lower_bound(X_209,greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))) = greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)),
    inference(subst,[],[refute_0_357:[bind(Y,$fot(X_208)),bind(X_38,$fot(Y)),bind(X_39,$fot(X_209))]]) ).

cnf(refute_0_762,plain,
    greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208) = greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(Y)),bind(Y,$fot(X_209)),bind(Z,$fot(X_208))]]) ).

cnf(refute_0_763,plain,
    greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) = greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)))]]) ).

cnf(refute_0_764,plain,
    ( greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) != greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208))
    | greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208) != greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))
    | greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) = greatest_lower_bound(X_209,greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)),greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)))]]) ).

cnf(refute_0_765,plain,
    ( greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208) != greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))
    | greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) = greatest_lower_bound(X_209,greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)),greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208))) )],[refute_0_763,refute_0_764]) ).

cnf(refute_0_766,plain,
    greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) = greatest_lower_bound(X_209,greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208),greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))) )],[refute_0_762,refute_0_765]) ).

cnf(refute_0_767,plain,
    ( greatest_lower_bound(X_209,greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))) != greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))
    | greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) != greatest_lower_bound(X_209,greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)))
    | greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) = greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)))),bind(Y0,$fot(greatest_lower_bound(X_209,greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))))]]) ).

cnf(refute_0_768,plain,
    ( greatest_lower_bound(X_209,greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))) != greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))
    | greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) = greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)),greatest_lower_bound(X_209,greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)))) )],[refute_0_766,refute_0_767]) ).

cnf(refute_0_769,plain,
    greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) = greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_209,greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))),greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))) )],[refute_0_761,refute_0_768]) ).

cnf(refute_0_770,plain,
    ( greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)) != greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208))
    | greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)) != greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))
    | greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))) ),[0],$fot(greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)))]]) ).

cnf(refute_0_771,plain,
    ( greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)) != greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208))
    | greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208)),greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))) )],[refute_0_769,refute_0_770]) ).

cnf(refute_0_772,plain,
    greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)),greatest_lower_bound(X_209,greatest_lower_bound(greatest_lower_bound(Y,X_209),X_208))) )],[refute_0_760,refute_0_771]) ).

cnf(refute_0_773,plain,
    ( greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)) != greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))
    | greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)) = greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))))]]) ).

cnf(refute_0_774,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208)) = greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_208,greatest_lower_bound(X_209,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_209,X_208))) )],[refute_0_772,refute_0_773]) ).

cnf(refute_0_775,plain,
    greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) = greatest_lower_bound(X_210,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_210))),
    inference(subst,[],[refute_0_774:[bind(Y,$fot(greatest_lower_bound(Y,X_210))),bind(X_208,$fot(X_210))]]) ).

cnf(refute_0_776,plain,
    ( greatest_lower_bound(X_210,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_210))) != greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y))
    | greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) != greatest_lower_bound(X_210,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_210)))
    | greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) = greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)))),bind(Y0,$fot(greatest_lower_bound(X_210,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_210))))),bind(Z0,$fot(greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y))))]]) ).

cnf(refute_0_777,plain,
    ( greatest_lower_bound(X_210,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_210))) != greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y))
    | greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) = greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)),greatest_lower_bound(X_210,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_210)))) )],[refute_0_775,refute_0_776]) ).

cnf(refute_0_778,plain,
    greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) = greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_210,greatest_lower_bound(X_209,greatest_lower_bound(Y,X_210))),greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y))) )],[refute_0_755,refute_0_777]) ).

cnf(refute_0_779,plain,
    ( greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) != greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y))
    | greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) != greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y))
    | greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)) = greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)),greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y))) ),[0],$fot(greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)))]]) ).

cnf(refute_0_780,plain,
    ( greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)) != greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y))
    | greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)) = greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)),greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y))) )],[refute_0_778,refute_0_779]) ).

cnf(refute_0_781,plain,
    greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)) = greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_210),greatest_lower_bound(X_209,X_210)),greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y))) )],[refute_0_747,refute_0_780]) ).

cnf(refute_0_782,plain,
    ( greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)) != greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y))
    | greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y)) = greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)))),bind(Y0,$fot(greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y))))]]) ).

cnf(refute_0_783,plain,
    greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y)) = greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_210,greatest_lower_bound(X_209,Y)),greatest_lower_bound(X_209,greatest_lower_bound(X_210,Y))) )],[refute_0_781,refute_0_782]) ).

cnf(refute_0_784,plain,
    greatest_lower_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(c))) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))),
    inference(subst,[],[refute_0_783:[bind(Y,$fot(inverse(c))),bind(X_209,$fot(inverse(b))),bind(X_210,$fot(inverse(a)))]]) ).

cnf(refute_0_785,plain,
    inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))) = greatest_lower_bound(inverse(a),inverse(c)),
    inference(subst,[],[p12_2:[bind(X,$fot(greatest_lower_bound(inverse(a),inverse(c))))]]) ).

cnf(refute_0_786,plain,
    greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))) = greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))]]) ).

cnf(refute_0_787,plain,
    ( greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))) != greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))
    | inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))) != greatest_lower_bound(inverse(a),inverse(c))
    | greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))) = greatest_lower_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(c))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))),greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))) ),[1,1],$fot(greatest_lower_bound(inverse(a),inverse(c)))]]) ).

cnf(refute_0_788,plain,
    ( inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))) != greatest_lower_bound(inverse(a),inverse(c))
    | greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))) = greatest_lower_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))),greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))) )],[refute_0_786,refute_0_787]) ).

cnf(refute_0_789,plain,
    greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))) = greatest_lower_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(c))),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),greatest_lower_bound(inverse(a),inverse(c))) )],[refute_0_785,refute_0_788]) ).

cnf(refute_0_790,plain,
    ( greatest_lower_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(c))) != greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))
    | greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))) != greatest_lower_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(c)))
    | greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))),bind(Y0,$fot(greatest_lower_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(c))))),bind(Z0,$fot(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_791,plain,
    ( greatest_lower_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(c))) != greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))
    | greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))),greatest_lower_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(c)))) )],[refute_0_789,refute_0_790]) ).

cnf(refute_0_792,plain,
    greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(c))),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_784,refute_0_791]) ).

cnf(refute_0_793,plain,
    inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))) = inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))))]]) ).

cnf(refute_0_794,plain,
    ( greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))) != greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))
    | inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))) != inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))
    | inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))) = inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))),inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))) ),[1,0],$fot(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))]]) ).

cnf(refute_0_795,plain,
    ( greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))) != greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))
    | inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))) = inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))),inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))) )],[refute_0_793,refute_0_794]) ).

cnf(refute_0_796,plain,
    inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))) = inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_792,refute_0_795]) ).

cnf(refute_0_797,plain,
    inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(b))) = inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))),
    inference(subst,[],[refute_0_482:[bind(X_112,$fot(inverse(b))),bind(X_113,$fot(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))]]) ).

cnf(refute_0_798,plain,
    inverse(greatest_lower_bound(X_134,inverse(X_229))) = multiply(X_229,inverse(multiply(greatest_lower_bound(X_134,inverse(X_229)),X_229))),
    inference(subst,[],[refute_0_209:[bind(X_61,$fot(greatest_lower_bound(X_134,inverse(X_229)))),bind(X_63,$fot(X_229))]]) ).

cnf(refute_0_799,plain,
    multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133) = greatest_lower_bound(multiply(X_134,X_133),multiply(inverse(X_133),X_133)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_133)),bind(Y,$fot(X_134)),bind(Z,$fot(inverse(X_133)))]]) ).

cnf(refute_0_800,plain,
    multiply(inverse(X_133),X_133) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_133))]]) ).

cnf(refute_0_801,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133) != greatest_lower_bound(multiply(X_134,X_133),multiply(inverse(X_133),X_133))
    | multiply(inverse(X_133),X_133) != identity
    | multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133) = greatest_lower_bound(multiply(X_134,X_133),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133),greatest_lower_bound(multiply(X_134,X_133),multiply(inverse(X_133),X_133))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_802,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133) != greatest_lower_bound(multiply(X_134,X_133),multiply(inverse(X_133),X_133))
    | multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133) = greatest_lower_bound(multiply(X_134,X_133),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_133),X_133),identity) )],[refute_0_800,refute_0_801]) ).

cnf(refute_0_803,plain,
    multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133) = greatest_lower_bound(multiply(X_134,X_133),identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133),greatest_lower_bound(multiply(X_134,X_133),multiply(inverse(X_133),X_133))) )],[refute_0_799,refute_0_802]) ).

cnf(refute_0_804,plain,
    greatest_lower_bound(multiply(X_134,X_133),identity) = greatest_lower_bound(identity,multiply(X_134,X_133)),
    inference(subst,[],[refute_0_46:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_134,X_133)))]]) ).

cnf(refute_0_805,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133) != greatest_lower_bound(multiply(X_134,X_133),identity)
    | greatest_lower_bound(multiply(X_134,X_133),identity) != greatest_lower_bound(identity,multiply(X_134,X_133))
    | multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133) = greatest_lower_bound(identity,multiply(X_134,X_133)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133),greatest_lower_bound(identity,multiply(X_134,X_133))) ),[0],$fot(greatest_lower_bound(multiply(X_134,X_133),identity))]]) ).

cnf(refute_0_806,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133) != greatest_lower_bound(multiply(X_134,X_133),identity)
    | multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133) = greatest_lower_bound(identity,multiply(X_134,X_133)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_134,X_133),identity),greatest_lower_bound(identity,multiply(X_134,X_133))) )],[refute_0_804,refute_0_805]) ).

cnf(refute_0_807,plain,
    multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133) = greatest_lower_bound(identity,multiply(X_134,X_133)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,inverse(X_133)),X_133),greatest_lower_bound(multiply(X_134,X_133),identity)) )],[refute_0_803,refute_0_806]) ).

cnf(refute_0_808,plain,
    multiply(greatest_lower_bound(X_134,inverse(X_229)),X_229) = greatest_lower_bound(identity,multiply(X_134,X_229)),
    inference(subst,[],[refute_0_807:[bind(X_133,$fot(X_229))]]) ).

cnf(refute_0_809,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(X_229)),X_229) != greatest_lower_bound(identity,multiply(X_134,X_229))
    | inverse(greatest_lower_bound(X_134,inverse(X_229))) != multiply(X_229,inverse(multiply(greatest_lower_bound(X_134,inverse(X_229)),X_229)))
    | inverse(greatest_lower_bound(X_134,inverse(X_229))) = multiply(X_229,inverse(greatest_lower_bound(identity,multiply(X_134,X_229)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_134,inverse(X_229))),multiply(X_229,inverse(multiply(greatest_lower_bound(X_134,inverse(X_229)),X_229)))) ),[1,1,0],$fot(greatest_lower_bound(identity,multiply(X_134,X_229)))]]) ).

cnf(refute_0_810,plain,
    ( inverse(greatest_lower_bound(X_134,inverse(X_229))) != multiply(X_229,inverse(multiply(greatest_lower_bound(X_134,inverse(X_229)),X_229)))
    | inverse(greatest_lower_bound(X_134,inverse(X_229))) = multiply(X_229,inverse(greatest_lower_bound(identity,multiply(X_134,X_229)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,inverse(X_229)),X_229),greatest_lower_bound(identity,multiply(X_134,X_229))) )],[refute_0_808,refute_0_809]) ).

cnf(refute_0_811,plain,
    inverse(greatest_lower_bound(X_134,inverse(X_229))) = multiply(X_229,inverse(greatest_lower_bound(identity,multiply(X_134,X_229)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_134,inverse(X_229))),multiply(X_229,inverse(multiply(greatest_lower_bound(X_134,inverse(X_229)),X_229)))) )],[refute_0_798,refute_0_810]) ).

cnf(refute_0_812,plain,
    ( inverse(greatest_lower_bound(X_134,inverse(X_229))) != multiply(X_229,inverse(greatest_lower_bound(identity,multiply(X_134,X_229))))
    | multiply(X_229,inverse(greatest_lower_bound(identity,multiply(X_134,X_229)))) = inverse(greatest_lower_bound(X_134,inverse(X_229))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(X_134,inverse(X_229))))),bind(Y0,$fot(multiply(X_229,inverse(greatest_lower_bound(identity,multiply(X_134,X_229))))))]]) ).

cnf(refute_0_813,plain,
    multiply(X_229,inverse(greatest_lower_bound(identity,multiply(X_134,X_229)))) = inverse(greatest_lower_bound(X_134,inverse(X_229))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_134,inverse(X_229))),multiply(X_229,inverse(greatest_lower_bound(identity,multiply(X_134,X_229))))) )],[refute_0_811,refute_0_812]) ).

cnf(refute_0_814,plain,
    multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(b))),
    inference(subst,[],[refute_0_813:[bind(X_134,$fot(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))),bind(X_229,$fot(b))]]) ).

cnf(refute_0_815,plain,
    ( multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) != inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(b)))
    | inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(b))) != inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))
    | multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) = inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))))),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(b))))),bind(Z0,$fot(inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))))]]) ).

cnf(refute_0_816,plain,
    ( inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(b))) != inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))
    | multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) = inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))) ),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))),inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(b)))) )],[refute_0_814,refute_0_815]) ).

cnf(refute_0_817,plain,
    multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) = inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),inverse(b))),inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))) )],[refute_0_797,refute_0_816]) ).

cnf(refute_0_818,plain,
    ( multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) != inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))
    | inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))) != inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) = inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))))),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))))),bind(Z0,$fot(inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_819,plain,
    ( inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))) != inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) = inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))),inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c))))))) )],[refute_0_817,refute_0_818]) ).

cnf(refute_0_820,plain,
    multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) = inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(b),inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))))),inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_796,refute_0_819]) ).

cnf(refute_0_821,plain,
    ( multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))) != inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))
    | inverse(greatest_lower_bound(inverse(a),inverse(c))) != multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))))
    | inverse(greatest_lower_bound(inverse(a),inverse(c))) = inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(a),inverse(c))),multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))))) ),[1],$fot(inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_822,plain,
    ( inverse(greatest_lower_bound(inverse(a),inverse(c))) != multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))))
    | inverse(greatest_lower_bound(inverse(a),inverse(c))) = inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))),inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_820,refute_0_821]) ).

cnf(refute_0_823,plain,
    inverse(greatest_lower_bound(inverse(a),inverse(c))) = inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(a),inverse(c))),multiply(b,inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))))) )],[refute_0_742,refute_0_822]) ).

cnf(refute_0_824,plain,
    ( inverse(greatest_lower_bound(inverse(a),inverse(c))) != inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))
    | inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) = inverse(greatest_lower_bound(inverse(a),inverse(c))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(a),inverse(c))))),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_825,plain,
    inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) = inverse(greatest_lower_bound(inverse(a),inverse(c))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(a),inverse(c))),inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_823,refute_0_824]) ).

cnf(refute_0_826,plain,
    ( inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) != inverse(greatest_lower_bound(inverse(a),inverse(c)))
    | inverse(inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))) != greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))
    | inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) ),[0,0],$fot(inverse(greatest_lower_bound(inverse(a),inverse(c))))]]) ).

cnf(refute_0_827,plain,
    ( inverse(inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))) != greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))
    | inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))),inverse(greatest_lower_bound(inverse(a),inverse(c)))) )],[refute_0_825,refute_0_826]) ).

cnf(refute_0_828,plain,
    inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_142,refute_0_827]) ).

cnf(refute_0_829,plain,
    ( inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))) != greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))
    | inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))) != greatest_lower_bound(inverse(a),inverse(c))
    | greatest_lower_bound(inverse(a),inverse(c)) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) ),[0],$fot(greatest_lower_bound(inverse(a),inverse(c)))]]) ).

cnf(refute_0_830,plain,
    ( inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))) != greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))
    | greatest_lower_bound(inverse(a),inverse(c)) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),greatest_lower_bound(inverse(a),inverse(c))) )],[refute_0_785,refute_0_829]) ).

cnf(refute_0_831,plain,
    greatest_lower_bound(inverse(a),inverse(c)) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_828,refute_0_830]) ).

cnf(refute_0_832,plain,
    ( greatest_lower_bound(inverse(a),inverse(c)) != greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))
    | greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))) = greatest_lower_bound(inverse(a),inverse(c)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(inverse(a),inverse(c)))),bind(Y0,$fot(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_833,plain,
    greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))) = greatest_lower_bound(inverse(a),inverse(c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(a),inverse(c)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_831,refute_0_832]) ).

cnf(refute_0_834,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) != multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))
    | greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))) != greatest_lower_bound(inverse(a),inverse(c))
    | multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) = multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))),multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))) ),[1,1],$fot(greatest_lower_bound(inverse(a),inverse(c)))]]) ).

cnf(refute_0_835,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) != multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) = multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))),greatest_lower_bound(inverse(a),inverse(c))) )],[refute_0_833,refute_0_834]) ).

cnf(refute_0_836,plain,
    multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) = multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))),multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_141,refute_0_835]) ).

cnf(refute_0_837,plain,
    inverse(inverse(a)) = a,
    inference(subst,[],[p12_2:[bind(X,$fot(a))]]) ).

cnf(refute_0_838,plain,
    multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))) = multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))),
    introduced(tautology,[refl,[$fot(multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))))]]) ).

cnf(refute_0_839,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))) != multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))
    | inverse(inverse(a)) != a
    | multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))) = multiply(a,greatest_lower_bound(inverse(b),inverse(c))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))),multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))) ),[1,0],$fot(a)]]) ).

cnf(refute_0_840,plain,
    ( inverse(inverse(a)) != a
    | multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))) = multiply(a,greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))),multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_838,refute_0_839]) ).

cnf(refute_0_841,plain,
    multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))) = multiply(a,greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_837,refute_0_840]) ).

cnf(refute_0_842,plain,
    greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))) = greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_843,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))) != multiply(a,greatest_lower_bound(inverse(b),inverse(c)))
    | greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))) != greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))))
    | greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))) = greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))),greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))))) ),[1,1],$fot(multiply(a,greatest_lower_bound(inverse(b),inverse(c))))]]) ).

cnf(refute_0_844,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))) != multiply(a,greatest_lower_bound(inverse(b),inverse(c)))
    | greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))) = greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))),greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_842,refute_0_843]) ).

cnf(refute_0_845,plain,
    greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))) = greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))),multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_841,refute_0_844]) ).

cnf(refute_0_846,plain,
    multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) = greatest_lower_bound(identity,multiply(inverse(X_105),greatest_lower_bound(X_110,X_105))),
    inference(subst,[],[refute_0_134:[bind(X_104,$fot(greatest_lower_bound(X_110,X_105)))]]) ).

cnf(refute_0_847,plain,
    multiply(inverse(X_105),greatest_lower_bound(X_110,X_105)) = greatest_lower_bound(identity,multiply(inverse(X_105),X_110)),
    inference(subst,[],[refute_0_134:[bind(X_104,$fot(X_110))]]) ).

cnf(refute_0_848,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_110,X_105)) != greatest_lower_bound(identity,multiply(inverse(X_105),X_110))
    | multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) != greatest_lower_bound(identity,multiply(inverse(X_105),greatest_lower_bound(X_110,X_105)))
    | multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)),greatest_lower_bound(identity,multiply(inverse(X_105),greatest_lower_bound(X_110,X_105)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(inverse(X_105),X_110)))]]) ).

cnf(refute_0_849,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) != greatest_lower_bound(identity,multiply(inverse(X_105),greatest_lower_bound(X_110,X_105)))
    | multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_110,X_105)),greatest_lower_bound(identity,multiply(inverse(X_105),X_110))) )],[refute_0_847,refute_0_848]) ).

cnf(refute_0_850,plain,
    multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)),greatest_lower_bound(identity,multiply(inverse(X_105),greatest_lower_bound(X_110,X_105)))) )],[refute_0_846,refute_0_849]) ).

cnf(refute_0_851,plain,
    greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105)) = greatest_lower_bound(X_105,X_110),
    inference(subst,[],[refute_0_83:[bind(Y,$fot(X_110)),bind(X_30,$fot(X_105))]]) ).

cnf(refute_0_852,plain,
    multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))) = multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))),
    introduced(tautology,[refl,[$fot(multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))))]]) ).

cnf(refute_0_853,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))) != multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105)))
    | greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105)) != greatest_lower_bound(X_105,X_110)
    | multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))) = multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))),multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105)))) ),[1,1],$fot(greatest_lower_bound(X_105,X_110))]]) ).

cnf(refute_0_854,plain,
    ( greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105)) != greatest_lower_bound(X_105,X_110)
    | multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))) = multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))),multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105)))) )],[refute_0_852,refute_0_853]) ).

cnf(refute_0_855,plain,
    multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))) = multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105)),greatest_lower_bound(X_105,X_110)) )],[refute_0_851,refute_0_854]) ).

cnf(refute_0_856,plain,
    greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)) = greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105)),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(multiply(X_103,X_105))),bind(Y,$fot(multiply(X_103,X_104)))]]) ).

cnf(refute_0_857,plain,
    multiply(X_103,greatest_lower_bound(X_104,X_105)) = greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_103)),bind(Y,$fot(X_104)),bind(Z,$fot(X_105))]]) ).

cnf(refute_0_858,plain,
    ( multiply(X_103,greatest_lower_bound(X_104,X_105)) != greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105))
    | greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105)) = multiply(X_103,greatest_lower_bound(X_104,X_105)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(X_103,greatest_lower_bound(X_104,X_105)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105))))]]) ).

cnf(refute_0_859,plain,
    greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105)) = multiply(X_103,greatest_lower_bound(X_104,X_105)),
    inference(resolve,[$cnf( $equal(multiply(X_103,greatest_lower_bound(X_104,X_105)),greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105))) )],[refute_0_857,refute_0_858]) ).

cnf(refute_0_860,plain,
    ( greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105)) != multiply(X_103,greatest_lower_bound(X_104,X_105))
    | greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)) != greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105))
    | greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)) = multiply(X_103,greatest_lower_bound(X_104,X_105)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)),greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105))) ),[1],$fot(multiply(X_103,greatest_lower_bound(X_104,X_105)))]]) ).

cnf(refute_0_861,plain,
    ( greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)) != greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105))
    | greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)) = multiply(X_103,greatest_lower_bound(X_104,X_105)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105)),multiply(X_103,greatest_lower_bound(X_104,X_105))) )],[refute_0_859,refute_0_860]) ).

cnf(refute_0_862,plain,
    greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)) = multiply(X_103,greatest_lower_bound(X_104,X_105)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)),greatest_lower_bound(multiply(X_103,X_104),multiply(X_103,X_105))) )],[refute_0_856,refute_0_861]) ).

cnf(refute_0_863,plain,
    greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)) = multiply(X_103,greatest_lower_bound(X_105,X_104)),
    inference(subst,[],[refute_0_458:[bind(X,$fot(X_103)),bind(Y,$fot(X_105)),bind(Z,$fot(X_104))]]) ).

cnf(refute_0_864,plain,
    ( greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)) != multiply(X_103,greatest_lower_bound(X_104,X_105))
    | greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)) != multiply(X_103,greatest_lower_bound(X_105,X_104))
    | multiply(X_103,greatest_lower_bound(X_105,X_104)) = multiply(X_103,greatest_lower_bound(X_104,X_105)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)),multiply(X_103,greatest_lower_bound(X_104,X_105))) ),[0],$fot(multiply(X_103,greatest_lower_bound(X_105,X_104)))]]) ).

cnf(refute_0_865,plain,
    ( greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)) != multiply(X_103,greatest_lower_bound(X_104,X_105))
    | multiply(X_103,greatest_lower_bound(X_105,X_104)) = multiply(X_103,greatest_lower_bound(X_104,X_105)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)),multiply(X_103,greatest_lower_bound(X_105,X_104))) )],[refute_0_863,refute_0_864]) ).

cnf(refute_0_866,plain,
    multiply(X_103,greatest_lower_bound(X_105,X_104)) = multiply(X_103,greatest_lower_bound(X_104,X_105)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_103,X_105),multiply(X_103,X_104)),multiply(X_103,greatest_lower_bound(X_104,X_105))) )],[refute_0_862,refute_0_865]) ).

cnf(refute_0_867,plain,
    ( multiply(X_103,greatest_lower_bound(X_105,X_104)) != multiply(X_103,greatest_lower_bound(X_104,X_105))
    | multiply(X_103,greatest_lower_bound(X_104,X_105)) = multiply(X_103,greatest_lower_bound(X_105,X_104)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(X_103,greatest_lower_bound(X_105,X_104)))),bind(Y0,$fot(multiply(X_103,greatest_lower_bound(X_104,X_105))))]]) ).

cnf(refute_0_868,plain,
    multiply(X_103,greatest_lower_bound(X_104,X_105)) = multiply(X_103,greatest_lower_bound(X_105,X_104)),
    inference(resolve,[$cnf( $equal(multiply(X_103,greatest_lower_bound(X_105,X_104)),multiply(X_103,greatest_lower_bound(X_104,X_105))) )],[refute_0_866,refute_0_867]) ).

cnf(refute_0_869,plain,
    multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) = multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))),
    inference(subst,[],[refute_0_868:[bind(X_103,$fot(inverse(X_105))),bind(X_104,$fot(greatest_lower_bound(X_110,X_105)))]]) ).

cnf(refute_0_870,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))) != multiply(inverse(X_105),greatest_lower_bound(X_105,X_110))
    | multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) != multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105)))
    | multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) = multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)))),bind(Y0,$fot(multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))))),bind(Z0,$fot(multiply(inverse(X_105),greatest_lower_bound(X_105,X_110))))]]) ).

cnf(refute_0_871,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))) != multiply(inverse(X_105),greatest_lower_bound(X_105,X_110))
    | multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) = multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)),multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105)))) )],[refute_0_869,refute_0_870]) ).

cnf(refute_0_872,plain,
    multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) = multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_105,greatest_lower_bound(X_110,X_105))),multiply(inverse(X_105),greatest_lower_bound(X_105,X_110))) )],[refute_0_855,refute_0_871]) ).

cnf(refute_0_873,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) != multiply(inverse(X_105),greatest_lower_bound(X_105,X_110))
    | multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110)))
    | multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110)))) ),[0],$fot(multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)))]]) ).

cnf(refute_0_874,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110)))
    | multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)),multiply(inverse(X_105),greatest_lower_bound(X_105,X_110))) )],[refute_0_872,refute_0_873]) ).

cnf(refute_0_875,plain,
    greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110))) = greatest_lower_bound(identity,multiply(inverse(X_105),X_110)),
    inference(subst,[],[refute_0_319:[bind(X_31,$fot(multiply(inverse(X_105),X_110))),bind(X_32,$fot(identity))]]) ).

cnf(refute_0_876,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110)))
    | greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110))) != greatest_lower_bound(identity,multiply(inverse(X_105),X_110))
    | multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) = greatest_lower_bound(identity,multiply(inverse(X_105),X_110)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)),greatest_lower_bound(identity,multiply(inverse(X_105),X_110))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110))))]]) ).

cnf(refute_0_877,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110)))
    | multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) = greatest_lower_bound(identity,multiply(inverse(X_105),X_110)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110))),greatest_lower_bound(identity,multiply(inverse(X_105),X_110))) )],[refute_0_875,refute_0_876]) ).

cnf(refute_0_878,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110)))
    | multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) = greatest_lower_bound(identity,multiply(inverse(X_105),X_110)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110)))) )],[refute_0_874,refute_0_877]) ).

cnf(refute_0_879,plain,
    multiply(inverse(X_105),greatest_lower_bound(X_105,X_110)) = greatest_lower_bound(identity,multiply(inverse(X_105),X_110)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(greatest_lower_bound(X_110,X_105),X_105)),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(inverse(X_105),X_110)))) )],[refute_0_850,refute_0_878]) ).

cnf(refute_0_880,plain,
    multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) = greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))),
    inference(subst,[],[refute_0_879:[bind(X_105,$fot(inverse(a))),bind(X_110,$fot(greatest_lower_bound(inverse(b),inverse(c))))]]) ).

cnf(refute_0_881,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) != multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) != greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) = greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))))),bind(Y0,$fot(multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_882,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))) != greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) = greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))),multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_141,refute_0_881]) ).

cnf(refute_0_883,plain,
    multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) = greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c)))),greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_880,refute_0_882]) ).

cnf(refute_0_884,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) != greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))))
    | greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))) != greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) = greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_885,plain,
    ( greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))) != greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) = greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))),greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_883,refute_0_884]) ).

cnf(refute_0_886,plain,
    multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) = greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(a)),greatest_lower_bound(inverse(b),inverse(c)))),greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_845,refute_0_885]) ).

cnf(refute_0_887,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) != multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c)))
    | multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) != greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c))))
    | greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) = multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))),multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c)))) ),[0],$fot(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_888,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) != multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c)))
    | greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) = multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))),greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_886,refute_0_887]) ).

cnf(refute_0_889,plain,
    multiply(greatest_lower_bound(X_134,inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_807:[bind(X_133,$fot(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_890,plain,
    inverse(inverse(X_112)) = multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(multiply(inverse(X_112),greatest_lower_bound(a,greatest_lower_bound(c,X_112))))),
    inference(subst,[],[refute_0_209:[bind(X_61,$fot(inverse(X_112))),bind(X_63,$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_112))))]]) ).

cnf(refute_0_891,plain,
    multiply(inverse(X_112),greatest_lower_bound(X_112,greatest_lower_bound(a,c))) = greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_94:[bind(X_104,$fot(X_112)),bind(X_105,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_892,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,X_112)) = greatest_lower_bound(X_112,greatest_lower_bound(a,c)),
    inference(subst,[],[refute_0_453:[bind(X_66,$fot(X_112))]]) ).

cnf(refute_0_893,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,X_112)) != greatest_lower_bound(X_112,greatest_lower_bound(a,c))
    | greatest_lower_bound(X_112,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(c,X_112)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_112)))),bind(Y0,$fot(greatest_lower_bound(X_112,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_894,plain,
    greatest_lower_bound(X_112,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(c,X_112)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),greatest_lower_bound(X_112,greatest_lower_bound(a,c))) )],[refute_0_892,refute_0_893]) ).

cnf(refute_0_895,plain,
    ( multiply(inverse(X_112),greatest_lower_bound(X_112,greatest_lower_bound(a,c))) != greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c)))
    | greatest_lower_bound(X_112,greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(c,X_112))
    | multiply(inverse(X_112),greatest_lower_bound(a,greatest_lower_bound(c,X_112))) = greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_112),greatest_lower_bound(X_112,greatest_lower_bound(a,c))),greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c)))) ),[0,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_112)))]]) ).

cnf(refute_0_896,plain,
    ( multiply(inverse(X_112),greatest_lower_bound(X_112,greatest_lower_bound(a,c))) != greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c)))
    | multiply(inverse(X_112),greatest_lower_bound(a,greatest_lower_bound(c,X_112))) = greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_112,greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(c,X_112))) )],[refute_0_894,refute_0_895]) ).

cnf(refute_0_897,plain,
    multiply(inverse(X_112),greatest_lower_bound(a,greatest_lower_bound(c,X_112))) = greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_112),greatest_lower_bound(X_112,greatest_lower_bound(a,c))),greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c)))) )],[refute_0_891,refute_0_896]) ).

cnf(refute_0_898,plain,
    ( multiply(inverse(X_112),greatest_lower_bound(a,greatest_lower_bound(c,X_112))) != greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c)))
    | inverse(inverse(X_112)) != multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(multiply(inverse(X_112),greatest_lower_bound(a,greatest_lower_bound(c,X_112)))))
    | inverse(inverse(X_112)) = multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_112)),multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(multiply(inverse(X_112),greatest_lower_bound(a,greatest_lower_bound(c,X_112)))))) ),[1,1,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_899,plain,
    ( inverse(inverse(X_112)) != multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(multiply(inverse(X_112),greatest_lower_bound(a,greatest_lower_bound(c,X_112)))))
    | inverse(inverse(X_112)) = multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_112),greatest_lower_bound(a,greatest_lower_bound(c,X_112))),greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c)))) )],[refute_0_897,refute_0_898]) ).

cnf(refute_0_900,plain,
    inverse(inverse(X_112)) = multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_112)),multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(multiply(inverse(X_112),greatest_lower_bound(a,greatest_lower_bound(c,X_112)))))) )],[refute_0_890,refute_0_899]) ).

cnf(refute_0_901,plain,
    ( inverse(inverse(X_112)) != X_112
    | inverse(inverse(X_112)) != multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c)))))
    | X_112 = multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_112)),multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c)))))) ),[0],$fot(X_112)]]) ).

cnf(refute_0_902,plain,
    ( inverse(inverse(X_112)) != multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c)))))
    | X_112 = multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_112)),X_112) )],[refute_0_99,refute_0_901]) ).

cnf(refute_0_903,plain,
    X_112 = multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_112)),multiply(greatest_lower_bound(a,greatest_lower_bound(c,X_112)),inverse(greatest_lower_bound(identity,multiply(inverse(X_112),greatest_lower_bound(a,c)))))) )],[refute_0_900,refute_0_902]) ).

cnf(refute_0_904,plain,
    c = multiply(greatest_lower_bound(a,greatest_lower_bound(c,c)),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_903:[bind(X_112,$fot(c))]]) ).

cnf(refute_0_905,plain,
    greatest_lower_bound(c,c) = c,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(c))]]) ).

cnf(refute_0_906,plain,
    ( c != multiply(greatest_lower_bound(a,greatest_lower_bound(c,c)),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c)))))
    | greatest_lower_bound(c,c) != c
    | c = multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(c,multiply(greatest_lower_bound(a,greatest_lower_bound(c,c)),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c)))))) ),[1,0,1],$fot(c)]]) ).

cnf(refute_0_907,plain,
    ( c != multiply(greatest_lower_bound(a,greatest_lower_bound(c,c)),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c)))))
    | c = multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,c),c) )],[refute_0_905,refute_0_906]) ).

cnf(refute_0_908,plain,
    c = multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(c,multiply(greatest_lower_bound(a,greatest_lower_bound(c,c)),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c)))))) )],[refute_0_904,refute_0_907]) ).

cnf(refute_0_909,plain,
    multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_813:[bind(X_134,$fot(inverse(c))),bind(X_229,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_910,plain,
    ( multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))
    | c != multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c)))))
    | c = inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(c,multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c)))))) ),[1],$fot(inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_911,plain,
    ( c != multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c)))))
    | c = inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_909,refute_0_910]) ).

cnf(refute_0_912,plain,
    c = inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(c,multiply(greatest_lower_bound(a,c),inverse(greatest_lower_bound(identity,multiply(inverse(c),greatest_lower_bound(a,c)))))) )],[refute_0_908,refute_0_911]) ).

cnf(refute_0_913,plain,
    ( c != inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))
    | inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = c ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(c)),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_914,plain,
    inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = c,
    inference(resolve,[$cnf( $equal(c,inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_912,refute_0_913]) ).

cnf(refute_0_915,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))
    | inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != c
    | multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_134,inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))) ),[0,0,1],$fot(c)]]) ).

cnf(refute_0_916,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))
    | multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),c) )],[refute_0_914,refute_0_915]) ).

cnf(refute_0_917,plain,
    multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))) )],[refute_0_889,refute_0_916]) ).

cnf(refute_0_918,plain,
    inverse(inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))),
    inference(subst,[],[p12_2:[bind(X,$fot(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_919,plain,
    ( inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != c
    | inverse(inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))
    | inverse(c) = greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) ),[0,0],$fot(c)]]) ).

cnf(refute_0_920,plain,
    ( inverse(inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))
    | inverse(c) = greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),c) )],[refute_0_914,refute_0_919]) ).

cnf(refute_0_921,plain,
    inverse(c) = greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) )],[refute_0_918,refute_0_920]) ).

cnf(refute_0_922,plain,
    ( inverse(c) != greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))
    | greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))) = inverse(c) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(c))),bind(Y0,$fot(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_923,plain,
    greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))) = inverse(c),
    inference(resolve,[$cnf( $equal(inverse(c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) )],[refute_0_921,refute_0_922]) ).

cnf(refute_0_924,plain,
    multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_925,plain,
    ( multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))
    | greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))) != inverse(c)
    | multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = multiply(greatest_lower_bound(X_134,c),inverse(c)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) ),[1,1],$fot(inverse(c))]]) ).

cnf(refute_0_926,plain,
    ( greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))) != inverse(c)
    | multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = multiply(greatest_lower_bound(X_134,c),inverse(c)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_924,refute_0_925]) ).

cnf(refute_0_927,plain,
    multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = multiply(greatest_lower_bound(X_134,c),inverse(c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))),inverse(c)) )],[refute_0_923,refute_0_926]) ).

cnf(refute_0_928,plain,
    ( multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != multiply(greatest_lower_bound(X_134,c),inverse(c))
    | multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))
    | multiply(greatest_lower_bound(X_134,c),inverse(c)) = greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))) ),[0],$fot(multiply(greatest_lower_bound(X_134,c),inverse(c)))]]) ).

cnf(refute_0_929,plain,
    ( multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))
    | multiply(greatest_lower_bound(X_134,c),inverse(c)) = greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),multiply(greatest_lower_bound(X_134,c),inverse(c))) )],[refute_0_927,refute_0_928]) ).

cnf(refute_0_930,plain,
    greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)) = greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133)),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(multiply(X_135,X_133))),bind(Y,$fot(multiply(X_134,X_133)))]]) ).

cnf(refute_0_931,plain,
    multiply(greatest_lower_bound(X_134,X_135),X_133) = greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_133)),bind(Y,$fot(X_134)),bind(Z,$fot(X_135))]]) ).

cnf(refute_0_932,plain,
    ( multiply(greatest_lower_bound(X_134,X_135),X_133) != greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133))
    | greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133)) = multiply(greatest_lower_bound(X_134,X_135),X_133) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(greatest_lower_bound(X_134,X_135),X_133))),bind(Y0,$fot(greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133))))]]) ).

cnf(refute_0_933,plain,
    greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133)) = multiply(greatest_lower_bound(X_134,X_135),X_133),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,X_135),X_133),greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133))) )],[refute_0_931,refute_0_932]) ).

cnf(refute_0_934,plain,
    ( greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133)) != multiply(greatest_lower_bound(X_134,X_135),X_133)
    | greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)) != greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133))
    | greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)) = multiply(greatest_lower_bound(X_134,X_135),X_133) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)),greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133))) ),[1],$fot(multiply(greatest_lower_bound(X_134,X_135),X_133))]]) ).

cnf(refute_0_935,plain,
    ( greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)) != greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133))
    | greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)) = multiply(greatest_lower_bound(X_134,X_135),X_133) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133)),multiply(greatest_lower_bound(X_134,X_135),X_133)) )],[refute_0_933,refute_0_934]) ).

cnf(refute_0_936,plain,
    greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)) = multiply(greatest_lower_bound(X_134,X_135),X_133),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)),greatest_lower_bound(multiply(X_134,X_133),multiply(X_135,X_133))) )],[refute_0_930,refute_0_935]) ).

cnf(refute_0_937,plain,
    ( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
    | greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).

cnf(refute_0_938,plain,
    greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_937]) ).

cnf(refute_0_939,plain,
    greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)) = multiply(greatest_lower_bound(X_135,X_134),X_133),
    inference(subst,[],[refute_0_938:[bind(X,$fot(X_133)),bind(Y,$fot(X_135)),bind(Z,$fot(X_134))]]) ).

cnf(refute_0_940,plain,
    ( greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)) != multiply(greatest_lower_bound(X_134,X_135),X_133)
    | greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)) != multiply(greatest_lower_bound(X_135,X_134),X_133)
    | multiply(greatest_lower_bound(X_135,X_134),X_133) = multiply(greatest_lower_bound(X_134,X_135),X_133) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)),multiply(greatest_lower_bound(X_134,X_135),X_133)) ),[0],$fot(multiply(greatest_lower_bound(X_135,X_134),X_133))]]) ).

cnf(refute_0_941,plain,
    ( greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)) != multiply(greatest_lower_bound(X_134,X_135),X_133)
    | multiply(greatest_lower_bound(X_135,X_134),X_133) = multiply(greatest_lower_bound(X_134,X_135),X_133) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)),multiply(greatest_lower_bound(X_135,X_134),X_133)) )],[refute_0_939,refute_0_940]) ).

cnf(refute_0_942,plain,
    multiply(greatest_lower_bound(X_135,X_134),X_133) = multiply(greatest_lower_bound(X_134,X_135),X_133),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_135,X_133),multiply(X_134,X_133)),multiply(greatest_lower_bound(X_134,X_135),X_133)) )],[refute_0_936,refute_0_941]) ).

cnf(refute_0_943,plain,
    multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) = multiply(greatest_lower_bound(X_135,X_134),inverse(X_135)),
    inference(subst,[],[refute_0_942:[bind(X_133,$fot(inverse(X_135))),bind(X_134,$fot(X_135)),bind(X_135,$fot(X_134))]]) ).

cnf(refute_0_944,plain,
    ( multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) != multiply(greatest_lower_bound(X_135,X_134),inverse(X_135))
    | multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) != greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))
    | multiply(greatest_lower_bound(X_135,X_134),inverse(X_135)) = greatest_lower_bound(identity,multiply(X_134,inverse(X_135))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)),greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) ),[0],$fot(multiply(greatest_lower_bound(X_135,X_134),inverse(X_135)))]]) ).

cnf(refute_0_945,plain,
    ( multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) != greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))
    | multiply(greatest_lower_bound(X_135,X_134),inverse(X_135)) = greatest_lower_bound(identity,multiply(X_134,inverse(X_135))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)),multiply(greatest_lower_bound(X_135,X_134),inverse(X_135))) )],[refute_0_943,refute_0_944]) ).

cnf(refute_0_946,plain,
    multiply(greatest_lower_bound(X_135,X_134),inverse(X_135)) = greatest_lower_bound(identity,multiply(X_134,inverse(X_135))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)),greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) )],[refute_0_64,refute_0_945]) ).

cnf(refute_0_947,plain,
    ( multiply(greatest_lower_bound(X_135,X_134),inverse(X_135)) != greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))
    | greatest_lower_bound(identity,multiply(X_134,inverse(X_135))) = multiply(greatest_lower_bound(X_135,X_134),inverse(X_135)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(greatest_lower_bound(X_135,X_134),inverse(X_135)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))))]]) ).

cnf(refute_0_948,plain,
    greatest_lower_bound(identity,multiply(X_134,inverse(X_135))) = multiply(greatest_lower_bound(X_135,X_134),inverse(X_135)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_135,X_134),inverse(X_135)),greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) )],[refute_0_946,refute_0_947]) ).

cnf(refute_0_949,plain,
    greatest_lower_bound(identity,multiply(X_134,inverse(c))) = multiply(greatest_lower_bound(c,X_134),inverse(c)),
    inference(subst,[],[refute_0_948:[bind(X_135,$fot(c))]]) ).

cnf(refute_0_950,plain,
    multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),
    introduced(tautology,[refl,[$fot(multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_951,plain,
    ( multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))
    | greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))) != inverse(c)
    | multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = multiply(X_134,inverse(c)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) ),[1,1],$fot(inverse(c))]]) ).

cnf(refute_0_952,plain,
    ( greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))) != inverse(c)
    | multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = multiply(X_134,inverse(c)) ),
    inference(resolve,[$cnf( $equal(multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_950,refute_0_951]) ).

cnf(refute_0_953,plain,
    multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) = multiply(X_134,inverse(c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))),inverse(c)) )],[refute_0_923,refute_0_952]) ).

cnf(refute_0_954,plain,
    greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_955,plain,
    ( multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != multiply(X_134,inverse(c))
    | greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))
    | greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(identity,multiply(X_134,inverse(c))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))) ),[1,1],$fot(multiply(X_134,inverse(c)))]]) ).

cnf(refute_0_956,plain,
    ( multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != multiply(X_134,inverse(c))
    | greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(identity,multiply(X_134,inverse(c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))) )],[refute_0_954,refute_0_955]) ).

cnf(refute_0_957,plain,
    greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(identity,multiply(X_134,inverse(c))),
    inference(resolve,[$cnf( $equal(multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),multiply(X_134,inverse(c))) )],[refute_0_953,refute_0_956]) ).

cnf(refute_0_958,plain,
    ( greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(identity,multiply(X_134,inverse(c)))
    | greatest_lower_bound(identity,multiply(X_134,inverse(c))) != multiply(greatest_lower_bound(c,X_134),inverse(c))
    | greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(c,X_134),inverse(c)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_134,inverse(c))))),bind(Z0,$fot(multiply(greatest_lower_bound(c,X_134),inverse(c))))]]) ).

cnf(refute_0_959,plain,
    ( greatest_lower_bound(identity,multiply(X_134,inverse(c))) != multiply(greatest_lower_bound(c,X_134),inverse(c))
    | greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(c,X_134),inverse(c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(identity,multiply(X_134,inverse(c)))) )],[refute_0_957,refute_0_958]) ).

cnf(refute_0_960,plain,
    greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(c,X_134),inverse(c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_134,inverse(c))),multiply(greatest_lower_bound(c,X_134),inverse(c))) )],[refute_0_949,refute_0_959]) ).

cnf(refute_0_961,plain,
    ( multiply(greatest_lower_bound(X_134,c),inverse(c)) != greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))
    | greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))) != multiply(greatest_lower_bound(c,X_134),inverse(c))
    | multiply(greatest_lower_bound(X_134,c),inverse(c)) = multiply(greatest_lower_bound(c,X_134),inverse(c)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_134,c),inverse(c)),multiply(greatest_lower_bound(c,X_134),inverse(c))) ),[0],$fot(greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_962,plain,
    ( multiply(greatest_lower_bound(X_134,c),inverse(c)) != greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))
    | multiply(greatest_lower_bound(X_134,c),inverse(c)) = multiply(greatest_lower_bound(c,X_134),inverse(c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c))))),multiply(greatest_lower_bound(c,X_134),inverse(c))) )],[refute_0_960,refute_0_961]) ).

cnf(refute_0_963,plain,
    ( multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))
    | multiply(greatest_lower_bound(X_134,c),inverse(c)) = multiply(greatest_lower_bound(c,X_134),inverse(c)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,c),inverse(c)),greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))) )],[refute_0_929,refute_0_962]) ).

cnf(refute_0_964,plain,
    multiply(greatest_lower_bound(X_134,c),inverse(c)) = multiply(greatest_lower_bound(c,X_134),inverse(c)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,c),greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(identity,multiply(X_134,greatest_lower_bound(inverse(c),inverse(greatest_lower_bound(a,c)))))) )],[refute_0_917,refute_0_963]) ).

cnf(refute_0_965,plain,
    ( multiply(greatest_lower_bound(X_134,c),inverse(c)) != multiply(greatest_lower_bound(c,X_134),inverse(c))
    | multiply(greatest_lower_bound(c,X_134),inverse(c)) = multiply(greatest_lower_bound(X_134,c),inverse(c)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(greatest_lower_bound(X_134,c),inverse(c)))),bind(Y0,$fot(multiply(greatest_lower_bound(c,X_134),inverse(c))))]]) ).

cnf(refute_0_966,plain,
    multiply(greatest_lower_bound(c,X_134),inverse(c)) = multiply(greatest_lower_bound(X_134,c),inverse(c)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,c),inverse(c)),multiply(greatest_lower_bound(c,X_134),inverse(c))) )],[refute_0_964,refute_0_965]) ).

cnf(refute_0_967,plain,
    multiply(greatest_lower_bound(c,a),inverse(c)) = multiply(greatest_lower_bound(a,c),inverse(c)),
    inference(subst,[],[refute_0_966:[bind(X_134,$fot(a))]]) ).

cnf(refute_0_968,plain,
    greatest_lower_bound(identity,multiply(a,inverse(c))) = multiply(greatest_lower_bound(c,a),inverse(c)),
    inference(subst,[],[refute_0_948:[bind(X_134,$fot(a)),bind(X_135,$fot(c))]]) ).

cnf(refute_0_969,plain,
    ( multiply(greatest_lower_bound(c,a),inverse(c)) != multiply(greatest_lower_bound(a,c),inverse(c))
    | greatest_lower_bound(identity,multiply(a,inverse(c))) != multiply(greatest_lower_bound(c,a),inverse(c))
    | greatest_lower_bound(identity,multiply(a,inverse(c))) = multiply(greatest_lower_bound(a,c),inverse(c)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(identity,multiply(a,inverse(c))))),bind(Y0,$fot(multiply(greatest_lower_bound(c,a),inverse(c)))),bind(Z0,$fot(multiply(greatest_lower_bound(a,c),inverse(c))))]]) ).

cnf(refute_0_970,plain,
    ( multiply(greatest_lower_bound(c,a),inverse(c)) != multiply(greatest_lower_bound(a,c),inverse(c))
    | greatest_lower_bound(identity,multiply(a,inverse(c))) = multiply(greatest_lower_bound(a,c),inverse(c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,inverse(c))),multiply(greatest_lower_bound(c,a),inverse(c))) )],[refute_0_968,refute_0_969]) ).

cnf(refute_0_971,plain,
    greatest_lower_bound(identity,multiply(a,inverse(c))) = multiply(greatest_lower_bound(a,c),inverse(c)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(c,a),inverse(c)),multiply(greatest_lower_bound(a,c),inverse(c))) )],[refute_0_967,refute_0_970]) ).

cnf(refute_0_972,plain,
    inverse(multiply(c,inverse(a))) = multiply(a,inverse(c)),
    inference(subst,[],[refute_0_146:[bind(X,$fot(a)),bind(X_17,$fot(c))]]) ).

cnf(refute_0_973,plain,
    greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))) = greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))))]]) ).

cnf(refute_0_974,plain,
    ( greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))) != greatest_lower_bound(identity,inverse(multiply(c,inverse(a))))
    | inverse(multiply(c,inverse(a))) != multiply(a,inverse(c))
    | greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))) = greatest_lower_bound(identity,multiply(a,inverse(c))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))),greatest_lower_bound(identity,inverse(multiply(c,inverse(a))))) ),[1,1],$fot(multiply(a,inverse(c)))]]) ).

cnf(refute_0_975,plain,
    ( inverse(multiply(c,inverse(a))) != multiply(a,inverse(c))
    | greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))) = greatest_lower_bound(identity,multiply(a,inverse(c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))),greatest_lower_bound(identity,inverse(multiply(c,inverse(a))))) )],[refute_0_973,refute_0_974]) ).

cnf(refute_0_976,plain,
    greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))) = greatest_lower_bound(identity,multiply(a,inverse(c))),
    inference(resolve,[$cnf( $equal(inverse(multiply(c,inverse(a))),multiply(a,inverse(c))) )],[refute_0_972,refute_0_975]) ).

cnf(refute_0_977,plain,
    ( greatest_lower_bound(identity,multiply(a,inverse(c))) != multiply(greatest_lower_bound(a,c),inverse(c))
    | greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))) != greatest_lower_bound(identity,multiply(a,inverse(c)))
    | greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))) = multiply(greatest_lower_bound(a,c),inverse(c)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(a,inverse(c))))),bind(Z0,$fot(multiply(greatest_lower_bound(a,c),inverse(c))))]]) ).

cnf(refute_0_978,plain,
    ( greatest_lower_bound(identity,multiply(a,inverse(c))) != multiply(greatest_lower_bound(a,c),inverse(c))
    | greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))) = multiply(greatest_lower_bound(a,c),inverse(c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))),greatest_lower_bound(identity,multiply(a,inverse(c)))) )],[refute_0_976,refute_0_977]) ).

cnf(refute_0_979,plain,
    greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))) = multiply(greatest_lower_bound(a,c),inverse(c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,inverse(c))),multiply(greatest_lower_bound(a,c),inverse(c))) )],[refute_0_971,refute_0_978]) ).

cnf(refute_0_980,plain,
    multiply(inverse(X_112),greatest_lower_bound(X_112,inverse(X))) = greatest_lower_bound(identity,multiply(inverse(X_112),inverse(X))),
    inference(subst,[],[refute_0_94:[bind(X_104,$fot(X_112)),bind(X_105,$fot(inverse(X)))]]) ).

cnf(refute_0_981,plain,
    inverse(multiply(X,X_112)) = multiply(inverse(X_112),inverse(X)),
    inference(subst,[],[p12_3:[bind(Y,$fot(X_112))]]) ).

cnf(refute_0_982,plain,
    ( inverse(multiply(X,X_112)) != multiply(inverse(X_112),inverse(X))
    | multiply(inverse(X_112),inverse(X)) = inverse(multiply(X,X_112)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(multiply(X,X_112)))),bind(Y0,$fot(multiply(inverse(X_112),inverse(X))))]]) ).

cnf(refute_0_983,plain,
    multiply(inverse(X_112),inverse(X)) = inverse(multiply(X,X_112)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,X_112)),multiply(inverse(X_112),inverse(X))) )],[refute_0_981,refute_0_982]) ).

cnf(refute_0_984,plain,
    ( multiply(inverse(X_112),greatest_lower_bound(X_112,inverse(X))) != greatest_lower_bound(identity,multiply(inverse(X_112),inverse(X)))
    | multiply(inverse(X_112),inverse(X)) != inverse(multiply(X,X_112))
    | multiply(inverse(X_112),greatest_lower_bound(X_112,inverse(X))) = greatest_lower_bound(identity,inverse(multiply(X,X_112))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_112),greatest_lower_bound(X_112,inverse(X))),greatest_lower_bound(identity,multiply(inverse(X_112),inverse(X)))) ),[1,1],$fot(inverse(multiply(X,X_112)))]]) ).

cnf(refute_0_985,plain,
    ( multiply(inverse(X_112),greatest_lower_bound(X_112,inverse(X))) != greatest_lower_bound(identity,multiply(inverse(X_112),inverse(X)))
    | multiply(inverse(X_112),greatest_lower_bound(X_112,inverse(X))) = greatest_lower_bound(identity,inverse(multiply(X,X_112))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_112),inverse(X)),inverse(multiply(X,X_112))) )],[refute_0_983,refute_0_984]) ).

cnf(refute_0_986,plain,
    multiply(inverse(X_112),greatest_lower_bound(X_112,inverse(X))) = greatest_lower_bound(identity,inverse(multiply(X,X_112))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_112),greatest_lower_bound(X_112,inverse(X))),greatest_lower_bound(identity,multiply(inverse(X_112),inverse(X)))) )],[refute_0_980,refute_0_985]) ).

cnf(refute_0_987,plain,
    multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))) = greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))),
    inference(subst,[],[refute_0_986:[bind(X,$fot(c)),bind(X_112,$fot(inverse(a)))]]) ).

cnf(refute_0_988,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))) != greatest_lower_bound(identity,inverse(multiply(c,inverse(a))))
    | greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))) != multiply(greatest_lower_bound(a,c),inverse(c))
    | multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))) = multiply(greatest_lower_bound(a,c),inverse(c)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))))),bind(Z0,$fot(multiply(greatest_lower_bound(a,c),inverse(c))))]]) ).

cnf(refute_0_989,plain,
    ( greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))) != multiply(greatest_lower_bound(a,c),inverse(c))
    | multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))) = multiply(greatest_lower_bound(a,c),inverse(c)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))),greatest_lower_bound(identity,inverse(multiply(c,inverse(a))))) )],[refute_0_987,refute_0_988]) ).

cnf(refute_0_990,plain,
    multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))) = multiply(greatest_lower_bound(a,c),inverse(c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(c,inverse(a)))),multiply(greatest_lower_bound(a,c),inverse(c))) )],[refute_0_979,refute_0_989]) ).

cnf(refute_0_991,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))) != multiply(greatest_lower_bound(a,c),inverse(c))
    | greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) != multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c)))
    | greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) = multiply(greatest_lower_bound(a,c),inverse(c)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))),multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c)))) ),[1],$fot(multiply(greatest_lower_bound(a,c),inverse(c)))]]) ).

cnf(refute_0_992,plain,
    ( greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) != multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c)))
    | greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) = multiply(greatest_lower_bound(a,c),inverse(c)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c))),multiply(greatest_lower_bound(a,c),inverse(c))) )],[refute_0_990,refute_0_991]) ).

cnf(refute_0_993,plain,
    ( multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))) != multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c)))
    | greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) = multiply(greatest_lower_bound(a,c),inverse(c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))),multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c)))) )],[refute_0_888,refute_0_992]) ).

cnf(refute_0_994,plain,
    greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) = multiply(greatest_lower_bound(a,c),inverse(c)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(a)),greatest_lower_bound(greatest_lower_bound(inverse(b),inverse(c)),inverse(a))),multiply(inverse(inverse(a)),greatest_lower_bound(inverse(a),inverse(c)))) )],[refute_0_836,refute_0_993]) ).

cnf(refute_0_995,plain,
    ( greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) != multiply(greatest_lower_bound(a,c),inverse(c))
    | identity != greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))))))
    | identity = greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))))))) ),[1,1,1,0],$fot(multiply(greatest_lower_bound(a,c),inverse(c)))]]) ).

cnf(refute_0_996,plain,
    ( identity != greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))))))
    | identity = greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))),multiply(greatest_lower_bound(a,c),inverse(c))) )],[refute_0_994,refute_0_995]) ).

cnf(refute_0_997,plain,
    identity = greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))),
    inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))))))) )],[refute_0_125,refute_0_996]) ).

cnf(refute_0_998,plain,
    multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) = greatest_lower_bound(multiply(Y,inverse(b)),multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(b))),bind(Z,$fot(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_999,plain,
    multiply(least_upper_bound(inverse(X_118),X_120),X_118) = least_upper_bound(multiply(inverse(X_118),X_118),multiply(X_120,X_118)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_118)),bind(Y,$fot(inverse(X_118))),bind(Z,$fot(X_120))]]) ).

cnf(refute_0_1000,plain,
    multiply(inverse(X_118),X_118) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_118))]]) ).

cnf(refute_0_1001,plain,
    ( multiply(inverse(X_118),X_118) != identity
    | multiply(least_upper_bound(inverse(X_118),X_120),X_118) != least_upper_bound(multiply(inverse(X_118),X_118),multiply(X_120,X_118))
    | multiply(least_upper_bound(inverse(X_118),X_120),X_118) = least_upper_bound(identity,multiply(X_120,X_118)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_118),X_120),X_118),least_upper_bound(multiply(inverse(X_118),X_118),multiply(X_120,X_118))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1002,plain,
    ( multiply(least_upper_bound(inverse(X_118),X_120),X_118) != least_upper_bound(multiply(inverse(X_118),X_118),multiply(X_120,X_118))
    | multiply(least_upper_bound(inverse(X_118),X_120),X_118) = least_upper_bound(identity,multiply(X_120,X_118)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_118),X_118),identity) )],[refute_0_1000,refute_0_1001]) ).

cnf(refute_0_1003,plain,
    multiply(least_upper_bound(inverse(X_118),X_120),X_118) = least_upper_bound(identity,multiply(X_120,X_118)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_118),X_120),X_118),least_upper_bound(multiply(inverse(X_118),X_118),multiply(X_120,X_118))) )],[refute_0_999,refute_0_1002]) ).

cnf(refute_0_1004,plain,
    multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) = least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))),
    inference(subst,[],[refute_0_1003:[bind(X_118,$fot(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))),bind(X_120,$fot(greatest_lower_bound(inverse(a),inverse(c))))]]) ).

cnf(refute_0_1005,plain,
    multiply(least_upper_bound(X_119,X_120),inverse(X_119)) = least_upper_bound(multiply(X_119,inverse(X_119)),multiply(X_120,inverse(X_119))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_119))),bind(Y,$fot(X_119)),bind(Z,$fot(X_120))]]) ).

cnf(refute_0_1006,plain,
    multiply(X_119,inverse(X_119)) = identity,
    inference(subst,[],[refute_0_40:[bind(X,$fot(X_119))]]) ).

cnf(refute_0_1007,plain,
    ( multiply(X_119,inverse(X_119)) != identity
    | multiply(least_upper_bound(X_119,X_120),inverse(X_119)) != least_upper_bound(multiply(X_119,inverse(X_119)),multiply(X_120,inverse(X_119)))
    | multiply(least_upper_bound(X_119,X_120),inverse(X_119)) = least_upper_bound(identity,multiply(X_120,inverse(X_119))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_119,X_120),inverse(X_119)),least_upper_bound(multiply(X_119,inverse(X_119)),multiply(X_120,inverse(X_119)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1008,plain,
    ( multiply(least_upper_bound(X_119,X_120),inverse(X_119)) != least_upper_bound(multiply(X_119,inverse(X_119)),multiply(X_120,inverse(X_119)))
    | multiply(least_upper_bound(X_119,X_120),inverse(X_119)) = least_upper_bound(identity,multiply(X_120,inverse(X_119))) ),
    inference(resolve,[$cnf( $equal(multiply(X_119,inverse(X_119)),identity) )],[refute_0_1006,refute_0_1007]) ).

cnf(refute_0_1009,plain,
    multiply(least_upper_bound(X_119,X_120),inverse(X_119)) = least_upper_bound(identity,multiply(X_120,inverse(X_119))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,X_120),inverse(X_119)),least_upper_bound(multiply(X_119,inverse(X_119)),multiply(X_120,inverse(X_119)))) )],[refute_0_1005,refute_0_1008]) ).

cnf(refute_0_1010,plain,
    multiply(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))),
    inference(subst,[],[refute_0_1009:[bind(X_119,$fot(multiply(b,inverse(greatest_lower_bound(a,c))))),bind(X_120,$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),b)))]]) ).

cnf(refute_0_1011,plain,
    least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(X_14,Y),X_16)) = least_upper_bound(least_upper_bound(X_14,greatest_lower_bound(X_14,Y)),X_16),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_14)),bind(Y,$fot(greatest_lower_bound(X_14,Y))),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_1012,plain,
    least_upper_bound(X_14,greatest_lower_bound(X_14,Y)) = X_14,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_14))]]) ).

cnf(refute_0_1013,plain,
    ( least_upper_bound(X_14,greatest_lower_bound(X_14,Y)) != X_14
    | least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(X_14,Y),X_16)) != least_upper_bound(least_upper_bound(X_14,greatest_lower_bound(X_14,Y)),X_16)
    | least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(X_14,Y),X_16)) = least_upper_bound(X_14,X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(X_14,Y),X_16)),least_upper_bound(least_upper_bound(X_14,greatest_lower_bound(X_14,Y)),X_16)) ),[1,0],$fot(X_14)]]) ).

cnf(refute_0_1014,plain,
    ( least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(X_14,Y),X_16)) != least_upper_bound(least_upper_bound(X_14,greatest_lower_bound(X_14,Y)),X_16)
    | least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(X_14,Y),X_16)) = least_upper_bound(X_14,X_16) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,greatest_lower_bound(X_14,Y)),X_14) )],[refute_0_1012,refute_0_1013]) ).

cnf(refute_0_1015,plain,
    least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(X_14,Y),X_16)) = least_upper_bound(X_14,X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(X_14,Y),X_16)),least_upper_bound(least_upper_bound(X_14,greatest_lower_bound(X_14,Y)),X_16)) )],[refute_0_1011,refute_0_1014]) ).

cnf(refute_0_1016,plain,
    least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))) = least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_1015:[bind(Y,$fot(X_332)),bind(X_14,$fot(identity)),bind(X_16,$fot(multiply(b,inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_1017,plain,
    multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_533:[bind(X_119,$fot(b)),bind(X_120,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_1018,plain,
    least_upper_bound(b,greatest_lower_bound(b,c)) = b,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).

cnf(refute_0_1019,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | least_upper_bound(b,greatest_lower_bound(b,c)) != b
    | least_upper_bound(b,greatest_lower_bound(a,c)) = b ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,c)),b) ),[0,1],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_1020,plain,
    ( least_upper_bound(b,greatest_lower_bound(b,c)) != b
    | least_upper_bound(b,greatest_lower_bound(a,c)) = b ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_294,refute_0_1019]) ).

cnf(refute_0_1021,plain,
    least_upper_bound(b,greatest_lower_bound(a,c)) = b,
    inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,c)),b) )],[refute_0_1018,refute_0_1020]) ).

cnf(refute_0_1022,plain,
    ( multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(b,greatest_lower_bound(a,c)) != b
    | multiply(b,inverse(greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))) ),[0,0],$fot(b)]]) ).

cnf(refute_0_1023,plain,
    ( multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))
    | multiply(b,inverse(greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,c)),b) )],[refute_0_1021,refute_0_1022]) ).

cnf(refute_0_1024,plain,
    multiply(b,inverse(greatest_lower_bound(a,c))) = least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1017,refute_0_1023]) ).

cnf(refute_0_1025,plain,
    ( multiply(b,inverse(greatest_lower_bound(a,c))) != least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(b,inverse(greatest_lower_bound(a,c))))),bind(Y0,$fot(least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1026,plain,
    least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1024,refute_0_1025]) ).

cnf(refute_0_1027,plain,
    ( least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) != multiply(b,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))) != least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))),least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))) ),[1],$fot(multiply(b,inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1028,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))) != least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),multiply(b,inverse(greatest_lower_bound(a,c)))) )],[refute_0_1026,refute_0_1027]) ).

cnf(refute_0_1029,plain,
    least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))) = multiply(b,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))),least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1016,refute_0_1028]) ).

cnf(refute_0_1030,plain,
    least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)) = least_upper_bound(X_14,least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_588:[bind(X,$fot(multiply(b,inverse(greatest_lower_bound(a,c))))),bind(X_15,$fot(identity))]]) ).

cnf(refute_0_1031,plain,
    ( least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)) != least_upper_bound(X_14,least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))))
    | least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))) != multiply(b,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)) = least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)),least_upper_bound(X_14,least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))))) ),[1,1],$fot(multiply(b,inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1032,plain,
    ( least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)) != least_upper_bound(X_14,least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))))
    | least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)) = least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))),multiply(b,inverse(greatest_lower_bound(a,c)))) )],[refute_0_1026,refute_0_1031]) ).

cnf(refute_0_1033,plain,
    least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)) = least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)),least_upper_bound(X_14,least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_1030,refute_0_1032]) ).

cnf(refute_0_1034,plain,
    least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_92,Y))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)),
    inference(subst,[],[associativity_of_lub:[bind(Z,$fot(least_upper_bound(X_92,Y)))]]) ).

cnf(refute_0_1035,plain,
    least_upper_bound(X_92,Y) = least_upper_bound(Y,least_upper_bound(X_92,Y)),
    inference(subst,[],[refute_0_613:[bind(X_15,$fot(X_92)),bind(X_16,$fot(Y))]]) ).

cnf(refute_0_1036,plain,
    ( least_upper_bound(X_92,Y) != least_upper_bound(Y,least_upper_bound(X_92,Y))
    | least_upper_bound(Y,least_upper_bound(X_92,Y)) = least_upper_bound(X_92,Y) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_92,Y))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_92,Y))))]]) ).

cnf(refute_0_1037,plain,
    least_upper_bound(Y,least_upper_bound(X_92,Y)) = least_upper_bound(X_92,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_92,Y),least_upper_bound(Y,least_upper_bound(X_92,Y))) )],[refute_0_1035,refute_0_1036]) ).

cnf(refute_0_1038,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_92,Y))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y))
    | least_upper_bound(Y,least_upper_bound(X_92,Y)) != least_upper_bound(X_92,Y)
    | least_upper_bound(X,least_upper_bound(X_92,Y)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_92,Y))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y))) ),[0,1],$fot(least_upper_bound(X_92,Y))]]) ).

cnf(refute_0_1039,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_92,Y))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y))
    | least_upper_bound(X,least_upper_bound(X_92,Y)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_92,Y)),least_upper_bound(X_92,Y)) )],[refute_0_1037,refute_0_1038]) ).

cnf(refute_0_1040,plain,
    least_upper_bound(X,least_upper_bound(X_92,Y)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_92,Y))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y))) )],[refute_0_1034,refute_0_1039]) ).

cnf(refute_0_1041,plain,
    least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_55,X_56))) = least_upper_bound(X_15,least_upper_bound(X_55,X_56)),
    inference(subst,[],[refute_0_606:[bind(X_16,$fot(least_upper_bound(X_55,X_56)))]]) ).

cnf(refute_0_1042,plain,
    least_upper_bound(X_15,least_upper_bound(X_55,X_56)) = least_upper_bound(X_55,least_upper_bound(X_56,X_15)),
    inference(subst,[],[refute_0_588:[bind(X,$fot(X_15)),bind(X_14,$fot(X_55)),bind(X_15,$fot(X_56))]]) ).

cnf(refute_0_1043,plain,
    ( least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_55,X_56))) != least_upper_bound(X_15,least_upper_bound(X_55,X_56))
    | least_upper_bound(X_15,least_upper_bound(X_55,X_56)) != least_upper_bound(X_55,least_upper_bound(X_56,X_15))
    | least_upper_bound(X_15,least_upper_bound(X_55,least_upper_bound(X_56,X_15))) = least_upper_bound(X_15,least_upper_bound(X_55,X_56)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_55,X_56))),least_upper_bound(X_15,least_upper_bound(X_55,X_56))) ),[0,1],$fot(least_upper_bound(X_55,least_upper_bound(X_56,X_15)))]]) ).

cnf(refute_0_1044,plain,
    ( least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_55,X_56))) != least_upper_bound(X_15,least_upper_bound(X_55,X_56))
    | least_upper_bound(X_15,least_upper_bound(X_55,least_upper_bound(X_56,X_15))) = least_upper_bound(X_15,least_upper_bound(X_55,X_56)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_55,X_56)),least_upper_bound(X_55,least_upper_bound(X_56,X_15))) )],[refute_0_1042,refute_0_1043]) ).

cnf(refute_0_1045,plain,
    least_upper_bound(X_15,least_upper_bound(X_55,least_upper_bound(X_56,X_15))) = least_upper_bound(X_15,least_upper_bound(X_55,X_56)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,least_upper_bound(X_55,X_56))),least_upper_bound(X_15,least_upper_bound(X_55,X_56))) )],[refute_0_1041,refute_0_1044]) ).

cnf(refute_0_1046,plain,
    least_upper_bound(Y,least_upper_bound(X_92,least_upper_bound(X,Y))) = least_upper_bound(Y,least_upper_bound(X_92,X)),
    inference(subst,[],[refute_0_1045:[bind(X_15,$fot(Y)),bind(X_55,$fot(X_92)),bind(X_56,$fot(X))]]) ).

cnf(refute_0_1047,plain,
    least_upper_bound(X_54,least_upper_bound(X_55,X_56)) = least_upper_bound(X_55,least_upper_bound(X_56,X_54)),
    inference(subst,[],[refute_0_588:[bind(X,$fot(X_54)),bind(X_14,$fot(X_55)),bind(X_15,$fot(X_56))]]) ).

cnf(refute_0_1048,plain,
    least_upper_bound(X_56,X_55) = least_upper_bound(X_55,X_56),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_56)),bind(Y,$fot(X_55))]]) ).

cnf(refute_0_1049,plain,
    ( least_upper_bound(X_56,X_55) != least_upper_bound(X_55,X_56)
    | least_upper_bound(X_55,X_56) = least_upper_bound(X_56,X_55) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_56,X_55))),bind(Y0,$fot(least_upper_bound(X_55,X_56)))]]) ).

cnf(refute_0_1050,plain,
    least_upper_bound(X_55,X_56) = least_upper_bound(X_56,X_55),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_56,X_55),least_upper_bound(X_55,X_56)) )],[refute_0_1048,refute_0_1049]) ).

cnf(refute_0_1051,plain,
    ( least_upper_bound(X_54,least_upper_bound(X_55,X_56)) != least_upper_bound(X_55,least_upper_bound(X_56,X_54))
    | least_upper_bound(X_55,X_56) != least_upper_bound(X_56,X_55)
    | least_upper_bound(X_54,least_upper_bound(X_56,X_55)) = least_upper_bound(X_55,least_upper_bound(X_56,X_54)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_54,least_upper_bound(X_55,X_56)),least_upper_bound(X_55,least_upper_bound(X_56,X_54))) ),[0,1],$fot(least_upper_bound(X_56,X_55))]]) ).

cnf(refute_0_1052,plain,
    ( least_upper_bound(X_54,least_upper_bound(X_55,X_56)) != least_upper_bound(X_55,least_upper_bound(X_56,X_54))
    | least_upper_bound(X_54,least_upper_bound(X_56,X_55)) = least_upper_bound(X_55,least_upper_bound(X_56,X_54)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_55,X_56),least_upper_bound(X_56,X_55)) )],[refute_0_1050,refute_0_1051]) ).

cnf(refute_0_1053,plain,
    least_upper_bound(X_54,least_upper_bound(X_56,X_55)) = least_upper_bound(X_55,least_upper_bound(X_56,X_54)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_54,least_upper_bound(X_55,X_56)),least_upper_bound(X_55,least_upper_bound(X_56,X_54))) )],[refute_0_1047,refute_0_1052]) ).

cnf(refute_0_1054,plain,
    ( least_upper_bound(X_54,least_upper_bound(X_56,X_55)) != least_upper_bound(X_55,least_upper_bound(X_56,X_54))
    | least_upper_bound(X_55,least_upper_bound(X_56,X_54)) = least_upper_bound(X_54,least_upper_bound(X_56,X_55)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_54,least_upper_bound(X_56,X_55)))),bind(Y0,$fot(least_upper_bound(X_55,least_upper_bound(X_56,X_54))))]]) ).

cnf(refute_0_1055,plain,
    least_upper_bound(X_55,least_upper_bound(X_56,X_54)) = least_upper_bound(X_54,least_upper_bound(X_56,X_55)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_54,least_upper_bound(X_56,X_55)),least_upper_bound(X_55,least_upper_bound(X_56,X_54))) )],[refute_0_1053,refute_0_1054]) ).

cnf(refute_0_1056,plain,
    least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)) = least_upper_bound(Y,least_upper_bound(X_92,least_upper_bound(X,Y))),
    inference(subst,[],[refute_0_1055:[bind(X_54,$fot(Y)),bind(X_55,$fot(least_upper_bound(X,Y))),bind(X_56,$fot(X_92))]]) ).

cnf(refute_0_1057,plain,
    ( least_upper_bound(Y,least_upper_bound(X_92,least_upper_bound(X,Y))) != least_upper_bound(Y,least_upper_bound(X_92,X))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)) != least_upper_bound(Y,least_upper_bound(X_92,least_upper_bound(X,Y)))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)) = least_upper_bound(Y,least_upper_bound(X_92,X)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_92,least_upper_bound(X,Y))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_92,X))))]]) ).

cnf(refute_0_1058,plain,
    ( least_upper_bound(Y,least_upper_bound(X_92,least_upper_bound(X,Y))) != least_upper_bound(Y,least_upper_bound(X_92,X))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)) = least_upper_bound(Y,least_upper_bound(X_92,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)),least_upper_bound(Y,least_upper_bound(X_92,least_upper_bound(X,Y)))) )],[refute_0_1056,refute_0_1057]) ).

cnf(refute_0_1059,plain,
    least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)) = least_upper_bound(Y,least_upper_bound(X_92,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_92,least_upper_bound(X,Y))),least_upper_bound(Y,least_upper_bound(X_92,X))) )],[refute_0_1046,refute_0_1058]) ).

cnf(refute_0_1060,plain,
    ( least_upper_bound(X,least_upper_bound(X_92,Y)) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)) != least_upper_bound(Y,least_upper_bound(X_92,X))
    | least_upper_bound(X,least_upper_bound(X_92,Y)) = least_upper_bound(Y,least_upper_bound(X_92,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_92,Y)),least_upper_bound(Y,least_upper_bound(X_92,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)))]]) ).

cnf(refute_0_1061,plain,
    ( least_upper_bound(X,least_upper_bound(X_92,Y)) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y))
    | least_upper_bound(X,least_upper_bound(X_92,Y)) = least_upper_bound(Y,least_upper_bound(X_92,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y)),least_upper_bound(Y,least_upper_bound(X_92,X))) )],[refute_0_1059,refute_0_1060]) ).

cnf(refute_0_1062,plain,
    least_upper_bound(X,least_upper_bound(X_92,Y)) = least_upper_bound(Y,least_upper_bound(X_92,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_92,Y)),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_92,Y))) )],[refute_0_1040,refute_0_1061]) ).

cnf(refute_0_1063,plain,
    ( least_upper_bound(X,least_upper_bound(X_92,Y)) != least_upper_bound(Y,least_upper_bound(X_92,X))
    | least_upper_bound(Y,least_upper_bound(X_92,X)) = least_upper_bound(X,least_upper_bound(X_92,Y)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_92,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_92,X))))]]) ).

cnf(refute_0_1064,plain,
    least_upper_bound(Y,least_upper_bound(X_92,X)) = least_upper_bound(X,least_upper_bound(X_92,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_92,Y)),least_upper_bound(Y,least_upper_bound(X_92,X))) )],[refute_0_1062,refute_0_1063]) ).

cnf(refute_0_1065,plain,
    least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)) = least_upper_bound(identity,least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_1064:[bind(X,$fot(identity)),bind(Y,$fot(multiply(b,inverse(greatest_lower_bound(a,c))))),bind(X_92,$fot(X_14))]]) ).

cnf(refute_0_1066,plain,
    ( least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)) != least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)) != least_upper_bound(identity,least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c)))))
    | least_upper_bound(identity,least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c))))) = least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)),least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c))))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1067,plain,
    ( least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)) != least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(identity,least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c))))) = least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)),least_upper_bound(identity,least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_1065,refute_0_1066]) ).

cnf(refute_0_1068,plain,
    least_upper_bound(identity,least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c))))) = least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),least_upper_bound(X_14,identity)),least_upper_bound(X_14,multiply(b,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1033,refute_0_1067]) ).

cnf(refute_0_1069,plain,
    least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))) = least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_1068:[bind(X_14,$fot(greatest_lower_bound(identity,X_332)))]]) ).

cnf(refute_0_1070,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))) != multiply(b,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))) != least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))),multiply(b,inverse(greatest_lower_bound(a,c)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_1071,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))) != multiply(b,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))),least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1069,refute_0_1070]) ).

cnf(refute_0_1072,plain,
    least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X_332),multiply(b,inverse(greatest_lower_bound(a,c))))),multiply(b,inverse(greatest_lower_bound(a,c)))) )],[refute_0_1029,refute_0_1071]) ).

cnf(refute_0_1073,plain,
    least_upper_bound(greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_1072:[bind(X_332,$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),b)))]]) ).

cnf(refute_0_1074,plain,
    multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c))))) = greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)),
    inference(subst,[],[refute_0_134:[bind(X_104,$fot(b)),bind(X_105,$fot(inverse(greatest_lower_bound(inverse(a),inverse(c)))))]]) ).

cnf(refute_0_1075,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c))))) != greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))
    | greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))) != b
    | multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) = greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c))))),greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))) ),[0,1],$fot(b)]]) ).

cnf(refute_0_1076,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c))))) != greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))
    | multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) = greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) )],[refute_0_739,refute_0_1075]) ).

cnf(refute_0_1077,plain,
    multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) = greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),greatest_lower_bound(b,inverse(greatest_lower_bound(inverse(a),inverse(c))))),greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))) )],[refute_0_1074,refute_0_1076]) ).

cnf(refute_0_1078,plain,
    multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) = multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b),
    introduced(tautology,[refl,[$fot(multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))]]) ).

cnf(refute_0_1079,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) != multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)
    | inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))) != greatest_lower_bound(inverse(a),inverse(c))
    | multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) = multiply(greatest_lower_bound(inverse(a),inverse(c)),b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b),multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) ),[1,0],$fot(greatest_lower_bound(inverse(a),inverse(c)))]]) ).

cnf(refute_0_1080,plain,
    ( inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))) != greatest_lower_bound(inverse(a),inverse(c))
    | multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) = multiply(greatest_lower_bound(inverse(a),inverse(c)),b) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b),multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) )],[refute_0_1078,refute_0_1079]) ).

cnf(refute_0_1081,plain,
    multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) = multiply(greatest_lower_bound(inverse(a),inverse(c)),b),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),greatest_lower_bound(inverse(a),inverse(c))) )],[refute_0_785,refute_0_1080]) ).

cnf(refute_0_1082,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) != multiply(greatest_lower_bound(inverse(a),inverse(c)),b)
    | multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) != greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))
    | multiply(greatest_lower_bound(inverse(a),inverse(c)),b) = greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b),greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))) ),[0],$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),b))]]) ).

cnf(refute_0_1083,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) != greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))
    | multiply(greatest_lower_bound(inverse(a),inverse(c)),b) = greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) )],[refute_0_1081,refute_0_1082]) ).

cnf(refute_0_1084,plain,
    greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) = greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))]]) ).

cnf(refute_0_1085,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) != multiply(greatest_lower_bound(inverse(a),inverse(c)),b)
    | greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) != greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))
    | greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)),greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))) ),[1,1],$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),b))]]) ).

cnf(refute_0_1086,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) != multiply(greatest_lower_bound(inverse(a),inverse(c)),b)
    | greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)),greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))) )],[refute_0_1084,refute_0_1085]) ).

cnf(refute_0_1087,plain,
    greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) )],[refute_0_1081,refute_0_1086]) ).

cnf(refute_0_1088,plain,
    ( multiply(greatest_lower_bound(inverse(a),inverse(c)),b) != greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))
    | greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b))
    | multiply(greatest_lower_bound(inverse(a),inverse(c)),b) = greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)))]]) ).

cnf(refute_0_1089,plain,
    ( multiply(greatest_lower_bound(inverse(a),inverse(c)),b) != greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))
    | multiply(greatest_lower_bound(inverse(a),inverse(c)),b) = greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b)),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b))) )],[refute_0_1087,refute_0_1088]) ).

cnf(refute_0_1090,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b) != greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))
    | multiply(greatest_lower_bound(inverse(a),inverse(c)),b) = greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))) )],[refute_0_1083,refute_0_1089]) ).

cnf(refute_0_1091,plain,
    multiply(greatest_lower_bound(inverse(a),inverse(c)),b) = greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b),greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(inverse(a),inverse(c)))),b))) )],[refute_0_1077,refute_0_1090]) ).

cnf(refute_0_1092,plain,
    ( multiply(greatest_lower_bound(inverse(a),inverse(c)),b) != greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b))
    | greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) = multiply(greatest_lower_bound(inverse(a),inverse(c)),b) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),b))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b))))]]) ).

cnf(refute_0_1093,plain,
    greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) = multiply(greatest_lower_bound(inverse(a),inverse(c)),b),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b))) )],[refute_0_1091,refute_0_1092]) ).

cnf(refute_0_1094,plain,
    ( greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) != multiply(greatest_lower_bound(inverse(a),inverse(c)),b)
    | least_upper_bound(greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(b,inverse(greatest_lower_bound(a,c)))) != multiply(b,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(b,inverse(greatest_lower_bound(a,c)))),multiply(b,inverse(greatest_lower_bound(a,c)))) ),[0,0],$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),b))]]) ).

cnf(refute_0_1095,plain,
    ( least_upper_bound(greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(b,inverse(greatest_lower_bound(a,c)))) != multiply(b,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) )],[refute_0_1093,refute_0_1094]) ).

cnf(refute_0_1096,plain,
    least_upper_bound(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(b,inverse(greatest_lower_bound(a,c)))),multiply(b,inverse(greatest_lower_bound(a,c)))) )],[refute_0_1073,refute_0_1095]) ).

cnf(refute_0_1097,plain,
    least_upper_bound(X,least_upper_bound(X_14,greatest_lower_bound(a,greatest_lower_bound(X_14,c)))) = least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X)),
    inference(subst,[],[refute_0_588:[bind(X_15,$fot(greatest_lower_bound(a,greatest_lower_bound(X_14,c))))]]) ).

cnf(refute_0_1098,plain,
    least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(a,c))) = X,
    inference(subst,[],[lub_absorbtion:[bind(Y,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_1099,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_65)) != greatest_lower_bound(a,greatest_lower_bound(c,X_65))
    | greatest_lower_bound(c,X_65) != greatest_lower_bound(X_65,c)
    | greatest_lower_bound(b,greatest_lower_bound(c,X_65)) = greatest_lower_bound(a,greatest_lower_bound(X_65,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_65)),greatest_lower_bound(a,greatest_lower_bound(c,X_65))) ),[1,1],$fot(greatest_lower_bound(X_65,c))]]) ).

cnf(refute_0_1100,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_65)) != greatest_lower_bound(a,greatest_lower_bound(c,X_65))
    | greatest_lower_bound(b,greatest_lower_bound(c,X_65)) = greatest_lower_bound(a,greatest_lower_bound(X_65,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,X_65),greatest_lower_bound(X_65,c)) )],[refute_0_305,refute_0_1099]) ).

cnf(refute_0_1101,plain,
    greatest_lower_bound(b,greatest_lower_bound(c,X_65)) = greatest_lower_bound(a,greatest_lower_bound(X_65,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_65)),greatest_lower_bound(a,greatest_lower_bound(c,X_65))) )],[refute_0_302,refute_0_1100]) ).

cnf(refute_0_1102,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_65)) != greatest_lower_bound(a,greatest_lower_bound(X_65,c))
    | greatest_lower_bound(b,greatest_lower_bound(c,X_65)) != greatest_lower_bound(a,greatest_lower_bound(c,X_65))
    | greatest_lower_bound(a,greatest_lower_bound(c,X_65)) = greatest_lower_bound(a,greatest_lower_bound(X_65,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_65)),greatest_lower_bound(a,greatest_lower_bound(X_65,c))) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_65)))]]) ).

cnf(refute_0_1103,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_65)) != greatest_lower_bound(a,greatest_lower_bound(X_65,c))
    | greatest_lower_bound(a,greatest_lower_bound(c,X_65)) = greatest_lower_bound(a,greatest_lower_bound(X_65,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_65)),greatest_lower_bound(a,greatest_lower_bound(c,X_65))) )],[refute_0_302,refute_0_1102]) ).

cnf(refute_0_1104,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,X_65)) = greatest_lower_bound(a,greatest_lower_bound(X_65,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_65)),greatest_lower_bound(a,greatest_lower_bound(X_65,c))) )],[refute_0_1101,refute_0_1103]) ).

cnf(refute_0_1105,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,X_66)) = greatest_lower_bound(a,greatest_lower_bound(X_66,c)),
    inference(subst,[],[refute_0_1104:[bind(X_65,$fot(X_66))]]) ).

cnf(refute_0_1106,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,X_66)) != greatest_lower_bound(X_66,greatest_lower_bound(a,c))
    | greatest_lower_bound(a,greatest_lower_bound(c,X_66)) != greatest_lower_bound(a,greatest_lower_bound(X_66,c))
    | greatest_lower_bound(a,greatest_lower_bound(X_66,c)) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_66)),greatest_lower_bound(X_66,greatest_lower_bound(a,c))) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(X_66,c)))]]) ).

cnf(refute_0_1107,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,X_66)) != greatest_lower_bound(X_66,greatest_lower_bound(a,c))
    | greatest_lower_bound(a,greatest_lower_bound(X_66,c)) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_66)),greatest_lower_bound(a,greatest_lower_bound(X_66,c))) )],[refute_0_1105,refute_0_1106]) ).

cnf(refute_0_1108,plain,
    greatest_lower_bound(a,greatest_lower_bound(X_66,c)) = greatest_lower_bound(X_66,greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,X_66)),greatest_lower_bound(X_66,greatest_lower_bound(a,c))) )],[refute_0_453,refute_0_1107]) ).

cnf(refute_0_1109,plain,
    greatest_lower_bound(a,greatest_lower_bound(X,c)) = greatest_lower_bound(X,greatest_lower_bound(a,c)),
    inference(subst,[],[refute_0_1108:[bind(X_66,$fot(X))]]) ).

cnf(refute_0_1110,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(X,c)) != greatest_lower_bound(X,greatest_lower_bound(a,c))
    | greatest_lower_bound(X,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(X,c)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(X,c)))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1111,plain,
    greatest_lower_bound(X,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(X,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(X,c)),greatest_lower_bound(X,greatest_lower_bound(a,c))) )],[refute_0_1109,refute_0_1110]) ).

cnf(refute_0_1112,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(X,c))
    | least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(a,c))) != X
    | least_upper_bound(X,greatest_lower_bound(a,greatest_lower_bound(X,c))) = X ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(a,c))),X) ),[0,1],$fot(greatest_lower_bound(a,greatest_lower_bound(X,c)))]]) ).

cnf(refute_0_1113,plain,
    ( least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(a,c))) != X
    | least_upper_bound(X,greatest_lower_bound(a,greatest_lower_bound(X,c))) = X ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(X,c))) )],[refute_0_1111,refute_0_1112]) ).

cnf(refute_0_1114,plain,
    least_upper_bound(X,greatest_lower_bound(a,greatest_lower_bound(X,c))) = X,
    inference(resolve,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,greatest_lower_bound(a,c))),X) )],[refute_0_1098,refute_0_1113]) ).

cnf(refute_0_1115,plain,
    least_upper_bound(X_14,greatest_lower_bound(a,greatest_lower_bound(X_14,c))) = X_14,
    inference(subst,[],[refute_0_1114:[bind(X,$fot(X_14))]]) ).

cnf(refute_0_1116,plain,
    ( least_upper_bound(X,least_upper_bound(X_14,greatest_lower_bound(a,greatest_lower_bound(X_14,c)))) != least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X))
    | least_upper_bound(X_14,greatest_lower_bound(a,greatest_lower_bound(X_14,c))) != X_14
    | least_upper_bound(X,X_14) = least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_14,greatest_lower_bound(a,greatest_lower_bound(X_14,c)))),least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X))) ),[0,1],$fot(X_14)]]) ).

cnf(refute_0_1117,plain,
    ( least_upper_bound(X,least_upper_bound(X_14,greatest_lower_bound(a,greatest_lower_bound(X_14,c)))) != least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X))
    | least_upper_bound(X,X_14) = least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,greatest_lower_bound(a,greatest_lower_bound(X_14,c))),X_14) )],[refute_0_1115,refute_0_1116]) ).

cnf(refute_0_1118,plain,
    least_upper_bound(X,X_14) = least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_14,greatest_lower_bound(a,greatest_lower_bound(X_14,c)))),least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X))) )],[refute_0_1097,refute_0_1117]) ).

cnf(refute_0_1119,plain,
    least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),Z)) = least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_27,X)),Z),
    inference(subst,[],[associativity_of_lub:[bind(Y,$fot(greatest_lower_bound(X_27,X)))]]) ).

cnf(refute_0_1120,plain,
    least_upper_bound(X,greatest_lower_bound(X_27,X)) = X,
    inference(subst,[],[refute_0_281:[bind(X_8,$fot(X)),bind(X_9,$fot(X_27))]]) ).

cnf(refute_0_1121,plain,
    ( least_upper_bound(X,greatest_lower_bound(X_27,X)) != X
    | least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),Z)) != least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_27,X)),Z)
    | least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),Z)) = least_upper_bound(X,Z) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),Z)),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_27,X)),Z)) ),[1,0],$fot(X)]]) ).

cnf(refute_0_1122,plain,
    ( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),Z)) != least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_27,X)),Z)
    | least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),Z)) = least_upper_bound(X,Z) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X_27,X)),X) )],[refute_0_1120,refute_0_1121]) ).

cnf(refute_0_1123,plain,
    least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),Z)) = least_upper_bound(X,Z),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),Z)),least_upper_bound(least_upper_bound(X,greatest_lower_bound(X_27,X)),Z)) )],[refute_0_1119,refute_0_1122]) ).

cnf(refute_0_1124,plain,
    least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)),
    inference(subst,[],[refute_0_1123:[bind(Z,$fot(least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)))]]) ).

cnf(refute_0_1125,plain,
    least_upper_bound(greatest_lower_bound(X_27,X),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) = least_upper_bound(greatest_lower_bound(X_27,X),X_334),
    inference(subst,[],[refute_0_1015:[bind(Y,$fot(X_332)),bind(X_14,$fot(greatest_lower_bound(X_27,X))),bind(X_16,$fot(X_334))]]) ).

cnf(refute_0_1126,plain,
    ( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))
    | least_upper_bound(greatest_lower_bound(X_27,X),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) != least_upper_bound(greatest_lower_bound(X_27,X),X_334)
    | least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),X_334)) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))),least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))) ),[0,1],$fot(least_upper_bound(greatest_lower_bound(X_27,X),X_334))]]) ).

cnf(refute_0_1127,plain,
    ( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))
    | least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),X_334)) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_27,X),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)),least_upper_bound(greatest_lower_bound(X_27,X),X_334)) )],[refute_0_1125,refute_0_1126]) ).

cnf(refute_0_1128,plain,
    least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),X_334)) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))),least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))) )],[refute_0_1124,refute_0_1127]) ).

cnf(refute_0_1129,plain,
    least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),X_334)) = least_upper_bound(X,X_334),
    inference(subst,[],[refute_0_1123:[bind(Z,$fot(X_334))]]) ).

cnf(refute_0_1130,plain,
    ( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),X_334)) != least_upper_bound(X,X_334)
    | least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),X_334)) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))
    | least_upper_bound(X,X_334) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),X_334)),least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))) ),[0],$fot(least_upper_bound(X,X_334))]]) ).

cnf(refute_0_1131,plain,
    ( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),X_334)) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))
    | least_upper_bound(X,X_334) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),X_334)),least_upper_bound(X,X_334)) )],[refute_0_1129,refute_0_1130]) ).

cnf(refute_0_1132,plain,
    greatest_lower_bound(greatest_lower_bound(X_27,X),X_332) = greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_27)),bind(Y,$fot(X)),bind(Z,$fot(X_332))]]) ).

cnf(refute_0_1133,plain,
    least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334),
    introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))]]) ).

cnf(refute_0_1134,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_27,X),X_332) != greatest_lower_bound(X_27,greatest_lower_bound(X,X_332))
    | least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334) != least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)
    | least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334) = least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) ),[1,0],$fot(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)))]]) ).

cnf(refute_0_1135,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_27,X),X_332) != greatest_lower_bound(X_27,greatest_lower_bound(X,X_332))
    | least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334) = least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334),least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) )],[refute_0_1133,refute_0_1134]) ).

cnf(refute_0_1136,plain,
    least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334) = least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),greatest_lower_bound(X_27,greatest_lower_bound(X,X_332))) )],[refute_0_1132,refute_0_1135]) ).

cnf(refute_0_1137,plain,
    least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)))]]) ).

cnf(refute_0_1138,plain,
    ( least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))
    | least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334) != least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)
    | least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)),least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))) ),[1,1],$fot(least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334))]]) ).

cnf(refute_0_1139,plain,
    ( least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334) != least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)
    | least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)),least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))) )],[refute_0_1137,refute_0_1138]) ).

cnf(refute_0_1140,plain,
    least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334),least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)) )],[refute_0_1136,refute_0_1139]) ).

cnf(refute_0_1141,plain,
    ( least_upper_bound(X,X_334) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))
    | least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334))
    | least_upper_bound(X,X_334) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,X_334),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334))) ),[0],$fot(least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)))]]) ).

cnf(refute_0_1142,plain,
    ( least_upper_bound(X,X_334) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))
    | least_upper_bound(X,X_334) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334)),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334))) )],[refute_0_1140,refute_0_1141]) ).

cnf(refute_0_1143,plain,
    ( least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),X_334)) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))
    | least_upper_bound(X,X_334) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,X_334),least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))) )],[refute_0_1131,refute_0_1142]) ).

cnf(refute_0_1144,plain,
    least_upper_bound(X,X_334) = least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,X),X_334)),least_upper_bound(X,least_upper_bound(greatest_lower_bound(greatest_lower_bound(X_27,X),X_332),X_334))) )],[refute_0_1128,refute_0_1143]) ).

cnf(refute_0_1145,plain,
    ( least_upper_bound(X,X_334) != least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334))
    | least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)) = least_upper_bound(X,X_334) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X,X_334))),bind(Y0,$fot(least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334))))]]) ).

cnf(refute_0_1146,plain,
    least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334)) = least_upper_bound(X,X_334),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,X_334),least_upper_bound(X,least_upper_bound(greatest_lower_bound(X_27,greatest_lower_bound(X,X_332)),X_334))) )],[refute_0_1144,refute_0_1145]) ).

cnf(refute_0_1147,plain,
    least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X)) = least_upper_bound(X_14,X),
    inference(subst,[],[refute_0_1146:[bind(X,$fot(X_14)),bind(X_27,$fot(a)),bind(X_332,$fot(c)),bind(X_334,$fot(X))]]) ).

cnf(refute_0_1148,plain,
    ( least_upper_bound(X,X_14) != least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X))
    | least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X)) != least_upper_bound(X_14,X)
    | least_upper_bound(X,X_14) = least_upper_bound(X_14,X) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,X_14),least_upper_bound(X_14,X)) ),[0],$fot(least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X)))]]) ).

cnf(refute_0_1149,plain,
    ( least_upper_bound(X,X_14) != least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X))
    | least_upper_bound(X,X_14) = least_upper_bound(X_14,X) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X)),least_upper_bound(X_14,X)) )],[refute_0_1147,refute_0_1148]) ).

cnf(refute_0_1150,plain,
    least_upper_bound(X,X_14) = least_upper_bound(X_14,X),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,X_14),least_upper_bound(X_14,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(X_14,c)),X))) )],[refute_0_1118,refute_0_1149]) ).

cnf(refute_0_1151,plain,
    ( least_upper_bound(X,X_14) != least_upper_bound(X_14,X)
    | least_upper_bound(X_14,X) = least_upper_bound(X,X_14) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X,X_14))),bind(Y0,$fot(least_upper_bound(X_14,X)))]]) ).

cnf(refute_0_1152,plain,
    least_upper_bound(X_14,X) = least_upper_bound(X,X_14),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,X_14),least_upper_bound(X_14,X)) )],[refute_0_1150,refute_0_1151]) ).

cnf(refute_0_1153,plain,
    least_upper_bound(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),multiply(b,inverse(greatest_lower_bound(a,c)))) = least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),
    inference(subst,[],[refute_0_1152:[bind(X,$fot(multiply(b,inverse(greatest_lower_bound(a,c))))),bind(X_14,$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),b)))]]) ).

cnf(refute_0_1154,plain,
    ( least_upper_bound(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),multiply(b,inverse(greatest_lower_bound(a,c)))) != multiply(b,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),multiply(b,inverse(greatest_lower_bound(a,c)))) != least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b))
    | least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),multiply(b,inverse(greatest_lower_bound(a,c)))),multiply(b,inverse(greatest_lower_bound(a,c)))) ),[0],$fot(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)))]]) ).

cnf(refute_0_1155,plain,
    ( least_upper_bound(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),multiply(b,inverse(greatest_lower_bound(a,c)))) != multiply(b,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) = multiply(b,inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),multiply(b,inverse(greatest_lower_bound(a,c)))),least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b))) )],[refute_0_1153,refute_0_1154]) ).

cnf(refute_0_1156,plain,
    least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) = multiply(b,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),multiply(b,inverse(greatest_lower_bound(a,c)))),multiply(b,inverse(greatest_lower_bound(a,c)))) )],[refute_0_1096,refute_0_1155]) ).

cnf(refute_0_1157,plain,
    ( multiply(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))
    | least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)) != multiply(b,inverse(greatest_lower_bound(a,c)))
    | multiply(multiply(b,inverse(greatest_lower_bound(a,c))),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))) ),[0,0],$fot(multiply(b,inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1158,plain,
    ( multiply(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))
    | multiply(multiply(b,inverse(greatest_lower_bound(a,c))),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(b,inverse(greatest_lower_bound(a,c)))) )],[refute_0_1156,refute_0_1157]) ).

cnf(refute_0_1159,plain,
    multiply(multiply(b,inverse(greatest_lower_bound(a,c))),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(multiply(b,inverse(greatest_lower_bound(a,c))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))) )],[refute_0_1010,refute_0_1158]) ).

cnf(refute_0_1160,plain,
    multiply(multiply(b,inverse(greatest_lower_bound(a,c))),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = identity,
    inference(subst,[],[refute_0_40:[bind(X,$fot(multiply(b,inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_1161,plain,
    ( multiply(multiply(b,inverse(greatest_lower_bound(a,c))),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != identity
    | multiply(multiply(b,inverse(greatest_lower_bound(a,c))),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))
    | identity = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(b,inverse(greatest_lower_bound(a,c))),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))) ),[0],$fot(identity)]]) ).

cnf(refute_0_1162,plain,
    ( multiply(multiply(b,inverse(greatest_lower_bound(a,c))),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))
    | identity = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,inverse(greatest_lower_bound(a,c))),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),identity) )],[refute_0_1160,refute_0_1161]) ).

cnf(refute_0_1163,plain,
    inverse(multiply(b,inverse(greatest_lower_bound(a,c)))) = multiply(greatest_lower_bound(a,c),inverse(b)),
    inference(subst,[],[refute_0_146:[bind(X,$fot(greatest_lower_bound(a,c))),bind(X_17,$fot(b))]]) ).

cnf(refute_0_1164,plain,
    multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),
    introduced(tautology,[refl,[$fot(multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1165,plain,
    ( multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))
    | inverse(multiply(b,inverse(greatest_lower_bound(a,c)))) != multiply(greatest_lower_bound(a,c),inverse(b))
    | multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) ),[1,1],$fot(multiply(greatest_lower_bound(a,c),inverse(b)))]]) ).

cnf(refute_0_1166,plain,
    ( inverse(multiply(b,inverse(greatest_lower_bound(a,c)))) != multiply(greatest_lower_bound(a,c),inverse(b))
    | multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))) ),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_1164,refute_0_1165]) ).

cnf(refute_0_1167,plain,
    multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))),
    inference(resolve,[$cnf( $equal(inverse(multiply(b,inverse(greatest_lower_bound(a,c)))),multiply(greatest_lower_bound(a,c),inverse(b))) )],[refute_0_1163,refute_0_1166]) ).

cnf(refute_0_1168,plain,
    multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) = multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_1169,plain,
    ( multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))
    | multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) != multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))
    | multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) = multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))),multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))) ),[1,1],$fot(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))]]) ).

cnf(refute_0_1170,plain,
    ( multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))
    | multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) = multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))),multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))) )],[refute_0_1168,refute_0_1169]) ).

cnf(refute_0_1171,plain,
    multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) = multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) )],[refute_0_1167,refute_0_1170]) ).

cnf(refute_0_1172,plain,
    multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))),
    inference(subst,[],[associativity:[bind(X,$fot(greatest_lower_bound(inverse(a),inverse(c)))),bind(Y,$fot(b)),bind(Z,$fot(inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1173,plain,
    ( multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))
    | multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) != multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))
    | multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))))),bind(Z0,$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))))]]) ).

cnf(refute_0_1174,plain,
    ( multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) != multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))
    | multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))) )],[refute_0_1172,refute_0_1173]) ).

cnf(refute_0_1175,plain,
    multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))),multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))) )],[refute_0_1171,refute_0_1174]) ).

cnf(refute_0_1176,plain,
    least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) = least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_1177,plain,
    ( multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))
    | least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))
    | least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) = least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))) ),[1,1],$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))]]) ).

cnf(refute_0_1178,plain,
    ( multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))
    | least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) = least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))) )],[refute_0_1176,refute_0_1177]) ).

cnf(refute_0_1179,plain,
    least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) = least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))),
    inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))) )],[refute_0_1175,refute_0_1178]) ).

cnf(refute_0_1180,plain,
    ( identity != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))
    | least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))) != least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))
    | identity = least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(identity,least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))) ),[0],$fot(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_1181,plain,
    ( identity != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))
    | identity = least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c)))))),least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))) )],[refute_0_1179,refute_0_1180]) ).

cnf(refute_0_1182,plain,
    ( multiply(multiply(b,inverse(greatest_lower_bound(a,c))),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))) != least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))
    | identity = least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))) ),
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))) )],[refute_0_1162,refute_0_1181]) ).

cnf(refute_0_1183,plain,
    identity = least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,inverse(greatest_lower_bound(a,c))),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))),least_upper_bound(identity,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),inverse(multiply(b,inverse(greatest_lower_bound(a,c))))))) )],[refute_0_1159,refute_0_1182]) ).

cnf(refute_0_1184,plain,
    ( identity != least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))
    | least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))) = identity ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))))]]) ).

cnf(refute_0_1185,plain,
    least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))) = identity,
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))) )],[refute_0_1183,refute_0_1184]) ).

cnf(refute_0_1186,plain,
    ( multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) != least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))
    | least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))) != identity
    | multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) = identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),identity) ),[0],$fot(least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))))]]) ).

cnf(refute_0_1187,plain,
    ( multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) != least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))
    | multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b))))),identity) )],[refute_0_1185,refute_0_1186]) ).

cnf(refute_0_1188,plain,
    multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) = identity,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))) )],[refute_0_1004,refute_0_1187]) ).

cnf(refute_0_1189,plain,
    multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)) = multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))),
    inference(subst,[],[associativity:[bind(X,$fot(greatest_lower_bound(inverse(a),inverse(c)))),bind(Y,$fot(b)),bind(Z,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_1190,plain,
    least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))) = least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),
    introduced(tautology,[refl,[$fot(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1191,plain,
    ( multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)) != multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))
    | least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))) != least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)))
    | least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))) = least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)))) ),[1,1],$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1192,plain,
    ( multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)) != multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))
    | least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))) = least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)))) )],[refute_0_1190,refute_0_1191]) ).

cnf(refute_0_1193,plain,
    least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))) = least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)),multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) )],[refute_0_1189,refute_0_1192]) ).

cnf(refute_0_1194,plain,
    multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) = multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)))]]) ).

cnf(refute_0_1195,plain,
    ( multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) != multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))
    | least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))) != least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))
    | multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) = multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)),multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))) ),[1,0],$fot(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_1196,plain,
    ( least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))) != least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))
    | multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) = multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)),multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))) )],[refute_0_1194,refute_0_1195]) ).

cnf(refute_0_1197,plain,
    multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) = multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) )],[refute_0_1193,refute_0_1196]) ).

cnf(refute_0_1198,plain,
    multiply(least_upper_bound(identity,multiply(X_128,inverse(X_129))),inverse(multiply(X_128,inverse(X_129)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))),
    inference(subst,[],[refute_0_533:[bind(X_119,$fot(identity)),bind(X_120,$fot(multiply(X_128,inverse(X_129))))]]) ).

cnf(refute_0_1199,plain,
    multiply(least_upper_bound(X_128,X_129),inverse(X_129)) = least_upper_bound(identity,multiply(X_128,inverse(X_129))),
    inference(subst,[],[refute_0_533:[bind(X_119,$fot(X_128)),bind(X_120,$fot(X_129))]]) ).

cnf(refute_0_1200,plain,
    ( multiply(least_upper_bound(X_128,X_129),inverse(X_129)) != least_upper_bound(identity,multiply(X_128,inverse(X_129)))
    | least_upper_bound(identity,multiply(X_128,inverse(X_129))) = multiply(least_upper_bound(X_128,X_129),inverse(X_129)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_128,X_129),inverse(X_129)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_128,inverse(X_129)))))]]) ).

cnf(refute_0_1201,plain,
    least_upper_bound(identity,multiply(X_128,inverse(X_129))) = multiply(least_upper_bound(X_128,X_129),inverse(X_129)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),least_upper_bound(identity,multiply(X_128,inverse(X_129)))) )],[refute_0_1199,refute_0_1200]) ).

cnf(refute_0_1202,plain,
    ( multiply(least_upper_bound(identity,multiply(X_128,inverse(X_129))),inverse(multiply(X_128,inverse(X_129)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))
    | least_upper_bound(identity,multiply(X_128,inverse(X_129))) != multiply(least_upper_bound(X_128,X_129),inverse(X_129))
    | multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_128,inverse(X_129))),inverse(multiply(X_128,inverse(X_129)))),least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))) ),[0,0],$fot(multiply(least_upper_bound(X_128,X_129),inverse(X_129)))]]) ).

cnf(refute_0_1203,plain,
    ( multiply(least_upper_bound(identity,multiply(X_128,inverse(X_129))),inverse(multiply(X_128,inverse(X_129)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))
    | multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_128,inverse(X_129))),multiply(least_upper_bound(X_128,X_129),inverse(X_129))) )],[refute_0_1201,refute_0_1202]) ).

cnf(refute_0_1204,plain,
    multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_128,inverse(X_129))),inverse(multiply(X_128,inverse(X_129)))),least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))) )],[refute_0_1198,refute_0_1203]) ).

cnf(refute_0_1205,plain,
    ( inverse(X_61) != multiply(X_63,inverse(multiply(X_61,X_63)))
    | multiply(X_63,inverse(multiply(X_61,X_63))) = inverse(X_61) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(X_61))),bind(Y0,$fot(multiply(X_63,inverse(multiply(X_61,X_63)))))]]) ).

cnf(refute_0_1206,plain,
    multiply(X_63,inverse(multiply(X_61,X_63))) = inverse(X_61),
    inference(resolve,[$cnf( $equal(inverse(X_61),multiply(X_63,inverse(multiply(X_61,X_63)))) )],[refute_0_209,refute_0_1205]) ).

cnf(refute_0_1207,plain,
    multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129)))) = inverse(X_128),
    inference(subst,[],[refute_0_1206:[bind(X_61,$fot(X_128)),bind(X_63,$fot(inverse(X_129)))]]) ).

cnf(refute_0_1208,plain,
    multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))) = multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))))]]) ).

cnf(refute_0_1209,plain,
    ( multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129)))) != inverse(X_128)
    | multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))) != multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129)))))
    | multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))) = multiply(least_upper_bound(X_128,X_129),inverse(X_128)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))),multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129)))))) ),[1,1],$fot(inverse(X_128))]]) ).

cnf(refute_0_1210,plain,
    ( multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129)))) != inverse(X_128)
    | multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))) = multiply(least_upper_bound(X_128,X_129),inverse(X_128)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))),multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129)))))) )],[refute_0_1208,refute_0_1209]) ).

cnf(refute_0_1211,plain,
    multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))) = multiply(least_upper_bound(X_128,X_129),inverse(X_128)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129)))),inverse(X_128)) )],[refute_0_1207,refute_0_1210]) ).

cnf(refute_0_1212,plain,
    multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) = multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))),
    inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(X_128,X_129))),bind(Y,$fot(inverse(X_129))),bind(Z,$fot(inverse(multiply(X_128,inverse(X_129)))))]]) ).

cnf(refute_0_1213,plain,
    ( multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) != multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129)))))
    | multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))) != multiply(least_upper_bound(X_128,X_129),inverse(X_128))
    | multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) = multiply(least_upper_bound(X_128,X_129),inverse(X_128)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))))),bind(Y0,$fot(multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))))),bind(Z0,$fot(multiply(least_upper_bound(X_128,X_129),inverse(X_128))))]]) ).

cnf(refute_0_1214,plain,
    ( multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))) != multiply(least_upper_bound(X_128,X_129),inverse(X_128))
    | multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) = multiply(least_upper_bound(X_128,X_129),inverse(X_128)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))),multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129)))))) )],[refute_0_1212,refute_0_1213]) ).

cnf(refute_0_1215,plain,
    multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) = multiply(least_upper_bound(X_128,X_129),inverse(X_128)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_128,X_129),multiply(inverse(X_129),inverse(multiply(X_128,inverse(X_129))))),multiply(least_upper_bound(X_128,X_129),inverse(X_128))) )],[refute_0_1211,refute_0_1214]) ).

cnf(refute_0_1216,plain,
    ( multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) != multiply(least_upper_bound(X_128,X_129),inverse(X_128))
    | multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))
    | multiply(least_upper_bound(X_128,X_129),inverse(X_128)) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))),least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))) ),[0],$fot(multiply(least_upper_bound(X_128,X_129),inverse(X_128)))]]) ).

cnf(refute_0_1217,plain,
    ( multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))
    | multiply(least_upper_bound(X_128,X_129),inverse(X_128)) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))),multiply(least_upper_bound(X_128,X_129),inverse(X_128))) )],[refute_0_1215,refute_0_1216]) ).

cnf(refute_0_1218,plain,
    inverse(multiply(X_128,inverse(X_129))) = multiply(X_129,inverse(X_128)),
    inference(subst,[],[refute_0_146:[bind(X,$fot(X_129)),bind(X_17,$fot(X_128))]]) ).

cnf(refute_0_1219,plain,
    least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))) = least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))))]]) ).

cnf(refute_0_1220,plain,
    ( inverse(multiply(X_128,inverse(X_129))) != multiply(X_129,inverse(X_128))
    | least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))) != least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))
    | least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))) = least_upper_bound(identity,multiply(X_129,inverse(X_128))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))),least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))) ),[1,1],$fot(multiply(X_129,inverse(X_128)))]]) ).

cnf(refute_0_1221,plain,
    ( inverse(multiply(X_128,inverse(X_129))) != multiply(X_129,inverse(X_128))
    | least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))) = least_upper_bound(identity,multiply(X_129,inverse(X_128))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))),least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))) )],[refute_0_1219,refute_0_1220]) ).

cnf(refute_0_1222,plain,
    least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))) = least_upper_bound(identity,multiply(X_129,inverse(X_128))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_128,inverse(X_129))),multiply(X_129,inverse(X_128))) )],[refute_0_1218,refute_0_1221]) ).

cnf(refute_0_1223,plain,
    multiply(identity,least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))) = least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))))]]) ).

cnf(refute_0_1224,plain,
    least_upper_bound(X_15,multiply(X_15,X_98)) = least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))),
    inference(subst,[],[refute_0_613:[bind(X_16,$fot(multiply(X_15,X_98)))]]) ).

cnf(refute_0_1225,plain,
    multiply(X_15,least_upper_bound(X_98,identity)) = least_upper_bound(X_15,multiply(X_15,X_98)),
    inference(subst,[],[refute_0_260:[bind(X_94,$fot(X_15)),bind(X_95,$fot(X_98))]]) ).

cnf(refute_0_1226,plain,
    ( multiply(X_15,least_upper_bound(X_98,identity)) != least_upper_bound(X_15,multiply(X_15,X_98))
    | least_upper_bound(X_15,multiply(X_15,X_98)) = multiply(X_15,least_upper_bound(X_98,identity)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(X_15,least_upper_bound(X_98,identity)))),bind(Y0,$fot(least_upper_bound(X_15,multiply(X_15,X_98))))]]) ).

cnf(refute_0_1227,plain,
    least_upper_bound(X_15,multiply(X_15,X_98)) = multiply(X_15,least_upper_bound(X_98,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_15,least_upper_bound(X_98,identity)),least_upper_bound(X_15,multiply(X_15,X_98))) )],[refute_0_1225,refute_0_1226]) ).

cnf(refute_0_1228,plain,
    ( least_upper_bound(X_15,multiply(X_15,X_98)) != multiply(X_15,least_upper_bound(X_98,identity))
    | least_upper_bound(X_15,multiply(X_15,X_98)) != least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98)))
    | multiply(X_15,least_upper_bound(X_98,identity)) = least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,multiply(X_15,X_98)),least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98)))) ),[0],$fot(multiply(X_15,least_upper_bound(X_98,identity)))]]) ).

cnf(refute_0_1229,plain,
    ( least_upper_bound(X_15,multiply(X_15,X_98)) != least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98)))
    | multiply(X_15,least_upper_bound(X_98,identity)) = least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_15,X_98)),multiply(X_15,least_upper_bound(X_98,identity))) )],[refute_0_1227,refute_0_1228]) ).

cnf(refute_0_1230,plain,
    multiply(X_15,least_upper_bound(X_98,identity)) = least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_15,X_98)),least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98)))) )],[refute_0_1224,refute_0_1229]) ).

cnf(refute_0_1231,plain,
    least_upper_bound(X_98,X_98) = X_98,
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_98))]]) ).

cnf(refute_0_1232,plain,
    least_upper_bound(identity,least_upper_bound(X_98,X_98)) = least_upper_bound(identity,least_upper_bound(X_98,X_98)),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(X_98,X_98)))]]) ).

cnf(refute_0_1233,plain,
    ( least_upper_bound(X_98,X_98) != X_98
    | least_upper_bound(identity,least_upper_bound(X_98,X_98)) != least_upper_bound(identity,least_upper_bound(X_98,X_98))
    | least_upper_bound(identity,least_upper_bound(X_98,X_98)) = least_upper_bound(identity,X_98) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_98,X_98)),least_upper_bound(identity,least_upper_bound(X_98,X_98))) ),[1,1],$fot(X_98)]]) ).

cnf(refute_0_1234,plain,
    ( least_upper_bound(X_98,X_98) != X_98
    | least_upper_bound(identity,least_upper_bound(X_98,X_98)) = least_upper_bound(identity,X_98) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_98,X_98)),least_upper_bound(identity,least_upper_bound(X_98,X_98))) )],[refute_0_1232,refute_0_1233]) ).

cnf(refute_0_1235,plain,
    least_upper_bound(identity,least_upper_bound(X_98,X_98)) = least_upper_bound(identity,X_98),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_98,X_98),X_98) )],[refute_0_1231,refute_0_1234]) ).

cnf(refute_0_1236,plain,
    multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))),
    introduced(tautology,[refl,[$fot(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))))]]) ).

cnf(refute_0_1237,plain,
    ( multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))
    | least_upper_bound(identity,least_upper_bound(X_98,X_98)) != least_upper_bound(identity,X_98)
    | multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))) = multiply(X_15,least_upper_bound(identity,X_98)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))),multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))) ),[1,1],$fot(least_upper_bound(identity,X_98))]]) ).

cnf(refute_0_1238,plain,
    ( least_upper_bound(identity,least_upper_bound(X_98,X_98)) != least_upper_bound(identity,X_98)
    | multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))) = multiply(X_15,least_upper_bound(identity,X_98)) ),
    inference(resolve,[$cnf( $equal(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))),multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))) )],[refute_0_1236,refute_0_1237]) ).

cnf(refute_0_1239,plain,
    multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))) = multiply(X_15,least_upper_bound(identity,X_98)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_98,X_98)),least_upper_bound(identity,X_98)) )],[refute_0_1235,refute_0_1238]) ).

cnf(refute_0_1240,plain,
    least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)),
    inference(subst,[],[refute_0_606:[bind(X_15,$fot(multiply(X_94,X_95))),bind(X_16,$fot(multiply(X_94,X_96)))]]) ).

cnf(refute_0_1241,plain,
    multiply(X_94,least_upper_bound(X_95,X_96)) = least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_94)),bind(Y,$fot(X_95)),bind(Z,$fot(X_96))]]) ).

cnf(refute_0_1242,plain,
    ( multiply(X_94,least_upper_bound(X_95,X_96)) != least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))
    | least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)) = multiply(X_94,least_upper_bound(X_95,X_96)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(X_94,least_upper_bound(X_95,X_96)))),bind(Y0,$fot(least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))))]]) ).

cnf(refute_0_1243,plain,
    least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)) = multiply(X_94,least_upper_bound(X_95,X_96)),
    inference(resolve,[$cnf( $equal(multiply(X_94,least_upper_bound(X_95,X_96)),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) )],[refute_0_1241,refute_0_1242]) ).

cnf(refute_0_1244,plain,
    ( least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)) != multiply(X_94,least_upper_bound(X_95,X_96))
    | least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) != least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))
    | least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = multiply(X_94,least_upper_bound(X_95,X_96)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) ),[1],$fot(multiply(X_94,least_upper_bound(X_95,X_96)))]]) ).

cnf(refute_0_1245,plain,
    ( least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) != least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))
    | least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = multiply(X_94,least_upper_bound(X_95,X_96)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)),multiply(X_94,least_upper_bound(X_95,X_96))) )],[refute_0_1243,refute_0_1244]) ).

cnf(refute_0_1246,plain,
    least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = multiply(X_94,least_upper_bound(X_95,X_96)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) )],[refute_0_1240,refute_0_1245]) ).

cnf(refute_0_1247,plain,
    least_upper_bound(X_95,X_95) = X_95,
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_95))]]) ).

cnf(refute_0_1248,plain,
    least_upper_bound(X_96,least_upper_bound(X_95,X_95)) = least_upper_bound(X_96,least_upper_bound(X_95,X_95)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_96,least_upper_bound(X_95,X_95)))]]) ).

cnf(refute_0_1249,plain,
    ( least_upper_bound(X_95,X_95) != X_95
    | least_upper_bound(X_96,least_upper_bound(X_95,X_95)) != least_upper_bound(X_96,least_upper_bound(X_95,X_95))
    | least_upper_bound(X_96,least_upper_bound(X_95,X_95)) = least_upper_bound(X_96,X_95) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_96,least_upper_bound(X_95,X_95)),least_upper_bound(X_96,least_upper_bound(X_95,X_95))) ),[1,1],$fot(X_95)]]) ).

cnf(refute_0_1250,plain,
    ( least_upper_bound(X_95,X_95) != X_95
    | least_upper_bound(X_96,least_upper_bound(X_95,X_95)) = least_upper_bound(X_96,X_95) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_96,least_upper_bound(X_95,X_95)),least_upper_bound(X_96,least_upper_bound(X_95,X_95))) )],[refute_0_1248,refute_0_1249]) ).

cnf(refute_0_1251,plain,
    least_upper_bound(X_96,least_upper_bound(X_95,X_95)) = least_upper_bound(X_96,X_95),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_95,X_95),X_95) )],[refute_0_1247,refute_0_1250]) ).

cnf(refute_0_1252,plain,
    multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))) = multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))),
    introduced(tautology,[refl,[$fot(multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))))]]) ).

cnf(refute_0_1253,plain,
    ( multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))) != multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95)))
    | least_upper_bound(X_96,least_upper_bound(X_95,X_95)) != least_upper_bound(X_96,X_95)
    | multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))) = multiply(X_94,least_upper_bound(X_96,X_95)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))),multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95)))) ),[1,1],$fot(least_upper_bound(X_96,X_95))]]) ).

cnf(refute_0_1254,plain,
    ( least_upper_bound(X_96,least_upper_bound(X_95,X_95)) != least_upper_bound(X_96,X_95)
    | multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))) = multiply(X_94,least_upper_bound(X_96,X_95)) ),
    inference(resolve,[$cnf( $equal(multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))),multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95)))) )],[refute_0_1252,refute_0_1253]) ).

cnf(refute_0_1255,plain,
    multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))) = multiply(X_94,least_upper_bound(X_96,X_95)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_96,least_upper_bound(X_95,X_95)),least_upper_bound(X_96,X_95)) )],[refute_0_1251,refute_0_1254]) ).

cnf(refute_0_1256,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_13:[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_1257,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_1256]) ).

cnf(refute_0_1258,plain,
    least_upper_bound(multiply(X_94,X_96),multiply(X_94,least_upper_bound(X_95,X_95))) = multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))),
    inference(subst,[],[refute_0_1257:[bind(X,$fot(X_94)),bind(Y,$fot(X_96)),bind(Z,$fot(least_upper_bound(X_95,X_95)))]]) ).

cnf(refute_0_1259,plain,
    least_upper_bound(X,least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X)),
    inference(subst,[],[refute_0_588:[bind(X_14,$fot(multiply(X_94,X_95))),bind(X_15,$fot(multiply(X_94,X_96)))]]) ).

cnf(refute_0_1260,plain,
    ( least_upper_bound(X,least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) != least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X))
    | least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)) != multiply(X_94,least_upper_bound(X_95,X_96))
    | least_upper_bound(X,multiply(X_94,least_upper_bound(X_95,X_96))) = least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))),least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X))) ),[0,1],$fot(multiply(X_94,least_upper_bound(X_95,X_96)))]]) ).

cnf(refute_0_1261,plain,
    ( least_upper_bound(X,least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) != least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X))
    | least_upper_bound(X,multiply(X_94,least_upper_bound(X_95,X_96))) = least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)),multiply(X_94,least_upper_bound(X_95,X_96))) )],[refute_0_1243,refute_0_1260]) ).

cnf(refute_0_1262,plain,
    least_upper_bound(X,multiply(X_94,least_upper_bound(X_95,X_96))) = least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))),least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X))) )],[refute_0_1259,refute_0_1261]) ).

cnf(refute_0_1263,plain,
    ( least_upper_bound(X,multiply(X_94,least_upper_bound(X_95,X_96))) != least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X))
    | least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X)) = least_upper_bound(X,multiply(X_94,least_upper_bound(X_95,X_96))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X,multiply(X_94,least_upper_bound(X_95,X_96))))),bind(Y0,$fot(least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X))))]]) ).

cnf(refute_0_1264,plain,
    least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X)) = least_upper_bound(X,multiply(X_94,least_upper_bound(X_95,X_96))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(X_94,least_upper_bound(X_95,X_96))),least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_96),X))) )],[refute_0_1262,refute_0_1263]) ).

cnf(refute_0_1265,plain,
    least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = least_upper_bound(multiply(X_94,X_96),multiply(X_94,least_upper_bound(X_95,X_95))),
    inference(subst,[],[refute_0_1264:[bind(X,$fot(multiply(X_94,X_96))),bind(X_96,$fot(X_95))]]) ).

cnf(refute_0_1266,plain,
    ( least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) != least_upper_bound(multiply(X_94,X_96),multiply(X_94,least_upper_bound(X_95,X_95)))
    | least_upper_bound(multiply(X_94,X_96),multiply(X_94,least_upper_bound(X_95,X_95))) != multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95)))
    | least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))))),bind(Y0,$fot(least_upper_bound(multiply(X_94,X_96),multiply(X_94,least_upper_bound(X_95,X_95))))),bind(Z0,$fot(multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95)))))]]) ).

cnf(refute_0_1267,plain,
    ( least_upper_bound(multiply(X_94,X_96),multiply(X_94,least_upper_bound(X_95,X_95))) != multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95)))
    | least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))),least_upper_bound(multiply(X_94,X_96),multiply(X_94,least_upper_bound(X_95,X_95)))) )],[refute_0_1265,refute_0_1266]) ).

cnf(refute_0_1268,plain,
    least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_96),multiply(X_94,least_upper_bound(X_95,X_95))),multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95)))) )],[refute_0_1258,refute_0_1267]) ).

cnf(refute_0_1269,plain,
    ( multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))) != multiply(X_94,least_upper_bound(X_96,X_95))
    | least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) != multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95)))
    | least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = multiply(X_94,least_upper_bound(X_96,X_95)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))))),bind(Y0,$fot(multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))))),bind(Z0,$fot(multiply(X_94,least_upper_bound(X_96,X_95))))]]) ).

cnf(refute_0_1270,plain,
    ( multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))) != multiply(X_94,least_upper_bound(X_96,X_95))
    | least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = multiply(X_94,least_upper_bound(X_96,X_95)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))),multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95)))) )],[refute_0_1268,refute_0_1269]) ).

cnf(refute_0_1271,plain,
    least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) = multiply(X_94,least_upper_bound(X_96,X_95)),
    inference(resolve,[$cnf( $equal(multiply(X_94,least_upper_bound(X_96,least_upper_bound(X_95,X_95))),multiply(X_94,least_upper_bound(X_96,X_95))) )],[refute_0_1255,refute_0_1270]) ).

cnf(refute_0_1272,plain,
    ( least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) != multiply(X_94,least_upper_bound(X_95,X_96))
    | least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) != multiply(X_94,least_upper_bound(X_96,X_95))
    | multiply(X_94,least_upper_bound(X_96,X_95)) = multiply(X_94,least_upper_bound(X_95,X_96)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))),multiply(X_94,least_upper_bound(X_95,X_96))) ),[0],$fot(multiply(X_94,least_upper_bound(X_96,X_95)))]]) ).

cnf(refute_0_1273,plain,
    ( least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))) != multiply(X_94,least_upper_bound(X_95,X_96))
    | multiply(X_94,least_upper_bound(X_96,X_95)) = multiply(X_94,least_upper_bound(X_95,X_96)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))),multiply(X_94,least_upper_bound(X_96,X_95))) )],[refute_0_1271,refute_0_1272]) ).

cnf(refute_0_1274,plain,
    multiply(X_94,least_upper_bound(X_96,X_95)) = multiply(X_94,least_upper_bound(X_95,X_96)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))),multiply(X_94,least_upper_bound(X_95,X_96))) )],[refute_0_1246,refute_0_1273]) ).

cnf(refute_0_1275,plain,
    ( multiply(X_94,least_upper_bound(X_96,X_95)) != multiply(X_94,least_upper_bound(X_95,X_96))
    | multiply(X_94,least_upper_bound(X_95,X_96)) = multiply(X_94,least_upper_bound(X_96,X_95)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(X_94,least_upper_bound(X_96,X_95)))),bind(Y0,$fot(multiply(X_94,least_upper_bound(X_95,X_96))))]]) ).

cnf(refute_0_1276,plain,
    multiply(X_94,least_upper_bound(X_95,X_96)) = multiply(X_94,least_upper_bound(X_96,X_95)),
    inference(resolve,[$cnf( $equal(multiply(X_94,least_upper_bound(X_96,X_95)),multiply(X_94,least_upper_bound(X_95,X_96))) )],[refute_0_1274,refute_0_1275]) ).

cnf(refute_0_1277,plain,
    multiply(X_15,least_upper_bound(least_upper_bound(X_98,X_98),identity)) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))),
    inference(subst,[],[refute_0_1276:[bind(X_94,$fot(X_15)),bind(X_95,$fot(least_upper_bound(X_98,X_98))),bind(X_96,$fot(identity))]]) ).

cnf(refute_0_1278,plain,
    ( multiply(X_94,least_upper_bound(X_95,identity)) != least_upper_bound(X_94,multiply(X_94,X_95))
    | least_upper_bound(X_94,multiply(X_94,X_95)) = multiply(X_94,least_upper_bound(X_95,identity)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(X_94,least_upper_bound(X_95,identity)))),bind(Y0,$fot(least_upper_bound(X_94,multiply(X_94,X_95))))]]) ).

cnf(refute_0_1279,plain,
    least_upper_bound(X_94,multiply(X_94,X_95)) = multiply(X_94,least_upper_bound(X_95,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_94,least_upper_bound(X_95,identity)),least_upper_bound(X_94,multiply(X_94,X_95))) )],[refute_0_260,refute_0_1278]) ).

cnf(refute_0_1280,plain,
    least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))) = multiply(X_15,least_upper_bound(least_upper_bound(X_98,X_98),identity)),
    inference(subst,[],[refute_0_1279:[bind(X_94,$fot(X_15)),bind(X_95,$fot(least_upper_bound(X_98,X_98)))]]) ).

cnf(refute_0_1281,plain,
    ( multiply(X_15,least_upper_bound(least_upper_bound(X_98,X_98),identity)) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))
    | least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))) != multiply(X_15,least_upper_bound(least_upper_bound(X_98,X_98),identity))
    | least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))))),bind(Y0,$fot(multiply(X_15,least_upper_bound(least_upper_bound(X_98,X_98),identity)))),bind(Z0,$fot(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))))]]) ).

cnf(refute_0_1282,plain,
    ( multiply(X_15,least_upper_bound(least_upper_bound(X_98,X_98),identity)) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))
    | least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))),multiply(X_15,least_upper_bound(least_upper_bound(X_98,X_98),identity))) )],[refute_0_1280,refute_0_1281]) ).

cnf(refute_0_1283,plain,
    least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))),
    inference(resolve,[$cnf( $equal(multiply(X_15,least_upper_bound(least_upper_bound(X_98,X_98),identity)),multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))) )],[refute_0_1277,refute_0_1282]) ).

cnf(refute_0_1284,plain,
    least_upper_bound(multiply(X_94,X_96),least_upper_bound(X_14,multiply(X_94,X_95))) = least_upper_bound(X_14,least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96))),
    inference(subst,[],[refute_0_588:[bind(X,$fot(multiply(X_94,X_96))),bind(X_15,$fot(multiply(X_94,X_95)))]]) ).

cnf(refute_0_1285,plain,
    ( least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)) != multiply(X_94,least_upper_bound(X_95,X_96))
    | least_upper_bound(multiply(X_94,X_96),least_upper_bound(X_14,multiply(X_94,X_95))) != least_upper_bound(X_14,least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)))
    | least_upper_bound(multiply(X_94,X_96),least_upper_bound(X_14,multiply(X_94,X_95))) = least_upper_bound(X_14,multiply(X_94,least_upper_bound(X_95,X_96))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_94,X_96),least_upper_bound(X_14,multiply(X_94,X_95))),least_upper_bound(X_14,least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)))) ),[1,1],$fot(multiply(X_94,least_upper_bound(X_95,X_96)))]]) ).

cnf(refute_0_1286,plain,
    ( least_upper_bound(multiply(X_94,X_96),least_upper_bound(X_14,multiply(X_94,X_95))) != least_upper_bound(X_14,least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)))
    | least_upper_bound(multiply(X_94,X_96),least_upper_bound(X_14,multiply(X_94,X_95))) = least_upper_bound(X_14,multiply(X_94,least_upper_bound(X_95,X_96))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)),multiply(X_94,least_upper_bound(X_95,X_96))) )],[refute_0_1243,refute_0_1285]) ).

cnf(refute_0_1287,plain,
    least_upper_bound(multiply(X_94,X_96),least_upper_bound(X_14,multiply(X_94,X_95))) = least_upper_bound(X_14,multiply(X_94,least_upper_bound(X_95,X_96))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_96),least_upper_bound(X_14,multiply(X_94,X_95))),least_upper_bound(X_14,least_upper_bound(multiply(X_94,X_95),multiply(X_94,X_96)))) )],[refute_0_1284,refute_0_1286]) ).

cnf(refute_0_1288,plain,
    least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) = least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))),
    inference(subst,[],[refute_0_1287:[bind(X_14,$fot(X_15)),bind(X_94,$fot(X_15)),bind(X_95,$fot(X_98)),bind(X_96,$fot(X_98))]]) ).

cnf(refute_0_1289,plain,
    ( least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))
    | least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) != least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98)))
    | least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))))),bind(Y0,$fot(least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))))),bind(Z0,$fot(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))))]]) ).

cnf(refute_0_1290,plain,
    ( least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))
    | least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))),least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98)))) )],[refute_0_1288,refute_0_1289]) ).

cnf(refute_0_1291,plain,
    least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_98,X_98))),multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))) )],[refute_0_1283,refute_0_1290]) ).

cnf(refute_0_1292,plain,
    ( multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))) != multiply(X_15,least_upper_bound(identity,X_98))
    | least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))
    | least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) = multiply(X_15,least_upper_bound(identity,X_98)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))))),bind(Y0,$fot(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))))),bind(Z0,$fot(multiply(X_15,least_upper_bound(identity,X_98))))]]) ).

cnf(refute_0_1293,plain,
    ( multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))) != multiply(X_15,least_upper_bound(identity,X_98))
    | least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) = multiply(X_15,least_upper_bound(identity,X_98)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))),multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98)))) )],[refute_0_1291,refute_0_1292]) ).

cnf(refute_0_1294,plain,
    least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) = multiply(X_15,least_upper_bound(identity,X_98)),
    inference(resolve,[$cnf( $equal(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_98,X_98))),multiply(X_15,least_upper_bound(identity,X_98))) )],[refute_0_1239,refute_0_1293]) ).

cnf(refute_0_1295,plain,
    ( multiply(X_15,least_upper_bound(X_98,identity)) != least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98)))
    | least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))) != multiply(X_15,least_upper_bound(identity,X_98))
    | multiply(X_15,least_upper_bound(X_98,identity)) = multiply(X_15,least_upper_bound(identity,X_98)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_15,least_upper_bound(X_98,identity)),multiply(X_15,least_upper_bound(identity,X_98))) ),[0],$fot(least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))))]]) ).

cnf(refute_0_1296,plain,
    ( multiply(X_15,least_upper_bound(X_98,identity)) != least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98)))
    | multiply(X_15,least_upper_bound(X_98,identity)) = multiply(X_15,least_upper_bound(identity,X_98)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98))),multiply(X_15,least_upper_bound(identity,X_98))) )],[refute_0_1294,refute_0_1295]) ).

cnf(refute_0_1297,plain,
    multiply(X_15,least_upper_bound(X_98,identity)) = multiply(X_15,least_upper_bound(identity,X_98)),
    inference(resolve,[$cnf( $equal(multiply(X_15,least_upper_bound(X_98,identity)),least_upper_bound(multiply(X_15,X_98),least_upper_bound(X_15,multiply(X_15,X_98)))) )],[refute_0_1230,refute_0_1296]) ).

cnf(refute_0_1298,plain,
    multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)) = multiply(identity,least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))),
    inference(subst,[],[refute_0_1297:[bind(X_15,$fot(identity)),bind(X_98,$fot(inverse(multiply(X_128,inverse(X_129)))))]]) ).

cnf(refute_0_1299,plain,
    ( multiply(identity,least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))) != least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))
    | multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)) != multiply(identity,least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))))
    | multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)) = least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))))),bind(Z0,$fot(least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))))]]) ).

cnf(refute_0_1300,plain,
    ( multiply(identity,least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))) != least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))
    | multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)) = least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))) ),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)),multiply(identity,least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))))) )],[refute_0_1298,refute_0_1299]) ).

cnf(refute_0_1301,plain,
    multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)) = least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))),least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))) )],[refute_0_1223,refute_0_1300]) ).

cnf(refute_0_1302,plain,
    least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) = multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)),
    inference(subst,[],[refute_0_1279:[bind(X_94,$fot(identity)),bind(X_95,$fot(inverse(multiply(X_128,inverse(X_129)))))]]) ).

cnf(refute_0_1303,plain,
    ( multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)) != least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))
    | least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) != multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity))
    | least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) = least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))))),bind(Y0,$fot(multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)))),bind(Z0,$fot(least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))))]]) ).

cnf(refute_0_1304,plain,
    ( multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)) != least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))
    | least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) = least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))),multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity))) )],[refute_0_1302,refute_0_1303]) ).

cnf(refute_0_1305,plain,
    least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) = least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(inverse(multiply(X_128,inverse(X_129))),identity)),least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))) )],[refute_0_1301,refute_0_1304]) ).

cnf(refute_0_1306,plain,
    ( least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) != least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))
    | least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))) != least_upper_bound(identity,multiply(X_129,inverse(X_128)))
    | least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) = least_upper_bound(identity,multiply(X_129,inverse(X_128))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_129,inverse(X_128)))))]]) ).

cnf(refute_0_1307,plain,
    ( least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))) != least_upper_bound(identity,multiply(X_129,inverse(X_128)))
    | least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) = least_upper_bound(identity,multiply(X_129,inverse(X_128))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))),least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129))))) )],[refute_0_1305,refute_0_1306]) ).

cnf(refute_0_1308,plain,
    least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) = least_upper_bound(identity,multiply(X_129,inverse(X_128))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_128,inverse(X_129)))),least_upper_bound(identity,multiply(X_129,inverse(X_128)))) )],[refute_0_1222,refute_0_1307]) ).

cnf(refute_0_1309,plain,
    ( multiply(least_upper_bound(X_128,X_129),inverse(X_128)) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))
    | least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))) != least_upper_bound(identity,multiply(X_129,inverse(X_128)))
    | multiply(least_upper_bound(X_128,X_129),inverse(X_128)) = least_upper_bound(identity,multiply(X_129,inverse(X_128))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_128,X_129),inverse(X_128)),least_upper_bound(identity,multiply(X_129,inverse(X_128)))) ),[0],$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))))]]) ).

cnf(refute_0_1310,plain,
    ( multiply(least_upper_bound(X_128,X_129),inverse(X_128)) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))
    | multiply(least_upper_bound(X_128,X_129),inverse(X_128)) = least_upper_bound(identity,multiply(X_129,inverse(X_128))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129))))),least_upper_bound(identity,multiply(X_129,inverse(X_128)))) )],[refute_0_1308,refute_0_1309]) ).

cnf(refute_0_1311,plain,
    ( multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))
    | multiply(least_upper_bound(X_128,X_129),inverse(X_128)) = least_upper_bound(identity,multiply(X_129,inverse(X_128))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_128,X_129),inverse(X_128)),least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))) )],[refute_0_1217,refute_0_1310]) ).

cnf(refute_0_1312,plain,
    multiply(least_upper_bound(X_128,X_129),inverse(X_128)) = least_upper_bound(identity,multiply(X_129,inverse(X_128))),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_128,X_129),inverse(X_129)),inverse(multiply(X_128,inverse(X_129)))),least_upper_bound(identity,multiply(identity,inverse(multiply(X_128,inverse(X_129)))))) )],[refute_0_1204,refute_0_1311]) ).

cnf(refute_0_1313,plain,
    ( multiply(least_upper_bound(X_128,X_129),inverse(X_128)) != least_upper_bound(identity,multiply(X_129,inverse(X_128)))
    | least_upper_bound(identity,multiply(X_129,inverse(X_128))) = multiply(least_upper_bound(X_128,X_129),inverse(X_128)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_128,X_129),inverse(X_128)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_129,inverse(X_128)))))]]) ).

cnf(refute_0_1314,plain,
    least_upper_bound(identity,multiply(X_129,inverse(X_128))) = multiply(least_upper_bound(X_128,X_129),inverse(X_128)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_128,X_129),inverse(X_128)),least_upper_bound(identity,multiply(X_129,inverse(X_128)))) )],[refute_0_1312,refute_0_1313]) ).

cnf(refute_0_1315,plain,
    least_upper_bound(identity,multiply(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)),inverse(b))) = multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)),
    inference(subst,[],[refute_0_1314:[bind(X_128,$fot(b)),bind(X_129,$fot(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1316,plain,
    multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) = least_upper_bound(identity,multiply(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)),inverse(b))),
    inference(subst,[],[refute_0_1003:[bind(X_118,$fot(inverse(b))),bind(X_120,$fot(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1317,plain,
    ( multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) != least_upper_bound(identity,multiply(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)),inverse(b)))
    | least_upper_bound(identity,multiply(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)),inverse(b))) != multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))
    | multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) = multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)))),bind(Y0,$fot(least_upper_bound(identity,multiply(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)),inverse(b))))),bind(Z0,$fot(multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))))]]) ).

cnf(refute_0_1318,plain,
    ( least_upper_bound(identity,multiply(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)),inverse(b))) != multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))
    | multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) = multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)),least_upper_bound(identity,multiply(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)),inverse(b)))) )],[refute_0_1316,refute_0_1317]) ).

cnf(refute_0_1319,plain,
    multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) = multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c)),inverse(b))),multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))) )],[refute_0_1315,refute_0_1318]) ).

cnf(refute_0_1320,plain,
    multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)) = least_upper_bound(multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)),multiply(Z,multiply(X_343,X_344))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(multiply(X_343,X_344))),bind(Y,$fot(inverse(multiply(X_343,X_345))))]]) ).

cnf(refute_0_1321,plain,
    multiply(multiply(inverse(multiply(Y,X_88)),Y),Z) = multiply(inverse(multiply(Y,X_88)),multiply(Y,Z)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(multiply(Y,X_88))))]]) ).

cnf(refute_0_1322,plain,
    inverse(X_88) = multiply(inverse(multiply(Y,X_88)),Y),
    inference(subst,[],[refute_0_34:[bind(X_83,$fot(Y)),bind(X_84,$fot(X_88))]]) ).

cnf(refute_0_1323,plain,
    ( inverse(X_88) != multiply(inverse(multiply(Y,X_88)),Y)
    | multiply(inverse(multiply(Y,X_88)),Y) = inverse(X_88) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(X_88))),bind(Y0,$fot(multiply(inverse(multiply(Y,X_88)),Y)))]]) ).

cnf(refute_0_1324,plain,
    multiply(inverse(multiply(Y,X_88)),Y) = inverse(X_88),
    inference(resolve,[$cnf( $equal(inverse(X_88),multiply(inverse(multiply(Y,X_88)),Y)) )],[refute_0_1322,refute_0_1323]) ).

cnf(refute_0_1325,plain,
    ( multiply(multiply(inverse(multiply(Y,X_88)),Y),Z) != multiply(inverse(multiply(Y,X_88)),multiply(Y,Z))
    | multiply(inverse(multiply(Y,X_88)),Y) != inverse(X_88)
    | multiply(inverse(X_88),Z) = multiply(inverse(multiply(Y,X_88)),multiply(Y,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(multiply(Y,X_88)),Y),Z),multiply(inverse(multiply(Y,X_88)),multiply(Y,Z))) ),[0,0],$fot(inverse(X_88))]]) ).

cnf(refute_0_1326,plain,
    ( multiply(multiply(inverse(multiply(Y,X_88)),Y),Z) != multiply(inverse(multiply(Y,X_88)),multiply(Y,Z))
    | multiply(inverse(X_88),Z) = multiply(inverse(multiply(Y,X_88)),multiply(Y,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(Y,X_88)),Y),inverse(X_88)) )],[refute_0_1324,refute_0_1325]) ).

cnf(refute_0_1327,plain,
    multiply(inverse(X_88),Z) = multiply(inverse(multiply(Y,X_88)),multiply(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(Y,X_88)),Y),Z),multiply(inverse(multiply(Y,X_88)),multiply(Y,Z))) )],[refute_0_1321,refute_0_1326]) ).

cnf(refute_0_1328,plain,
    multiply(inverse(X_345),X_344) = multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)),
    inference(subst,[],[refute_0_1327:[bind(Y,$fot(X_343)),bind(Z,$fot(X_344)),bind(X_88,$fot(X_345))]]) ).

cnf(refute_0_1329,plain,
    ( multiply(inverse(X_345),X_344) != multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344))
    | multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)) = multiply(inverse(X_345),X_344) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(inverse(X_345),X_344))),bind(Y0,$fot(multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344))))]]) ).

cnf(refute_0_1330,plain,
    multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)) = multiply(inverse(X_345),X_344),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_345),X_344),multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344))) )],[refute_0_1328,refute_0_1329]) ).

cnf(refute_0_1331,plain,
    ( multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)) != multiply(inverse(X_345),X_344)
    | multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)) != least_upper_bound(multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)),multiply(Z,multiply(X_343,X_344)))
    | multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)) = least_upper_bound(multiply(inverse(X_345),X_344),multiply(Z,multiply(X_343,X_344))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)),least_upper_bound(multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)),multiply(Z,multiply(X_343,X_344)))) ),[1,0],$fot(multiply(inverse(X_345),X_344))]]) ).

cnf(refute_0_1332,plain,
    ( multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)) != least_upper_bound(multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)),multiply(Z,multiply(X_343,X_344)))
    | multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)) = least_upper_bound(multiply(inverse(X_345),X_344),multiply(Z,multiply(X_343,X_344))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)),multiply(inverse(X_345),X_344)) )],[refute_0_1330,refute_0_1331]) ).

cnf(refute_0_1333,plain,
    multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)) = least_upper_bound(multiply(inverse(X_345),X_344),multiply(Z,multiply(X_343,X_344))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)),least_upper_bound(multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)),multiply(Z,multiply(X_343,X_344)))) )],[refute_0_1320,refute_0_1332]) ).

cnf(refute_0_1334,plain,
    multiply(least_upper_bound(X_119,multiply(X,Y)),X_118) = least_upper_bound(multiply(X_119,X_118),multiply(multiply(X,Y),X_118)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_118)),bind(Y,$fot(X_119)),bind(Z,$fot(multiply(X,Y)))]]) ).

cnf(refute_0_1335,plain,
    multiply(multiply(X,Y),X_118) = multiply(X,multiply(Y,X_118)),
    inference(subst,[],[associativity:[bind(Z,$fot(X_118))]]) ).

cnf(refute_0_1336,plain,
    ( multiply(multiply(X,Y),X_118) != multiply(X,multiply(Y,X_118))
    | multiply(least_upper_bound(X_119,multiply(X,Y)),X_118) != least_upper_bound(multiply(X_119,X_118),multiply(multiply(X,Y),X_118))
    | multiply(least_upper_bound(X_119,multiply(X,Y)),X_118) = least_upper_bound(multiply(X_119,X_118),multiply(X,multiply(Y,X_118))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_119,multiply(X,Y)),X_118),least_upper_bound(multiply(X_119,X_118),multiply(multiply(X,Y),X_118))) ),[1,1],$fot(multiply(X,multiply(Y,X_118)))]]) ).

cnf(refute_0_1337,plain,
    ( multiply(least_upper_bound(X_119,multiply(X,Y)),X_118) != least_upper_bound(multiply(X_119,X_118),multiply(multiply(X,Y),X_118))
    | multiply(least_upper_bound(X_119,multiply(X,Y)),X_118) = least_upper_bound(multiply(X_119,X_118),multiply(X,multiply(Y,X_118))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_118),multiply(X,multiply(Y,X_118))) )],[refute_0_1335,refute_0_1336]) ).

cnf(refute_0_1338,plain,
    multiply(least_upper_bound(X_119,multiply(X,Y)),X_118) = least_upper_bound(multiply(X_119,X_118),multiply(X,multiply(Y,X_118))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,multiply(X,Y)),X_118),least_upper_bound(multiply(X_119,X_118),multiply(multiply(X,Y),X_118))) )],[refute_0_1334,refute_0_1337]) ).

cnf(refute_0_1339,plain,
    ( multiply(least_upper_bound(X_119,multiply(X,Y)),X_118) != least_upper_bound(multiply(X_119,X_118),multiply(X,multiply(Y,X_118)))
    | least_upper_bound(multiply(X_119,X_118),multiply(X,multiply(Y,X_118))) = multiply(least_upper_bound(X_119,multiply(X,Y)),X_118) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_119,multiply(X,Y)),X_118))),bind(Y0,$fot(least_upper_bound(multiply(X_119,X_118),multiply(X,multiply(Y,X_118)))))]]) ).

cnf(refute_0_1340,plain,
    least_upper_bound(multiply(X_119,X_118),multiply(X,multiply(Y,X_118))) = multiply(least_upper_bound(X_119,multiply(X,Y)),X_118),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,multiply(X,Y)),X_118),least_upper_bound(multiply(X_119,X_118),multiply(X,multiply(Y,X_118)))) )],[refute_0_1338,refute_0_1339]) ).

cnf(refute_0_1341,plain,
    least_upper_bound(multiply(inverse(X_345),X_344),multiply(Z,multiply(X_343,X_344))) = multiply(least_upper_bound(inverse(X_345),multiply(Z,X_343)),X_344),
    inference(subst,[],[refute_0_1340:[bind(X,$fot(Z)),bind(Y,$fot(X_343)),bind(X_118,$fot(X_344)),bind(X_119,$fot(inverse(X_345)))]]) ).

cnf(refute_0_1342,plain,
    ( multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)) != least_upper_bound(multiply(inverse(X_345),X_344),multiply(Z,multiply(X_343,X_344)))
    | least_upper_bound(multiply(inverse(X_345),X_344),multiply(Z,multiply(X_343,X_344))) != multiply(least_upper_bound(inverse(X_345),multiply(Z,X_343)),X_344)
    | multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)) = multiply(least_upper_bound(inverse(X_345),multiply(Z,X_343)),X_344) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)),multiply(least_upper_bound(inverse(X_345),multiply(Z,X_343)),X_344)) ),[0],$fot(least_upper_bound(multiply(inverse(X_345),X_344),multiply(Z,multiply(X_343,X_344))))]]) ).

cnf(refute_0_1343,plain,
    ( multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)) != least_upper_bound(multiply(inverse(X_345),X_344),multiply(Z,multiply(X_343,X_344)))
    | multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)) = multiply(least_upper_bound(inverse(X_345),multiply(Z,X_343)),X_344) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_345),X_344),multiply(Z,multiply(X_343,X_344))),multiply(least_upper_bound(inverse(X_345),multiply(Z,X_343)),X_344)) )],[refute_0_1341,refute_0_1342]) ).

cnf(refute_0_1344,plain,
    multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)) = multiply(least_upper_bound(inverse(X_345),multiply(Z,X_343)),X_344),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(X_343,X_345)),Z),multiply(X_343,X_344)),least_upper_bound(multiply(inverse(X_345),X_344),multiply(Z,multiply(X_343,X_344)))) )],[refute_0_1333,refute_0_1343]) ).

cnf(refute_0_1345,plain,
    multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))) = multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)),
    inference(subst,[],[refute_0_1344:[bind(Z,$fot(multiply(greatest_lower_bound(inverse(a),inverse(c)),b))),bind(X_343,$fot(greatest_lower_bound(a,c))),bind(X_344,$fot(inverse(b))),bind(X_345,$fot(inverse(b)))]]) ).

cnf(refute_0_1346,plain,
    ( multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))) != multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))
    | multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) != multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))
    | multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))) = multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))))),bind(Y0,$fot(multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)))),bind(Z0,$fot(multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))))]]) ).

cnf(refute_0_1347,plain,
    ( multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) != multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))
    | multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))) = multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))),multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))) )],[refute_0_1345,refute_0_1346]) ).

cnf(refute_0_1348,plain,
    multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))) = multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(b)),multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)),multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))) )],[refute_0_1319,refute_0_1347]) ).

cnf(refute_0_1349,plain,
    multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) = multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))),
    inference(subst,[],[refute_0_1344:[bind(Z,$fot(greatest_lower_bound(inverse(a),inverse(c)))),bind(X_343,$fot(b)),bind(X_344,$fot(multiply(greatest_lower_bound(a,c),inverse(b)))),bind(X_345,$fot(multiply(greatest_lower_bound(a,c),inverse(b))))]]) ).

cnf(refute_0_1350,plain,
    ( multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) != multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b)))
    | multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))) != multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))
    | multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) = multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))),bind(Y0,$fot(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))))),bind(Z0,$fot(multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))))]]) ).

cnf(refute_0_1351,plain,
    ( multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))) != multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))
    | multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) = multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b)))) )],[refute_0_1349,refute_0_1350]) ).

cnf(refute_0_1352,plain,
    multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) = multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(greatest_lower_bound(a,c),inverse(b))),multiply(greatest_lower_bound(inverse(a),inverse(c)),b)),multiply(greatest_lower_bound(a,c),inverse(b))),multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))) )],[refute_0_1348,refute_0_1351]) ).

cnf(refute_0_1353,plain,
    ( multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) != multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))
    | multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) != multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))
    | multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) = multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))))),bind(Y0,$fot(multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)))),bind(Z0,$fot(multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))))]]) ).

cnf(refute_0_1354,plain,
    ( multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)) != multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))
    | multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) = multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b))) )],[refute_0_1352,refute_0_1353]) ).

cnf(refute_0_1355,plain,
    multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) = multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,multiply(multiply(greatest_lower_bound(inverse(a),inverse(c)),b),greatest_lower_bound(a,c))),inverse(b)),multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))) )],[refute_0_1197,refute_0_1354]) ).

cnf(refute_0_1356,plain,
    ( multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) != multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))
    | multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) != identity
    | multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),identity) ),[0],$fot(multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)))]]) ).

cnf(refute_0_1357,plain,
    ( multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))) != identity
    | multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)) = identity ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))) )],[refute_0_1355,refute_0_1356]) ).

cnf(refute_0_1358,plain,
    multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)) = identity,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),greatest_lower_bound(inverse(a),inverse(c))),multiply(b,multiply(greatest_lower_bound(a,c),inverse(b)))),identity) )],[refute_0_1188,refute_0_1357]) ).

cnf(refute_0_1359,plain,
    ( multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) != greatest_lower_bound(multiply(Y,inverse(b)),multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)))
    | multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)) != identity
    | multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) = greatest_lower_bound(multiply(Y,inverse(b)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)),greatest_lower_bound(multiply(Y,inverse(b)),multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1360,plain,
    ( multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) != greatest_lower_bound(multiply(Y,inverse(b)),multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)))
    | multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) = greatest_lower_bound(multiply(Y,inverse(b)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)),identity) )],[refute_0_1358,refute_0_1359]) ).

cnf(refute_0_1361,plain,
    multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) = greatest_lower_bound(multiply(Y,inverse(b)),identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)),greatest_lower_bound(multiply(Y,inverse(b)),multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)))) )],[refute_0_998,refute_0_1360]) ).

cnf(refute_0_1362,plain,
    greatest_lower_bound(identity,multiply(Y,inverse(b))) = multiply(greatest_lower_bound(b,Y),inverse(b)),
    inference(subst,[],[refute_0_948:[bind(X_134,$fot(Y)),bind(X_135,$fot(b))]]) ).

cnf(refute_0_1363,plain,
    greatest_lower_bound(multiply(Y,inverse(b)),identity) = greatest_lower_bound(identity,multiply(Y,inverse(b))),
    inference(subst,[],[refute_0_46:[bind(X,$fot(identity)),bind(Y,$fot(multiply(Y,inverse(b))))]]) ).

cnf(refute_0_1364,plain,
    ( greatest_lower_bound(multiply(Y,inverse(b)),identity) != greatest_lower_bound(identity,multiply(Y,inverse(b)))
    | greatest_lower_bound(identity,multiply(Y,inverse(b))) != multiply(greatest_lower_bound(b,Y),inverse(b))
    | greatest_lower_bound(multiply(Y,inverse(b)),identity) = multiply(greatest_lower_bound(b,Y),inverse(b)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(multiply(Y,inverse(b)),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(Y,inverse(b))))),bind(Z0,$fot(multiply(greatest_lower_bound(b,Y),inverse(b))))]]) ).

cnf(refute_0_1365,plain,
    ( greatest_lower_bound(identity,multiply(Y,inverse(b))) != multiply(greatest_lower_bound(b,Y),inverse(b))
    | greatest_lower_bound(multiply(Y,inverse(b)),identity) = multiply(greatest_lower_bound(b,Y),inverse(b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Y,inverse(b)),identity),greatest_lower_bound(identity,multiply(Y,inverse(b)))) )],[refute_0_1363,refute_0_1364]) ).

cnf(refute_0_1366,plain,
    greatest_lower_bound(multiply(Y,inverse(b)),identity) = multiply(greatest_lower_bound(b,Y),inverse(b)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(Y,inverse(b))),multiply(greatest_lower_bound(b,Y),inverse(b))) )],[refute_0_1362,refute_0_1365]) ).

cnf(refute_0_1367,plain,
    ( multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) != greatest_lower_bound(multiply(Y,inverse(b)),identity)
    | greatest_lower_bound(multiply(Y,inverse(b)),identity) != multiply(greatest_lower_bound(b,Y),inverse(b))
    | multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) = multiply(greatest_lower_bound(b,Y),inverse(b)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)),multiply(greatest_lower_bound(b,Y),inverse(b))) ),[0],$fot(greatest_lower_bound(multiply(Y,inverse(b)),identity))]]) ).

cnf(refute_0_1368,plain,
    ( multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) != greatest_lower_bound(multiply(Y,inverse(b)),identity)
    | multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) = multiply(greatest_lower_bound(b,Y),inverse(b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Y,inverse(b)),identity),multiply(greatest_lower_bound(b,Y),inverse(b))) )],[refute_0_1366,refute_0_1367]) ).

cnf(refute_0_1369,plain,
    multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) = multiply(greatest_lower_bound(b,Y),inverse(b)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)),greatest_lower_bound(multiply(Y,inverse(b)),identity)) )],[refute_0_1361,refute_0_1368]) ).

cnf(refute_0_1370,plain,
    inverse(inverse(b)) = multiply(inverse(multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_34:[bind(X_83,$fot(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))),bind(X_84,$fot(inverse(b)))]]) ).

cnf(refute_0_1371,plain,
    ( multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)) != identity
    | inverse(inverse(b)) != multiply(inverse(multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))
    | inverse(inverse(b)) = multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(b)),multiply(inverse(multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))) ),[1,0,0],$fot(identity)]]) ).

cnf(refute_0_1372,plain,
    ( inverse(inverse(b)) != multiply(inverse(multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))
    | inverse(inverse(b)) = multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b)),identity) )],[refute_0_1358,refute_0_1371]) ).

cnf(refute_0_1373,plain,
    inverse(inverse(b)) = multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),multiply(inverse(multiply(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),inverse(b))),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))) )],[refute_0_1370,refute_0_1372]) ).

cnf(refute_0_1374,plain,
    inverse(inverse(b)) = b,
    inference(subst,[],[p12_2:[bind(X,$fot(b))]]) ).

cnf(refute_0_1375,plain,
    ( inverse(inverse(b)) != multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))
    | inverse(inverse(b)) != b
    | b = multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(b)),multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))) ),[0],$fot(b)]]) ).

cnf(refute_0_1376,plain,
    ( inverse(inverse(b)) != multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))
    | b = multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),b) )],[refute_0_1374,refute_0_1375]) ).

cnf(refute_0_1377,plain,
    multiply(identity,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1378,plain,
    multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),
    introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1379,plain,
    ( multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) != multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))
    | inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1380,plain,
    ( inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))) )],[refute_0_1378,refute_0_1379]) ).

cnf(refute_0_1381,plain,
    multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = multiply(identity,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p12_1,refute_0_1380]) ).

cnf(refute_0_1382,plain,
    ( multiply(identity,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) != least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))
    | multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) != multiply(identity,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))
    | multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))))),bind(Y0,$fot(multiply(identity,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))))),bind(Z0,$fot(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1383,plain,
    ( multiply(identity,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) != least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))
    | multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),multiply(identity,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))) )],[refute_0_1381,refute_0_1382]) ).

cnf(refute_0_1384,plain,
    multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) )],[refute_0_1377,refute_0_1383]) ).

cnf(refute_0_1385,plain,
    ( multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) != least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))
    | b != multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))
    | b = least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))) ),[1],$fot(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_1386,plain,
    ( b != multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))
    | b = least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) )],[refute_0_1384,refute_0_1385]) ).

cnf(refute_0_1387,plain,
    ( inverse(inverse(b)) != multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))
    | b = least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(b,multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))) )],[refute_0_1376,refute_0_1386]) ).

cnf(refute_0_1388,plain,
    b = least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),multiply(inverse(identity),least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))) )],[refute_0_1373,refute_0_1387]) ).

cnf(refute_0_1389,plain,
    ( b != least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))
    | least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) = b ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(b)),bind(Y0,$fot(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1390,plain,
    least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) = b,
    inference(resolve,[$cnf( $equal(b,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) )],[refute_0_1388,refute_0_1389]) ).

cnf(refute_0_1391,plain,
    greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1392,plain,
    ( greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) != greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))
    | least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) != b
    | greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = greatest_lower_bound(Y,b) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))) ),[1,1],$fot(b)]]) ).

cnf(refute_0_1393,plain,
    ( least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))) != b
    | greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = greatest_lower_bound(Y,b) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))))) )],[refute_0_1391,refute_0_1392]) ).

cnf(refute_0_1394,plain,
    greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) = greatest_lower_bound(Y,b),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c)))),b) )],[refute_0_1390,refute_0_1393]) ).

cnf(refute_0_1395,plain,
    multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) = multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)))]]) ).

cnf(refute_0_1396,plain,
    ( multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) != multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b))
    | greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) != greatest_lower_bound(Y,b)
    | multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) = multiply(greatest_lower_bound(Y,b),inverse(b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)),multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b))) ),[1,0],$fot(greatest_lower_bound(Y,b))]]) ).

cnf(refute_0_1397,plain,
    ( greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))) != greatest_lower_bound(Y,b)
    | multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) = multiply(greatest_lower_bound(Y,b),inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)),multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b))) )],[refute_0_1395,refute_0_1396]) ).

cnf(refute_0_1398,plain,
    multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) = multiply(greatest_lower_bound(Y,b),inverse(b)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),greatest_lower_bound(Y,b)) )],[refute_0_1394,refute_0_1397]) ).

cnf(refute_0_1399,plain,
    ( multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) != multiply(greatest_lower_bound(Y,b),inverse(b))
    | multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) != multiply(greatest_lower_bound(b,Y),inverse(b))
    | multiply(greatest_lower_bound(Y,b),inverse(b)) = multiply(greatest_lower_bound(b,Y),inverse(b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)),multiply(greatest_lower_bound(b,Y),inverse(b))) ),[0],$fot(multiply(greatest_lower_bound(Y,b),inverse(b)))]]) ).

cnf(refute_0_1400,plain,
    ( multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)) != multiply(greatest_lower_bound(b,Y),inverse(b))
    | multiply(greatest_lower_bound(Y,b),inverse(b)) = multiply(greatest_lower_bound(b,Y),inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)),multiply(greatest_lower_bound(Y,b),inverse(b))) )],[refute_0_1398,refute_0_1399]) ).

cnf(refute_0_1401,plain,
    multiply(greatest_lower_bound(Y,b),inverse(b)) = multiply(greatest_lower_bound(b,Y),inverse(b)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,least_upper_bound(b,multiply(greatest_lower_bound(inverse(a),inverse(c)),multiply(b,greatest_lower_bound(a,c))))),inverse(b)),multiply(greatest_lower_bound(b,Y),inverse(b))) )],[refute_0_1369,refute_0_1400]) ).

cnf(refute_0_1402,plain,
    ( multiply(greatest_lower_bound(Y,b),inverse(b)) != multiply(greatest_lower_bound(b,Y),inverse(b))
    | multiply(greatest_lower_bound(b,Y),inverse(b)) = multiply(greatest_lower_bound(Y,b),inverse(b)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(greatest_lower_bound(Y,b),inverse(b)))),bind(Y0,$fot(multiply(greatest_lower_bound(b,Y),inverse(b))))]]) ).

cnf(refute_0_1403,plain,
    multiply(greatest_lower_bound(b,Y),inverse(b)) = multiply(greatest_lower_bound(Y,b),inverse(b)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,b),inverse(b)),multiply(greatest_lower_bound(b,Y),inverse(b))) )],[refute_0_1401,refute_0_1402]) ).

cnf(refute_0_1404,plain,
    multiply(greatest_lower_bound(b,a),inverse(b)) = multiply(greatest_lower_bound(a,b),inverse(b)),
    inference(subst,[],[refute_0_1403:[bind(Y,$fot(a))]]) ).

cnf(refute_0_1405,plain,
    greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(greatest_lower_bound(b,a),inverse(b)),
    inference(subst,[],[refute_0_948:[bind(X_134,$fot(a)),bind(X_135,$fot(b))]]) ).

cnf(refute_0_1406,plain,
    ( multiply(greatest_lower_bound(b,a),inverse(b)) != multiply(greatest_lower_bound(a,b),inverse(b))
    | greatest_lower_bound(identity,multiply(a,inverse(b))) != multiply(greatest_lower_bound(b,a),inverse(b))
    | greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(greatest_lower_bound(a,b),inverse(b)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(identity,multiply(a,inverse(b))))),bind(Y0,$fot(multiply(greatest_lower_bound(b,a),inverse(b)))),bind(Z0,$fot(multiply(greatest_lower_bound(a,b),inverse(b))))]]) ).

cnf(refute_0_1407,plain,
    ( multiply(greatest_lower_bound(b,a),inverse(b)) != multiply(greatest_lower_bound(a,b),inverse(b))
    | greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(greatest_lower_bound(a,b),inverse(b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,inverse(b))),multiply(greatest_lower_bound(b,a),inverse(b))) )],[refute_0_1405,refute_0_1406]) ).

cnf(refute_0_1408,plain,
    greatest_lower_bound(identity,multiply(a,inverse(b))) = multiply(greatest_lower_bound(a,b),inverse(b)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,a),inverse(b)),multiply(greatest_lower_bound(a,b),inverse(b))) )],[refute_0_1404,refute_0_1407]) ).

cnf(refute_0_1409,plain,
    multiply(multiply(X_80,inverse(X_80)),X_82) = multiply(X_80,multiply(inverse(X_80),X_82)),
    inference(subst,[],[associativity:[bind(X,$fot(X_80)),bind(Y,$fot(inverse(X_80))),bind(Z,$fot(X_82))]]) ).

cnf(refute_0_1410,plain,
    multiply(X_80,inverse(X_80)) = identity,
    inference(subst,[],[refute_0_40:[bind(X,$fot(X_80))]]) ).

cnf(refute_0_1411,plain,
    ( multiply(X_80,inverse(X_80)) != identity
    | multiply(multiply(X_80,inverse(X_80)),X_82) != multiply(X_80,multiply(inverse(X_80),X_82))
    | multiply(identity,X_82) = multiply(X_80,multiply(inverse(X_80),X_82)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_80,inverse(X_80)),X_82),multiply(X_80,multiply(inverse(X_80),X_82))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_1412,plain,
    ( multiply(multiply(X_80,inverse(X_80)),X_82) != multiply(X_80,multiply(inverse(X_80),X_82))
    | multiply(identity,X_82) = multiply(X_80,multiply(inverse(X_80),X_82)) ),
    inference(resolve,[$cnf( $equal(multiply(X_80,inverse(X_80)),identity) )],[refute_0_1410,refute_0_1411]) ).

cnf(refute_0_1413,plain,
    multiply(identity,X_82) = multiply(X_80,multiply(inverse(X_80),X_82)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_80,inverse(X_80)),X_82),multiply(X_80,multiply(inverse(X_80),X_82))) )],[refute_0_1409,refute_0_1412]) ).

cnf(refute_0_1414,plain,
    ( multiply(identity,X_82) != X_82
    | multiply(identity,X_82) != multiply(X_80,multiply(inverse(X_80),X_82))
    | X_82 = multiply(X_80,multiply(inverse(X_80),X_82)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_82),multiply(X_80,multiply(inverse(X_80),X_82))) ),[0],$fot(X_82)]]) ).

cnf(refute_0_1415,plain,
    ( multiply(identity,X_82) != multiply(X_80,multiply(inverse(X_80),X_82))
    | X_82 = multiply(X_80,multiply(inverse(X_80),X_82)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_82),X_82) )],[refute_0_6,refute_0_1414]) ).

cnf(refute_0_1416,plain,
    X_82 = multiply(X_80,multiply(inverse(X_80),X_82)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_82),multiply(X_80,multiply(inverse(X_80),X_82))) )],[refute_0_1413,refute_0_1415]) ).

cnf(refute_0_1417,plain,
    ( X_82 != multiply(X_80,multiply(inverse(X_80),X_82))
    | multiply(X_80,multiply(inverse(X_80),X_82)) = X_82 ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(X_82)),bind(Y0,$fot(multiply(X_80,multiply(inverse(X_80),X_82))))]]) ).

cnf(refute_0_1418,plain,
    multiply(X_80,multiply(inverse(X_80),X_82)) = X_82,
    inference(resolve,[$cnf( $equal(X_82,multiply(X_80,multiply(inverse(X_80),X_82))) )],[refute_0_1416,refute_0_1417]) ).

cnf(refute_0_1419,plain,
    multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),b)) = b,
    inference(subst,[],[refute_0_1418:[bind(X_80,$fot(greatest_lower_bound(a,c))),bind(X_82,$fot(b))]]) ).

cnf(refute_0_1420,plain,
    inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(b,c)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(b,c)))]]) ).

cnf(refute_0_1421,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | inverse(greatest_lower_bound(b,c)) != inverse(greatest_lower_bound(b,c))
    | inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,c)),inverse(greatest_lower_bound(b,c))) ),[1,0],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_1422,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,c)),inverse(greatest_lower_bound(b,c))) )],[refute_0_1420,refute_0_1421]) ).

cnf(refute_0_1423,plain,
    inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_294,refute_0_1422]) ).

cnf(refute_0_1424,plain,
    multiply(inverse(greatest_lower_bound(b,c)),b) = multiply(inverse(greatest_lower_bound(b,c)),b),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(b,c)),b))]]) ).

cnf(refute_0_1425,plain,
    ( multiply(inverse(greatest_lower_bound(b,c)),b) != multiply(inverse(greatest_lower_bound(b,c)),b)
    | inverse(greatest_lower_bound(b,c)) != inverse(greatest_lower_bound(a,c))
    | multiply(inverse(greatest_lower_bound(b,c)),b) = multiply(inverse(greatest_lower_bound(a,c)),b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(b,c)),b),multiply(inverse(greatest_lower_bound(b,c)),b)) ),[1,0],$fot(inverse(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_1426,plain,
    ( inverse(greatest_lower_bound(b,c)) != inverse(greatest_lower_bound(a,c))
    | multiply(inverse(greatest_lower_bound(b,c)),b) = multiply(inverse(greatest_lower_bound(a,c)),b) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(b,c)),b),multiply(inverse(greatest_lower_bound(b,c)),b)) )],[refute_0_1424,refute_0_1425]) ).

cnf(refute_0_1427,plain,
    multiply(inverse(greatest_lower_bound(b,c)),b) = multiply(inverse(greatest_lower_bound(a,c)),b),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,c)),inverse(greatest_lower_bound(a,c))) )],[refute_0_1423,refute_0_1426]) ).

cnf(refute_0_1428,plain,
    multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)) = multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))]]) ).

cnf(refute_0_1429,plain,
    ( multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)) != multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))
    | multiply(inverse(greatest_lower_bound(b,c)),b) != multiply(inverse(greatest_lower_bound(a,c)),b)
    | multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)) = multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)),multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) ),[1,1],$fot(multiply(inverse(greatest_lower_bound(a,c)),b))]]) ).

cnf(refute_0_1430,plain,
    ( multiply(inverse(greatest_lower_bound(b,c)),b) != multiply(inverse(greatest_lower_bound(a,c)),b)
    | multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)) = multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),b)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)),multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) )],[refute_0_1428,refute_0_1429]) ).

cnf(refute_0_1431,plain,
    multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)) = multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),b)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(b,c)),b),multiply(inverse(greatest_lower_bound(a,c)),b)) )],[refute_0_1427,refute_0_1430]) ).

cnf(refute_0_1432,plain,
    ( multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),b)) != b
    | multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)) != multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),b))
    | multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)) = b ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))),bind(Y0,$fot(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),b)))),bind(Z0,$fot(b))]]) ).

cnf(refute_0_1433,plain,
    ( multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),b)) != b
    | multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)) = b ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)),multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),b))) )],[refute_0_1431,refute_0_1432]) ).

cnf(refute_0_1434,plain,
    multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)) = b,
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),b)),b) )],[refute_0_1419,refute_0_1433]) ).

cnf(refute_0_1435,plain,
    inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) = inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))),
    introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))))]]) ).

cnf(refute_0_1436,plain,
    ( multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)) != b
    | inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) != inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))
    | inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) = inverse(b) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))),inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))) ),[1,0],$fot(b)]]) ).

cnf(refute_0_1437,plain,
    ( multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)) != b
    | inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) = inverse(b) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))),inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))) )],[refute_0_1435,refute_0_1436]) ).

cnf(refute_0_1438,plain,
    inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) = inverse(b),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)),b) )],[refute_0_1434,refute_0_1437]) ).

cnf(refute_0_1439,plain,
    inverse(multiply(X,multiply(inverse(X_21),X_22))) = multiply(inverse(multiply(inverse(X_21),X_22)),inverse(X)),
    inference(subst,[],[p12_3:[bind(Y,$fot(multiply(inverse(X_21),X_22)))]]) ).

cnf(refute_0_1440,plain,
    inverse(multiply(inverse(X_21),X_22)) = multiply(inverse(X_22),X_21),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_21)),bind(X_18,$fot(X_22))]]) ).

cnf(refute_0_1441,plain,
    ( inverse(multiply(X,multiply(inverse(X_21),X_22))) != multiply(inverse(multiply(inverse(X_21),X_22)),inverse(X))
    | inverse(multiply(inverse(X_21),X_22)) != multiply(inverse(X_22),X_21)
    | inverse(multiply(X,multiply(inverse(X_21),X_22))) = multiply(multiply(inverse(X_22),X_21),inverse(X)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,multiply(inverse(X_21),X_22))),multiply(inverse(multiply(inverse(X_21),X_22)),inverse(X))) ),[1,0],$fot(multiply(inverse(X_22),X_21))]]) ).

cnf(refute_0_1442,plain,
    ( inverse(multiply(X,multiply(inverse(X_21),X_22))) != multiply(inverse(multiply(inverse(X_21),X_22)),inverse(X))
    | inverse(multiply(X,multiply(inverse(X_21),X_22))) = multiply(multiply(inverse(X_22),X_21),inverse(X)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_21),X_22)),multiply(inverse(X_22),X_21)) )],[refute_0_1440,refute_0_1441]) ).

cnf(refute_0_1443,plain,
    inverse(multiply(X,multiply(inverse(X_21),X_22))) = multiply(multiply(inverse(X_22),X_21),inverse(X)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,multiply(inverse(X_21),X_22))),multiply(inverse(multiply(inverse(X_21),X_22)),inverse(X))) )],[refute_0_1439,refute_0_1442]) ).

cnf(refute_0_1444,plain,
    multiply(multiply(inverse(X_22),X_21),inverse(X)) = multiply(inverse(X_22),multiply(X_21,inverse(X))),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_22))),bind(Y,$fot(X_21)),bind(Z,$fot(inverse(X)))]]) ).

cnf(refute_0_1445,plain,
    ( multiply(multiply(inverse(X_22),X_21),inverse(X)) != multiply(inverse(X_22),multiply(X_21,inverse(X)))
    | inverse(multiply(X,multiply(inverse(X_21),X_22))) != multiply(multiply(inverse(X_22),X_21),inverse(X))
    | inverse(multiply(X,multiply(inverse(X_21),X_22))) = multiply(inverse(X_22),multiply(X_21,inverse(X))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,multiply(inverse(X_21),X_22))),multiply(multiply(inverse(X_22),X_21),inverse(X))) ),[1],$fot(multiply(inverse(X_22),multiply(X_21,inverse(X))))]]) ).

cnf(refute_0_1446,plain,
    ( inverse(multiply(X,multiply(inverse(X_21),X_22))) != multiply(multiply(inverse(X_22),X_21),inverse(X))
    | inverse(multiply(X,multiply(inverse(X_21),X_22))) = multiply(inverse(X_22),multiply(X_21,inverse(X))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_22),X_21),inverse(X)),multiply(inverse(X_22),multiply(X_21,inverse(X)))) )],[refute_0_1444,refute_0_1445]) ).

cnf(refute_0_1447,plain,
    inverse(multiply(X,multiply(inverse(X_21),X_22))) = multiply(inverse(X_22),multiply(X_21,inverse(X))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,multiply(inverse(X_21),X_22))),multiply(multiply(inverse(X_22),X_21),inverse(X))) )],[refute_0_1443,refute_0_1446]) ).

cnf(refute_0_1448,plain,
    ( inverse(multiply(X,multiply(inverse(X_21),X_22))) != multiply(inverse(X_22),multiply(X_21,inverse(X)))
    | multiply(inverse(X_22),multiply(X_21,inverse(X))) = inverse(multiply(X,multiply(inverse(X_21),X_22))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(multiply(X,multiply(inverse(X_21),X_22))))),bind(Y0,$fot(multiply(inverse(X_22),multiply(X_21,inverse(X)))))]]) ).

cnf(refute_0_1449,plain,
    multiply(inverse(X_22),multiply(X_21,inverse(X))) = inverse(multiply(X,multiply(inverse(X_21),X_22))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,multiply(inverse(X_21),X_22))),multiply(inverse(X_22),multiply(X_21,inverse(X)))) )],[refute_0_1447,refute_0_1448]) ).

cnf(refute_0_1450,plain,
    multiply(inverse(b),multiply(greatest_lower_bound(b,c),inverse(greatest_lower_bound(a,c)))) = inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))),
    inference(subst,[],[refute_0_1449:[bind(X,$fot(greatest_lower_bound(a,c))),bind(X_21,$fot(greatest_lower_bound(b,c))),bind(X_22,$fot(b))]]) ).

cnf(refute_0_1451,plain,
    multiply(multiply(inverse(X_366),greatest_lower_bound(X_365,X_366)),Z) = multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_366))),bind(Y,$fot(greatest_lower_bound(X_365,X_366)))]]) ).

cnf(refute_0_1452,plain,
    multiply(inverse(X_366),greatest_lower_bound(X_365,X_366)) = multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)),
    inference(subst,[],[refute_0_140:[bind(X_104,$fot(X_365)),bind(X_105,$fot(X_366))]]) ).

cnf(refute_0_1453,plain,
    ( multiply(multiply(inverse(X_366),greatest_lower_bound(X_365,X_366)),Z) != multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z))
    | multiply(inverse(X_366),greatest_lower_bound(X_365,X_366)) != multiply(inverse(X_366),greatest_lower_bound(X_366,X_365))
    | multiply(multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)),Z) = multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_366),greatest_lower_bound(X_365,X_366)),Z),multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z))) ),[0,0],$fot(multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)))]]) ).

cnf(refute_0_1454,plain,
    ( multiply(multiply(inverse(X_366),greatest_lower_bound(X_365,X_366)),Z) != multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z))
    | multiply(multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)),Z) = multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_366),greatest_lower_bound(X_365,X_366)),multiply(inverse(X_366),greatest_lower_bound(X_366,X_365))) )],[refute_0_1452,refute_0_1453]) ).

cnf(refute_0_1455,plain,
    multiply(multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)),Z) = multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_366),greatest_lower_bound(X_365,X_366)),Z),multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z))) )],[refute_0_1451,refute_0_1454]) ).

cnf(refute_0_1456,plain,
    multiply(multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)),Z) = multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_366))),bind(Y,$fot(greatest_lower_bound(X_366,X_365)))]]) ).

cnf(refute_0_1457,plain,
    ( multiply(multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)),Z) != multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z))
    | multiply(multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)),Z) != multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z))
    | multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z)) = multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)),Z),multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z))) ),[0],$fot(multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z)))]]) ).

cnf(refute_0_1458,plain,
    ( multiply(multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)),Z) != multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z))
    | multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z)) = multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)),Z),multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z))) )],[refute_0_1456,refute_0_1457]) ).

cnf(refute_0_1459,plain,
    multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z)) = multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_366),greatest_lower_bound(X_366,X_365)),Z),multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z))) )],[refute_0_1455,refute_0_1458]) ).

cnf(refute_0_1460,plain,
    ( multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z)) != multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z))
    | multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z)) = multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z)))),bind(Y0,$fot(multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z))))]]) ).

cnf(refute_0_1461,plain,
    multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z)) = multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_366),multiply(greatest_lower_bound(X_366,X_365),Z)),multiply(inverse(X_366),multiply(greatest_lower_bound(X_365,X_366),Z))) )],[refute_0_1459,refute_0_1460]) ).

cnf(refute_0_1462,plain,
    multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))) = multiply(inverse(b),multiply(greatest_lower_bound(b,c),inverse(greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_1461:[bind(Z,$fot(inverse(greatest_lower_bound(a,c)))),bind(X_365,$fot(c)),bind(X_366,$fot(b))]]) ).

cnf(refute_0_1463,plain,
    ( multiply(inverse(b),multiply(greatest_lower_bound(b,c),inverse(greatest_lower_bound(a,c)))) != inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))
    | multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))) != multiply(inverse(b),multiply(greatest_lower_bound(b,c),inverse(greatest_lower_bound(a,c))))
    | multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))) = inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))))),bind(Y0,$fot(multiply(inverse(b),multiply(greatest_lower_bound(b,c),inverse(greatest_lower_bound(a,c)))))),bind(Z0,$fot(inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))))]]) ).

cnf(refute_0_1464,plain,
    ( multiply(inverse(b),multiply(greatest_lower_bound(b,c),inverse(greatest_lower_bound(a,c)))) != inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))
    | multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))) = inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))),multiply(inverse(b),multiply(greatest_lower_bound(b,c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_1462,refute_0_1463]) ).

cnf(refute_0_1465,plain,
    multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))) = inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),multiply(greatest_lower_bound(b,c),inverse(greatest_lower_bound(a,c)))),inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))) )],[refute_0_1450,refute_0_1464]) ).

cnf(refute_0_1466,plain,
    multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) = multiply(inverse(multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372))))),multiply(greatest_lower_bound(X_372,X_373),Z)),
    inference(subst,[],[refute_0_1327:[bind(Y,$fot(greatest_lower_bound(X_372,X_373))),bind(X_88,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))))]]) ).

cnf(refute_0_1467,plain,
    X_373 = multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),
    inference(subst,[],[refute_0_217:[bind(X_104,$fot(X_372)),bind(X_105,$fot(X_373))]]) ).

cnf(refute_0_1468,plain,
    ( X_373 != multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372))))
    | multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))) = X_373 ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(X_373)),bind(Y0,$fot(multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372))))))]]) ).

cnf(refute_0_1469,plain,
    multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))) = X_373,
    inference(resolve,[$cnf( $equal(X_373,multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372))))) )],[refute_0_1467,refute_0_1468]) ).

cnf(refute_0_1470,plain,
    ( multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))) != X_373
    | multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) != multiply(inverse(multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372))))),multiply(greatest_lower_bound(X_372,X_373),Z))
    | multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) = multiply(inverse(X_373),multiply(greatest_lower_bound(X_372,X_373),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z),multiply(inverse(multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372))))),multiply(greatest_lower_bound(X_372,X_373),Z))) ),[1,0,0],$fot(X_373)]]) ).

cnf(refute_0_1471,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) != multiply(inverse(multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372))))),multiply(greatest_lower_bound(X_372,X_373),Z))
    | multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) = multiply(inverse(X_373),multiply(greatest_lower_bound(X_372,X_373),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),X_373) )],[refute_0_1469,refute_0_1470]) ).

cnf(refute_0_1472,plain,
    multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) = multiply(inverse(X_373),multiply(greatest_lower_bound(X_372,X_373),Z)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z),multiply(inverse(multiply(greatest_lower_bound(X_372,X_373),inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372))))),multiply(greatest_lower_bound(X_372,X_373),Z))) )],[refute_0_1466,refute_0_1471]) ).

cnf(refute_0_1473,plain,
    inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))) = greatest_lower_bound(identity,multiply(inverse(X_373),X_372)),
    inference(subst,[],[p12_2:[bind(X,$fot(greatest_lower_bound(identity,multiply(inverse(X_373),X_372))))]]) ).

cnf(refute_0_1474,plain,
    multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) = multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z),
    introduced(tautology,[refl,[$fot(multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z))]]) ).

cnf(refute_0_1475,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) != multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z)
    | inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))) != greatest_lower_bound(identity,multiply(inverse(X_373),X_372))
    | multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) = multiply(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z),multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z)) ),[1,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))]]) ).

cnf(refute_0_1476,plain,
    ( inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))) != greatest_lower_bound(identity,multiply(inverse(X_373),X_372))
    | multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) = multiply(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)),Z) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z),multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z)) )],[refute_0_1474,refute_0_1475]) ).

cnf(refute_0_1477,plain,
    multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) = multiply(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)),Z),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),greatest_lower_bound(identity,multiply(inverse(X_373),X_372))) )],[refute_0_1473,refute_0_1476]) ).

cnf(refute_0_1478,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) != multiply(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)),Z)
    | multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) != multiply(inverse(X_373),multiply(greatest_lower_bound(X_372,X_373),Z))
    | multiply(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)),Z) = multiply(inverse(X_373),multiply(greatest_lower_bound(X_372,X_373),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z),multiply(inverse(X_373),multiply(greatest_lower_bound(X_372,X_373),Z))) ),[0],$fot(multiply(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)),Z))]]) ).

cnf(refute_0_1479,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z) != multiply(inverse(X_373),multiply(greatest_lower_bound(X_372,X_373),Z))
    | multiply(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)),Z) = multiply(inverse(X_373),multiply(greatest_lower_bound(X_372,X_373),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z),multiply(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)),Z)) )],[refute_0_1477,refute_0_1478]) ).

cnf(refute_0_1480,plain,
    multiply(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)),Z) = multiply(inverse(X_373),multiply(greatest_lower_bound(X_372,X_373),Z)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,multiply(inverse(X_373),X_372)))),Z),multiply(inverse(X_373),multiply(greatest_lower_bound(X_372,X_373),Z))) )],[refute_0_1472,refute_0_1479]) ).

cnf(refute_0_1481,plain,
    multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))) = multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_1480:[bind(Z,$fot(inverse(greatest_lower_bound(a,c)))),bind(X_372,$fot(c)),bind(X_373,$fot(b))]]) ).

cnf(refute_0_1482,plain,
    ( multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))) != multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c))))
    | multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))) != inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))
    | multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))) = inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))))),bind(Y0,$fot(multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))))),bind(Z0,$fot(inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))))]]) ).

cnf(refute_0_1483,plain,
    ( multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))) != inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))
    | multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))) = inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))),multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c))))) )],[refute_0_1481,refute_0_1482]) ).

cnf(refute_0_1484,plain,
    multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))) = inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),multiply(greatest_lower_bound(c,b),inverse(greatest_lower_bound(a,c)))),inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))) )],[refute_0_1465,refute_0_1483]) ).

cnf(refute_0_1485,plain,
    ( multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))) != inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))
    | inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) != inverse(b)
    | multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))) = inverse(b) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))))),bind(Z0,$fot(inverse(b)))]]) ).

cnf(refute_0_1486,plain,
    ( inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))) != inverse(b)
    | multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))) = inverse(b) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))),inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b)))) )],[refute_0_1484,refute_0_1485]) ).

cnf(refute_0_1487,plain,
    multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))) = inverse(b),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(b,c)),b))),inverse(b)) )],[refute_0_1438,refute_0_1486]) ).

cnf(refute_0_1488,plain,
    multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) = greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),multiply(inverse(X_81),multiply(X_81,X_82))),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(multiply(X_81,X_82))),bind(Y,$fot(X_134)),bind(Z,$fot(inverse(X_81)))]]) ).

cnf(refute_0_1489,plain,
    ( X_82 != multiply(inverse(X_81),multiply(X_81,X_82))
    | multiply(inverse(X_81),multiply(X_81,X_82)) = X_82 ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(X_82)),bind(Y0,$fot(multiply(inverse(X_81),multiply(X_81,X_82))))]]) ).

cnf(refute_0_1490,plain,
    multiply(inverse(X_81),multiply(X_81,X_82)) = X_82,
    inference(resolve,[$cnf( $equal(X_82,multiply(inverse(X_81),multiply(X_81,X_82))) )],[refute_0_9,refute_0_1489]) ).

cnf(refute_0_1491,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) != greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),multiply(inverse(X_81),multiply(X_81,X_82)))
    | multiply(inverse(X_81),multiply(X_81,X_82)) != X_82
    | multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) = greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),X_82) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)),greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),multiply(inverse(X_81),multiply(X_81,X_82)))) ),[1,1],$fot(X_82)]]) ).

cnf(refute_0_1492,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) != greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),multiply(inverse(X_81),multiply(X_81,X_82)))
    | multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) = greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),X_82) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_81),multiply(X_81,X_82)),X_82) )],[refute_0_1490,refute_0_1491]) ).

cnf(refute_0_1493,plain,
    multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) = greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),X_82),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)),greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),multiply(inverse(X_81),multiply(X_81,X_82)))) )],[refute_0_1488,refute_0_1492]) ).

cnf(refute_0_1494,plain,
    greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),X_82) = greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82))),
    inference(subst,[],[refute_0_46:[bind(X,$fot(X_82)),bind(Y,$fot(multiply(X_134,multiply(X_81,X_82))))]]) ).

cnf(refute_0_1495,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) != greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),X_82)
    | greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),X_82) != greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82)))
    | multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) = greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)),greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82)))) ),[0],$fot(greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),X_82))]]) ).

cnf(refute_0_1496,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) != greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),X_82)
    | multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) = greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),X_82),greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82)))) )],[refute_0_1494,refute_0_1495]) ).

cnf(refute_0_1497,plain,
    multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) = greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)),greatest_lower_bound(multiply(X_134,multiply(X_81,X_82)),X_82)) )],[refute_0_1493,refute_0_1496]) ).

cnf(refute_0_1498,plain,
    multiply(greatest_lower_bound(X_134,identity),X_133) = greatest_lower_bound(multiply(X_134,X_133),multiply(identity,X_133)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_133)),bind(Y,$fot(X_134)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_1499,plain,
    multiply(identity,X_133) = X_133,
    inference(subst,[],[left_identity:[bind(X,$fot(X_133))]]) ).

cnf(refute_0_1500,plain,
    ( multiply(greatest_lower_bound(X_134,identity),X_133) != greatest_lower_bound(multiply(X_134,X_133),multiply(identity,X_133))
    | multiply(identity,X_133) != X_133
    | multiply(greatest_lower_bound(X_134,identity),X_133) = greatest_lower_bound(multiply(X_134,X_133),X_133) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_134,identity),X_133),greatest_lower_bound(multiply(X_134,X_133),multiply(identity,X_133))) ),[1,1],$fot(X_133)]]) ).

cnf(refute_0_1501,plain,
    ( multiply(greatest_lower_bound(X_134,identity),X_133) != greatest_lower_bound(multiply(X_134,X_133),multiply(identity,X_133))
    | multiply(greatest_lower_bound(X_134,identity),X_133) = greatest_lower_bound(multiply(X_134,X_133),X_133) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_133),X_133) )],[refute_0_1499,refute_0_1500]) ).

cnf(refute_0_1502,plain,
    multiply(greatest_lower_bound(X_134,identity),X_133) = greatest_lower_bound(multiply(X_134,X_133),X_133),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,identity),X_133),greatest_lower_bound(multiply(X_134,X_133),multiply(identity,X_133))) )],[refute_0_1498,refute_0_1501]) ).

cnf(refute_0_1503,plain,
    greatest_lower_bound(multiply(X_134,X_133),X_133) = greatest_lower_bound(X_133,multiply(X_134,X_133)),
    inference(subst,[],[refute_0_46:[bind(X,$fot(X_133)),bind(Y,$fot(multiply(X_134,X_133)))]]) ).

cnf(refute_0_1504,plain,
    ( multiply(greatest_lower_bound(X_134,identity),X_133) != greatest_lower_bound(multiply(X_134,X_133),X_133)
    | greatest_lower_bound(multiply(X_134,X_133),X_133) != greatest_lower_bound(X_133,multiply(X_134,X_133))
    | multiply(greatest_lower_bound(X_134,identity),X_133) = greatest_lower_bound(X_133,multiply(X_134,X_133)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_134,identity),X_133),greatest_lower_bound(X_133,multiply(X_134,X_133))) ),[0],$fot(greatest_lower_bound(multiply(X_134,X_133),X_133))]]) ).

cnf(refute_0_1505,plain,
    ( multiply(greatest_lower_bound(X_134,identity),X_133) != greatest_lower_bound(multiply(X_134,X_133),X_133)
    | multiply(greatest_lower_bound(X_134,identity),X_133) = greatest_lower_bound(X_133,multiply(X_134,X_133)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_134,X_133),X_133),greatest_lower_bound(X_133,multiply(X_134,X_133))) )],[refute_0_1503,refute_0_1504]) ).

cnf(refute_0_1506,plain,
    multiply(greatest_lower_bound(X_134,identity),X_133) = greatest_lower_bound(X_133,multiply(X_134,X_133)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,identity),X_133),greatest_lower_bound(multiply(X_134,X_133),X_133)) )],[refute_0_1502,refute_0_1505]) ).

cnf(refute_0_1507,plain,
    multiply(greatest_lower_bound(multiply(X,Y),identity),X_136) = greatest_lower_bound(X_136,multiply(multiply(X,Y),X_136)),
    inference(subst,[],[refute_0_1506:[bind(X_133,$fot(X_136)),bind(X_134,$fot(multiply(X,Y)))]]) ).

cnf(refute_0_1508,plain,
    multiply(multiply(X,Y),X_136) = multiply(X,multiply(Y,X_136)),
    inference(subst,[],[associativity:[bind(Z,$fot(X_136))]]) ).

cnf(refute_0_1509,plain,
    ( multiply(multiply(X,Y),X_136) != multiply(X,multiply(Y,X_136))
    | multiply(greatest_lower_bound(multiply(X,Y),identity),X_136) != greatest_lower_bound(X_136,multiply(multiply(X,Y),X_136))
    | multiply(greatest_lower_bound(multiply(X,Y),identity),X_136) = greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(multiply(X,Y),identity),X_136),greatest_lower_bound(X_136,multiply(multiply(X,Y),X_136))) ),[1,1],$fot(multiply(X,multiply(Y,X_136)))]]) ).

cnf(refute_0_1510,plain,
    ( multiply(greatest_lower_bound(multiply(X,Y),identity),X_136) != greatest_lower_bound(X_136,multiply(multiply(X,Y),X_136))
    | multiply(greatest_lower_bound(multiply(X,Y),identity),X_136) = greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_136),multiply(X,multiply(Y,X_136))) )],[refute_0_1508,refute_0_1509]) ).

cnf(refute_0_1511,plain,
    multiply(greatest_lower_bound(multiply(X,Y),identity),X_136) = greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(multiply(X,Y),identity),X_136),greatest_lower_bound(X_136,multiply(multiply(X,Y),X_136))) )],[refute_0_1507,refute_0_1510]) ).

cnf(refute_0_1512,plain,
    multiply(greatest_lower_bound(X_137,identity),X_136) = greatest_lower_bound(X_136,multiply(X_137,X_136)),
    inference(subst,[],[refute_0_1506:[bind(X_133,$fot(X_136)),bind(X_134,$fot(X_137))]]) ).

cnf(refute_0_1513,plain,
    greatest_lower_bound(identity,X_137) = greatest_lower_bound(X_137,identity),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_137))]]) ).

cnf(refute_0_1514,plain,
    ( greatest_lower_bound(identity,X_137) != greatest_lower_bound(X_137,identity)
    | greatest_lower_bound(X_137,identity) = greatest_lower_bound(identity,X_137) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(identity,X_137))),bind(Y0,$fot(greatest_lower_bound(X_137,identity)))]]) ).

cnf(refute_0_1515,plain,
    greatest_lower_bound(X_137,identity) = greatest_lower_bound(identity,X_137),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_137),greatest_lower_bound(X_137,identity)) )],[refute_0_1513,refute_0_1514]) ).

cnf(refute_0_1516,plain,
    ( multiply(greatest_lower_bound(X_137,identity),X_136) != greatest_lower_bound(X_136,multiply(X_137,X_136))
    | greatest_lower_bound(X_137,identity) != greatest_lower_bound(identity,X_137)
    | multiply(greatest_lower_bound(identity,X_137),X_136) = greatest_lower_bound(X_136,multiply(X_137,X_136)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_137,identity),X_136),greatest_lower_bound(X_136,multiply(X_137,X_136))) ),[0,0],$fot(greatest_lower_bound(identity,X_137))]]) ).

cnf(refute_0_1517,plain,
    ( multiply(greatest_lower_bound(X_137,identity),X_136) != greatest_lower_bound(X_136,multiply(X_137,X_136))
    | multiply(greatest_lower_bound(identity,X_137),X_136) = greatest_lower_bound(X_136,multiply(X_137,X_136)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_137,identity),greatest_lower_bound(identity,X_137)) )],[refute_0_1515,refute_0_1516]) ).

cnf(refute_0_1518,plain,
    multiply(greatest_lower_bound(identity,X_137),X_136) = greatest_lower_bound(X_136,multiply(X_137,X_136)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_137,identity),X_136),greatest_lower_bound(X_136,multiply(X_137,X_136))) )],[refute_0_1512,refute_0_1517]) ).

cnf(refute_0_1519,plain,
    ( multiply(greatest_lower_bound(X_134,identity),X_133) != greatest_lower_bound(X_133,multiply(X_134,X_133))
    | greatest_lower_bound(X_133,multiply(X_134,X_133)) = multiply(greatest_lower_bound(X_134,identity),X_133) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(greatest_lower_bound(X_134,identity),X_133))),bind(Y0,$fot(greatest_lower_bound(X_133,multiply(X_134,X_133))))]]) ).

cnf(refute_0_1520,plain,
    greatest_lower_bound(X_133,multiply(X_134,X_133)) = multiply(greatest_lower_bound(X_134,identity),X_133),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,identity),X_133),greatest_lower_bound(X_133,multiply(X_134,X_133))) )],[refute_0_1506,refute_0_1519]) ).

cnf(refute_0_1521,plain,
    greatest_lower_bound(X_136,multiply(X_137,X_136)) = multiply(greatest_lower_bound(X_137,identity),X_136),
    inference(subst,[],[refute_0_1520:[bind(X_133,$fot(X_136)),bind(X_134,$fot(X_137))]]) ).

cnf(refute_0_1522,plain,
    ( multiply(greatest_lower_bound(identity,X_137),X_136) != greatest_lower_bound(X_136,multiply(X_137,X_136))
    | greatest_lower_bound(X_136,multiply(X_137,X_136)) != multiply(greatest_lower_bound(X_137,identity),X_136)
    | multiply(greatest_lower_bound(identity,X_137),X_136) = multiply(greatest_lower_bound(X_137,identity),X_136) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_137),X_136),multiply(greatest_lower_bound(X_137,identity),X_136)) ),[0],$fot(greatest_lower_bound(X_136,multiply(X_137,X_136)))]]) ).

cnf(refute_0_1523,plain,
    ( multiply(greatest_lower_bound(identity,X_137),X_136) != greatest_lower_bound(X_136,multiply(X_137,X_136))
    | multiply(greatest_lower_bound(identity,X_137),X_136) = multiply(greatest_lower_bound(X_137,identity),X_136) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_136,multiply(X_137,X_136)),multiply(greatest_lower_bound(X_137,identity),X_136)) )],[refute_0_1521,refute_0_1522]) ).

cnf(refute_0_1524,plain,
    multiply(greatest_lower_bound(identity,X_137),X_136) = multiply(greatest_lower_bound(X_137,identity),X_136),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_137),X_136),greatest_lower_bound(X_136,multiply(X_137,X_136))) )],[refute_0_1518,refute_0_1523]) ).

cnf(refute_0_1525,plain,
    ( multiply(greatest_lower_bound(identity,X_137),X_136) != multiply(greatest_lower_bound(X_137,identity),X_136)
    | multiply(greatest_lower_bound(X_137,identity),X_136) = multiply(greatest_lower_bound(identity,X_137),X_136) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_137),X_136))),bind(Y0,$fot(multiply(greatest_lower_bound(X_137,identity),X_136)))]]) ).

cnf(refute_0_1526,plain,
    multiply(greatest_lower_bound(X_137,identity),X_136) = multiply(greatest_lower_bound(identity,X_137),X_136),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_137),X_136),multiply(greatest_lower_bound(X_137,identity),X_136)) )],[refute_0_1524,refute_0_1525]) ).

cnf(refute_0_1527,plain,
    multiply(greatest_lower_bound(multiply(X,Y),identity),X_136) = multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136),
    inference(subst,[],[refute_0_1526:[bind(X_137,$fot(multiply(X,Y)))]]) ).

cnf(refute_0_1528,plain,
    ( multiply(greatest_lower_bound(multiply(X,Y),identity),X_136) != multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136)
    | multiply(greatest_lower_bound(multiply(X,Y),identity),X_136) != greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136)))
    | multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136) = greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(multiply(X,Y),identity),X_136),greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136)))) ),[0],$fot(multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136))]]) ).

cnf(refute_0_1529,plain,
    ( multiply(greatest_lower_bound(multiply(X,Y),identity),X_136) != greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136)))
    | multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136) = greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(multiply(X,Y),identity),X_136),multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136)) )],[refute_0_1527,refute_0_1528]) ).

cnf(refute_0_1530,plain,
    multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136) = greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(multiply(X,Y),identity),X_136),greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136)))) )],[refute_0_1511,refute_0_1529]) ).

cnf(refute_0_1531,plain,
    ( multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136) != greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136)))
    | greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136))) = multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136))),bind(Y0,$fot(greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136)))))]]) ).

cnf(refute_0_1532,plain,
    greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136))) = multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X,Y)),X_136),greatest_lower_bound(X_136,multiply(X,multiply(Y,X_136)))) )],[refute_0_1530,refute_0_1531]) ).

cnf(refute_0_1533,plain,
    greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82))) = multiply(greatest_lower_bound(identity,multiply(X_134,X_81)),X_82),
    inference(subst,[],[refute_0_1532:[bind(X,$fot(X_134)),bind(Y,$fot(X_81)),bind(X_136,$fot(X_82))]]) ).

cnf(refute_0_1534,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) != greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82)))
    | greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82))) != multiply(greatest_lower_bound(identity,multiply(X_134,X_81)),X_82)
    | multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) = multiply(greatest_lower_bound(identity,multiply(X_134,X_81)),X_82) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)),multiply(greatest_lower_bound(identity,multiply(X_134,X_81)),X_82)) ),[0],$fot(greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82))))]]) ).

cnf(refute_0_1535,plain,
    ( multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) != greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82)))
    | multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) = multiply(greatest_lower_bound(identity,multiply(X_134,X_81)),X_82) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82))),multiply(greatest_lower_bound(identity,multiply(X_134,X_81)),X_82)) )],[refute_0_1533,refute_0_1534]) ).

cnf(refute_0_1536,plain,
    multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)) = multiply(greatest_lower_bound(identity,multiply(X_134,X_81)),X_82),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,inverse(X_81)),multiply(X_81,X_82)),greatest_lower_bound(X_82,multiply(X_134,multiply(X_81,X_82)))) )],[refute_0_1497,refute_0_1535]) ).

cnf(refute_0_1537,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_1536:[bind(X_134,$fot(inverse(b))),bind(X_81,$fot(c)),bind(X_82,$fot(inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1538,plain,
    ( multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))) != inverse(b)
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))) != multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c)))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))) = inverse(b) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))))),bind(Z0,$fot(inverse(b)))]]) ).

cnf(refute_0_1539,plain,
    ( multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))) != inverse(b)
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))) = inverse(b) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))),multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c)))) )],[refute_0_1537,refute_0_1538]) ).

cnf(refute_0_1540,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))) = inverse(b),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),inverse(greatest_lower_bound(a,c))),inverse(b)) )],[refute_0_1487,refute_0_1539]) ).

cnf(refute_0_1541,plain,
    inverse(multiply(greatest_lower_bound(a,c),inverse(c))) = multiply(c,inverse(greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_146:[bind(X,$fot(c)),bind(X_17,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_1542,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) = multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))]]) ).

cnf(refute_0_1543,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) != multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))
    | inverse(multiply(greatest_lower_bound(a,c),inverse(c))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) = multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))),multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) ),[1,1],$fot(multiply(c,inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1544,plain,
    ( inverse(multiply(greatest_lower_bound(a,c),inverse(c))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) = multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))),multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) )],[refute_0_1542,refute_0_1543]) ).

cnf(refute_0_1545,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) = multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(a,c),inverse(c))),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_1541,refute_0_1544]) ).

cnf(refute_0_1546,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))) != inverse(b)
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) != multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c))))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) = inverse(b) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))))),bind(Z0,$fot(inverse(b)))]]) ).

cnf(refute_0_1547,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))) != inverse(b)
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) = inverse(b) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))),multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1545,refute_0_1546]) ).

cnf(refute_0_1548,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) = inverse(b),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,inverse(greatest_lower_bound(a,c)))),inverse(b)) )],[refute_0_1540,refute_0_1547]) ).

cnf(refute_0_1549,plain,
    multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) = multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))),
    introduced(tautology,[refl,[$fot(multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))))]]) ).

cnf(refute_0_1550,plain,
    ( multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) != multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) != inverse(b)
    | multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) = multiply(a,inverse(b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))),multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))) ),[1,1],$fot(inverse(b))]]) ).

cnf(refute_0_1551,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) != inverse(b)
    | multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) = multiply(a,inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))),multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))) )],[refute_0_1549,refute_0_1550]) ).

cnf(refute_0_1552,plain,
    multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) = multiply(a,inverse(b)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))),inverse(b)) )],[refute_0_1548,refute_0_1551]) ).

cnf(refute_0_1553,plain,
    multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) = multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))),
    inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(greatest_lower_bound(inverse(b),inverse(c)))),bind(Z,$fot(inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))]]) ).

cnf(refute_0_1554,plain,
    ( multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) != multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))
    | multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) != multiply(a,inverse(b))
    | multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) = multiply(a,inverse(b)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))),bind(Y0,$fot(multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))))),bind(Z0,$fot(multiply(a,inverse(b))))]]) ).

cnf(refute_0_1555,plain,
    ( multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) != multiply(a,inverse(b))
    | multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) = multiply(a,inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))),multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))) )],[refute_0_1553,refute_0_1554]) ).

cnf(refute_0_1556,plain,
    multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) = multiply(a,inverse(b)),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))),multiply(a,inverse(b))) )],[refute_0_1552,refute_0_1555]) ).

cnf(refute_0_1557,plain,
    greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) = greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))))]]) ).

cnf(refute_0_1558,plain,
    ( multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) != multiply(a,inverse(b))
    | greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) != greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))
    | greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) = greatest_lower_bound(identity,multiply(a,inverse(b))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))),greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))) ),[1,1],$fot(multiply(a,inverse(b)))]]) ).

cnf(refute_0_1559,plain,
    ( multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))) != multiply(a,inverse(b))
    | greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) = greatest_lower_bound(identity,multiply(a,inverse(b))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))),greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))) )],[refute_0_1557,refute_0_1558]) ).

cnf(refute_0_1560,plain,
    greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) = greatest_lower_bound(identity,multiply(a,inverse(b))),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))),multiply(a,inverse(b))) )],[refute_0_1556,refute_0_1559]) ).

cnf(refute_0_1561,plain,
    ( greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) != greatest_lower_bound(identity,multiply(a,inverse(b)))
    | greatest_lower_bound(identity,multiply(a,inverse(b))) != multiply(greatest_lower_bound(a,b),inverse(b))
    | greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) = multiply(greatest_lower_bound(a,b),inverse(b)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(a,inverse(b))))),bind(Z0,$fot(multiply(greatest_lower_bound(a,b),inverse(b))))]]) ).

cnf(refute_0_1562,plain,
    ( greatest_lower_bound(identity,multiply(a,inverse(b))) != multiply(greatest_lower_bound(a,b),inverse(b))
    | greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) = multiply(greatest_lower_bound(a,b),inverse(b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))),greatest_lower_bound(identity,multiply(a,inverse(b)))) )],[refute_0_1560,refute_0_1561]) ).

cnf(refute_0_1563,plain,
    greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) = multiply(greatest_lower_bound(a,b),inverse(b)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,inverse(b))),multiply(greatest_lower_bound(a,b),inverse(b))) )],[refute_0_1408,refute_0_1562]) ).

cnf(refute_0_1564,plain,
    ( greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))) != multiply(greatest_lower_bound(a,b),inverse(b))
    | identity != greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))
    | identity = multiply(greatest_lower_bound(a,b),inverse(b)) ),
    introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))) ),[1],$fot(multiply(greatest_lower_bound(a,b),inverse(b)))]]) ).

cnf(refute_0_1565,plain,
    ( identity != greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))
    | identity = multiply(greatest_lower_bound(a,b),inverse(b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c))))),multiply(greatest_lower_bound(a,b),inverse(b))) )],[refute_0_1563,refute_0_1564]) ).

cnf(refute_0_1566,plain,
    identity = multiply(greatest_lower_bound(a,b),inverse(b)),
    inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(multiply(a,greatest_lower_bound(inverse(b),inverse(c))),inverse(multiply(greatest_lower_bound(a,c),inverse(c)))))) )],[refute_0_997,refute_0_1565]) ).

cnf(refute_0_1567,plain,
    ( identity != multiply(greatest_lower_bound(a,b),inverse(b))
    | multiply(greatest_lower_bound(a,b),inverse(b)) = identity ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(greatest_lower_bound(a,b),inverse(b))))]]) ).

cnf(refute_0_1568,plain,
    multiply(greatest_lower_bound(a,b),inverse(b)) = identity,
    inference(resolve,[$cnf( $equal(identity,multiply(greatest_lower_bound(a,b),inverse(b))) )],[refute_0_1566,refute_0_1567]) ).

cnf(refute_0_1569,plain,
    ( multiply(greatest_lower_bound(a,b),inverse(b)) != identity
    | inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))) != multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(a,b),inverse(b)))),greatest_lower_bound(a,b))
    | inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))) = multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))),multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(a,b),inverse(b)))),greatest_lower_bound(a,b))) ),[1,0,0,1],$fot(identity)]]) ).

cnf(refute_0_1570,plain,
    ( inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))) != multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(a,b),inverse(b)))),greatest_lower_bound(a,b))
    | inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))) = multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,b),inverse(b)),identity) )],[refute_0_1568,refute_0_1569]) ).

cnf(refute_0_1571,plain,
    inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))) = multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))),multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(a,b),inverse(b)))),greatest_lower_bound(a,b))) )],[refute_0_55,refute_0_1570]) ).

cnf(refute_0_1572,plain,
    inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))) = multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)))),greatest_lower_bound(X_134,X_135)),
    inference(subst,[],[refute_0_54:[bind(X_107,$fot(inverse(X_135))),bind(X_83,$fot(greatest_lower_bound(X_134,X_135)))]]) ).

cnf(refute_0_1573,plain,
    ( multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)) != greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))
    | inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))) != multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)))),greatest_lower_bound(X_134,X_135))
    | inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))) = multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))),multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)))),greatest_lower_bound(X_134,X_135))) ),[1,0,0,1],$fot(greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))]]) ).

cnf(refute_0_1574,plain,
    ( inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))) != multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)))),greatest_lower_bound(X_134,X_135))
    | inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))) = multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)),greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) )],[refute_0_64,refute_0_1573]) ).

cnf(refute_0_1575,plain,
    inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))) = multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))),multiply(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_134,X_135),inverse(X_135)))),greatest_lower_bound(X_134,X_135))) )],[refute_0_1572,refute_0_1574]) ).

cnf(refute_0_1576,plain,
    inverse(inverse(X_141)) = multiply(inverse(multiply(greatest_lower_bound(X_140,X_141),inverse(X_141))),greatest_lower_bound(X_140,X_141)),
    inference(subst,[],[refute_0_34:[bind(X_83,$fot(greatest_lower_bound(X_140,X_141))),bind(X_84,$fot(inverse(X_141)))]]) ).

cnf(refute_0_1577,plain,
    multiply(greatest_lower_bound(X_140,X_141),inverse(X_141)) = greatest_lower_bound(identity,multiply(X_140,inverse(X_141))),
    inference(subst,[],[refute_0_64:[bind(X_134,$fot(X_140)),bind(X_135,$fot(X_141))]]) ).

cnf(refute_0_1578,plain,
    ( multiply(greatest_lower_bound(X_140,X_141),inverse(X_141)) != greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))
    | inverse(inverse(X_141)) != multiply(inverse(multiply(greatest_lower_bound(X_140,X_141),inverse(X_141))),greatest_lower_bound(X_140,X_141))
    | inverse(inverse(X_141)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_141)),multiply(inverse(multiply(greatest_lower_bound(X_140,X_141),inverse(X_141))),greatest_lower_bound(X_140,X_141))) ),[1,0,0],$fot(greatest_lower_bound(identity,multiply(X_140,inverse(X_141))))]]) ).

cnf(refute_0_1579,plain,
    ( inverse(inverse(X_141)) != multiply(inverse(multiply(greatest_lower_bound(X_140,X_141),inverse(X_141))),greatest_lower_bound(X_140,X_141))
    | inverse(inverse(X_141)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_140,X_141),inverse(X_141)),greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))) )],[refute_0_1577,refute_0_1578]) ).

cnf(refute_0_1580,plain,
    inverse(inverse(X_141)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141)),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_141)),multiply(inverse(multiply(greatest_lower_bound(X_140,X_141),inverse(X_141))),greatest_lower_bound(X_140,X_141))) )],[refute_0_1576,refute_0_1579]) ).

cnf(refute_0_1581,plain,
    inverse(inverse(X_141)) = X_141,
    inference(subst,[],[p12_2:[bind(X,$fot(X_141))]]) ).

cnf(refute_0_1582,plain,
    ( inverse(inverse(X_141)) != X_141
    | inverse(inverse(X_141)) != multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141))
    | X_141 = multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_141)),multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141))) ),[0],$fot(X_141)]]) ).

cnf(refute_0_1583,plain,
    ( inverse(inverse(X_141)) != multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141))
    | X_141 = multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_141)),X_141) )],[refute_0_1581,refute_0_1582]) ).

cnf(refute_0_1584,plain,
    X_141 = multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141)),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_141)),multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141))) )],[refute_0_1580,refute_0_1583]) ).

cnf(refute_0_1585,plain,
    ( X_141 != multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141))
    | multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141)) = X_141 ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(X_141)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141))))]]) ).

cnf(refute_0_1586,plain,
    multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141)) = X_141,
    inference(resolve,[$cnf( $equal(X_141,multiply(inverse(greatest_lower_bound(identity,multiply(X_140,inverse(X_141)))),greatest_lower_bound(X_140,X_141))) )],[refute_0_1584,refute_0_1585]) ).

cnf(refute_0_1587,plain,
    multiply(inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),greatest_lower_bound(X_134,X_135)) = X_135,
    inference(subst,[],[refute_0_1586:[bind(X_140,$fot(X_134)),bind(X_141,$fot(X_135))]]) ).

cnf(refute_0_1588,plain,
    greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) = greatest_lower_bound(identity,multiply(X_134,inverse(X_135))),
    inference(subst,[],[refute_0_319:[bind(X_31,$fot(multiply(X_134,inverse(X_135)))),bind(X_32,$fot(identity))]]) ).

cnf(refute_0_1589,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))))]]) ).

cnf(refute_0_1590,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) != greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))) = inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))]]) ).

cnf(refute_0_1591,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) != greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))) = inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))))) )],[refute_0_1589,refute_0_1590]) ).

cnf(refute_0_1592,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))) = inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))) )],[refute_0_1588,refute_0_1591]) ).

cnf(refute_0_1593,plain,
    multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) = multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)))]]) ).

cnf(refute_0_1594,plain,
    ( multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) != multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))) != inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))
    | multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),greatest_lower_bound(X_134,X_135)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)),multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135))) ),[1,0],$fot(inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))))]]) ).

cnf(refute_0_1595,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))) != inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))
    | multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),greatest_lower_bound(X_134,X_135)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)),multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135))) )],[refute_0_1593,refute_0_1594]) ).

cnf(refute_0_1596,plain,
    multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) = multiply(inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),greatest_lower_bound(X_134,X_135)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))) )],[refute_0_1592,refute_0_1595]) ).

cnf(refute_0_1597,plain,
    ( multiply(inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),greatest_lower_bound(X_134,X_135)) != X_135
    | multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) != multiply(inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),greatest_lower_bound(X_134,X_135))
    | multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) = X_135 ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),greatest_lower_bound(X_134,X_135)))),bind(Z0,$fot(X_135))]]) ).

cnf(refute_0_1598,plain,
    ( multiply(inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),greatest_lower_bound(X_134,X_135)) != X_135
    | multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) = X_135 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)),multiply(inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),greatest_lower_bound(X_134,X_135))) )],[refute_0_1596,refute_0_1597]) ).

cnf(refute_0_1599,plain,
    multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) = X_135,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(X_134,inverse(X_135)))),greatest_lower_bound(X_134,X_135)),X_135) )],[refute_0_1587,refute_0_1598]) ).

cnf(refute_0_1600,plain,
    ( multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)) != X_135
    | inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))) != multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135))
    | inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))) = X_135 ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))),multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135))) ),[1],$fot(X_135)]]) ).

cnf(refute_0_1601,plain,
    ( inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))) != multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135))
    | inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))) = X_135 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135)),X_135) )],[refute_0_1599,refute_0_1600]) ).

cnf(refute_0_1602,plain,
    inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))) = X_135,
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_135),inverse(greatest_lower_bound(X_134,X_135)))),multiply(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_134,inverse(X_135))))),greatest_lower_bound(X_134,X_135))) )],[refute_0_1575,refute_0_1601]) ).

cnf(refute_0_1603,plain,
    inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))) = b,
    inference(subst,[],[refute_0_1602:[bind(X_134,$fot(a)),bind(X_135,$fot(b))]]) ).

cnf(refute_0_1604,plain,
    ( inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))) != multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))
    | inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))) != b
    | b = multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))),multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))) ),[0],$fot(b)]]) ).

cnf(refute_0_1605,plain,
    ( inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))) != multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))
    | b = multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))),b) )],[refute_0_1603,refute_0_1604]) ).

cnf(refute_0_1606,plain,
    multiply(identity,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b),
    inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(a,b)))]]) ).

cnf(refute_0_1607,plain,
    inverse(greatest_lower_bound(identity,identity)) = inverse(greatest_lower_bound(identity,identity)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,identity)))]]) ).

cnf(refute_0_1608,plain,
    ( greatest_lower_bound(identity,identity) != identity
    | inverse(greatest_lower_bound(identity,identity)) != inverse(greatest_lower_bound(identity,identity))
    | inverse(greatest_lower_bound(identity,identity)) = inverse(identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,identity)),inverse(greatest_lower_bound(identity,identity))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1609,plain,
    ( greatest_lower_bound(identity,identity) != identity
    | inverse(greatest_lower_bound(identity,identity)) = inverse(identity) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,identity)),inverse(greatest_lower_bound(identity,identity))) )],[refute_0_1607,refute_0_1608]) ).

cnf(refute_0_1610,plain,
    inverse(greatest_lower_bound(identity,identity)) = inverse(identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,identity),identity) )],[refute_0_502,refute_0_1609]) ).

cnf(refute_0_1611,plain,
    ( inverse(greatest_lower_bound(identity,identity)) != inverse(identity)
    | inverse(identity) != identity
    | inverse(greatest_lower_bound(identity,identity)) = identity ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(inverse(greatest_lower_bound(identity,identity)))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_1612,plain,
    ( inverse(identity) != identity
    | inverse(greatest_lower_bound(identity,identity)) = identity ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,identity)),inverse(identity)) )],[refute_0_1610,refute_0_1611]) ).

cnf(refute_0_1613,plain,
    inverse(greatest_lower_bound(identity,identity)) = identity,
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p12_1,refute_0_1612]) ).

cnf(refute_0_1614,plain,
    multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) = multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)))]]) ).

cnf(refute_0_1615,plain,
    ( multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) != multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))
    | inverse(greatest_lower_bound(identity,identity)) != identity
    | multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) = multiply(identity,greatest_lower_bound(a,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)),multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1616,plain,
    ( inverse(greatest_lower_bound(identity,identity)) != identity
    | multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) = multiply(identity,greatest_lower_bound(a,b)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)),multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))) )],[refute_0_1614,refute_0_1615]) ).

cnf(refute_0_1617,plain,
    multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) = multiply(identity,greatest_lower_bound(a,b)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,identity)),identity) )],[refute_0_1613,refute_0_1616]) ).

cnf(refute_0_1618,plain,
    ( multiply(identity,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b)
    | multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) != multiply(identity,greatest_lower_bound(a,b))
    | multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) = greatest_lower_bound(a,b) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(a,b)))),bind(Z0,$fot(greatest_lower_bound(a,b)))]]) ).

cnf(refute_0_1619,plain,
    ( multiply(identity,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b)
    | multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) = greatest_lower_bound(a,b) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)),multiply(identity,greatest_lower_bound(a,b))) )],[refute_0_1617,refute_0_1618]) ).

cnf(refute_0_1620,plain,
    multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) = greatest_lower_bound(a,b),
    inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(a,b)),greatest_lower_bound(a,b)) )],[refute_0_1606,refute_0_1619]) ).

cnf(refute_0_1621,plain,
    ( multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)) != greatest_lower_bound(a,b)
    | b != multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))
    | b = greatest_lower_bound(a,b) ),
    introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))) ),[1],$fot(greatest_lower_bound(a,b))]]) ).

cnf(refute_0_1622,plain,
    ( b != multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))
    | b = greatest_lower_bound(a,b) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b)),greatest_lower_bound(a,b)) )],[refute_0_1620,refute_0_1621]) ).

cnf(refute_0_1623,plain,
    ( inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))) != multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))
    | b = greatest_lower_bound(a,b) ),
    inference(resolve,[$cnf( $equal(b,multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))) )],[refute_0_1605,refute_0_1622]) ).

cnf(refute_0_1624,plain,
    b = greatest_lower_bound(a,b),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,b)))),multiply(inverse(greatest_lower_bound(identity,identity)),greatest_lower_bound(a,b))) )],[refute_0_1571,refute_0_1623]) ).

cnf(refute_0_1625,plain,
    greatest_lower_bound(a,a) = a,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(a))]]) ).

cnf(refute_0_1626,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(least_upper_bound(X_38,Y),X_40)) = greatest_lower_bound(greatest_lower_bound(X_38,least_upper_bound(X_38,Y)),X_40),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_38)),bind(Y,$fot(least_upper_bound(X_38,Y))),bind(Z,$fot(X_40))]]) ).

cnf(refute_0_1627,plain,
    greatest_lower_bound(X_38,least_upper_bound(X_38,Y)) = X_38,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_38))]]) ).

cnf(refute_0_1628,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(least_upper_bound(X_38,Y),X_40)) != greatest_lower_bound(greatest_lower_bound(X_38,least_upper_bound(X_38,Y)),X_40)
    | greatest_lower_bound(X_38,least_upper_bound(X_38,Y)) != X_38
    | greatest_lower_bound(X_38,greatest_lower_bound(least_upper_bound(X_38,Y),X_40)) = greatest_lower_bound(X_38,X_40) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(least_upper_bound(X_38,Y),X_40)),greatest_lower_bound(greatest_lower_bound(X_38,least_upper_bound(X_38,Y)),X_40)) ),[1,0],$fot(X_38)]]) ).

cnf(refute_0_1629,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(least_upper_bound(X_38,Y),X_40)) != greatest_lower_bound(greatest_lower_bound(X_38,least_upper_bound(X_38,Y)),X_40)
    | greatest_lower_bound(X_38,greatest_lower_bound(least_upper_bound(X_38,Y),X_40)) = greatest_lower_bound(X_38,X_40) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,least_upper_bound(X_38,Y)),X_38) )],[refute_0_1627,refute_0_1628]) ).

cnf(refute_0_1630,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(least_upper_bound(X_38,Y),X_40)) = greatest_lower_bound(X_38,X_40),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(least_upper_bound(X_38,Y),X_40)),greatest_lower_bound(greatest_lower_bound(X_38,least_upper_bound(X_38,Y)),X_40)) )],[refute_0_1626,refute_0_1629]) ).

cnf(refute_0_1631,plain,
    greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),X_40)) = greatest_lower_bound(a,X_40),
    inference(subst,[],[refute_0_1630:[bind(Y,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))),bind(X_38,$fot(a))]]) ).

cnf(refute_0_1632,plain,
    least_upper_bound(b,least_upper_bound(c,X_16)) = least_upper_bound(least_upper_bound(b,c),X_16),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(b)),bind(Y,$fot(c)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_1633,plain,
    ( least_upper_bound(b,c) != least_upper_bound(a,c)
    | least_upper_bound(b,least_upper_bound(c,X_16)) != least_upper_bound(least_upper_bound(b,c),X_16)
    | least_upper_bound(b,least_upper_bound(c,X_16)) = least_upper_bound(least_upper_bound(a,c),X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_16)),least_upper_bound(least_upper_bound(b,c),X_16)) ),[1,0],$fot(least_upper_bound(a,c))]]) ).

cnf(refute_0_1634,plain,
    ( least_upper_bound(b,least_upper_bound(c,X_16)) != least_upper_bound(least_upper_bound(b,c),X_16)
    | least_upper_bound(b,least_upper_bound(c,X_16)) = least_upper_bound(least_upper_bound(a,c),X_16) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,c),least_upper_bound(a,c)) )],[refute_0_222,refute_0_1633]) ).

cnf(refute_0_1635,plain,
    least_upper_bound(b,least_upper_bound(c,X_16)) = least_upper_bound(least_upper_bound(a,c),X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_16)),least_upper_bound(least_upper_bound(b,c),X_16)) )],[refute_0_1632,refute_0_1634]) ).

cnf(refute_0_1636,plain,
    least_upper_bound(least_upper_bound(a,c),X_16) = least_upper_bound(a,least_upper_bound(c,X_16)),
    inference(subst,[],[refute_0_237:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_1637,plain,
    ( least_upper_bound(b,least_upper_bound(c,X_16)) != least_upper_bound(least_upper_bound(a,c),X_16)
    | least_upper_bound(least_upper_bound(a,c),X_16) != least_upper_bound(a,least_upper_bound(c,X_16))
    | least_upper_bound(b,least_upper_bound(c,X_16)) = least_upper_bound(a,least_upper_bound(c,X_16)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(b,least_upper_bound(c,X_16)),least_upper_bound(a,least_upper_bound(c,X_16))) ),[0],$fot(least_upper_bound(least_upper_bound(a,c),X_16))]]) ).

cnf(refute_0_1638,plain,
    ( least_upper_bound(b,least_upper_bound(c,X_16)) != least_upper_bound(least_upper_bound(a,c),X_16)
    | least_upper_bound(b,least_upper_bound(c,X_16)) = least_upper_bound(a,least_upper_bound(c,X_16)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,c),X_16),least_upper_bound(a,least_upper_bound(c,X_16))) )],[refute_0_1636,refute_0_1637]) ).

cnf(refute_0_1639,plain,
    least_upper_bound(b,least_upper_bound(c,X_16)) = least_upper_bound(a,least_upper_bound(c,X_16)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_16)),least_upper_bound(least_upper_bound(a,c),X_16)) )],[refute_0_1635,refute_0_1638]) ).

cnf(refute_0_1640,plain,
    least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_15,X))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_15,X))),
    inference(subst,[],[refute_0_1639:[bind(X_16,$fot(least_upper_bound(X_15,X)))]]) ).

cnf(refute_0_1641,plain,
    least_upper_bound(X,least_upper_bound(c,X_15)) = least_upper_bound(c,least_upper_bound(X_15,X)),
    inference(subst,[],[refute_0_588:[bind(X_14,$fot(c))]]) ).

cnf(refute_0_1642,plain,
    ( least_upper_bound(X,least_upper_bound(c,X_15)) != least_upper_bound(c,least_upper_bound(X_15,X))
    | least_upper_bound(c,least_upper_bound(X_15,X)) = least_upper_bound(X,least_upper_bound(c,X_15)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(c,X_15)))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_15,X))))]]) ).

cnf(refute_0_1643,plain,
    least_upper_bound(c,least_upper_bound(X_15,X)) = least_upper_bound(X,least_upper_bound(c,X_15)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(c,X_15)),least_upper_bound(c,least_upper_bound(X_15,X))) )],[refute_0_1641,refute_0_1642]) ).

cnf(refute_0_1644,plain,
    ( least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_15,X))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_15,X)))
    | least_upper_bound(c,least_upper_bound(X_15,X)) != least_upper_bound(X,least_upper_bound(c,X_15))
    | least_upper_bound(b,least_upper_bound(X,least_upper_bound(c,X_15))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_15,X))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_15,X))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_15,X)))) ),[0,1],$fot(least_upper_bound(X,least_upper_bound(c,X_15)))]]) ).

cnf(refute_0_1645,plain,
    ( least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_15,X))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_15,X)))
    | least_upper_bound(b,least_upper_bound(X,least_upper_bound(c,X_15))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_15,X))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_15,X)),least_upper_bound(X,least_upper_bound(c,X_15))) )],[refute_0_1643,refute_0_1644]) ).

cnf(refute_0_1646,plain,
    least_upper_bound(b,least_upper_bound(X,least_upper_bound(c,X_15))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_15,X))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,least_upper_bound(X_15,X))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(X_15,X)))) )],[refute_0_1640,refute_0_1645]) ).

cnf(refute_0_1647,plain,
    least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) = least_upper_bound(a,least_upper_bound(c,least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),
    inference(subst,[],[refute_0_1646:[bind(X,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))),bind(X_15,$fot(b))]]) ).

cnf(refute_0_1648,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) = inverse(greatest_lower_bound(inverse(b),inverse(c))),
    inference(subst,[],[refute_0_281:[bind(X_8,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))),bind(X_9,$fot(a))]]) ).

cnf(refute_0_1649,plain,
    inverse(inverse(b)) = multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),
    inference(subst,[],[refute_0_209:[bind(X_61,$fot(inverse(b))),bind(X_63,$fot(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_1650,plain,
    multiply(inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))))]]) ).

cnf(refute_0_1651,plain,
    X_82 = multiply(inverse(greatest_lower_bound(X_139,inverse(X_82))),multiply(greatest_lower_bound(X_139,inverse(X_82)),X_82)),
    inference(subst,[],[refute_0_9:[bind(X_81,$fot(greatest_lower_bound(X_139,inverse(X_82))))]]) ).

cnf(refute_0_1652,plain,
    multiply(greatest_lower_bound(X_139,inverse(X_82)),X_82) = greatest_lower_bound(identity,multiply(X_139,X_82)),
    inference(subst,[],[refute_0_807:[bind(X_133,$fot(X_82)),bind(X_134,$fot(X_139))]]) ).

cnf(refute_0_1653,plain,
    ( X_82 != multiply(inverse(greatest_lower_bound(X_139,inverse(X_82))),multiply(greatest_lower_bound(X_139,inverse(X_82)),X_82))
    | multiply(greatest_lower_bound(X_139,inverse(X_82)),X_82) != greatest_lower_bound(identity,multiply(X_139,X_82))
    | X_82 = multiply(inverse(greatest_lower_bound(X_139,inverse(X_82))),greatest_lower_bound(identity,multiply(X_139,X_82))) ),
    introduced(tautology,[equality,[$cnf( $equal(X_82,multiply(inverse(greatest_lower_bound(X_139,inverse(X_82))),multiply(greatest_lower_bound(X_139,inverse(X_82)),X_82))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_139,X_82)))]]) ).

cnf(refute_0_1654,plain,
    ( X_82 != multiply(inverse(greatest_lower_bound(X_139,inverse(X_82))),multiply(greatest_lower_bound(X_139,inverse(X_82)),X_82))
    | X_82 = multiply(inverse(greatest_lower_bound(X_139,inverse(X_82))),greatest_lower_bound(identity,multiply(X_139,X_82))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_139,inverse(X_82)),X_82),greatest_lower_bound(identity,multiply(X_139,X_82))) )],[refute_0_1652,refute_0_1653]) ).

cnf(refute_0_1655,plain,
    X_82 = multiply(inverse(greatest_lower_bound(X_139,inverse(X_82))),greatest_lower_bound(identity,multiply(X_139,X_82))),
    inference(resolve,[$cnf( $equal(X_82,multiply(inverse(greatest_lower_bound(X_139,inverse(X_82))),multiply(greatest_lower_bound(X_139,inverse(X_82)),X_82))) )],[refute_0_1651,refute_0_1654]) ).

cnf(refute_0_1656,plain,
    greatest_lower_bound(inverse(b),inverse(c)) = multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c))))),
    inference(subst,[],[refute_0_1655:[bind(X_139,$fot(a)),bind(X_82,$fot(greatest_lower_bound(inverse(b),inverse(c))))]]) ).

cnf(refute_0_1657,plain,
    ( greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))) != multiply(greatest_lower_bound(a,c),inverse(c))
    | greatest_lower_bound(inverse(b),inverse(c)) != multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))))
    | greatest_lower_bound(inverse(b),inverse(c)) = multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),multiply(greatest_lower_bound(a,c),inverse(c))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(c)),multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))))) ),[1,1],$fot(multiply(greatest_lower_bound(a,c),inverse(c)))]]) ).

cnf(refute_0_1658,plain,
    ( greatest_lower_bound(inverse(b),inverse(c)) != multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))))
    | greatest_lower_bound(inverse(b),inverse(c)) = multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),multiply(greatest_lower_bound(a,c),inverse(c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))),multiply(greatest_lower_bound(a,c),inverse(c))) )],[refute_0_994,refute_0_1657]) ).

cnf(refute_0_1659,plain,
    greatest_lower_bound(inverse(b),inverse(c)) = multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),multiply(greatest_lower_bound(a,c),inverse(c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(c)),multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),greatest_lower_bound(identity,multiply(a,greatest_lower_bound(inverse(b),inverse(c)))))) )],[refute_0_1656,refute_0_1658]) ).

cnf(refute_0_1660,plain,
    multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),multiply(greatest_lower_bound(a,c),inverse(c))) = inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),
    inference(subst,[],[refute_0_1449:[bind(X,$fot(c)),bind(X_21,$fot(greatest_lower_bound(a,c))),bind(X_22,$fot(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_1661,plain,
    ( multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),multiply(greatest_lower_bound(a,c),inverse(c))) != inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))
    | greatest_lower_bound(inverse(b),inverse(c)) != multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),multiply(greatest_lower_bound(a,c),inverse(c)))
    | greatest_lower_bound(inverse(b),inverse(c)) = inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(c)),multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),multiply(greatest_lower_bound(a,c),inverse(c)))) ),[1],$fot(inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))))]]) ).

cnf(refute_0_1662,plain,
    ( greatest_lower_bound(inverse(b),inverse(c)) != multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),multiply(greatest_lower_bound(a,c),inverse(c)))
    | greatest_lower_bound(inverse(b),inverse(c)) = inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),multiply(greatest_lower_bound(a,c),inverse(c))),inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))) )],[refute_0_1660,refute_0_1661]) ).

cnf(refute_0_1663,plain,
    greatest_lower_bound(inverse(b),inverse(c)) = inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(c)),multiply(inverse(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),multiply(greatest_lower_bound(a,c),inverse(c)))) )],[refute_0_1659,refute_0_1662]) ).

cnf(refute_0_1664,plain,
    ( greatest_lower_bound(inverse(b),inverse(c)) != inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))
    | inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = greatest_lower_bound(inverse(b),inverse(c)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(inverse(b),inverse(c)))),bind(Y0,$fot(inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))))]]) ).

cnf(refute_0_1665,plain,
    inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = greatest_lower_bound(inverse(b),inverse(c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(c)),inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))) )],[refute_0_1663,refute_0_1664]) ).

cnf(refute_0_1666,plain,
    ( multiply(inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != identity
    | inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != greatest_lower_bound(inverse(b),inverse(c))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),identity) ),[0,0],$fot(greatest_lower_bound(inverse(b),inverse(c)))]]) ).

cnf(refute_0_1667,plain,
    ( multiply(inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != identity
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = identity ),
    inference(resolve,[$cnf( $equal(inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),greatest_lower_bound(inverse(b),inverse(c))) )],[refute_0_1665,refute_0_1666]) ).

cnf(refute_0_1668,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),identity) )],[refute_0_1650,refute_0_1667]) ).

cnf(refute_0_1669,plain,
    multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),
    inference(subst,[],[refute_0_1418:[bind(X_80,$fot(greatest_lower_bound(a,c))),bind(X_82,$fot(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_1670,plain,
    multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))]]) ).

cnf(refute_0_1671,plain,
    ( multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) != multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))
    | greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) ),[1,0],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_1672,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) )],[refute_0_1670,refute_0_1671]) ).

cnf(refute_0_1673,plain,
    multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_294,refute_0_1672]) ).

cnf(refute_0_1674,plain,
    ( multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) != greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) != multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))
    | multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))),bind(Y0,$fot(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))),bind(Z0,$fot(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_1675,plain,
    ( multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) != greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) )],[refute_0_1673,refute_0_1674]) ).

cnf(refute_0_1676,plain,
    multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_1669,refute_0_1675]) ).

cnf(refute_0_1677,plain,
    multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),
    introduced(tautology,[refl,[$fot(multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))))]]) ).

cnf(refute_0_1678,plain,
    ( multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) != greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))
    | multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))) ),[1,1],$fot(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_1679,plain,
    ( multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) != greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))) )],[refute_0_1677,refute_0_1678]) ).

cnf(refute_0_1680,plain,
    multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_1676,refute_0_1679]) ).

cnf(refute_0_1681,plain,
    multiply(inverse(b),multiply(greatest_lower_bound(c,b),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),
    inference(subst,[],[refute_0_1461:[bind(Z,$fot(multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),bind(X_365,$fot(c)),bind(X_366,$fot(b))]]) ).

cnf(refute_0_1682,plain,
    multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = multiply(inverse(b),multiply(greatest_lower_bound(c,b),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),
    inference(subst,[],[refute_0_1480:[bind(Z,$fot(multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),bind(X_372,$fot(c)),bind(X_373,$fot(b))]]) ).

cnf(refute_0_1683,plain,
    ( multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) != multiply(inverse(b),multiply(greatest_lower_bound(c,b),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))
    | multiply(inverse(b),multiply(greatest_lower_bound(c,b),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))
    | multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))),bind(Y0,$fot(multiply(inverse(b),multiply(greatest_lower_bound(c,b),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))))),bind(Z0,$fot(multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))))]]) ).

cnf(refute_0_1684,plain,
    ( multiply(inverse(b),multiply(greatest_lower_bound(c,b),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))
    | multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),multiply(inverse(b),multiply(greatest_lower_bound(c,b),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))) )],[refute_0_1682,refute_0_1683]) ).

cnf(refute_0_1685,plain,
    multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) = multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),multiply(greatest_lower_bound(c,b),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))) )],[refute_0_1681,refute_0_1684]) ).

cnf(refute_0_1686,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),
    inference(subst,[],[refute_0_1536:[bind(X_134,$fot(inverse(b))),bind(X_81,$fot(c)),bind(X_82,$fot(multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))]]) ).

cnf(refute_0_1687,plain,
    ( multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) != multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))),bind(Z0,$fot(multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))))]]) ).

cnf(refute_0_1688,plain,
    ( multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) != multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) )],[refute_0_1686,refute_0_1687]) ).

cnf(refute_0_1689,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(b),c)),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))) )],[refute_0_1685,refute_0_1688]) ).

cnf(refute_0_1690,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))
    | multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))))),bind(Y0,$fot(multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))))),bind(Z0,$fot(multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))]]) ).

cnf(refute_0_1691,plain,
    ( multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))) )],[refute_0_1689,refute_0_1690]) ).

cnf(refute_0_1692,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) = multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),multiply(greatest_lower_bound(b,c),multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) )],[refute_0_1680,refute_0_1691]) ).

cnf(refute_0_1693,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))
    | multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != identity
    | multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),identity) ),[0],$fot(multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_1694,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) != identity
    | multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) )],[refute_0_1692,refute_0_1693]) ).

cnf(refute_0_1695,plain,
    multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) = identity,
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(c)),multiply(c,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))),identity) )],[refute_0_1668,refute_0_1694]) ).

cnf(refute_0_1696,plain,
    ( multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) != identity
    | inverse(inverse(b)) != multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))
    | inverse(inverse(b)) = multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(b)),multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))) ),[1,1,0],$fot(identity)]]) ).

cnf(refute_0_1697,plain,
    ( inverse(inverse(b)) != multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))
    | inverse(inverse(b)) = multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),identity) )],[refute_0_1695,refute_0_1696]) ).

cnf(refute_0_1698,plain,
    inverse(inverse(b)) = multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(multiply(inverse(b),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))))) )],[refute_0_1649,refute_0_1697]) ).

cnf(refute_0_1699,plain,
    ( inverse(inverse(b)) != multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))
    | inverse(inverse(b)) != b
    | b = multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(b)),multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))) ),[0],$fot(b)]]) ).

cnf(refute_0_1700,plain,
    ( inverse(inverse(b)) != multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))
    | b = multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),b) )],[refute_0_1374,refute_0_1699]) ).

cnf(refute_0_1701,plain,
    multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),identity) = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),
    inference(subst,[],[refute_0_189:[bind(X,$fot(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_1702,plain,
    multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) = multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)))]]) ).

cnf(refute_0_1703,plain,
    ( multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) != multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))
    | inverse(identity) != identity
    | multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) = multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)),multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1704,plain,
    ( inverse(identity) != identity
    | multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) = multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),identity) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)),multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))) )],[refute_0_1702,refute_0_1703]) ).

cnf(refute_0_1705,plain,
    multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) = multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),identity),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p12_1,refute_0_1704]) ).

cnf(refute_0_1706,plain,
    ( multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),identity) != greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) != multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),identity)
    | multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),identity))),bind(Z0,$fot(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_1707,plain,
    ( multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),identity) != greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)),multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),identity)) )],[refute_0_1705,refute_0_1706]) ).

cnf(refute_0_1708,plain,
    multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),identity),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_1701,refute_0_1707]) ).

cnf(refute_0_1709,plain,
    ( multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)) != greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | b != multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))
    | b = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(b,multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))) ),[1],$fot(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_1710,plain,
    ( b != multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))
    | b = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity)),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_1708,refute_0_1709]) ).

cnf(refute_0_1711,plain,
    ( inverse(inverse(b)) != multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))
    | b = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(b,multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))) )],[refute_0_1700,refute_0_1710]) ).

cnf(refute_0_1712,plain,
    b = greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),multiply(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(identity))) )],[refute_0_1698,refute_0_1711]) ).

cnf(refute_0_1713,plain,
    ( b != greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) = b ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(b)),bind(Y0,$fot(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_1714,plain,
    greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) = b,
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_1712,refute_0_1713]) ).

cnf(refute_0_1715,plain,
    ( greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) != b
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),b) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),[0,1],$fot(b)]]) ).

cnf(refute_0_1716,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),b) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),b) )],[refute_0_1714,refute_0_1715]) ).

cnf(refute_0_1717,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),b) = inverse(greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),inverse(greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_1648,refute_0_1716]) ).

cnf(refute_0_1718,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))),X_16)) = least_upper_bound(b,X_16),
    inference(subst,[],[refute_0_1015:[bind(Y,$fot(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))))),bind(X_14,$fot(b))]]) ).

cnf(refute_0_1719,plain,
    greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16))) = least_upper_bound(greatest_lower_bound(a,c),X_16),
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(least_upper_bound(greatest_lower_bound(a,c),X_16))),bind(X_13,$fot(b))]]) ).

cnf(refute_0_1720,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16)) = least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_16),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(b)),bind(Y,$fot(greatest_lower_bound(a,c))),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_1721,plain,
    ( least_upper_bound(b,greatest_lower_bound(a,c)) != b
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16)) != least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_16)
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16)) = least_upper_bound(b,X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16)),least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_16)) ),[1,0],$fot(b)]]) ).

cnf(refute_0_1722,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16)) != least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_16)
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16)) = least_upper_bound(b,X_16) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,c)),b) )],[refute_0_1021,refute_0_1721]) ).

cnf(refute_0_1723,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16)) = least_upper_bound(b,X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16)),least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_16)) )],[refute_0_1720,refute_0_1722]) ).

cnf(refute_0_1724,plain,
    ( greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16))) != least_upper_bound(greatest_lower_bound(a,c),X_16)
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16)) != least_upper_bound(b,X_16)
    | greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,X_16)) = least_upper_bound(greatest_lower_bound(a,c),X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16))),least_upper_bound(greatest_lower_bound(a,c),X_16)) ),[0,1],$fot(least_upper_bound(b,X_16))]]) ).

cnf(refute_0_1725,plain,
    ( greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16))) != least_upper_bound(greatest_lower_bound(a,c),X_16)
    | greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,X_16)) = least_upper_bound(greatest_lower_bound(a,c),X_16) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16)),least_upper_bound(b,X_16)) )],[refute_0_1723,refute_0_1724]) ).

cnf(refute_0_1726,plain,
    greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,X_16)) = least_upper_bound(greatest_lower_bound(a,c),X_16),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_16))),least_upper_bound(greatest_lower_bound(a,c),X_16)) )],[refute_0_1719,refute_0_1725]) ).

cnf(refute_0_1727,plain,
    greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,X_16)) = greatest_lower_bound(least_upper_bound(b,X_16),least_upper_bound(greatest_lower_bound(a,c),X_16)),
    inference(subst,[],[refute_0_46:[bind(X,$fot(least_upper_bound(b,X_16))),bind(Y,$fot(least_upper_bound(greatest_lower_bound(a,c),X_16)))]]) ).

cnf(refute_0_1728,plain,
    ( greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,X_16)) != greatest_lower_bound(least_upper_bound(b,X_16),least_upper_bound(greatest_lower_bound(a,c),X_16))
    | greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,X_16)) != least_upper_bound(greatest_lower_bound(a,c),X_16)
    | greatest_lower_bound(least_upper_bound(b,X_16),least_upper_bound(greatest_lower_bound(a,c),X_16)) = least_upper_bound(greatest_lower_bound(a,c),X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,X_16)),least_upper_bound(greatest_lower_bound(a,c),X_16)) ),[0],$fot(greatest_lower_bound(least_upper_bound(b,X_16),least_upper_bound(greatest_lower_bound(a,c),X_16)))]]) ).

cnf(refute_0_1729,plain,
    ( greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,X_16)) != least_upper_bound(greatest_lower_bound(a,c),X_16)
    | greatest_lower_bound(least_upper_bound(b,X_16),least_upper_bound(greatest_lower_bound(a,c),X_16)) = least_upper_bound(greatest_lower_bound(a,c),X_16) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,X_16)),greatest_lower_bound(least_upper_bound(b,X_16),least_upper_bound(greatest_lower_bound(a,c),X_16))) )],[refute_0_1727,refute_0_1728]) ).

cnf(refute_0_1730,plain,
    greatest_lower_bound(least_upper_bound(b,X_16),least_upper_bound(greatest_lower_bound(a,c),X_16)) = least_upper_bound(greatest_lower_bound(a,c),X_16),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(greatest_lower_bound(a,c),X_16),least_upper_bound(b,X_16)),least_upper_bound(greatest_lower_bound(a,c),X_16)) )],[refute_0_1726,refute_0_1729]) ).

cnf(refute_0_1731,plain,
    greatest_lower_bound(least_upper_bound(b,X_34),least_upper_bound(greatest_lower_bound(a,c),X_34)) = least_upper_bound(greatest_lower_bound(a,c),X_34),
    inference(subst,[],[refute_0_1730:[bind(X_16,$fot(X_34))]]) ).

cnf(refute_0_1732,plain,
    least_upper_bound(X_34,greatest_lower_bound(a,c)) = least_upper_bound(greatest_lower_bound(a,c),X_34),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_34)),bind(Y,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_1733,plain,
    ( least_upper_bound(X_34,greatest_lower_bound(a,c)) != least_upper_bound(greatest_lower_bound(a,c),X_34)
    | least_upper_bound(greatest_lower_bound(a,c),X_34) = least_upper_bound(X_34,greatest_lower_bound(a,c)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_34,greatest_lower_bound(a,c)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,c),X_34)))]]) ).

cnf(refute_0_1734,plain,
    least_upper_bound(greatest_lower_bound(a,c),X_34) = least_upper_bound(X_34,greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_34,greatest_lower_bound(a,c)),least_upper_bound(greatest_lower_bound(a,c),X_34)) )],[refute_0_1732,refute_0_1733]) ).

cnf(refute_0_1735,plain,
    ( greatest_lower_bound(least_upper_bound(b,X_34),least_upper_bound(greatest_lower_bound(a,c),X_34)) != least_upper_bound(greatest_lower_bound(a,c),X_34)
    | least_upper_bound(greatest_lower_bound(a,c),X_34) != least_upper_bound(X_34,greatest_lower_bound(a,c))
    | greatest_lower_bound(least_upper_bound(b,X_34),least_upper_bound(X_34,greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),X_34) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,X_34),least_upper_bound(greatest_lower_bound(a,c),X_34)),least_upper_bound(greatest_lower_bound(a,c),X_34)) ),[0,1],$fot(least_upper_bound(X_34,greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_1736,plain,
    ( greatest_lower_bound(least_upper_bound(b,X_34),least_upper_bound(greatest_lower_bound(a,c),X_34)) != least_upper_bound(greatest_lower_bound(a,c),X_34)
    | greatest_lower_bound(least_upper_bound(b,X_34),least_upper_bound(X_34,greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),X_34) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),X_34),least_upper_bound(X_34,greatest_lower_bound(a,c))) )],[refute_0_1734,refute_0_1735]) ).

cnf(refute_0_1737,plain,
    greatest_lower_bound(least_upper_bound(b,X_34),least_upper_bound(X_34,greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),X_34),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,X_34),least_upper_bound(greatest_lower_bound(a,c),X_34)),least_upper_bound(greatest_lower_bound(a,c),X_34)) )],[refute_0_1731,refute_0_1736]) ).

cnf(refute_0_1738,plain,
    greatest_lower_bound(least_upper_bound(b,multiply(b,X_98)),least_upper_bound(multiply(b,X_98),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),multiply(b,X_98)),
    inference(subst,[],[refute_0_1737:[bind(X_34,$fot(multiply(b,X_98)))]]) ).

cnf(refute_0_1739,plain,
    multiply(b,least_upper_bound(X_98,identity)) = least_upper_bound(b,multiply(b,X_98)),
    inference(subst,[],[refute_0_260:[bind(X_94,$fot(b)),bind(X_95,$fot(X_98))]]) ).

cnf(refute_0_1740,plain,
    ( multiply(b,least_upper_bound(X_98,identity)) != least_upper_bound(b,multiply(b,X_98))
    | least_upper_bound(b,multiply(b,X_98)) = multiply(b,least_upper_bound(X_98,identity)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(b,least_upper_bound(X_98,identity)))),bind(Y0,$fot(least_upper_bound(b,multiply(b,X_98))))]]) ).

cnf(refute_0_1741,plain,
    least_upper_bound(b,multiply(b,X_98)) = multiply(b,least_upper_bound(X_98,identity)),
    inference(resolve,[$cnf( $equal(multiply(b,least_upper_bound(X_98,identity)),least_upper_bound(b,multiply(b,X_98))) )],[refute_0_1739,refute_0_1740]) ).

cnf(refute_0_1742,plain,
    ( greatest_lower_bound(least_upper_bound(b,multiply(b,X_98)),least_upper_bound(multiply(b,X_98),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),multiply(b,X_98))
    | least_upper_bound(b,multiply(b,X_98)) != multiply(b,least_upper_bound(X_98,identity))
    | greatest_lower_bound(multiply(b,least_upper_bound(X_98,identity)),least_upper_bound(multiply(b,X_98),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),multiply(b,X_98)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,multiply(b,X_98)),least_upper_bound(multiply(b,X_98),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),multiply(b,X_98))) ),[0,0],$fot(multiply(b,least_upper_bound(X_98,identity)))]]) ).

cnf(refute_0_1743,plain,
    ( greatest_lower_bound(least_upper_bound(b,multiply(b,X_98)),least_upper_bound(multiply(b,X_98),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),multiply(b,X_98))
    | greatest_lower_bound(multiply(b,least_upper_bound(X_98,identity)),least_upper_bound(multiply(b,X_98),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),multiply(b,X_98)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,multiply(b,X_98)),multiply(b,least_upper_bound(X_98,identity))) )],[refute_0_1741,refute_0_1742]) ).

cnf(refute_0_1744,plain,
    greatest_lower_bound(multiply(b,least_upper_bound(X_98,identity)),least_upper_bound(multiply(b,X_98),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),multiply(b,X_98)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,multiply(b,X_98)),least_upper_bound(multiply(b,X_98),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),multiply(b,X_98))) )],[refute_0_1738,refute_0_1743]) ).

cnf(refute_0_1745,plain,
    greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(multiply(b,inverse(least_upper_bound(b,identity))),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_1744:[bind(X_98,$fot(inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_1746,plain,
    inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127))) = multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))),
    inference(subst,[],[p12_3:[bind(X,$fot(least_upper_bound(X_127,identity))),bind(Y,$fot(inverse(X_127)))]]) ).

cnf(refute_0_1747,plain,
    multiply(least_upper_bound(X_122,identity),inverse(X_122)) = least_upper_bound(inverse(X_122),multiply(X_122,inverse(X_122))),
    inference(subst,[],[refute_0_557:[bind(X_118,$fot(inverse(X_122))),bind(X_119,$fot(X_122))]]) ).

cnf(refute_0_1748,plain,
    multiply(X_122,inverse(X_122)) = identity,
    inference(subst,[],[refute_0_40:[bind(X,$fot(X_122))]]) ).

cnf(refute_0_1749,plain,
    ( multiply(X_122,inverse(X_122)) != identity
    | multiply(least_upper_bound(X_122,identity),inverse(X_122)) != least_upper_bound(inverse(X_122),multiply(X_122,inverse(X_122)))
    | multiply(least_upper_bound(X_122,identity),inverse(X_122)) = least_upper_bound(inverse(X_122),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_122,identity),inverse(X_122)),least_upper_bound(inverse(X_122),multiply(X_122,inverse(X_122)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1750,plain,
    ( multiply(least_upper_bound(X_122,identity),inverse(X_122)) != least_upper_bound(inverse(X_122),multiply(X_122,inverse(X_122)))
    | multiply(least_upper_bound(X_122,identity),inverse(X_122)) = least_upper_bound(inverse(X_122),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_122,inverse(X_122)),identity) )],[refute_0_1748,refute_0_1749]) ).

cnf(refute_0_1751,plain,
    multiply(least_upper_bound(X_122,identity),inverse(X_122)) = least_upper_bound(inverse(X_122),identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_122,identity),inverse(X_122)),least_upper_bound(inverse(X_122),multiply(X_122,inverse(X_122)))) )],[refute_0_1747,refute_0_1750]) ).

cnf(refute_0_1752,plain,
    least_upper_bound(inverse(X_122),identity) = least_upper_bound(identity,inverse(X_122)),
    inference(subst,[],[refute_0_256:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_122)))]]) ).

cnf(refute_0_1753,plain,
    ( multiply(least_upper_bound(X_122,identity),inverse(X_122)) != least_upper_bound(inverse(X_122),identity)
    | least_upper_bound(inverse(X_122),identity) != least_upper_bound(identity,inverse(X_122))
    | multiply(least_upper_bound(X_122,identity),inverse(X_122)) = least_upper_bound(identity,inverse(X_122)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_122,identity),inverse(X_122)),least_upper_bound(identity,inverse(X_122))) ),[0],$fot(least_upper_bound(inverse(X_122),identity))]]) ).

cnf(refute_0_1754,plain,
    ( multiply(least_upper_bound(X_122,identity),inverse(X_122)) != least_upper_bound(inverse(X_122),identity)
    | multiply(least_upper_bound(X_122,identity),inverse(X_122)) = least_upper_bound(identity,inverse(X_122)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_122),identity),least_upper_bound(identity,inverse(X_122))) )],[refute_0_1752,refute_0_1753]) ).

cnf(refute_0_1755,plain,
    multiply(least_upper_bound(X_122,identity),inverse(X_122)) = least_upper_bound(identity,inverse(X_122)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_122,identity),inverse(X_122)),least_upper_bound(inverse(X_122),identity)) )],[refute_0_1751,refute_0_1754]) ).

cnf(refute_0_1756,plain,
    multiply(least_upper_bound(X_127,identity),inverse(X_127)) = least_upper_bound(identity,inverse(X_127)),
    inference(subst,[],[refute_0_1755:[bind(X_122,$fot(X_127))]]) ).

cnf(refute_0_1757,plain,
    ( multiply(least_upper_bound(X_127,identity),inverse(X_127)) != least_upper_bound(identity,inverse(X_127))
    | inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127))) != multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity)))
    | inverse(least_upper_bound(identity,inverse(X_127))) = multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127))),multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity)))) ),[0,0],$fot(least_upper_bound(identity,inverse(X_127)))]]) ).

cnf(refute_0_1758,plain,
    ( inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127))) != multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity)))
    | inverse(least_upper_bound(identity,inverse(X_127))) = multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_127,identity),inverse(X_127)),least_upper_bound(identity,inverse(X_127))) )],[refute_0_1756,refute_0_1757]) ).

cnf(refute_0_1759,plain,
    inverse(least_upper_bound(identity,inverse(X_127))) = multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127))),multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity)))) )],[refute_0_1746,refute_0_1758]) ).

cnf(refute_0_1760,plain,
    inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127))) = multiply(X_127,inverse(least_upper_bound(X_127,identity))),
    inference(subst,[],[refute_0_146:[bind(X,$fot(X_127)),bind(X_17,$fot(least_upper_bound(X_127,identity)))]]) ).

cnf(refute_0_1761,plain,
    multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))) = inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127))),
    inference(subst,[],[refute_0_25:[bind(X,$fot(least_upper_bound(X_127,identity))),bind(Y,$fot(inverse(X_127)))]]) ).

cnf(refute_0_1762,plain,
    ( multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))) != inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127)))
    | inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127))) != multiply(X_127,inverse(least_upper_bound(X_127,identity)))
    | multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))) = multiply(X_127,inverse(least_upper_bound(X_127,identity))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127))))),bind(Z0,$fot(multiply(X_127,inverse(least_upper_bound(X_127,identity)))))]]) ).

cnf(refute_0_1763,plain,
    ( inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127))) != multiply(X_127,inverse(least_upper_bound(X_127,identity)))
    | multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))) = multiply(X_127,inverse(least_upper_bound(X_127,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))),inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127)))) )],[refute_0_1761,refute_0_1762]) ).

cnf(refute_0_1764,plain,
    multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))) = multiply(X_127,inverse(least_upper_bound(X_127,identity))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_127,identity),inverse(X_127))),multiply(X_127,inverse(least_upper_bound(X_127,identity)))) )],[refute_0_1760,refute_0_1763]) ).

cnf(refute_0_1765,plain,
    ( multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))) != multiply(X_127,inverse(least_upper_bound(X_127,identity)))
    | inverse(least_upper_bound(identity,inverse(X_127))) != multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity)))
    | inverse(least_upper_bound(identity,inverse(X_127))) = multiply(X_127,inverse(least_upper_bound(X_127,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_127))),multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity)))) ),[1],$fot(multiply(X_127,inverse(least_upper_bound(X_127,identity))))]]) ).

cnf(refute_0_1766,plain,
    ( inverse(least_upper_bound(identity,inverse(X_127))) != multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity)))
    | inverse(least_upper_bound(identity,inverse(X_127))) = multiply(X_127,inverse(least_upper_bound(X_127,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity))),multiply(X_127,inverse(least_upper_bound(X_127,identity)))) )],[refute_0_1764,refute_0_1765]) ).

cnf(refute_0_1767,plain,
    inverse(least_upper_bound(identity,inverse(X_127))) = multiply(X_127,inverse(least_upper_bound(X_127,identity))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_127))),multiply(inverse(inverse(X_127)),inverse(least_upper_bound(X_127,identity)))) )],[refute_0_1759,refute_0_1766]) ).

cnf(refute_0_1768,plain,
    inverse(least_upper_bound(identity,inverse(b))) = multiply(b,inverse(least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_1767:[bind(X_127,$fot(b))]]) ).

cnf(refute_0_1769,plain,
    ( inverse(least_upper_bound(identity,inverse(b))) != multiply(b,inverse(least_upper_bound(b,identity)))
    | multiply(b,inverse(least_upper_bound(b,identity))) = inverse(least_upper_bound(identity,inverse(b))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(b))))),bind(Y0,$fot(multiply(b,inverse(least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_1770,plain,
    multiply(b,inverse(least_upper_bound(b,identity))) = inverse(least_upper_bound(identity,inverse(b))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(b))),multiply(b,inverse(least_upper_bound(b,identity)))) )],[refute_0_1768,refute_0_1769]) ).

cnf(refute_0_1771,plain,
    ( multiply(b,inverse(least_upper_bound(b,identity))) != inverse(least_upper_bound(identity,inverse(b)))
    | greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(multiply(b,inverse(least_upper_bound(b,identity))),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))
    | greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(multiply(b,inverse(least_upper_bound(b,identity))),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))) ),[0,1,0],$fot(inverse(least_upper_bound(identity,inverse(b))))]]) ).

cnf(refute_0_1772,plain,
    ( greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(multiply(b,inverse(least_upper_bound(b,identity))),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))
    | greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,inverse(b)))) )],[refute_0_1770,refute_0_1771]) ).

cnf(refute_0_1773,plain,
    greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(multiply(b,inverse(least_upper_bound(b,identity))),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))) )],[refute_0_1745,refute_0_1772]) ).

cnf(refute_0_1774,plain,
    multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) = least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),multiply(inverse(X_112),greatest_lower_bound(X_112,identity))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(greatest_lower_bound(X_112,identity))),bind(Y,$fot(X_119)),bind(Z,$fot(inverse(X_112)))]]) ).

cnf(refute_0_1775,plain,
    multiply(inverse(X_112),greatest_lower_bound(X_112,identity)) = greatest_lower_bound(identity,multiply(inverse(X_112),identity)),
    inference(subst,[],[refute_0_94:[bind(X_104,$fot(X_112)),bind(X_105,$fot(identity))]]) ).

cnf(refute_0_1776,plain,
    inverse(X_112) = multiply(inverse(X_112),identity),
    inference(subst,[],[refute_0_187:[bind(X,$fot(inverse(X_112)))]]) ).

cnf(refute_0_1777,plain,
    ( inverse(X_112) != multiply(inverse(X_112),identity)
    | multiply(inverse(X_112),identity) = inverse(X_112) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(X_112))),bind(Y0,$fot(multiply(inverse(X_112),identity)))]]) ).

cnf(refute_0_1778,plain,
    multiply(inverse(X_112),identity) = inverse(X_112),
    inference(resolve,[$cnf( $equal(inverse(X_112),multiply(inverse(X_112),identity)) )],[refute_0_1776,refute_0_1777]) ).

cnf(refute_0_1779,plain,
    ( multiply(inverse(X_112),greatest_lower_bound(X_112,identity)) != greatest_lower_bound(identity,multiply(inverse(X_112),identity))
    | multiply(inverse(X_112),identity) != inverse(X_112)
    | multiply(inverse(X_112),greatest_lower_bound(X_112,identity)) = greatest_lower_bound(identity,inverse(X_112)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_112),greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,multiply(inverse(X_112),identity))) ),[1,1],$fot(inverse(X_112))]]) ).

cnf(refute_0_1780,plain,
    ( multiply(inverse(X_112),greatest_lower_bound(X_112,identity)) != greatest_lower_bound(identity,multiply(inverse(X_112),identity))
    | multiply(inverse(X_112),greatest_lower_bound(X_112,identity)) = greatest_lower_bound(identity,inverse(X_112)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_112),identity),inverse(X_112)) )],[refute_0_1778,refute_0_1779]) ).

cnf(refute_0_1781,plain,
    multiply(inverse(X_112),greatest_lower_bound(X_112,identity)) = greatest_lower_bound(identity,inverse(X_112)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_112),greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,multiply(inverse(X_112),identity))) )],[refute_0_1775,refute_0_1780]) ).

cnf(refute_0_1782,plain,
    ( multiply(inverse(X_112),greatest_lower_bound(X_112,identity)) != greatest_lower_bound(identity,inverse(X_112))
    | multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) != least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),multiply(inverse(X_112),greatest_lower_bound(X_112,identity)))
    | multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) = least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,inverse(X_112))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)),least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),multiply(inverse(X_112),greatest_lower_bound(X_112,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_112)))]]) ).

cnf(refute_0_1783,plain,
    ( multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) != least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),multiply(inverse(X_112),greatest_lower_bound(X_112,identity)))
    | multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) = least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,inverse(X_112))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_112),greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,inverse(X_112))) )],[refute_0_1781,refute_0_1782]) ).

cnf(refute_0_1784,plain,
    multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) = least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,inverse(X_112))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)),least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),multiply(inverse(X_112),greatest_lower_bound(X_112,identity)))) )],[refute_0_1774,refute_0_1783]) ).

cnf(refute_0_1785,plain,
    least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,inverse(X_112))) = least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity))),
    inference(subst,[],[refute_0_256:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_112)))),bind(Y,$fot(multiply(X_119,greatest_lower_bound(X_112,identity))))]]) ).

cnf(refute_0_1786,plain,
    ( multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) != least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,inverse(X_112)))
    | least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,inverse(X_112))) != least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity)))
    | multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity)))) ),[0],$fot(least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,inverse(X_112))))]]) ).

cnf(refute_0_1787,plain,
    ( multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) != least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,inverse(X_112)))
    | multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,inverse(X_112))),least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity)))) )],[refute_0_1785,refute_0_1786]) ).

cnf(refute_0_1788,plain,
    multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)),least_upper_bound(multiply(X_119,greatest_lower_bound(X_112,identity)),greatest_lower_bound(identity,inverse(X_112)))) )],[refute_0_1784,refute_0_1787]) ).

cnf(refute_0_1789,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))),
    inference(subst,[],[refute_0_1788:[bind(X_112,$fot(least_upper_bound(identity,X_99))),bind(X_119,$fot(X_391))]]) ).

cnf(refute_0_1790,plain,
    inverse(least_upper_bound(X_99,identity)) = multiply(inverse(multiply(inverse(X_99),least_upper_bound(X_99,identity))),inverse(X_99)),
    inference(subst,[],[refute_0_34:[bind(X_83,$fot(inverse(X_99))),bind(X_84,$fot(least_upper_bound(X_99,identity)))]]) ).

cnf(refute_0_1791,plain,
    multiply(inverse(X_98),least_upper_bound(X_98,identity)) = least_upper_bound(inverse(X_98),multiply(inverse(X_98),X_98)),
    inference(subst,[],[refute_0_260:[bind(X_94,$fot(inverse(X_98))),bind(X_95,$fot(X_98))]]) ).

cnf(refute_0_1792,plain,
    multiply(inverse(X_98),X_98) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_98))]]) ).

cnf(refute_0_1793,plain,
    ( multiply(inverse(X_98),X_98) != identity
    | multiply(inverse(X_98),least_upper_bound(X_98,identity)) != least_upper_bound(inverse(X_98),multiply(inverse(X_98),X_98))
    | multiply(inverse(X_98),least_upper_bound(X_98,identity)) = least_upper_bound(inverse(X_98),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_98),least_upper_bound(X_98,identity)),least_upper_bound(inverse(X_98),multiply(inverse(X_98),X_98))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1794,plain,
    ( multiply(inverse(X_98),least_upper_bound(X_98,identity)) != least_upper_bound(inverse(X_98),multiply(inverse(X_98),X_98))
    | multiply(inverse(X_98),least_upper_bound(X_98,identity)) = least_upper_bound(inverse(X_98),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_98),X_98),identity) )],[refute_0_1792,refute_0_1793]) ).

cnf(refute_0_1795,plain,
    multiply(inverse(X_98),least_upper_bound(X_98,identity)) = least_upper_bound(inverse(X_98),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_98),least_upper_bound(X_98,identity)),least_upper_bound(inverse(X_98),multiply(inverse(X_98),X_98))) )],[refute_0_1791,refute_0_1794]) ).

cnf(refute_0_1796,plain,
    least_upper_bound(inverse(X_98),identity) = least_upper_bound(identity,inverse(X_98)),
    inference(subst,[],[refute_0_256:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_98)))]]) ).

cnf(refute_0_1797,plain,
    ( multiply(inverse(X_98),least_upper_bound(X_98,identity)) != least_upper_bound(inverse(X_98),identity)
    | least_upper_bound(inverse(X_98),identity) != least_upper_bound(identity,inverse(X_98))
    | multiply(inverse(X_98),least_upper_bound(X_98,identity)) = least_upper_bound(identity,inverse(X_98)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_98),least_upper_bound(X_98,identity)),least_upper_bound(identity,inverse(X_98))) ),[0],$fot(least_upper_bound(inverse(X_98),identity))]]) ).

cnf(refute_0_1798,plain,
    ( multiply(inverse(X_98),least_upper_bound(X_98,identity)) != least_upper_bound(inverse(X_98),identity)
    | multiply(inverse(X_98),least_upper_bound(X_98,identity)) = least_upper_bound(identity,inverse(X_98)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_98),identity),least_upper_bound(identity,inverse(X_98))) )],[refute_0_1796,refute_0_1797]) ).

cnf(refute_0_1799,plain,
    multiply(inverse(X_98),least_upper_bound(X_98,identity)) = least_upper_bound(identity,inverse(X_98)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_98),least_upper_bound(X_98,identity)),least_upper_bound(inverse(X_98),identity)) )],[refute_0_1795,refute_0_1798]) ).

cnf(refute_0_1800,plain,
    multiply(inverse(X_99),least_upper_bound(X_99,identity)) = least_upper_bound(identity,inverse(X_99)),
    inference(subst,[],[refute_0_1799:[bind(X_98,$fot(X_99))]]) ).

cnf(refute_0_1801,plain,
    ( multiply(inverse(X_99),least_upper_bound(X_99,identity)) != least_upper_bound(identity,inverse(X_99))
    | inverse(least_upper_bound(X_99,identity)) != multiply(inverse(multiply(inverse(X_99),least_upper_bound(X_99,identity))),inverse(X_99))
    | inverse(least_upper_bound(X_99,identity)) = multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_99,identity)),multiply(inverse(multiply(inverse(X_99),least_upper_bound(X_99,identity))),inverse(X_99))) ),[1,0,0],$fot(least_upper_bound(identity,inverse(X_99)))]]) ).

cnf(refute_0_1802,plain,
    ( inverse(least_upper_bound(X_99,identity)) != multiply(inverse(multiply(inverse(X_99),least_upper_bound(X_99,identity))),inverse(X_99))
    | inverse(least_upper_bound(X_99,identity)) = multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_99),least_upper_bound(X_99,identity)),least_upper_bound(identity,inverse(X_99))) )],[refute_0_1800,refute_0_1801]) ).

cnf(refute_0_1803,plain,
    inverse(least_upper_bound(X_99,identity)) = multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_99,identity)),multiply(inverse(multiply(inverse(X_99),least_upper_bound(X_99,identity))),inverse(X_99))) )],[refute_0_1790,refute_0_1802]) ).

cnf(refute_0_1804,plain,
    multiply(X_99,identity) = X_99,
    inference(subst,[],[refute_0_189:[bind(X,$fot(X_99))]]) ).

cnf(refute_0_1805,plain,
    least_upper_bound(identity,multiply(X_99,identity)) = least_upper_bound(identity,multiply(X_99,identity)),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_99,identity)))]]) ).

cnf(refute_0_1806,plain,
    ( multiply(X_99,identity) != X_99
    | least_upper_bound(identity,multiply(X_99,identity)) != least_upper_bound(identity,multiply(X_99,identity))
    | least_upper_bound(identity,multiply(X_99,identity)) = least_upper_bound(identity,X_99) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_99,identity)),least_upper_bound(identity,multiply(X_99,identity))) ),[1,1],$fot(X_99)]]) ).

cnf(refute_0_1807,plain,
    ( multiply(X_99,identity) != X_99
    | least_upper_bound(identity,multiply(X_99,identity)) = least_upper_bound(identity,X_99) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_99,identity)),least_upper_bound(identity,multiply(X_99,identity))) )],[refute_0_1805,refute_0_1806]) ).

cnf(refute_0_1808,plain,
    least_upper_bound(identity,multiply(X_99,identity)) = least_upper_bound(identity,X_99),
    inference(resolve,[$cnf( $equal(multiply(X_99,identity),X_99) )],[refute_0_1804,refute_0_1807]) ).

cnf(refute_0_1809,plain,
    multiply(X_94,least_upper_bound(X_95,inverse(X_94))) = least_upper_bound(multiply(X_94,X_95),multiply(X_94,inverse(X_94))),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_94)),bind(Y,$fot(X_95)),bind(Z,$fot(inverse(X_94)))]]) ).

cnf(refute_0_1810,plain,
    multiply(X_94,inverse(X_94)) = identity,
    inference(subst,[],[refute_0_40:[bind(X,$fot(X_94))]]) ).

cnf(refute_0_1811,plain,
    ( multiply(X_94,inverse(X_94)) != identity
    | multiply(X_94,least_upper_bound(X_95,inverse(X_94))) != least_upper_bound(multiply(X_94,X_95),multiply(X_94,inverse(X_94)))
    | multiply(X_94,least_upper_bound(X_95,inverse(X_94))) = least_upper_bound(multiply(X_94,X_95),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_94,least_upper_bound(X_95,inverse(X_94))),least_upper_bound(multiply(X_94,X_95),multiply(X_94,inverse(X_94)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1812,plain,
    ( multiply(X_94,least_upper_bound(X_95,inverse(X_94))) != least_upper_bound(multiply(X_94,X_95),multiply(X_94,inverse(X_94)))
    | multiply(X_94,least_upper_bound(X_95,inverse(X_94))) = least_upper_bound(multiply(X_94,X_95),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_94,inverse(X_94)),identity) )],[refute_0_1810,refute_0_1811]) ).

cnf(refute_0_1813,plain,
    multiply(X_94,least_upper_bound(X_95,inverse(X_94))) = least_upper_bound(multiply(X_94,X_95),identity),
    inference(resolve,[$cnf( $equal(multiply(X_94,least_upper_bound(X_95,inverse(X_94))),least_upper_bound(multiply(X_94,X_95),multiply(X_94,inverse(X_94)))) )],[refute_0_1809,refute_0_1812]) ).

cnf(refute_0_1814,plain,
    least_upper_bound(multiply(X_94,X_95),identity) = least_upper_bound(identity,multiply(X_94,X_95)),
    inference(subst,[],[refute_0_256:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_94,X_95)))]]) ).

cnf(refute_0_1815,plain,
    ( multiply(X_94,least_upper_bound(X_95,inverse(X_94))) != least_upper_bound(multiply(X_94,X_95),identity)
    | least_upper_bound(multiply(X_94,X_95),identity) != least_upper_bound(identity,multiply(X_94,X_95))
    | multiply(X_94,least_upper_bound(X_95,inverse(X_94))) = least_upper_bound(identity,multiply(X_94,X_95)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_94,least_upper_bound(X_95,inverse(X_94))),least_upper_bound(identity,multiply(X_94,X_95))) ),[0],$fot(least_upper_bound(multiply(X_94,X_95),identity))]]) ).

cnf(refute_0_1816,plain,
    ( multiply(X_94,least_upper_bound(X_95,inverse(X_94))) != least_upper_bound(multiply(X_94,X_95),identity)
    | multiply(X_94,least_upper_bound(X_95,inverse(X_94))) = least_upper_bound(identity,multiply(X_94,X_95)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_94,X_95),identity),least_upper_bound(identity,multiply(X_94,X_95))) )],[refute_0_1814,refute_0_1815]) ).

cnf(refute_0_1817,plain,
    multiply(X_94,least_upper_bound(X_95,inverse(X_94))) = least_upper_bound(identity,multiply(X_94,X_95)),
    inference(resolve,[$cnf( $equal(multiply(X_94,least_upper_bound(X_95,inverse(X_94))),least_upper_bound(multiply(X_94,X_95),identity)) )],[refute_0_1813,refute_0_1816]) ).

cnf(refute_0_1818,plain,
    multiply(X_99,least_upper_bound(identity,inverse(X_99))) = least_upper_bound(identity,multiply(X_99,identity)),
    inference(subst,[],[refute_0_1817:[bind(X_94,$fot(X_99)),bind(X_95,$fot(identity))]]) ).

cnf(refute_0_1819,plain,
    ( multiply(X_99,least_upper_bound(identity,inverse(X_99))) != least_upper_bound(identity,multiply(X_99,identity))
    | least_upper_bound(identity,multiply(X_99,identity)) != least_upper_bound(identity,X_99)
    | multiply(X_99,least_upper_bound(identity,inverse(X_99))) = least_upper_bound(identity,X_99) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(X_99,least_upper_bound(identity,inverse(X_99))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_99,identity)))),bind(Z0,$fot(least_upper_bound(identity,X_99)))]]) ).

cnf(refute_0_1820,plain,
    ( least_upper_bound(identity,multiply(X_99,identity)) != least_upper_bound(identity,X_99)
    | multiply(X_99,least_upper_bound(identity,inverse(X_99))) = least_upper_bound(identity,X_99) ),
    inference(resolve,[$cnf( $equal(multiply(X_99,least_upper_bound(identity,inverse(X_99))),least_upper_bound(identity,multiply(X_99,identity))) )],[refute_0_1818,refute_0_1819]) ).

cnf(refute_0_1821,plain,
    multiply(X_99,least_upper_bound(identity,inverse(X_99))) = least_upper_bound(identity,X_99),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_99,identity)),least_upper_bound(identity,X_99)) )],[refute_0_1808,refute_0_1820]) ).

cnf(refute_0_1822,plain,
    inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))) = inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))),
    introduced(tautology,[refl,[$fot(inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))))]]) ).

cnf(refute_0_1823,plain,
    ( multiply(X_99,least_upper_bound(identity,inverse(X_99))) != least_upper_bound(identity,X_99)
    | inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))) != inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99))))
    | inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))) = inverse(least_upper_bound(identity,X_99)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))),inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99))))) ),[1,0],$fot(least_upper_bound(identity,X_99))]]) ).

cnf(refute_0_1824,plain,
    ( multiply(X_99,least_upper_bound(identity,inverse(X_99))) != least_upper_bound(identity,X_99)
    | inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))) = inverse(least_upper_bound(identity,X_99)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))),inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99))))) )],[refute_0_1822,refute_0_1823]) ).

cnf(refute_0_1825,plain,
    inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))) = inverse(least_upper_bound(identity,X_99)),
    inference(resolve,[$cnf( $equal(multiply(X_99,least_upper_bound(identity,inverse(X_99))),least_upper_bound(identity,X_99)) )],[refute_0_1821,refute_0_1824]) ).

cnf(refute_0_1826,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) = inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))),
    inference(subst,[],[refute_0_25:[bind(X,$fot(X_99)),bind(Y,$fot(least_upper_bound(identity,inverse(X_99))))]]) ).

cnf(refute_0_1827,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) != inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99))))
    | inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))) != inverse(least_upper_bound(identity,X_99))
    | multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) = inverse(least_upper_bound(identity,X_99)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)))),bind(Y0,$fot(inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_99))))]]) ).

cnf(refute_0_1828,plain,
    ( inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))) != inverse(least_upper_bound(identity,X_99))
    | multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) = inverse(least_upper_bound(identity,X_99)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)),inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99))))) )],[refute_0_1826,refute_0_1827]) ).

cnf(refute_0_1829,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) = inverse(least_upper_bound(identity,X_99)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_99,least_upper_bound(identity,inverse(X_99)))),inverse(least_upper_bound(identity,X_99))) )],[refute_0_1825,refute_0_1828]) ).

cnf(refute_0_1830,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)) != inverse(least_upper_bound(identity,X_99))
    | inverse(least_upper_bound(X_99,identity)) != multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99))
    | inverse(least_upper_bound(X_99,identity)) = inverse(least_upper_bound(identity,X_99)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_99,identity)),multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99))) ),[1],$fot(inverse(least_upper_bound(identity,X_99)))]]) ).

cnf(refute_0_1831,plain,
    ( inverse(least_upper_bound(X_99,identity)) != multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99))
    | inverse(least_upper_bound(X_99,identity)) = inverse(least_upper_bound(identity,X_99)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99)),inverse(least_upper_bound(identity,X_99))) )],[refute_0_1829,refute_0_1830]) ).

cnf(refute_0_1832,plain,
    inverse(least_upper_bound(X_99,identity)) = inverse(least_upper_bound(identity,X_99)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_99,identity)),multiply(inverse(least_upper_bound(identity,inverse(X_99))),inverse(X_99))) )],[refute_0_1803,refute_0_1831]) ).

cnf(refute_0_1833,plain,
    ( inverse(least_upper_bound(X_99,identity)) != inverse(least_upper_bound(identity,X_99))
    | inverse(least_upper_bound(identity,X_99)) = inverse(least_upper_bound(X_99,identity)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(least_upper_bound(X_99,identity)))),bind(Y0,$fot(inverse(least_upper_bound(identity,X_99))))]]) ).

cnf(refute_0_1834,plain,
    inverse(least_upper_bound(identity,X_99)) = inverse(least_upper_bound(X_99,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_99,identity)),inverse(least_upper_bound(identity,X_99))) )],[refute_0_1832,refute_0_1833]) ).

cnf(refute_0_1835,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))
    | inverse(least_upper_bound(identity,X_99)) != inverse(least_upper_bound(X_99,identity))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))) ),[0,0,1],$fot(inverse(least_upper_bound(X_99,identity)))]]) ).

cnf(refute_0_1836,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_99)),inverse(least_upper_bound(X_99,identity))) )],[refute_0_1834,refute_0_1835]) ).

cnf(refute_0_1837,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))) )],[refute_0_1789,refute_0_1836]) ).

cnf(refute_0_1838,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),
    inference(subst,[],[refute_0_189:[bind(X,$fot(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))))]]) ).

cnf(refute_0_1839,plain,
    greatest_lower_bound(identity,least_upper_bound(identity,X_99)) = identity,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_99))]]) ).

cnf(refute_0_1840,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))))]]) ).

cnf(refute_0_1841,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))
    | greatest_lower_bound(identity,least_upper_bound(identity,X_99)) != identity
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1842,plain,
    ( greatest_lower_bound(identity,least_upper_bound(identity,X_99)) != identity
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))) )],[refute_0_1840,refute_0_1841]) ).

cnf(refute_0_1843,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_99)),identity) )],[refute_0_1839,refute_0_1842]) ).

cnf(refute_0_1844,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity)
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity) != least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))))),bind(Y0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity))),bind(Z0,$fot(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))))]]) ).

cnf(refute_0_1845,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity) != least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity)) )],[refute_0_1843,refute_0_1844]) ).

cnf(refute_0_1846,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity),least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))) )],[refute_0_1838,refute_0_1845]) ).

cnf(refute_0_1847,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),
    inference(subst,[],[refute_0_868:[bind(X_103,$fot(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))))),bind(X_104,$fot(least_upper_bound(identity,X_99))),bind(X_105,$fot(identity))]]) ).

cnf(refute_0_1848,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) != least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))))),bind(Z0,$fot(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))))]]) ).

cnf(refute_0_1849,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) != least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)),multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))) )],[refute_0_1847,refute_0_1848]) ).

cnf(refute_0_1850,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))) )],[refute_0_1846,refute_0_1849]) ).

cnf(refute_0_1851,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) != least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))
    | least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))) ),[0],$fot(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))))]]) ).

cnf(refute_0_1852,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))
    | least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)),least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))) )],[refute_0_1850,refute_0_1851]) ).

cnf(refute_0_1853,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),identity) = least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),
    inference(subst,[],[refute_0_189:[bind(X,$fot(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))))]]) ).

cnf(refute_0_1854,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))))]]) ).

cnf(refute_0_1855,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))
    | greatest_lower_bound(identity,least_upper_bound(identity,X_99)) != identity
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1856,plain,
    ( greatest_lower_bound(identity,least_upper_bound(identity,X_99)) != identity
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))) )],[refute_0_1854,refute_0_1855]) ).

cnf(refute_0_1857,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_99)),identity) )],[refute_0_1839,refute_0_1856]) ).

cnf(refute_0_1858,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),identity)
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),identity) != least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))))),bind(Y0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),identity))),bind(Z0,$fot(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))))]]) ).

cnf(refute_0_1859,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),identity) != least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),identity)) )],[refute_0_1857,refute_0_1858]) ).

cnf(refute_0_1860,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) = least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),identity),least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))) )],[refute_0_1853,refute_0_1859]) ).

cnf(refute_0_1861,plain,
    multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity))),
    inference(subst,[],[refute_0_1788:[bind(X_112,$fot(X_390)),bind(X_119,$fot(X_391))]]) ).

cnf(refute_0_1862,plain,
    greatest_lower_bound(identity,X_390) = greatest_lower_bound(X_390,identity),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_390))]]) ).

cnf(refute_0_1863,plain,
    ( greatest_lower_bound(identity,X_390) != greatest_lower_bound(X_390,identity)
    | greatest_lower_bound(X_390,identity) = greatest_lower_bound(identity,X_390) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(identity,X_390))),bind(Y0,$fot(greatest_lower_bound(X_390,identity)))]]) ).

cnf(refute_0_1864,plain,
    greatest_lower_bound(X_390,identity) = greatest_lower_bound(identity,X_390),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_390),greatest_lower_bound(X_390,identity)) )],[refute_0_1862,refute_0_1863]) ).

cnf(refute_0_1865,plain,
    ( multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity)))
    | greatest_lower_bound(X_390,identity) != greatest_lower_bound(identity,X_390)
    | multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity)))) ),[0,1],$fot(greatest_lower_bound(identity,X_390))]]) ).

cnf(refute_0_1866,plain,
    ( multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity)))
    | multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_390,identity),greatest_lower_bound(identity,X_390)) )],[refute_0_1864,refute_0_1865]) ).

cnf(refute_0_1867,plain,
    multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)) = least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity)))) )],[refute_0_1861,refute_0_1866]) ).

cnf(refute_0_1868,plain,
    ( multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity)))
    | least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity))) = multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity)))))]]) ).

cnf(refute_0_1869,plain,
    least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity))) = multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,inverse(X_112)),greatest_lower_bound(X_112,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(X_112)),multiply(X_119,greatest_lower_bound(X_112,identity)))) )],[refute_0_1788,refute_0_1868]) ).

cnf(refute_0_1870,plain,
    least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity))) = multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity)),
    inference(subst,[],[refute_0_1869:[bind(X_112,$fot(X_390)),bind(X_119,$fot(X_391))]]) ).

cnf(refute_0_1871,plain,
    ( multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity)))
    | least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity))) != multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity))
    | multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)) = multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)),multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity))))]]) ).

cnf(refute_0_1872,plain,
    ( multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)) != least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity)))
    | multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)) = multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity))),multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity))) )],[refute_0_1870,refute_0_1871]) ).

cnf(refute_0_1873,plain,
    multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)) = multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)),least_upper_bound(greatest_lower_bound(identity,inverse(X_390)),multiply(X_391,greatest_lower_bound(X_390,identity)))) )],[refute_0_1867,refute_0_1872]) ).

cnf(refute_0_1874,plain,
    ( multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)) != multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity))
    | multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity)) = multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)))),bind(Y0,$fot(multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity))))]]) ).

cnf(refute_0_1875,plain,
    multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity)) = multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(identity,X_390)),multiply(least_upper_bound(X_391,inverse(X_390)),greatest_lower_bound(X_390,identity))) )],[refute_0_1873,refute_0_1874]) ).

cnf(refute_0_1876,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),
    inference(subst,[],[refute_0_1875:[bind(X_390,$fot(least_upper_bound(identity,X_99)))]]) ).

cnf(refute_0_1877,plain,
    least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)),
    inference(subst,[],[refute_0_1869:[bind(X_112,$fot(least_upper_bound(identity,X_99))),bind(X_119,$fot(X_391))]]) ).

cnf(refute_0_1878,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity))
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))))),bind(Y0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)))),bind(Z0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))))]]) ).

cnf(refute_0_1879,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))),multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity))) )],[refute_0_1877,refute_0_1878]) ).

cnf(refute_0_1880,plain,
    least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)),multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))) )],[refute_0_1876,refute_0_1879]) ).

cnf(refute_0_1881,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) != least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) = least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))))),bind(Y0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))))),bind(Z0,$fot(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))))]]) ).

cnf(refute_0_1882,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))) != least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) = least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))),multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99)))) )],[refute_0_1880,refute_0_1881]) ).

cnf(refute_0_1883,plain,
    least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) = least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),greatest_lower_bound(identity,least_upper_bound(identity,X_99))),least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))) )],[refute_0_1860,refute_0_1882]) ).

cnf(refute_0_1884,plain,
    ( least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))) != least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))
    | least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))))]]) ).

cnf(refute_0_1885,plain,
    ( least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))
    | least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity))),least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99)))) )],[refute_0_1883,refute_0_1884]) ).

cnf(refute_0_1886,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))
    | least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))) )],[refute_0_1852,refute_0_1885]) ).

cnf(refute_0_1887,plain,
    least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(X_391,inverse(least_upper_bound(identity,X_99))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(identity,X_99),identity)),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(identity,X_99),identity)))) )],[refute_0_1837,refute_0_1886]) ).

cnf(refute_0_1888,plain,
    least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(inverse(b),identity))) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),
    inference(subst,[],[refute_0_1887:[bind(X_391,$fot(greatest_lower_bound(a,c))),bind(X_99,$fot(inverse(b)))]]) ).

cnf(refute_0_1889,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(X_99,identity))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),
    inference(subst,[],[refute_0_1788:[bind(X_112,$fot(least_upper_bound(X_99,identity))),bind(X_119,$fot(X_391))]]) ).

cnf(refute_0_1890,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(X_99,identity))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))
    | inverse(least_upper_bound(X_99,identity)) != inverse(least_upper_bound(identity,X_99))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(X_99,identity))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))) ),[1,0,1],$fot(inverse(least_upper_bound(identity,X_99)))]]) ).

cnf(refute_0_1891,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(X_99,identity))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_99,identity)),inverse(least_upper_bound(identity,X_99))) )],[refute_0_1832,refute_0_1890]) ).

cnf(refute_0_1892,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(X_99,identity))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))) )],[refute_0_1889,refute_0_1891]) ).

cnf(refute_0_1893,plain,
    greatest_lower_bound(identity,least_upper_bound(X_99,identity)) = identity,
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(identity)),bind(X_13,$fot(X_99))]]) ).

cnf(refute_0_1894,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))))]]) ).

cnf(refute_0_1895,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity)))
    | greatest_lower_bound(identity,least_upper_bound(X_99,identity)) != identity
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))),multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1896,plain,
    ( greatest_lower_bound(identity,least_upper_bound(X_99,identity)) != identity
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))),multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity)))) )],[refute_0_1894,refute_0_1895]) ).

cnf(refute_0_1897,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_99,identity)),identity) )],[refute_0_1893,refute_0_1896]) ).

cnf(refute_0_1898,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity)
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity) != least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))))),bind(Y0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity))),bind(Z0,$fot(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))))]]) ).

cnf(refute_0_1899,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity) != least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))),multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity)) )],[refute_0_1897,refute_0_1898]) ).

cnf(refute_0_1900,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),identity),least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))) )],[refute_0_1838,refute_0_1899]) ).

cnf(refute_0_1901,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))),
    inference(subst,[],[refute_0_1875:[bind(X_390,$fot(least_upper_bound(X_99,identity)))]]) ).

cnf(refute_0_1902,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))) != least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) != multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))))),bind(Z0,$fot(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))))]]) ).

cnf(refute_0_1903,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))) != least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)),multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity)))) )],[refute_0_1901,refute_0_1902]) ).

cnf(refute_0_1904,plain,
    multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(identity,least_upper_bound(X_99,identity))),least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))) )],[refute_0_1900,refute_0_1903]) ).

cnf(refute_0_1905,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) != least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))
    | multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))
    | least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))) ),[0],$fot(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))))]]) ).

cnf(refute_0_1906,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))
    | least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)),least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity)))) )],[refute_0_1904,refute_0_1905]) ).

cnf(refute_0_1907,plain,
    multiply(X_391,identity) = X_391,
    inference(subst,[],[refute_0_189:[bind(X,$fot(X_391))]]) ).

cnf(refute_0_1908,plain,
    multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))),
    introduced(tautology,[refl,[$fot(multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))))]]) ).

cnf(refute_0_1909,plain,
    ( multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))) != multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity)))
    | greatest_lower_bound(identity,least_upper_bound(X_99,identity)) != identity
    | multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = multiply(X_391,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))),multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1910,plain,
    ( greatest_lower_bound(identity,least_upper_bound(X_99,identity)) != identity
    | multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = multiply(X_391,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))),multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity)))) )],[refute_0_1908,refute_0_1909]) ).

cnf(refute_0_1911,plain,
    multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = multiply(X_391,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_99,identity)),identity) )],[refute_0_1893,refute_0_1910]) ).

cnf(refute_0_1912,plain,
    ( multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))) != multiply(X_391,identity)
    | multiply(X_391,identity) != X_391
    | multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = X_391 ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))))),bind(Y0,$fot(multiply(X_391,identity))),bind(Z0,$fot(X_391))]]) ).

cnf(refute_0_1913,plain,
    ( multiply(X_391,identity) != X_391
    | multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = X_391 ),
    inference(resolve,[$cnf( $equal(multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))),multiply(X_391,identity)) )],[refute_0_1911,refute_0_1912]) ).

cnf(refute_0_1914,plain,
    multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))) = X_391,
    inference(resolve,[$cnf( $equal(multiply(X_391,identity),X_391) )],[refute_0_1907,refute_0_1913]) ).

cnf(refute_0_1915,plain,
    multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))),
    inference(subst,[],[refute_0_868:[bind(X_103,$fot(X_391)),bind(X_104,$fot(least_upper_bound(X_99,identity))),bind(X_105,$fot(identity))]]) ).

cnf(refute_0_1916,plain,
    ( multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))) != X_391
    | multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)) != multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity)))
    | multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = X_391 ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))),bind(Y0,$fot(multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))))),bind(Z0,$fot(X_391))]]) ).

cnf(refute_0_1917,plain,
    ( multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))) != X_391
    | multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = X_391 ),
    inference(resolve,[$cnf( $equal(multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)),multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity)))) )],[refute_0_1915,refute_0_1916]) ).

cnf(refute_0_1918,plain,
    multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)) = X_391,
    inference(resolve,[$cnf( $equal(multiply(X_391,greatest_lower_bound(identity,least_upper_bound(X_99,identity))),X_391) )],[refute_0_1914,refute_0_1917]) ).

cnf(refute_0_1919,plain,
    least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),
    introduced(tautology,[refl,[$fot(least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))))]]) ).

cnf(refute_0_1920,plain,
    ( multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)) != X_391
    | least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) != least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))
    | least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))) ),[1,1],$fot(X_391)]]) ).

cnf(refute_0_1921,plain,
    ( multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)) != X_391
    | least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))) )],[refute_0_1919,refute_0_1920]) ).

cnf(refute_0_1922,plain,
    least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391),
    inference(resolve,[$cnf( $equal(multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)),X_391) )],[refute_0_1918,refute_0_1921]) ).

cnf(refute_0_1923,plain,
    multiply(inverse(X_111),greatest_lower_bound(identity,X_111)) = greatest_lower_bound(identity,multiply(inverse(X_111),identity)),
    inference(subst,[],[refute_0_134:[bind(X_104,$fot(identity)),bind(X_105,$fot(X_111))]]) ).

cnf(refute_0_1924,plain,
    inverse(X_111) = multiply(inverse(X_111),identity),
    inference(subst,[],[refute_0_187:[bind(X,$fot(inverse(X_111)))]]) ).

cnf(refute_0_1925,plain,
    ( inverse(X_111) != multiply(inverse(X_111),identity)
    | multiply(inverse(X_111),identity) = inverse(X_111) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(X_111))),bind(Y0,$fot(multiply(inverse(X_111),identity)))]]) ).

cnf(refute_0_1926,plain,
    multiply(inverse(X_111),identity) = inverse(X_111),
    inference(resolve,[$cnf( $equal(inverse(X_111),multiply(inverse(X_111),identity)) )],[refute_0_1924,refute_0_1925]) ).

cnf(refute_0_1927,plain,
    ( multiply(inverse(X_111),greatest_lower_bound(identity,X_111)) != greatest_lower_bound(identity,multiply(inverse(X_111),identity))
    | multiply(inverse(X_111),identity) != inverse(X_111)
    | multiply(inverse(X_111),greatest_lower_bound(identity,X_111)) = greatest_lower_bound(identity,inverse(X_111)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_111),greatest_lower_bound(identity,X_111)),greatest_lower_bound(identity,multiply(inverse(X_111),identity))) ),[1,1],$fot(inverse(X_111))]]) ).

cnf(refute_0_1928,plain,
    ( multiply(inverse(X_111),greatest_lower_bound(identity,X_111)) != greatest_lower_bound(identity,multiply(inverse(X_111),identity))
    | multiply(inverse(X_111),greatest_lower_bound(identity,X_111)) = greatest_lower_bound(identity,inverse(X_111)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_111),identity),inverse(X_111)) )],[refute_0_1926,refute_0_1927]) ).

cnf(refute_0_1929,plain,
    multiply(inverse(X_111),greatest_lower_bound(identity,X_111)) = greatest_lower_bound(identity,inverse(X_111)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_111),greatest_lower_bound(identity,X_111)),greatest_lower_bound(identity,multiply(inverse(X_111),identity))) )],[refute_0_1923,refute_0_1928]) ).

cnf(refute_0_1930,plain,
    multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
    inference(subst,[],[refute_0_1929:[bind(X_111,$fot(least_upper_bound(identity,Y)))]]) ).

cnf(refute_0_1931,plain,
    greatest_lower_bound(identity,least_upper_bound(identity,Y)) = identity,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity))]]) ).

cnf(refute_0_1932,plain,
    ( multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
    | greatest_lower_bound(identity,least_upper_bound(identity,Y)) != identity
    | multiply(inverse(least_upper_bound(identity,Y)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_1933,plain,
    ( multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
    | multiply(inverse(least_upper_bound(identity,Y)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,Y)),identity) )],[refute_0_1931,refute_0_1932]) ).

cnf(refute_0_1934,plain,
    multiply(inverse(least_upper_bound(identity,Y)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,least_upper_bound(identity,Y))),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1930,refute_0_1933]) ).

cnf(refute_0_1935,plain,
    multiply(inverse(least_upper_bound(identity,Y)),identity) = inverse(least_upper_bound(identity,Y)),
    inference(subst,[],[refute_0_189:[bind(X,$fot(inverse(least_upper_bound(identity,Y))))]]) ).

cnf(refute_0_1936,plain,
    ( multiply(inverse(least_upper_bound(identity,Y)),identity) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
    | multiply(inverse(least_upper_bound(identity,Y)),identity) != inverse(least_upper_bound(identity,Y))
    | inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),identity),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) ),[0],$fot(inverse(least_upper_bound(identity,Y)))]]) ).

cnf(refute_0_1937,plain,
    ( multiply(inverse(least_upper_bound(identity,Y)),identity) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
    | inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),identity),inverse(least_upper_bound(identity,Y))) )],[refute_0_1935,refute_0_1936]) ).

cnf(refute_0_1938,plain,
    inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,Y)),identity),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1934,refute_0_1937]) ).

cnf(refute_0_1939,plain,
    ( inverse(least_upper_bound(identity,Y)) != greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))
    | greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) = inverse(least_upper_bound(identity,Y)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(least_upper_bound(identity,Y)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))))]]) ).

cnf(refute_0_1940,plain,
    greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y))) = inverse(least_upper_bound(identity,Y)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1938,refute_0_1939]) ).

cnf(refute_0_1941,plain,
    greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))) = inverse(least_upper_bound(identity,X_99)),
    inference(subst,[],[refute_0_1940:[bind(Y,$fot(X_99))]]) ).

cnf(refute_0_1942,plain,
    least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) = least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),
    introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))))]]) ).

cnf(refute_0_1943,plain,
    ( greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))) != inverse(least_upper_bound(identity,X_99))
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))) ),[1,0],$fot(inverse(least_upper_bound(identity,X_99)))]]) ).

cnf(refute_0_1944,plain,
    ( greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))) != inverse(least_upper_bound(identity,X_99))
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))) )],[refute_0_1942,refute_0_1943]) ).

cnf(refute_0_1945,plain,
    least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),inverse(least_upper_bound(identity,X_99))) )],[refute_0_1941,refute_0_1944]) ).

cnf(refute_0_1946,plain,
    ( least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) != least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))
    | least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) != least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391)
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))))),bind(Z0,$fot(least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391)))]]) ).

cnf(refute_0_1947,plain,
    ( least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) != least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391)
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))) )],[refute_0_1945,refute_0_1946]) ).

cnf(refute_0_1948,plain,
    least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_99)),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391)) )],[refute_0_1922,refute_0_1947]) ).

cnf(refute_0_1949,plain,
    ( least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))
    | least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))) != least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391)
    | least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391)) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))))]]) ).

cnf(refute_0_1950,plain,
    ( least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))
    | least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity))),least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391)) )],[refute_0_1948,refute_0_1949]) ).

cnf(refute_0_1951,plain,
    ( multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)) != least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))
    | least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))) )],[refute_0_1906,refute_0_1950]) ).

cnf(refute_0_1952,plain,
    least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) = least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),greatest_lower_bound(least_upper_bound(X_99,identity),identity)),least_upper_bound(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X_99))),multiply(X_391,greatest_lower_bound(least_upper_bound(X_99,identity),identity)))) )],[refute_0_1892,refute_0_1951]) ).

cnf(refute_0_1953,plain,
    ( least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) != least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391)
    | least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391)))]]) ).

cnf(refute_0_1954,plain,
    least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391) = least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_391,inverse(least_upper_bound(X_99,identity))),least_upper_bound(inverse(least_upper_bound(identity,X_99)),X_391)) )],[refute_0_1952,refute_0_1953]) ).

cnf(refute_0_1955,plain,
    least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(inverse(b),identity))),
    inference(subst,[],[refute_0_1954:[bind(X_391,$fot(greatest_lower_bound(a,c))),bind(X_99,$fot(inverse(b)))]]) ).

cnf(refute_0_1956,plain,
    ( least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(inverse(b),identity))) != least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))
    | least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)) != least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(inverse(b),identity)))
    | least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(inverse(b),identity))))),bind(Z0,$fot(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))))]]) ).

cnf(refute_0_1957,plain,
    ( least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(inverse(b),identity))) != least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))
    | least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)),least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(inverse(b),identity)))) )],[refute_0_1955,refute_0_1956]) ).

cnf(refute_0_1958,plain,
    least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(inverse(b),identity))),least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) )],[refute_0_1888,refute_0_1957]) ).

cnf(refute_0_1959,plain,
    greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1960,plain,
    ( greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) != greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)))
    | least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)) != least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))
    | greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)))) ),[1,1],$fot(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))))]]) ).

cnf(refute_0_1961,plain,
    ( least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)) != least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))
    | greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)))) )],[refute_0_1959,refute_0_1960]) ).

cnf(refute_0_1962,plain,
    greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)),least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) )],[refute_0_1958,refute_0_1961]) ).

cnf(refute_0_1963,plain,
    multiply(b,identity) = b,
    inference(subst,[],[refute_0_189:[bind(X,$fot(b))]]) ).

cnf(refute_0_1964,plain,
    multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(X_182,identity))) = least_upper_bound(identity,inverse(least_upper_bound(X_182,identity))),
    inference(subst,[],[refute_0_1755:[bind(X_122,$fot(least_upper_bound(X_182,identity)))]]) ).

cnf(refute_0_1965,plain,
    inverse(least_upper_bound(X_182,identity)) = inverse(least_upper_bound(identity,X_182)),
    inference(subst,[],[refute_0_1832:[bind(X_99,$fot(X_182))]]) ).

cnf(refute_0_1966,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(X_182,identity))) != least_upper_bound(identity,inverse(least_upper_bound(X_182,identity)))
    | inverse(least_upper_bound(X_182,identity)) != inverse(least_upper_bound(identity,X_182))
    | multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))) = least_upper_bound(identity,inverse(least_upper_bound(X_182,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(X_182,identity))),least_upper_bound(identity,inverse(least_upper_bound(X_182,identity)))) ),[0,1],$fot(inverse(least_upper_bound(identity,X_182)))]]) ).

cnf(refute_0_1967,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(X_182,identity))) != least_upper_bound(identity,inverse(least_upper_bound(X_182,identity)))
    | multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))) = least_upper_bound(identity,inverse(least_upper_bound(X_182,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) )],[refute_0_1965,refute_0_1966]) ).

cnf(refute_0_1968,plain,
    multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))) = least_upper_bound(identity,inverse(least_upper_bound(X_182,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(X_182,identity))),least_upper_bound(identity,inverse(least_upper_bound(X_182,identity)))) )],[refute_0_1964,refute_0_1967]) ).

cnf(refute_0_1969,plain,
    multiply(least_upper_bound(X_128,least_upper_bound(X_15,X_128)),inverse(least_upper_bound(X_15,X_128))) = least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128)))),
    inference(subst,[],[refute_0_533:[bind(X_119,$fot(X_128)),bind(X_120,$fot(least_upper_bound(X_15,X_128)))]]) ).

cnf(refute_0_1970,plain,
    least_upper_bound(X_15,X_128) = least_upper_bound(X_128,least_upper_bound(X_15,X_128)),
    inference(subst,[],[refute_0_613:[bind(X_16,$fot(X_128))]]) ).

cnf(refute_0_1971,plain,
    ( least_upper_bound(X_15,X_128) != least_upper_bound(X_128,least_upper_bound(X_15,X_128))
    | least_upper_bound(X_128,least_upper_bound(X_15,X_128)) = least_upper_bound(X_15,X_128) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_15,X_128))),bind(Y0,$fot(least_upper_bound(X_128,least_upper_bound(X_15,X_128))))]]) ).

cnf(refute_0_1972,plain,
    least_upper_bound(X_128,least_upper_bound(X_15,X_128)) = least_upper_bound(X_15,X_128),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,X_128),least_upper_bound(X_128,least_upper_bound(X_15,X_128))) )],[refute_0_1970,refute_0_1971]) ).

cnf(refute_0_1973,plain,
    ( multiply(least_upper_bound(X_128,least_upper_bound(X_15,X_128)),inverse(least_upper_bound(X_15,X_128))) != least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128))))
    | least_upper_bound(X_128,least_upper_bound(X_15,X_128)) != least_upper_bound(X_15,X_128)
    | multiply(least_upper_bound(X_15,X_128),inverse(least_upper_bound(X_15,X_128))) = least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_128,least_upper_bound(X_15,X_128)),inverse(least_upper_bound(X_15,X_128))),least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128))))) ),[0,0],$fot(least_upper_bound(X_15,X_128))]]) ).

cnf(refute_0_1974,plain,
    ( multiply(least_upper_bound(X_128,least_upper_bound(X_15,X_128)),inverse(least_upper_bound(X_15,X_128))) != least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128))))
    | multiply(least_upper_bound(X_15,X_128),inverse(least_upper_bound(X_15,X_128))) = least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_128,least_upper_bound(X_15,X_128)),least_upper_bound(X_15,X_128)) )],[refute_0_1972,refute_0_1973]) ).

cnf(refute_0_1975,plain,
    multiply(least_upper_bound(X_15,X_128),inverse(least_upper_bound(X_15,X_128))) = least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_128,least_upper_bound(X_15,X_128)),inverse(least_upper_bound(X_15,X_128))),least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128))))) )],[refute_0_1969,refute_0_1974]) ).

cnf(refute_0_1976,plain,
    multiply(least_upper_bound(X_15,X_128),inverse(least_upper_bound(X_15,X_128))) = identity,
    inference(subst,[],[refute_0_40:[bind(X,$fot(least_upper_bound(X_15,X_128)))]]) ).

cnf(refute_0_1977,plain,
    ( multiply(least_upper_bound(X_15,X_128),inverse(least_upper_bound(X_15,X_128))) != identity
    | multiply(least_upper_bound(X_15,X_128),inverse(least_upper_bound(X_15,X_128))) != least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128))))
    | identity = least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_15,X_128),inverse(least_upper_bound(X_15,X_128))),least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128))))) ),[0],$fot(identity)]]) ).

cnf(refute_0_1978,plain,
    ( multiply(least_upper_bound(X_15,X_128),inverse(least_upper_bound(X_15,X_128))) != least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128))))
    | identity = least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_15,X_128),inverse(least_upper_bound(X_15,X_128))),identity) )],[refute_0_1976,refute_0_1977]) ).

cnf(refute_0_1979,plain,
    identity = least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_15,X_128),inverse(least_upper_bound(X_15,X_128))),least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128))))) )],[refute_0_1975,refute_0_1978]) ).

cnf(refute_0_1980,plain,
    ( identity != least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128))))
    | least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128)))) = identity ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128))))))]]) ).

cnf(refute_0_1981,plain,
    least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128)))) = identity,
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(X_128,inverse(least_upper_bound(X_15,X_128))))) )],[refute_0_1979,refute_0_1980]) ).

cnf(refute_0_1982,plain,
    least_upper_bound(identity,multiply(identity,inverse(least_upper_bound(X_182,identity)))) = identity,
    inference(subst,[],[refute_0_1981:[bind(X_128,$fot(identity)),bind(X_15,$fot(X_182))]]) ).

cnf(refute_0_1983,plain,
    multiply(least_upper_bound(X_119,least_upper_bound(X_182,identity)),inverse(least_upper_bound(X_182,identity))) = least_upper_bound(identity,multiply(X_119,inverse(least_upper_bound(X_182,identity)))),
    inference(subst,[],[refute_0_533:[bind(X_120,$fot(least_upper_bound(X_182,identity)))]]) ).

cnf(refute_0_1984,plain,
    ( multiply(least_upper_bound(X_119,least_upper_bound(X_182,identity)),inverse(least_upper_bound(X_182,identity))) != least_upper_bound(identity,multiply(X_119,inverse(least_upper_bound(X_182,identity))))
    | inverse(least_upper_bound(X_182,identity)) != inverse(least_upper_bound(identity,X_182))
    | multiply(least_upper_bound(X_119,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) = least_upper_bound(identity,multiply(X_119,inverse(least_upper_bound(X_182,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_119,least_upper_bound(X_182,identity)),inverse(least_upper_bound(X_182,identity))),least_upper_bound(identity,multiply(X_119,inverse(least_upper_bound(X_182,identity))))) ),[0,1],$fot(inverse(least_upper_bound(identity,X_182)))]]) ).

cnf(refute_0_1985,plain,
    ( multiply(least_upper_bound(X_119,least_upper_bound(X_182,identity)),inverse(least_upper_bound(X_182,identity))) != least_upper_bound(identity,multiply(X_119,inverse(least_upper_bound(X_182,identity))))
    | multiply(least_upper_bound(X_119,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) = least_upper_bound(identity,multiply(X_119,inverse(least_upper_bound(X_182,identity)))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) )],[refute_0_1965,refute_0_1984]) ).

cnf(refute_0_1986,plain,
    multiply(least_upper_bound(X_119,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) = least_upper_bound(identity,multiply(X_119,inverse(least_upper_bound(X_182,identity)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,least_upper_bound(X_182,identity)),inverse(least_upper_bound(X_182,identity))),least_upper_bound(identity,multiply(X_119,inverse(least_upper_bound(X_182,identity))))) )],[refute_0_1983,refute_0_1985]) ).

cnf(refute_0_1987,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) = least_upper_bound(identity,multiply(identity,inverse(least_upper_bound(X_182,identity)))),
    inference(subst,[],[refute_0_1986:[bind(X_119,$fot(identity))]]) ).

cnf(refute_0_1988,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) != least_upper_bound(identity,multiply(identity,inverse(least_upper_bound(X_182,identity))))
    | least_upper_bound(identity,multiply(identity,inverse(least_upper_bound(X_182,identity)))) != identity
    | multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) = identity ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))))),bind(Y0,$fot(least_upper_bound(identity,multiply(identity,inverse(least_upper_bound(X_182,identity)))))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_1989,plain,
    ( least_upper_bound(identity,multiply(identity,inverse(least_upper_bound(X_182,identity)))) != identity
    | multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))),least_upper_bound(identity,multiply(identity,inverse(least_upper_bound(X_182,identity))))) )],[refute_0_1987,refute_0_1988]) ).

cnf(refute_0_1990,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) = identity,
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(least_upper_bound(X_182,identity)))),identity) )],[refute_0_1982,refute_0_1989]) ).

cnf(refute_0_1991,plain,
    multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))) = multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))),
    inference(subst,[],[refute_0_687:[bind(X_122,$fot(least_upper_bound(X_182,identity))),bind(X_15,$fot(inverse(least_upper_bound(identity,X_182))))]]) ).

cnf(refute_0_1992,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) != identity
    | multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))) != multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182)))
    | multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))) = identity ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_1993,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) != identity
    | multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))),multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182)))) )],[refute_0_1991,refute_0_1992]) ).

cnf(refute_0_1994,plain,
    multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))) = identity,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))),identity) )],[refute_0_1990,refute_0_1993]) ).

cnf(refute_0_1995,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))) != identity
    | multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))) != least_upper_bound(identity,inverse(least_upper_bound(X_182,identity)))
    | identity = least_upper_bound(identity,inverse(least_upper_bound(X_182,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))),least_upper_bound(identity,inverse(least_upper_bound(X_182,identity)))) ),[0],$fot(identity)]]) ).

cnf(refute_0_1996,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))) != least_upper_bound(identity,inverse(least_upper_bound(X_182,identity)))
    | identity = least_upper_bound(identity,inverse(least_upper_bound(X_182,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))),identity) )],[refute_0_1994,refute_0_1995]) ).

cnf(refute_0_1997,plain,
    identity = least_upper_bound(identity,inverse(least_upper_bound(X_182,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_182,identity),identity),inverse(least_upper_bound(identity,X_182))),least_upper_bound(identity,inverse(least_upper_bound(X_182,identity)))) )],[refute_0_1968,refute_0_1996]) ).

cnf(refute_0_1998,plain,
    ( identity != least_upper_bound(identity,inverse(least_upper_bound(X_182,identity)))
    | least_upper_bound(identity,inverse(least_upper_bound(X_182,identity))) = identity ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,inverse(least_upper_bound(X_182,identity)))))]]) ).

cnf(refute_0_1999,plain,
    least_upper_bound(identity,inverse(least_upper_bound(X_182,identity))) = identity,
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,inverse(least_upper_bound(X_182,identity)))) )],[refute_0_1997,refute_0_1998]) ).

cnf(refute_0_2000,plain,
    least_upper_bound(identity,inverse(least_upper_bound(b,identity))) = identity,
    inference(subst,[],[refute_0_1999:[bind(X_182,$fot(b))]]) ).

cnf(refute_0_2001,plain,
    multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))) = multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2002,plain,
    ( multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))) != multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity))))
    | least_upper_bound(identity,inverse(least_upper_bound(b,identity))) != identity
    | multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))) = multiply(b,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))),multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_2003,plain,
    ( least_upper_bound(identity,inverse(least_upper_bound(b,identity))) != identity
    | multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))) = multiply(b,identity) ),
    inference(resolve,[$cnf( $equal(multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))),multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity))))) )],[refute_0_2001,refute_0_2002]) ).

cnf(refute_0_2004,plain,
    multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))) = multiply(b,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(b,identity))),identity) )],[refute_0_2000,refute_0_2003]) ).

cnf(refute_0_2005,plain,
    ( multiply(b,identity) != b
    | multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))) != multiply(b,identity)
    | multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))) = b ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))))),bind(Y0,$fot(multiply(b,identity))),bind(Z0,$fot(b))]]) ).

cnf(refute_0_2006,plain,
    ( multiply(b,identity) != b
    | multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))) = b ),
    inference(resolve,[$cnf( $equal(multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))),multiply(b,identity)) )],[refute_0_2004,refute_0_2005]) ).

cnf(refute_0_2007,plain,
    multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))) = b,
    inference(resolve,[$cnf( $equal(multiply(b,identity),b) )],[refute_0_1963,refute_0_2006]) ).

cnf(refute_0_2008,plain,
    multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)) = multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_1297:[bind(X_15,$fot(b)),bind(X_98,$fot(inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2009,plain,
    ( multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))) != b
    | multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)) != multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity))))
    | multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)) = b ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)))),bind(Y0,$fot(multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))))),bind(Z0,$fot(b))]]) ).

cnf(refute_0_2010,plain,
    ( multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))) != b
    | multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)) = b ),
    inference(resolve,[$cnf( $equal(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity))))) )],[refute_0_2008,refute_0_2009]) ).

cnf(refute_0_2011,plain,
    multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)) = b,
    inference(resolve,[$cnf( $equal(multiply(b,least_upper_bound(identity,inverse(least_upper_bound(b,identity)))),b) )],[refute_0_2007,refute_0_2010]) ).

cnf(refute_0_2012,plain,
    greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2013,plain,
    ( multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)) != b
    | greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) != greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)))
    | greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)))) ),[1,0],$fot(b)]]) ).

cnf(refute_0_2014,plain,
    ( multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)) != b
    | greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)))) )],[refute_0_2012,refute_0_2013]) ).

cnf(refute_0_2015,plain,
    greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),b) )],[refute_0_2011,refute_0_2014]) ).

cnf(refute_0_2016,plain,
    ( greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) != greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)))
    | greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) != greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))))
    | greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))))),bind(Y0,$fot(greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))))),bind(Z0,$fot(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))))))]]) ).

cnf(refute_0_2017,plain,
    ( greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) != greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))))
    | greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c)))) )],[refute_0_2015,refute_0_2016]) ).

cnf(refute_0_2018,plain,
    greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) = greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))))) )],[refute_0_1962,refute_0_2017]) ).

cnf(refute_0_2019,plain,
    ( greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) != greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))))
    | greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) = least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))) ),[0],$fot(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))))]]) ).

cnf(refute_0_2020,plain,
    ( greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) = least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))))) )],[refute_0_2018,refute_0_2019]) ).

cnf(refute_0_2021,plain,
    least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))) = least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2022,plain,
    ( multiply(b,inverse(least_upper_bound(b,identity))) != inverse(least_upper_bound(identity,inverse(b)))
    | least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))) != least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))
    | least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))),least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))) ),[1,1],$fot(inverse(least_upper_bound(identity,inverse(b))))]]) ).

cnf(refute_0_2023,plain,
    ( multiply(b,inverse(least_upper_bound(b,identity))) != inverse(least_upper_bound(identity,inverse(b)))
    | least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))),least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))) )],[refute_0_2021,refute_0_2022]) ).

cnf(refute_0_2024,plain,
    least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(least_upper_bound(b,identity))),inverse(least_upper_bound(identity,inverse(b)))) )],[refute_0_1770,refute_0_2023]) ).

cnf(refute_0_2025,plain,
    ( greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) != least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))
    | least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))) != least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))),least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) ),[0],$fot(least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2026,plain,
    ( greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) != least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity)))),least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) )],[refute_0_2024,refute_0_2025]) ).

cnf(refute_0_2027,plain,
    ( greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))),least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))) )],[refute_0_2020,refute_0_2026]) ).

cnf(refute_0_2028,plain,
    greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,least_upper_bound(inverse(least_upper_bound(b,identity)),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),multiply(b,inverse(least_upper_bound(b,identity))))) )],[refute_0_1773,refute_0_2027]) ).

cnf(refute_0_2029,plain,
    ( greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) != least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))),X_16)) != least_upper_bound(b,X_16)
    | least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) = least_upper_bound(b,X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))),X_16)),least_upper_bound(b,X_16)) ),[0,1,0],$fot(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))))]]) ).

cnf(refute_0_2030,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))),X_16)) != least_upper_bound(b,X_16)
    | least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) = least_upper_bound(b,X_16) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))),least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))) )],[refute_0_2028,refute_0_2029]) ).

cnf(refute_0_2031,plain,
    least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) = least_upper_bound(b,X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b))))),X_16)),least_upper_bound(b,X_16)) )],[refute_0_1718,refute_0_2030]) ).

cnf(refute_0_2032,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))) = least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)),
    inference(subst,[],[refute_0_1723:[bind(X_16,$fot(least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)))]]) ).

cnf(refute_0_2033,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)),
    inference(subst,[],[refute_0_237:[bind(X,$fot(greatest_lower_bound(a,c))),bind(Y,$fot(inverse(least_upper_bound(identity,inverse(b))))),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_2034,plain,
    least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) = least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)),
    introduced(tautology,[refl,[$fot(least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)))]]) ).

cnf(refute_0_2035,plain,
    ( least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) != least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16) != least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))
    | least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) = least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)),least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16))) ),[1,1],$fot(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)))]]) ).

cnf(refute_0_2036,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16) != least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))
    | least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) = least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)),least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16))) )],[refute_0_2034,refute_0_2035]) ).

cnf(refute_0_2037,plain,
    least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) = least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16),least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))) )],[refute_0_2033,refute_0_2036]) ).

cnf(refute_0_2038,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))) != least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))
    | least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) != least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)))
    | least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) = least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))))]]) ).

cnf(refute_0_2039,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))) != least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))
    | least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) = least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)))) )],[refute_0_2037,refute_0_2038]) ).

cnf(refute_0_2040,plain,
    least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) = least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))),least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))) )],[refute_0_2032,refute_0_2039]) ).

cnf(refute_0_2041,plain,
    ( least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) != least_upper_bound(b,X_16)
    | least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) != least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))
    | least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)) = least_upper_bound(b,X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)),least_upper_bound(b,X_16)) ),[0],$fot(least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)))]]) ).

cnf(refute_0_2042,plain,
    ( least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)) != least_upper_bound(b,X_16)
    | least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)) = least_upper_bound(b,X_16) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)),least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16))) )],[refute_0_2040,refute_0_2041]) ).

cnf(refute_0_2043,plain,
    least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)) = least_upper_bound(b,X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,inverse(b)))),X_16)),least_upper_bound(b,X_16)) )],[refute_0_2031,refute_0_2042]) ).

cnf(refute_0_2044,plain,
    least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)) = least_upper_bound(Y,least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92))))),
    inference(subst,[],[refute_0_1062:[bind(X,$fot(inverse(least_upper_bound(X_420,inverse(X_92)))))]]) ).

cnf(refute_0_2045,plain,
    multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) = least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379)))),
    inference(subst,[],[refute_0_260:[bind(X_94,$fot(inverse(least_upper_bound(X_378,inverse(X_379))))),bind(X_95,$fot(least_upper_bound(identity,multiply(X_378,X_379))))]]) ).

cnf(refute_0_2046,plain,
    X_82 = multiply(inverse(least_upper_bound(X_124,inverse(X_82))),multiply(least_upper_bound(X_124,inverse(X_82)),X_82)),
    inference(subst,[],[refute_0_9:[bind(X_81,$fot(least_upper_bound(X_124,inverse(X_82))))]]) ).

cnf(refute_0_2047,plain,
    multiply(least_upper_bound(X_119,inverse(X_118)),X_118) = least_upper_bound(multiply(X_119,X_118),multiply(inverse(X_118),X_118)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_118)),bind(Y,$fot(X_119)),bind(Z,$fot(inverse(X_118)))]]) ).

cnf(refute_0_2048,plain,
    ( multiply(inverse(X_118),X_118) != identity
    | multiply(least_upper_bound(X_119,inverse(X_118)),X_118) != least_upper_bound(multiply(X_119,X_118),multiply(inverse(X_118),X_118))
    | multiply(least_upper_bound(X_119,inverse(X_118)),X_118) = least_upper_bound(multiply(X_119,X_118),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_119,inverse(X_118)),X_118),least_upper_bound(multiply(X_119,X_118),multiply(inverse(X_118),X_118))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_2049,plain,
    ( multiply(least_upper_bound(X_119,inverse(X_118)),X_118) != least_upper_bound(multiply(X_119,X_118),multiply(inverse(X_118),X_118))
    | multiply(least_upper_bound(X_119,inverse(X_118)),X_118) = least_upper_bound(multiply(X_119,X_118),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_118),X_118),identity) )],[refute_0_1000,refute_0_2048]) ).

cnf(refute_0_2050,plain,
    multiply(least_upper_bound(X_119,inverse(X_118)),X_118) = least_upper_bound(multiply(X_119,X_118),identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,inverse(X_118)),X_118),least_upper_bound(multiply(X_119,X_118),multiply(inverse(X_118),X_118))) )],[refute_0_2047,refute_0_2049]) ).

cnf(refute_0_2051,plain,
    least_upper_bound(multiply(X_119,X_118),identity) = least_upper_bound(identity,multiply(X_119,X_118)),
    inference(subst,[],[refute_0_256:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_119,X_118)))]]) ).

cnf(refute_0_2052,plain,
    ( multiply(least_upper_bound(X_119,inverse(X_118)),X_118) != least_upper_bound(multiply(X_119,X_118),identity)
    | least_upper_bound(multiply(X_119,X_118),identity) != least_upper_bound(identity,multiply(X_119,X_118))
    | multiply(least_upper_bound(X_119,inverse(X_118)),X_118) = least_upper_bound(identity,multiply(X_119,X_118)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_119,inverse(X_118)),X_118),least_upper_bound(identity,multiply(X_119,X_118))) ),[0],$fot(least_upper_bound(multiply(X_119,X_118),identity))]]) ).

cnf(refute_0_2053,plain,
    ( multiply(least_upper_bound(X_119,inverse(X_118)),X_118) != least_upper_bound(multiply(X_119,X_118),identity)
    | multiply(least_upper_bound(X_119,inverse(X_118)),X_118) = least_upper_bound(identity,multiply(X_119,X_118)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,X_118),identity),least_upper_bound(identity,multiply(X_119,X_118))) )],[refute_0_2051,refute_0_2052]) ).

cnf(refute_0_2054,plain,
    multiply(least_upper_bound(X_119,inverse(X_118)),X_118) = least_upper_bound(identity,multiply(X_119,X_118)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,inverse(X_118)),X_118),least_upper_bound(multiply(X_119,X_118),identity)) )],[refute_0_2050,refute_0_2053]) ).

cnf(refute_0_2055,plain,
    multiply(least_upper_bound(X_124,inverse(X_82)),X_82) = least_upper_bound(identity,multiply(X_124,X_82)),
    inference(subst,[],[refute_0_2054:[bind(X_118,$fot(X_82)),bind(X_119,$fot(X_124))]]) ).

cnf(refute_0_2056,plain,
    ( X_82 != multiply(inverse(least_upper_bound(X_124,inverse(X_82))),multiply(least_upper_bound(X_124,inverse(X_82)),X_82))
    | multiply(least_upper_bound(X_124,inverse(X_82)),X_82) != least_upper_bound(identity,multiply(X_124,X_82))
    | X_82 = multiply(inverse(least_upper_bound(X_124,inverse(X_82))),least_upper_bound(identity,multiply(X_124,X_82))) ),
    introduced(tautology,[equality,[$cnf( $equal(X_82,multiply(inverse(least_upper_bound(X_124,inverse(X_82))),multiply(least_upper_bound(X_124,inverse(X_82)),X_82))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_124,X_82)))]]) ).

cnf(refute_0_2057,plain,
    ( X_82 != multiply(inverse(least_upper_bound(X_124,inverse(X_82))),multiply(least_upper_bound(X_124,inverse(X_82)),X_82))
    | X_82 = multiply(inverse(least_upper_bound(X_124,inverse(X_82))),least_upper_bound(identity,multiply(X_124,X_82))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_124,inverse(X_82)),X_82),least_upper_bound(identity,multiply(X_124,X_82))) )],[refute_0_2055,refute_0_2056]) ).

cnf(refute_0_2058,plain,
    X_82 = multiply(inverse(least_upper_bound(X_124,inverse(X_82))),least_upper_bound(identity,multiply(X_124,X_82))),
    inference(resolve,[$cnf( $equal(X_82,multiply(inverse(least_upper_bound(X_124,inverse(X_82))),multiply(least_upper_bound(X_124,inverse(X_82)),X_82))) )],[refute_0_2046,refute_0_2057]) ).

cnf(refute_0_2059,plain,
    X_379 = multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))),
    inference(subst,[],[refute_0_2058:[bind(X_124,$fot(X_378)),bind(X_82,$fot(X_379))]]) ).

cnf(refute_0_2060,plain,
    ( X_379 != multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379)))
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))) = X_379 ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(X_379)),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379)))))]]) ).

cnf(refute_0_2061,plain,
    multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))) = X_379,
    inference(resolve,[$cnf( $equal(X_379,multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379)))) )],[refute_0_2059,refute_0_2060]) ).

cnf(refute_0_2062,plain,
    ( multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))) != X_379
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) != least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))))
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) = least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)),least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))))) ),[1,1],$fot(X_379)]]) ).

cnf(refute_0_2063,plain,
    ( multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) != least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))))
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) = least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))),X_379) )],[refute_0_2061,refute_0_2062]) ).

cnf(refute_0_2064,plain,
    multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) = least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)),least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))))) )],[refute_0_2045,refute_0_2063]) ).

cnf(refute_0_2065,plain,
    least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379))) = least_upper_bound(identity,multiply(X_378,X_379)),
    inference(subst,[],[refute_0_606:[bind(X_15,$fot(identity)),bind(X_16,$fot(multiply(X_378,X_379)))]]) ).

cnf(refute_0_2066,plain,
    multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))) = multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))),
    introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))))]]) ).

cnf(refute_0_2067,plain,
    ( multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))) != multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379))))
    | least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379))) != least_upper_bound(identity,multiply(X_378,X_379))
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))) = multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))),multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379))))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_378,X_379)))]]) ).

cnf(refute_0_2068,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379))) != least_upper_bound(identity,multiply(X_378,X_379))
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))) = multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))),multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379))))) )],[refute_0_2066,refute_0_2067]) ).

cnf(refute_0_2069,plain,
    multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))) = multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379))),least_upper_bound(identity,multiply(X_378,X_379))) )],[refute_0_2065,refute_0_2068]) ).

cnf(refute_0_2070,plain,
    ( multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))) != X_379
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))) != multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379)))
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))) = X_379 ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))))),bind(Z0,$fot(X_379))]]) ).

cnf(refute_0_2071,plain,
    ( multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))) != X_379
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))) = X_379 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))),multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379)))) )],[refute_0_2069,refute_0_2070]) ).

cnf(refute_0_2072,plain,
    multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))) = X_379,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,multiply(X_378,X_379))),X_379) )],[refute_0_2061,refute_0_2071]) ).

cnf(refute_0_2073,plain,
    multiply(inverse(X_345),least_upper_bound(X_95,X_96)) = multiply(inverse(multiply(inverse(X_96),X_345)),multiply(inverse(X_96),least_upper_bound(X_95,X_96))),
    inference(subst,[],[refute_0_1327:[bind(Y,$fot(inverse(X_96))),bind(Z,$fot(least_upper_bound(X_95,X_96))),bind(X_88,$fot(X_345))]]) ).

cnf(refute_0_2074,plain,
    multiply(inverse(X_96),least_upper_bound(X_95,X_96)) = least_upper_bound(multiply(inverse(X_96),X_95),multiply(inverse(X_96),X_96)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_96))),bind(Y,$fot(X_95)),bind(Z,$fot(X_96))]]) ).

cnf(refute_0_2075,plain,
    multiply(inverse(X_96),X_96) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_96))]]) ).

cnf(refute_0_2076,plain,
    ( multiply(inverse(X_96),X_96) != identity
    | multiply(inverse(X_96),least_upper_bound(X_95,X_96)) != least_upper_bound(multiply(inverse(X_96),X_95),multiply(inverse(X_96),X_96))
    | multiply(inverse(X_96),least_upper_bound(X_95,X_96)) = least_upper_bound(multiply(inverse(X_96),X_95),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_96),least_upper_bound(X_95,X_96)),least_upper_bound(multiply(inverse(X_96),X_95),multiply(inverse(X_96),X_96))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_2077,plain,
    ( multiply(inverse(X_96),least_upper_bound(X_95,X_96)) != least_upper_bound(multiply(inverse(X_96),X_95),multiply(inverse(X_96),X_96))
    | multiply(inverse(X_96),least_upper_bound(X_95,X_96)) = least_upper_bound(multiply(inverse(X_96),X_95),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_96),X_96),identity) )],[refute_0_2075,refute_0_2076]) ).

cnf(refute_0_2078,plain,
    multiply(inverse(X_96),least_upper_bound(X_95,X_96)) = least_upper_bound(multiply(inverse(X_96),X_95),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_96),least_upper_bound(X_95,X_96)),least_upper_bound(multiply(inverse(X_96),X_95),multiply(inverse(X_96),X_96))) )],[refute_0_2074,refute_0_2077]) ).

cnf(refute_0_2079,plain,
    least_upper_bound(multiply(inverse(X_96),X_95),identity) = least_upper_bound(identity,multiply(inverse(X_96),X_95)),
    inference(subst,[],[refute_0_256:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_96),X_95)))]]) ).

cnf(refute_0_2080,plain,
    ( multiply(inverse(X_96),least_upper_bound(X_95,X_96)) != least_upper_bound(multiply(inverse(X_96),X_95),identity)
    | least_upper_bound(multiply(inverse(X_96),X_95),identity) != least_upper_bound(identity,multiply(inverse(X_96),X_95))
    | multiply(inverse(X_96),least_upper_bound(X_95,X_96)) = least_upper_bound(identity,multiply(inverse(X_96),X_95)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_96),least_upper_bound(X_95,X_96)),least_upper_bound(identity,multiply(inverse(X_96),X_95))) ),[0],$fot(least_upper_bound(multiply(inverse(X_96),X_95),identity))]]) ).

cnf(refute_0_2081,plain,
    ( multiply(inverse(X_96),least_upper_bound(X_95,X_96)) != least_upper_bound(multiply(inverse(X_96),X_95),identity)
    | multiply(inverse(X_96),least_upper_bound(X_95,X_96)) = least_upper_bound(identity,multiply(inverse(X_96),X_95)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_96),X_95),identity),least_upper_bound(identity,multiply(inverse(X_96),X_95))) )],[refute_0_2079,refute_0_2080]) ).

cnf(refute_0_2082,plain,
    multiply(inverse(X_96),least_upper_bound(X_95,X_96)) = least_upper_bound(identity,multiply(inverse(X_96),X_95)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_96),least_upper_bound(X_95,X_96)),least_upper_bound(multiply(inverse(X_96),X_95),identity)) )],[refute_0_2078,refute_0_2081]) ).

cnf(refute_0_2083,plain,
    ( multiply(inverse(X_345),least_upper_bound(X_95,X_96)) != multiply(inverse(multiply(inverse(X_96),X_345)),multiply(inverse(X_96),least_upper_bound(X_95,X_96)))
    | multiply(inverse(X_96),least_upper_bound(X_95,X_96)) != least_upper_bound(identity,multiply(inverse(X_96),X_95))
    | multiply(inverse(X_345),least_upper_bound(X_95,X_96)) = multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_345),least_upper_bound(X_95,X_96)),multiply(inverse(multiply(inverse(X_96),X_345)),multiply(inverse(X_96),least_upper_bound(X_95,X_96)))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_96),X_95)))]]) ).

cnf(refute_0_2084,plain,
    ( multiply(inverse(X_345),least_upper_bound(X_95,X_96)) != multiply(inverse(multiply(inverse(X_96),X_345)),multiply(inverse(X_96),least_upper_bound(X_95,X_96)))
    | multiply(inverse(X_345),least_upper_bound(X_95,X_96)) = multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_96),least_upper_bound(X_95,X_96)),least_upper_bound(identity,multiply(inverse(X_96),X_95))) )],[refute_0_2082,refute_0_2083]) ).

cnf(refute_0_2085,plain,
    multiply(inverse(X_345),least_upper_bound(X_95,X_96)) = multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_345),least_upper_bound(X_95,X_96)),multiply(inverse(multiply(inverse(X_96),X_345)),multiply(inverse(X_96),least_upper_bound(X_95,X_96)))) )],[refute_0_2073,refute_0_2084]) ).

cnf(refute_0_2086,plain,
    inverse(inverse(X_96)) = X_96,
    inference(subst,[],[p12_2:[bind(X,$fot(X_96))]]) ).

cnf(refute_0_2087,plain,
    least_upper_bound(inverse(inverse(X_96)),X_95) = least_upper_bound(inverse(inverse(X_96)),X_95),
    introduced(tautology,[refl,[$fot(least_upper_bound(inverse(inverse(X_96)),X_95))]]) ).

cnf(refute_0_2088,plain,
    ( inverse(inverse(X_96)) != X_96
    | least_upper_bound(inverse(inverse(X_96)),X_95) != least_upper_bound(inverse(inverse(X_96)),X_95)
    | least_upper_bound(inverse(inverse(X_96)),X_95) = least_upper_bound(X_96,X_95) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(X_96)),X_95),least_upper_bound(inverse(inverse(X_96)),X_95)) ),[1,0],$fot(X_96)]]) ).

cnf(refute_0_2089,plain,
    ( inverse(inverse(X_96)) != X_96
    | least_upper_bound(inverse(inverse(X_96)),X_95) = least_upper_bound(X_96,X_95) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_96)),X_95),least_upper_bound(inverse(inverse(X_96)),X_95)) )],[refute_0_2087,refute_0_2088]) ).

cnf(refute_0_2090,plain,
    least_upper_bound(inverse(inverse(X_96)),X_95) = least_upper_bound(X_96,X_95),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_96)),X_96) )],[refute_0_2086,refute_0_2089]) ).

cnf(refute_0_2091,plain,
    multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)) = multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)),
    introduced(tautology,[refl,[$fot(multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)))]]) ).

cnf(refute_0_2092,plain,
    ( multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)) != multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95))
    | least_upper_bound(inverse(inverse(X_96)),X_95) != least_upper_bound(X_96,X_95)
    | multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)) = multiply(inverse(X_345),least_upper_bound(X_96,X_95)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)),multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95))) ),[1,1],$fot(least_upper_bound(X_96,X_95))]]) ).

cnf(refute_0_2093,plain,
    ( least_upper_bound(inverse(inverse(X_96)),X_95) != least_upper_bound(X_96,X_95)
    | multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)) = multiply(inverse(X_345),least_upper_bound(X_96,X_95)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)),multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95))) )],[refute_0_2091,refute_0_2092]) ).

cnf(refute_0_2094,plain,
    multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)) = multiply(inverse(X_345),least_upper_bound(X_96,X_95)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_96)),X_95),least_upper_bound(X_96,X_95)) )],[refute_0_2090,refute_0_2093]) ).

cnf(refute_0_2095,plain,
    multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)) = least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344))),
    inference(subst,[],[refute_0_260:[bind(X_94,$fot(inverse(multiply(X_343,X_345)))),bind(X_95,$fot(multiply(X_343,X_344)))]]) ).

cnf(refute_0_2096,plain,
    ( multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)) != multiply(inverse(X_345),X_344)
    | multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)) != least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)))
    | multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)) = least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)),least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)))) ),[1,1],$fot(multiply(inverse(X_345),X_344))]]) ).

cnf(refute_0_2097,plain,
    ( multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)) != least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)))
    | multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)) = least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)),multiply(inverse(X_345),X_344)) )],[refute_0_1330,refute_0_2096]) ).

cnf(refute_0_2098,plain,
    multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)) = least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)),least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(multiply(X_343,X_345)),multiply(X_343,X_344)))) )],[refute_0_2095,refute_0_2097]) ).

cnf(refute_0_2099,plain,
    inverse(multiply(inverse(least_upper_bound(X_182,identity)),X_18)) = multiply(inverse(X_18),least_upper_bound(X_182,identity)),
    inference(subst,[],[refute_0_22:[bind(X,$fot(least_upper_bound(X_182,identity)))]]) ).

cnf(refute_0_2100,plain,
    ( inverse(multiply(inverse(least_upper_bound(X_182,identity)),X_18)) != multiply(inverse(X_18),least_upper_bound(X_182,identity))
    | inverse(least_upper_bound(X_182,identity)) != inverse(least_upper_bound(identity,X_182))
    | inverse(multiply(inverse(least_upper_bound(identity,X_182)),X_18)) = multiply(inverse(X_18),least_upper_bound(X_182,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(X_182,identity)),X_18)),multiply(inverse(X_18),least_upper_bound(X_182,identity))) ),[0,0,0],$fot(inverse(least_upper_bound(identity,X_182)))]]) ).

cnf(refute_0_2101,plain,
    ( inverse(multiply(inverse(least_upper_bound(X_182,identity)),X_18)) != multiply(inverse(X_18),least_upper_bound(X_182,identity))
    | inverse(multiply(inverse(least_upper_bound(identity,X_182)),X_18)) = multiply(inverse(X_18),least_upper_bound(X_182,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_182,identity)),inverse(least_upper_bound(identity,X_182))) )],[refute_0_1965,refute_0_2100]) ).

cnf(refute_0_2102,plain,
    inverse(multiply(inverse(least_upper_bound(identity,X_182)),X_18)) = multiply(inverse(X_18),least_upper_bound(X_182,identity)),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(X_182,identity)),X_18)),multiply(inverse(X_18),least_upper_bound(X_182,identity))) )],[refute_0_2099,refute_0_2101]) ).

cnf(refute_0_2103,plain,
    inverse(multiply(inverse(least_upper_bound(identity,X_182)),X_18)) = multiply(inverse(X_18),least_upper_bound(identity,X_182)),
    inference(subst,[],[refute_0_22:[bind(X,$fot(least_upper_bound(identity,X_182)))]]) ).

cnf(refute_0_2104,plain,
    ( inverse(multiply(inverse(least_upper_bound(identity,X_182)),X_18)) != multiply(inverse(X_18),least_upper_bound(X_182,identity))
    | inverse(multiply(inverse(least_upper_bound(identity,X_182)),X_18)) != multiply(inverse(X_18),least_upper_bound(identity,X_182))
    | multiply(inverse(X_18),least_upper_bound(identity,X_182)) = multiply(inverse(X_18),least_upper_bound(X_182,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,X_182)),X_18)),multiply(inverse(X_18),least_upper_bound(X_182,identity))) ),[0],$fot(multiply(inverse(X_18),least_upper_bound(identity,X_182)))]]) ).

cnf(refute_0_2105,plain,
    ( inverse(multiply(inverse(least_upper_bound(identity,X_182)),X_18)) != multiply(inverse(X_18),least_upper_bound(X_182,identity))
    | multiply(inverse(X_18),least_upper_bound(identity,X_182)) = multiply(inverse(X_18),least_upper_bound(X_182,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,X_182)),X_18)),multiply(inverse(X_18),least_upper_bound(identity,X_182))) )],[refute_0_2103,refute_0_2104]) ).

cnf(refute_0_2106,plain,
    multiply(inverse(X_18),least_upper_bound(identity,X_182)) = multiply(inverse(X_18),least_upper_bound(X_182,identity)),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(identity,X_182)),X_18)),multiply(inverse(X_18),least_upper_bound(X_182,identity))) )],[refute_0_2102,refute_0_2105]) ).

cnf(refute_0_2107,plain,
    ( multiply(inverse(X_18),least_upper_bound(identity,X_182)) != multiply(inverse(X_18),least_upper_bound(X_182,identity))
    | multiply(inverse(X_18),least_upper_bound(X_182,identity)) = multiply(inverse(X_18),least_upper_bound(identity,X_182)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(inverse(X_18),least_upper_bound(identity,X_182)))),bind(Y0,$fot(multiply(inverse(X_18),least_upper_bound(X_182,identity))))]]) ).

cnf(refute_0_2108,plain,
    multiply(inverse(X_18),least_upper_bound(X_182,identity)) = multiply(inverse(X_18),least_upper_bound(identity,X_182)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_18),least_upper_bound(identity,X_182)),multiply(inverse(X_18),least_upper_bound(X_182,identity))) )],[refute_0_2106,refute_0_2107]) ).

cnf(refute_0_2109,plain,
    multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)) = multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))),
    inference(subst,[],[refute_0_2108:[bind(X_18,$fot(multiply(X_343,X_345))),bind(X_182,$fot(multiply(X_343,X_344)))]]) ).

cnf(refute_0_2110,plain,
    ( multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)) != multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344)))
    | multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)) != least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344))
    | multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))) = least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)),least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344))) ),[0],$fot(multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))))]]) ).

cnf(refute_0_2111,plain,
    ( multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)) != least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344))
    | multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))) = least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)),multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344)))) )],[refute_0_2109,refute_0_2110]) ).

cnf(refute_0_2112,plain,
    multiply(inverse(Y),least_upper_bound(inverse(X),X_96)) = least_upper_bound(multiply(inverse(Y),inverse(X)),multiply(inverse(Y),X_96)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(Y))),bind(Y,$fot(inverse(X))),bind(Z,$fot(X_96))]]) ).

cnf(refute_0_2113,plain,
    ( multiply(inverse(Y),inverse(X)) != inverse(multiply(X,Y))
    | multiply(inverse(Y),least_upper_bound(inverse(X),X_96)) != least_upper_bound(multiply(inverse(Y),inverse(X)),multiply(inverse(Y),X_96))
    | multiply(inverse(Y),least_upper_bound(inverse(X),X_96)) = least_upper_bound(inverse(multiply(X,Y)),multiply(inverse(Y),X_96)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(Y),least_upper_bound(inverse(X),X_96)),least_upper_bound(multiply(inverse(Y),inverse(X)),multiply(inverse(Y),X_96))) ),[1,0],$fot(inverse(multiply(X,Y)))]]) ).

cnf(refute_0_2114,plain,
    ( multiply(inverse(Y),least_upper_bound(inverse(X),X_96)) != least_upper_bound(multiply(inverse(Y),inverse(X)),multiply(inverse(Y),X_96))
    | multiply(inverse(Y),least_upper_bound(inverse(X),X_96)) = least_upper_bound(inverse(multiply(X,Y)),multiply(inverse(Y),X_96)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(Y),inverse(X)),inverse(multiply(X,Y))) )],[refute_0_25,refute_0_2113]) ).

cnf(refute_0_2115,plain,
    multiply(inverse(Y),least_upper_bound(inverse(X),X_96)) = least_upper_bound(inverse(multiply(X,Y)),multiply(inverse(Y),X_96)),
    inference(resolve,[$cnf( $equal(multiply(inverse(Y),least_upper_bound(inverse(X),X_96)),least_upper_bound(multiply(inverse(Y),inverse(X)),multiply(inverse(Y),X_96))) )],[refute_0_2112,refute_0_2114]) ).

cnf(refute_0_2116,plain,
    ( multiply(inverse(Y),least_upper_bound(inverse(X),X_96)) != least_upper_bound(inverse(multiply(X,Y)),multiply(inverse(Y),X_96))
    | least_upper_bound(inverse(multiply(X,Y)),multiply(inverse(Y),X_96)) = multiply(inverse(Y),least_upper_bound(inverse(X),X_96)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(inverse(Y),least_upper_bound(inverse(X),X_96)))),bind(Y0,$fot(least_upper_bound(inverse(multiply(X,Y)),multiply(inverse(Y),X_96))))]]) ).

cnf(refute_0_2117,plain,
    least_upper_bound(inverse(multiply(X,Y)),multiply(inverse(Y),X_96)) = multiply(inverse(Y),least_upper_bound(inverse(X),X_96)),
    inference(resolve,[$cnf( $equal(multiply(inverse(Y),least_upper_bound(inverse(X),X_96)),least_upper_bound(inverse(multiply(X,Y)),multiply(inverse(Y),X_96))) )],[refute_0_2115,refute_0_2116]) ).

cnf(refute_0_2118,plain,
    least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344)) = multiply(inverse(X_345),least_upper_bound(inverse(X_343),X_344)),
    inference(subst,[],[refute_0_2117:[bind(X,$fot(X_343)),bind(Y,$fot(X_345)),bind(X_96,$fot(X_344))]]) ).

cnf(refute_0_2119,plain,
    ( multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))) != least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344))
    | least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344)) != multiply(inverse(X_345),least_upper_bound(inverse(X_343),X_344))
    | multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))) = multiply(inverse(X_345),least_upper_bound(inverse(X_343),X_344)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))),multiply(inverse(X_345),least_upper_bound(inverse(X_343),X_344))) ),[0],$fot(least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344)))]]) ).

cnf(refute_0_2120,plain,
    ( multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))) != least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344))
    | multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))) = multiply(inverse(X_345),least_upper_bound(inverse(X_343),X_344)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344)),multiply(inverse(X_345),least_upper_bound(inverse(X_343),X_344))) )],[refute_0_2118,refute_0_2119]) ).

cnf(refute_0_2121,plain,
    ( multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)) != least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344))
    | multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))) = multiply(inverse(X_345),least_upper_bound(inverse(X_343),X_344)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))),least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344))) )],[refute_0_2111,refute_0_2120]) ).

cnf(refute_0_2122,plain,
    multiply(inverse(multiply(X_343,X_345)),least_upper_bound(identity,multiply(X_343,X_344))) = multiply(inverse(X_345),least_upper_bound(inverse(X_343),X_344)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_343,X_345)),least_upper_bound(multiply(X_343,X_344),identity)),least_upper_bound(inverse(multiply(X_343,X_345)),multiply(inverse(X_345),X_344))) )],[refute_0_2098,refute_0_2121]) ).

cnf(refute_0_2123,plain,
    multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))) = multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)),
    inference(subst,[],[refute_0_2122:[bind(X_343,$fot(inverse(X_96))),bind(X_344,$fot(X_95))]]) ).

cnf(refute_0_2124,plain,
    ( multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)) != multiply(inverse(X_345),least_upper_bound(X_96,X_95))
    | multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))) != multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95))
    | multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))) = multiply(inverse(X_345),least_upper_bound(X_96,X_95)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))))),bind(Y0,$fot(multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)))),bind(Z0,$fot(multiply(inverse(X_345),least_upper_bound(X_96,X_95))))]]) ).

cnf(refute_0_2125,plain,
    ( multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)) != multiply(inverse(X_345),least_upper_bound(X_96,X_95))
    | multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))) = multiply(inverse(X_345),least_upper_bound(X_96,X_95)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))),multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95))) )],[refute_0_2123,refute_0_2124]) ).

cnf(refute_0_2126,plain,
    multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))) = multiply(inverse(X_345),least_upper_bound(X_96,X_95)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_345),least_upper_bound(inverse(inverse(X_96)),X_95)),multiply(inverse(X_345),least_upper_bound(X_96,X_95))) )],[refute_0_2094,refute_0_2125]) ).

cnf(refute_0_2127,plain,
    ( multiply(inverse(X_345),least_upper_bound(X_95,X_96)) != multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95)))
    | multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))) != multiply(inverse(X_345),least_upper_bound(X_96,X_95))
    | multiply(inverse(X_345),least_upper_bound(X_95,X_96)) = multiply(inverse(X_345),least_upper_bound(X_96,X_95)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_345),least_upper_bound(X_95,X_96)),multiply(inverse(X_345),least_upper_bound(X_96,X_95))) ),[0],$fot(multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))))]]) ).

cnf(refute_0_2128,plain,
    ( multiply(inverse(X_345),least_upper_bound(X_95,X_96)) != multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95)))
    | multiply(inverse(X_345),least_upper_bound(X_95,X_96)) = multiply(inverse(X_345),least_upper_bound(X_96,X_95)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95))),multiply(inverse(X_345),least_upper_bound(X_96,X_95))) )],[refute_0_2126,refute_0_2127]) ).

cnf(refute_0_2129,plain,
    multiply(inverse(X_345),least_upper_bound(X_95,X_96)) = multiply(inverse(X_345),least_upper_bound(X_96,X_95)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_345),least_upper_bound(X_95,X_96)),multiply(inverse(multiply(inverse(X_96),X_345)),least_upper_bound(identity,multiply(inverse(X_96),X_95)))) )],[refute_0_2085,refute_0_2128]) ).

cnf(refute_0_2130,plain,
    ( multiply(inverse(X_345),least_upper_bound(X_95,X_96)) != multiply(inverse(X_345),least_upper_bound(X_96,X_95))
    | multiply(inverse(X_345),least_upper_bound(X_96,X_95)) = multiply(inverse(X_345),least_upper_bound(X_95,X_96)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(inverse(X_345),least_upper_bound(X_95,X_96)))),bind(Y0,$fot(multiply(inverse(X_345),least_upper_bound(X_96,X_95))))]]) ).

cnf(refute_0_2131,plain,
    multiply(inverse(X_345),least_upper_bound(X_96,X_95)) = multiply(inverse(X_345),least_upper_bound(X_95,X_96)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_345),least_upper_bound(X_95,X_96)),multiply(inverse(X_345),least_upper_bound(X_96,X_95))) )],[refute_0_2129,refute_0_2130]) ).

cnf(refute_0_2132,plain,
    multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) = multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))),
    inference(subst,[],[refute_0_2131:[bind(X_345,$fot(least_upper_bound(X_378,inverse(X_379)))),bind(X_95,$fot(identity)),bind(X_96,$fot(least_upper_bound(identity,multiply(X_378,X_379))))]]) ).

cnf(refute_0_2133,plain,
    ( multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))) != X_379
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) != multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379))))
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) = X_379 ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))))),bind(Z0,$fot(X_379))]]) ).

cnf(refute_0_2134,plain,
    ( multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))) != X_379
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) = X_379 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)),multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379))))) )],[refute_0_2132,refute_0_2133]) ).

cnf(refute_0_2135,plain,
    multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) = X_379,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_378,X_379)))),X_379) )],[refute_0_2072,refute_0_2134]) ).

cnf(refute_0_2136,plain,
    ( multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) != X_379
    | multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) != least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379)
    | X_379 = least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)),least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379)) ),[0],$fot(X_379)]]) ).

cnf(refute_0_2137,plain,
    ( multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) != least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379)
    | X_379 = least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)),X_379) )],[refute_0_2135,refute_0_2136]) ).

cnf(refute_0_2138,plain,
    least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379) = least_upper_bound(X_379,inverse(least_upper_bound(X_378,inverse(X_379)))),
    inference(subst,[],[refute_0_1152:[bind(X,$fot(X_379)),bind(X_14,$fot(inverse(least_upper_bound(X_378,inverse(X_379)))))]]) ).

cnf(refute_0_2139,plain,
    ( X_379 != least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379)
    | least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379) != least_upper_bound(X_379,inverse(least_upper_bound(X_378,inverse(X_379))))
    | X_379 = least_upper_bound(X_379,inverse(least_upper_bound(X_378,inverse(X_379)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_379,least_upper_bound(X_379,inverse(least_upper_bound(X_378,inverse(X_379))))) ),[0],$fot(least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379))]]) ).

cnf(refute_0_2140,plain,
    ( X_379 != least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379)
    | X_379 = least_upper_bound(X_379,inverse(least_upper_bound(X_378,inverse(X_379)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379),least_upper_bound(X_379,inverse(least_upper_bound(X_378,inverse(X_379))))) )],[refute_0_2138,refute_0_2139]) ).

cnf(refute_0_2141,plain,
    ( multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)) != least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379)
    | X_379 = least_upper_bound(X_379,inverse(least_upper_bound(X_378,inverse(X_379)))) ),
    inference(resolve,[$cnf( $equal(X_379,least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379)) )],[refute_0_2137,refute_0_2140]) ).

cnf(refute_0_2142,plain,
    X_379 = least_upper_bound(X_379,inverse(least_upper_bound(X_378,inverse(X_379)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_378,inverse(X_379))),least_upper_bound(least_upper_bound(identity,multiply(X_378,X_379)),identity)),least_upper_bound(inverse(least_upper_bound(X_378,inverse(X_379))),X_379)) )],[refute_0_2064,refute_0_2141]) ).

cnf(refute_0_2143,plain,
    X_92 = least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92)))),
    inference(subst,[],[refute_0_2142:[bind(X_378,$fot(X_420)),bind(X_379,$fot(X_92))]]) ).

cnf(refute_0_2144,plain,
    ( X_92 != least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92))))
    | least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92)))) = X_92 ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(X_92)),bind(Y0,$fot(least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92))))))]]) ).

cnf(refute_0_2145,plain,
    least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92)))) = X_92,
    inference(resolve,[$cnf( $equal(X_92,least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92))))) )],[refute_0_2143,refute_0_2144]) ).

cnf(refute_0_2146,plain,
    ( least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92)))) != X_92
    | least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)) != least_upper_bound(Y,least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92)))))
    | least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)) = least_upper_bound(Y,X_92) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)),least_upper_bound(Y,least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92)))))) ),[1,1],$fot(X_92)]]) ).

cnf(refute_0_2147,plain,
    ( least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)) != least_upper_bound(Y,least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92)))))
    | least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)) = least_upper_bound(Y,X_92) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92)))),X_92) )],[refute_0_2145,refute_0_2146]) ).

cnf(refute_0_2148,plain,
    least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)) = least_upper_bound(Y,X_92),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)),least_upper_bound(Y,least_upper_bound(X_92,inverse(least_upper_bound(X_420,inverse(X_92)))))) )],[refute_0_2044,refute_0_2147]) ).

cnf(refute_0_2149,plain,
    least_upper_bound(least_upper_bound(X_172,X_171),Y) = least_upper_bound(Y,least_upper_bound(X_172,X_171)),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(least_upper_bound(X_172,X_171)))]]) ).

cnf(refute_0_2150,plain,
    least_upper_bound(Y,least_upper_bound(X_172,X_171)) = least_upper_bound(X_171,least_upper_bound(X_172,Y)),
    inference(subst,[],[refute_0_1062:[bind(X,$fot(Y)),bind(Y,$fot(X_171)),bind(X_92,$fot(X_172))]]) ).

cnf(refute_0_2151,plain,
    ( least_upper_bound(Y,least_upper_bound(X_172,X_171)) != least_upper_bound(X_171,least_upper_bound(X_172,Y))
    | least_upper_bound(least_upper_bound(X_172,X_171),Y) != least_upper_bound(Y,least_upper_bound(X_172,X_171))
    | least_upper_bound(least_upper_bound(X_172,X_171),Y) = least_upper_bound(X_171,least_upper_bound(X_172,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_172,X_171),Y),least_upper_bound(Y,least_upper_bound(X_172,X_171))) ),[1],$fot(least_upper_bound(X_171,least_upper_bound(X_172,Y)))]]) ).

cnf(refute_0_2152,plain,
    ( least_upper_bound(least_upper_bound(X_172,X_171),Y) != least_upper_bound(Y,least_upper_bound(X_172,X_171))
    | least_upper_bound(least_upper_bound(X_172,X_171),Y) = least_upper_bound(X_171,least_upper_bound(X_172,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_172,X_171)),least_upper_bound(X_171,least_upper_bound(X_172,Y))) )],[refute_0_2150,refute_0_2151]) ).

cnf(refute_0_2153,plain,
    least_upper_bound(least_upper_bound(X_172,X_171),Y) = least_upper_bound(X_171,least_upper_bound(X_172,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_172,X_171),Y),least_upper_bound(Y,least_upper_bound(X_172,X_171))) )],[refute_0_2149,refute_0_2152]) ).

cnf(refute_0_2154,plain,
    least_upper_bound(least_upper_bound(X_172,X_171),Y) = least_upper_bound(X_172,least_upper_bound(X_171,Y)),
    inference(subst,[],[refute_0_237:[bind(X,$fot(X_172)),bind(Y,$fot(X_171)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_2155,plain,
    ( least_upper_bound(least_upper_bound(X_172,X_171),Y) != least_upper_bound(X_171,least_upper_bound(X_172,Y))
    | least_upper_bound(least_upper_bound(X_172,X_171),Y) != least_upper_bound(X_172,least_upper_bound(X_171,Y))
    | least_upper_bound(X_172,least_upper_bound(X_171,Y)) = least_upper_bound(X_171,least_upper_bound(X_172,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_172,X_171),Y),least_upper_bound(X_171,least_upper_bound(X_172,Y))) ),[0],$fot(least_upper_bound(X_172,least_upper_bound(X_171,Y)))]]) ).

cnf(refute_0_2156,plain,
    ( least_upper_bound(least_upper_bound(X_172,X_171),Y) != least_upper_bound(X_171,least_upper_bound(X_172,Y))
    | least_upper_bound(X_172,least_upper_bound(X_171,Y)) = least_upper_bound(X_171,least_upper_bound(X_172,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_172,X_171),Y),least_upper_bound(X_172,least_upper_bound(X_171,Y))) )],[refute_0_2154,refute_0_2155]) ).

cnf(refute_0_2157,plain,
    least_upper_bound(X_172,least_upper_bound(X_171,Y)) = least_upper_bound(X_171,least_upper_bound(X_172,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_172,X_171),Y),least_upper_bound(X_171,least_upper_bound(X_172,Y))) )],[refute_0_2153,refute_0_2156]) ).

cnf(refute_0_2158,plain,
    ( least_upper_bound(X_172,least_upper_bound(X_171,Y)) != least_upper_bound(X_171,least_upper_bound(X_172,Y))
    | least_upper_bound(X_171,least_upper_bound(X_172,Y)) = least_upper_bound(X_172,least_upper_bound(X_171,Y)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_172,least_upper_bound(X_171,Y)))),bind(Y0,$fot(least_upper_bound(X_171,least_upper_bound(X_172,Y))))]]) ).

cnf(refute_0_2159,plain,
    least_upper_bound(X_171,least_upper_bound(X_172,Y)) = least_upper_bound(X_172,least_upper_bound(X_171,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_172,least_upper_bound(X_171,Y)),least_upper_bound(X_171,least_upper_bound(X_172,Y))) )],[refute_0_2157,refute_0_2158]) ).

cnf(refute_0_2160,plain,
    least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)) = least_upper_bound(X_92,least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),Y)),
    inference(subst,[],[refute_0_2159:[bind(X_171,$fot(inverse(least_upper_bound(X_420,inverse(X_92))))),bind(X_172,$fot(X_92))]]) ).

cnf(refute_0_2161,plain,
    ( least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)) != least_upper_bound(Y,X_92)
    | least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)) != least_upper_bound(X_92,least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),Y))
    | least_upper_bound(X_92,least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),Y)) = least_upper_bound(Y,X_92) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)),least_upper_bound(Y,X_92)) ),[0],$fot(least_upper_bound(X_92,least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),Y)))]]) ).

cnf(refute_0_2162,plain,
    ( least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)) != least_upper_bound(Y,X_92)
    | least_upper_bound(X_92,least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),Y)) = least_upper_bound(Y,X_92) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)),least_upper_bound(X_92,least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),Y))) )],[refute_0_2160,refute_0_2161]) ).

cnf(refute_0_2163,plain,
    least_upper_bound(X_92,least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),Y)) = least_upper_bound(Y,X_92),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_420,inverse(X_92))),least_upper_bound(X_92,Y)),least_upper_bound(Y,X_92)) )],[refute_0_2148,refute_0_2162]) ).

cnf(refute_0_2164,plain,
    least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)) = least_upper_bound(X_16,b),
    inference(subst,[],[refute_0_2163:[bind(Y,$fot(X_16)),bind(X_420,$fot(identity)),bind(X_92,$fot(b))]]) ).

cnf(refute_0_2165,plain,
    ( least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)) != least_upper_bound(X_16,b)
    | least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)) != least_upper_bound(b,X_16)
    | least_upper_bound(X_16,b) = least_upper_bound(b,X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)),least_upper_bound(b,X_16)) ),[0],$fot(least_upper_bound(X_16,b))]]) ).

cnf(refute_0_2166,plain,
    ( least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)) != least_upper_bound(b,X_16)
    | least_upper_bound(X_16,b) = least_upper_bound(b,X_16) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)),least_upper_bound(X_16,b)) )],[refute_0_2164,refute_0_2165]) ).

cnf(refute_0_2167,plain,
    least_upper_bound(X_16,b) = least_upper_bound(b,X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(inverse(least_upper_bound(identity,inverse(b))),X_16)),least_upper_bound(b,X_16)) )],[refute_0_2043,refute_0_2166]) ).

cnf(refute_0_2168,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),b) = least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c)))),
    inference(subst,[],[refute_0_2167:[bind(X_16,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_2169,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),b) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),b) != least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c)))) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),b),inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),[0],$fot(least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_2170,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),b) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c)))) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),b),least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_2168,refute_0_2169]) ).

cnf(refute_0_2171,plain,
    least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c)))) = inverse(greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),b),inverse(greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_1717,refute_0_2170]) ).

cnf(refute_0_2172,plain,
    ( least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c)))) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c))))))
    | least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) ),[1,1,1],$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))]]) ).

cnf(refute_0_2173,plain,
    ( least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) != least_upper_bound(a,least_upper_bound(c,least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c))))))
    | least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_2171,refute_0_2172]) ).

cnf(refute_0_2174,plain,
    least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))),least_upper_bound(a,least_upper_bound(c,least_upper_bound(b,inverse(greatest_lower_bound(inverse(b),inverse(c))))))) )],[refute_0_1647,refute_0_2173]) ).

cnf(refute_0_2175,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) = least_upper_bound(X_118,multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118)),
    inference(subst,[],[refute_0_557:[bind(X_119,$fot(inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))))]]) ).

cnf(refute_0_2176,plain,
    inverse(greatest_lower_bound(X_349,inverse(X_118))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118),
    inference(subst,[],[refute_0_54:[bind(X_107,$fot(X_349)),bind(X_83,$fot(X_118))]]) ).

cnf(refute_0_2177,plain,
    ( inverse(greatest_lower_bound(X_349,inverse(X_118))) != multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118)
    | multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118) = inverse(greatest_lower_bound(X_349,inverse(X_118))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(X_349,inverse(X_118))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118)))]]) ).

cnf(refute_0_2178,plain,
    multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118) = inverse(greatest_lower_bound(X_349,inverse(X_118))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_349,inverse(X_118))),multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118)) )],[refute_0_2176,refute_0_2177]) ).

cnf(refute_0_2179,plain,
    ( multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118) != inverse(greatest_lower_bound(X_349,inverse(X_118)))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) != least_upper_bound(X_118,multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) = least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118),least_upper_bound(X_118,multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118))) ),[1,1],$fot(inverse(greatest_lower_bound(X_349,inverse(X_118))))]]) ).

cnf(refute_0_2180,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) != least_upper_bound(X_118,multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) = least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118),inverse(greatest_lower_bound(X_349,inverse(X_118)))) )],[refute_0_2178,refute_0_2179]) ).

cnf(refute_0_2181,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) = least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118),least_upper_bound(X_118,multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118))) )],[refute_0_2175,refute_0_2180]) ).

cnf(refute_0_2182,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221)))) = inverse(greatest_lower_bound(identity,X_221)),
    inference(subst,[],[refute_0_281:[bind(X_8,$fot(inverse(greatest_lower_bound(identity,X_221)))),bind(X_9,$fot(identity))]]) ).

cnf(refute_0_2183,plain,
    multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135))),
    inference(subst,[],[refute_0_64:[bind(X_134,$fot(inverse(greatest_lower_bound(inverse(X_135),identity))))]]) ).

cnf(refute_0_2184,plain,
    inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity))) = multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))),
    inference(subst,[],[p12_3:[bind(X,$fot(inverse(X_117))),bind(Y,$fot(greatest_lower_bound(X_117,identity)))]]) ).

cnf(refute_0_2185,plain,
    multiply(inverse(X_117),greatest_lower_bound(X_117,identity)) = greatest_lower_bound(identity,inverse(X_117)),
    inference(subst,[],[refute_0_1781:[bind(X_112,$fot(X_117))]]) ).

cnf(refute_0_2186,plain,
    ( multiply(inverse(X_117),greatest_lower_bound(X_117,identity)) != greatest_lower_bound(identity,inverse(X_117))
    | inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity))) != multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117)))
    | inverse(greatest_lower_bound(identity,inverse(X_117))) = multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity))),multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117)))) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_117)))]]) ).

cnf(refute_0_2187,plain,
    ( inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity))) != multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117)))
    | inverse(greatest_lower_bound(identity,inverse(X_117))) = multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_117),greatest_lower_bound(X_117,identity)),greatest_lower_bound(identity,inverse(X_117))) )],[refute_0_2185,refute_0_2186]) ).

cnf(refute_0_2188,plain,
    inverse(greatest_lower_bound(identity,inverse(X_117))) = multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity))),multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117)))) )],[refute_0_2184,refute_0_2187]) ).

cnf(refute_0_2189,plain,
    inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity))) = multiply(inverse(greatest_lower_bound(X_117,identity)),X_117),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_117)),bind(X_18,$fot(greatest_lower_bound(X_117,identity)))]]) ).

cnf(refute_0_2190,plain,
    multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))) = inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity))),
    inference(subst,[],[refute_0_25:[bind(X,$fot(inverse(X_117))),bind(Y,$fot(greatest_lower_bound(X_117,identity)))]]) ).

cnf(refute_0_2191,plain,
    ( multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))) != inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity)))
    | inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity))) != multiply(inverse(greatest_lower_bound(X_117,identity)),X_117)
    | multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))) = multiply(inverse(greatest_lower_bound(X_117,identity)),X_117) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))))),bind(Y0,$fot(inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_117,identity)),X_117)))]]) ).

cnf(refute_0_2192,plain,
    ( inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity))) != multiply(inverse(greatest_lower_bound(X_117,identity)),X_117)
    | multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))) = multiply(inverse(greatest_lower_bound(X_117,identity)),X_117) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))),inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity)))) )],[refute_0_2190,refute_0_2191]) ).

cnf(refute_0_2193,plain,
    multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))) = multiply(inverse(greatest_lower_bound(X_117,identity)),X_117),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_117),greatest_lower_bound(X_117,identity))),multiply(inverse(greatest_lower_bound(X_117,identity)),X_117)) )],[refute_0_2189,refute_0_2192]) ).

cnf(refute_0_2194,plain,
    ( multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))) != multiply(inverse(greatest_lower_bound(X_117,identity)),X_117)
    | inverse(greatest_lower_bound(identity,inverse(X_117))) != multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117)))
    | inverse(greatest_lower_bound(identity,inverse(X_117))) = multiply(inverse(greatest_lower_bound(X_117,identity)),X_117) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_117))),multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_117,identity)),X_117))]]) ).

cnf(refute_0_2195,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_117))) != multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117)))
    | inverse(greatest_lower_bound(identity,inverse(X_117))) = multiply(inverse(greatest_lower_bound(X_117,identity)),X_117) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117))),multiply(inverse(greatest_lower_bound(X_117,identity)),X_117)) )],[refute_0_2193,refute_0_2194]) ).

cnf(refute_0_2196,plain,
    inverse(greatest_lower_bound(identity,inverse(X_117))) = multiply(inverse(greatest_lower_bound(X_117,identity)),X_117),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_117))),multiply(inverse(greatest_lower_bound(X_117,identity)),inverse(inverse(X_117)))) )],[refute_0_2188,refute_0_2195]) ).

cnf(refute_0_2197,plain,
    inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))) = multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135)),
    inference(subst,[],[refute_0_2196:[bind(X_117,$fot(inverse(X_135)))]]) ).

cnf(refute_0_2198,plain,
    ( inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))) != multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135))
    | multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135)) = inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135))))]]) ).

cnf(refute_0_2199,plain,
    multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135)) = inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))),multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135))) )],[refute_0_2197,refute_0_2198]) ).

cnf(refute_0_2200,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135)))
    | multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135)) != inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))
    | multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135)))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))]]) ).

cnf(refute_0_2201,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135)))
    | multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135)),inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) )],[refute_0_2199,refute_0_2200]) ).

cnf(refute_0_2202,plain,
    multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_135),identity)),inverse(X_135)))) )],[refute_0_2183,refute_0_2201]) ).

cnf(refute_0_2203,plain,
    multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,greatest_lower_bound(Y,identity))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity))),
    inference(subst,[],[refute_0_1929:[bind(X_111,$fot(greatest_lower_bound(Y,identity)))]]) ).

cnf(refute_0_2204,plain,
    greatest_lower_bound(identity,greatest_lower_bound(Y,identity)) = greatest_lower_bound(identity,Y),
    inference(subst,[],[refute_0_83:[bind(X_30,$fot(identity))]]) ).

cnf(refute_0_2205,plain,
    ( multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,greatest_lower_bound(Y,identity))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity)))
    | greatest_lower_bound(identity,greatest_lower_bound(Y,identity)) != greatest_lower_bound(identity,Y)
    | multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,Y)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,greatest_lower_bound(Y,identity))),greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity)))) ),[0,1],$fot(greatest_lower_bound(identity,Y))]]) ).

cnf(refute_0_2206,plain,
    ( multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,greatest_lower_bound(Y,identity))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity)))
    | multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,Y)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,Y)) )],[refute_0_2204,refute_0_2205]) ).

cnf(refute_0_2207,plain,
    multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,Y)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,greatest_lower_bound(Y,identity))),greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity)))) )],[refute_0_2203,refute_0_2206]) ).

cnf(refute_0_2208,plain,
    multiply(inverse(greatest_lower_bound(X_115,X_116)),greatest_lower_bound(X_115,X_116)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(greatest_lower_bound(X_115,X_116)))]]) ).

cnf(refute_0_2209,plain,
    ( multiply(inverse(greatest_lower_bound(X_115,X_116)),greatest_lower_bound(X_115,X_116)) != identity
    | inverse(greatest_lower_bound(X_115,X_116)) != inverse(greatest_lower_bound(X_116,X_115))
    | multiply(inverse(greatest_lower_bound(X_116,X_115)),greatest_lower_bound(X_115,X_116)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_115,X_116)),greatest_lower_bound(X_115,X_116)),identity) ),[0,0],$fot(inverse(greatest_lower_bound(X_116,X_115)))]]) ).

cnf(refute_0_2210,plain,
    ( multiply(inverse(greatest_lower_bound(X_115,X_116)),greatest_lower_bound(X_115,X_116)) != identity
    | multiply(inverse(greatest_lower_bound(X_116,X_115)),greatest_lower_bound(X_115,X_116)) = identity ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_115,X_116)),inverse(greatest_lower_bound(X_116,X_115))) )],[refute_0_117,refute_0_2209]) ).

cnf(refute_0_2211,plain,
    multiply(inverse(greatest_lower_bound(X_116,X_115)),greatest_lower_bound(X_115,X_116)) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_115,X_116)),greatest_lower_bound(X_115,X_116)),identity) )],[refute_0_2208,refute_0_2210]) ).

cnf(refute_0_2212,plain,
    multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,Y)) = identity,
    inference(subst,[],[refute_0_2211:[bind(X_115,$fot(identity)),bind(X_116,$fot(Y))]]) ).

cnf(refute_0_2213,plain,
    ( multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,Y)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity)))
    | multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,Y)) != identity
    | identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,Y)),greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity)))) ),[0],$fot(identity)]]) ).

cnf(refute_0_2214,plain,
    ( multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,Y)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity)))
    | identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,Y)),identity) )],[refute_0_2212,refute_0_2213]) ).

cnf(refute_0_2215,plain,
    identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,identity)),greatest_lower_bound(identity,Y)),greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity)))) )],[refute_0_2207,refute_0_2214]) ).

cnf(refute_0_2216,plain,
    ( identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity)))
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity))) = identity ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity)))))]]) ).

cnf(refute_0_2217,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity))) = identity,
    inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(Y,identity)))) )],[refute_0_2215,refute_0_2216]) ).

cnf(refute_0_2218,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(X_135,identity))) = identity,
    inference(subst,[],[refute_0_2217:[bind(Y,$fot(X_135))]]) ).

cnf(refute_0_2219,plain,
    multiply(greatest_lower_bound(X_135,identity),identity) = greatest_lower_bound(X_135,identity),
    inference(subst,[],[refute_0_189:[bind(X,$fot(greatest_lower_bound(X_135,identity)))]]) ).

cnf(refute_0_2220,plain,
    greatest_lower_bound(identity,multiply(X_135,identity)) = multiply(greatest_lower_bound(X_135,identity),identity),
    inference(subst,[],[refute_0_1520:[bind(X_133,$fot(identity)),bind(X_134,$fot(X_135))]]) ).

cnf(refute_0_2221,plain,
    ( multiply(greatest_lower_bound(X_135,identity),identity) != greatest_lower_bound(X_135,identity)
    | greatest_lower_bound(identity,multiply(X_135,identity)) != multiply(greatest_lower_bound(X_135,identity),identity)
    | greatest_lower_bound(identity,multiply(X_135,identity)) = greatest_lower_bound(X_135,identity) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_135,identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_135,identity),identity))),bind(Z0,$fot(greatest_lower_bound(X_135,identity)))]]) ).

cnf(refute_0_2222,plain,
    ( multiply(greatest_lower_bound(X_135,identity),identity) != greatest_lower_bound(X_135,identity)
    | greatest_lower_bound(identity,multiply(X_135,identity)) = greatest_lower_bound(X_135,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_135,identity)),multiply(greatest_lower_bound(X_135,identity),identity)) )],[refute_0_2220,refute_0_2221]) ).

cnf(refute_0_2223,plain,
    greatest_lower_bound(identity,multiply(X_135,identity)) = greatest_lower_bound(X_135,identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_135,identity),identity),greatest_lower_bound(X_135,identity)) )],[refute_0_2219,refute_0_2222]) ).

cnf(refute_0_2224,plain,
    multiply(X_135,greatest_lower_bound(identity,inverse(X_135))) = greatest_lower_bound(identity,multiply(X_135,identity)),
    inference(subst,[],[refute_0_50:[bind(X_103,$fot(X_135)),bind(X_104,$fot(identity))]]) ).

cnf(refute_0_2225,plain,
    ( multiply(X_135,greatest_lower_bound(identity,inverse(X_135))) != greatest_lower_bound(identity,multiply(X_135,identity))
    | greatest_lower_bound(identity,multiply(X_135,identity)) != greatest_lower_bound(X_135,identity)
    | multiply(X_135,greatest_lower_bound(identity,inverse(X_135))) = greatest_lower_bound(X_135,identity) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(X_135,greatest_lower_bound(identity,inverse(X_135))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_135,identity)))),bind(Z0,$fot(greatest_lower_bound(X_135,identity)))]]) ).

cnf(refute_0_2226,plain,
    ( greatest_lower_bound(identity,multiply(X_135,identity)) != greatest_lower_bound(X_135,identity)
    | multiply(X_135,greatest_lower_bound(identity,inverse(X_135))) = greatest_lower_bound(X_135,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_135,greatest_lower_bound(identity,inverse(X_135))),greatest_lower_bound(identity,multiply(X_135,identity))) )],[refute_0_2224,refute_0_2225]) ).

cnf(refute_0_2227,plain,
    multiply(X_135,greatest_lower_bound(identity,inverse(X_135))) = greatest_lower_bound(X_135,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_135,identity)),greatest_lower_bound(X_135,identity)) )],[refute_0_2223,refute_0_2226]) ).

cnf(refute_0_2228,plain,
    inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))) = inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))),
    introduced(tautology,[refl,[$fot(inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))))]]) ).

cnf(refute_0_2229,plain,
    ( multiply(X_135,greatest_lower_bound(identity,inverse(X_135))) != greatest_lower_bound(X_135,identity)
    | inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))) != inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135))))
    | inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))) = inverse(greatest_lower_bound(X_135,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))),inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135))))) ),[1,0],$fot(greatest_lower_bound(X_135,identity))]]) ).

cnf(refute_0_2230,plain,
    ( multiply(X_135,greatest_lower_bound(identity,inverse(X_135))) != greatest_lower_bound(X_135,identity)
    | inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))) = inverse(greatest_lower_bound(X_135,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))),inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135))))) )],[refute_0_2228,refute_0_2229]) ).

cnf(refute_0_2231,plain,
    inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))) = inverse(greatest_lower_bound(X_135,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_135,greatest_lower_bound(identity,inverse(X_135))),greatest_lower_bound(X_135,identity)) )],[refute_0_2227,refute_0_2230]) ).

cnf(refute_0_2232,plain,
    inverse(multiply(X,greatest_lower_bound(X_115,X_116))) = multiply(inverse(greatest_lower_bound(X_115,X_116)),inverse(X)),
    inference(subst,[],[p12_3:[bind(Y,$fot(greatest_lower_bound(X_115,X_116)))]]) ).

cnf(refute_0_2233,plain,
    ( inverse(multiply(X,greatest_lower_bound(X_115,X_116))) != multiply(inverse(greatest_lower_bound(X_115,X_116)),inverse(X))
    | inverse(greatest_lower_bound(X_115,X_116)) != inverse(greatest_lower_bound(X_116,X_115))
    | inverse(multiply(X,greatest_lower_bound(X_115,X_116))) = multiply(inverse(greatest_lower_bound(X_116,X_115)),inverse(X)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(X_115,X_116))),multiply(inverse(greatest_lower_bound(X_115,X_116)),inverse(X))) ),[1,0],$fot(inverse(greatest_lower_bound(X_116,X_115)))]]) ).

cnf(refute_0_2234,plain,
    ( inverse(multiply(X,greatest_lower_bound(X_115,X_116))) != multiply(inverse(greatest_lower_bound(X_115,X_116)),inverse(X))
    | inverse(multiply(X,greatest_lower_bound(X_115,X_116))) = multiply(inverse(greatest_lower_bound(X_116,X_115)),inverse(X)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_115,X_116)),inverse(greatest_lower_bound(X_116,X_115))) )],[refute_0_117,refute_0_2233]) ).

cnf(refute_0_2235,plain,
    inverse(multiply(X,greatest_lower_bound(X_115,X_116))) = multiply(inverse(greatest_lower_bound(X_116,X_115)),inverse(X)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(X_115,X_116))),multiply(inverse(greatest_lower_bound(X_115,X_116)),inverse(X))) )],[refute_0_2232,refute_0_2234]) ).

cnf(refute_0_2236,plain,
    multiply(inverse(greatest_lower_bound(X_116,X_115)),inverse(X)) = inverse(multiply(X,greatest_lower_bound(X_116,X_115))),
    inference(subst,[],[refute_0_25:[bind(Y,$fot(greatest_lower_bound(X_116,X_115)))]]) ).

cnf(refute_0_2237,plain,
    ( multiply(inverse(greatest_lower_bound(X_116,X_115)),inverse(X)) != inverse(multiply(X,greatest_lower_bound(X_116,X_115)))
    | inverse(multiply(X,greatest_lower_bound(X_115,X_116))) != multiply(inverse(greatest_lower_bound(X_116,X_115)),inverse(X))
    | inverse(multiply(X,greatest_lower_bound(X_115,X_116))) = inverse(multiply(X,greatest_lower_bound(X_116,X_115))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(X_115,X_116))),multiply(inverse(greatest_lower_bound(X_116,X_115)),inverse(X))) ),[1],$fot(inverse(multiply(X,greatest_lower_bound(X_116,X_115))))]]) ).

cnf(refute_0_2238,plain,
    ( inverse(multiply(X,greatest_lower_bound(X_115,X_116))) != multiply(inverse(greatest_lower_bound(X_116,X_115)),inverse(X))
    | inverse(multiply(X,greatest_lower_bound(X_115,X_116))) = inverse(multiply(X,greatest_lower_bound(X_116,X_115))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_116,X_115)),inverse(X)),inverse(multiply(X,greatest_lower_bound(X_116,X_115)))) )],[refute_0_2236,refute_0_2237]) ).

cnf(refute_0_2239,plain,
    inverse(multiply(X,greatest_lower_bound(X_115,X_116))) = inverse(multiply(X,greatest_lower_bound(X_116,X_115))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(X_115,X_116))),multiply(inverse(greatest_lower_bound(X_116,X_115)),inverse(X))) )],[refute_0_2235,refute_0_2238]) ).

cnf(refute_0_2240,plain,
    ( inverse(multiply(X,greatest_lower_bound(X_115,X_116))) != inverse(multiply(X,greatest_lower_bound(X_116,X_115)))
    | inverse(multiply(X,greatest_lower_bound(X_116,X_115))) = inverse(multiply(X,greatest_lower_bound(X_115,X_116))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(multiply(X,greatest_lower_bound(X_115,X_116))))),bind(Y0,$fot(inverse(multiply(X,greatest_lower_bound(X_116,X_115)))))]]) ).

cnf(refute_0_2241,plain,
    inverse(multiply(X,greatest_lower_bound(X_116,X_115))) = inverse(multiply(X,greatest_lower_bound(X_115,X_116))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,greatest_lower_bound(X_115,X_116))),inverse(multiply(X,greatest_lower_bound(X_116,X_115)))) )],[refute_0_2239,refute_0_2240]) ).

cnf(refute_0_2242,plain,
    inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))) = inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))),
    inference(subst,[],[refute_0_2241:[bind(X,$fot(X_135)),bind(X_115,$fot(identity)),bind(X_116,$fot(inverse(X_135)))]]) ).

cnf(refute_0_2243,plain,
    ( inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))) != inverse(greatest_lower_bound(X_135,identity))
    | inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))) != inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135))))
    | inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))) = inverse(greatest_lower_bound(X_135,identity)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))))),bind(Y0,$fot(inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_135,identity))))]]) ).

cnf(refute_0_2244,plain,
    ( inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))) != inverse(greatest_lower_bound(X_135,identity))
    | inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))) = inverse(greatest_lower_bound(X_135,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))),inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135))))) )],[refute_0_2242,refute_0_2243]) ).

cnf(refute_0_2245,plain,
    inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))) = inverse(greatest_lower_bound(X_135,identity)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_135,greatest_lower_bound(identity,inverse(X_135)))),inverse(greatest_lower_bound(X_135,identity))) )],[refute_0_2231,refute_0_2244]) ).

cnf(refute_0_2246,plain,
    greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))) = greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))))]]) ).

cnf(refute_0_2247,plain,
    ( greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))) != greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))))
    | inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))) != inverse(greatest_lower_bound(X_135,identity))
    | greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(X_135,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))),greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))))) ),[1,1],$fot(inverse(greatest_lower_bound(X_135,identity)))]]) ).

cnf(refute_0_2248,plain,
    ( inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))) != inverse(greatest_lower_bound(X_135,identity))
    | greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(X_135,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))),greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))))) )],[refute_0_2246,refute_0_2247]) ).

cnf(refute_0_2249,plain,
    greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(X_135,identity))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))),inverse(greatest_lower_bound(X_135,identity))) )],[refute_0_2245,refute_0_2248]) ).

cnf(refute_0_2250,plain,
    ( greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(X_135,identity)))
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(X_135,identity))) != identity
    | greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))) = identity ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(X_135,identity))))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_2251,plain,
    ( greatest_lower_bound(identity,inverse(greatest_lower_bound(X_135,identity))) != identity
    | greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(X_135,identity)))) )],[refute_0_2249,refute_0_2250]) ).

cnf(refute_0_2252,plain,
    greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))) = identity,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(X_135,identity))),identity) )],[refute_0_2218,refute_0_2251]) ).

cnf(refute_0_2253,plain,
    multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))) = greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141))),
    inference(subst,[],[refute_0_94:[bind(X_105,$fot(inverse(X_141)))]]) ).

cnf(refute_0_2254,plain,
    multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)) = greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141))),
    inference(subst,[],[refute_0_64:[bind(X_134,$fot(inverse(X_104))),bind(X_135,$fot(X_141))]]) ).

cnf(refute_0_2255,plain,
    ( multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)) != greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141)))
    | greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141))) = multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141)))))]]) ).

cnf(refute_0_2256,plain,
    greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141))) = multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)),greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141)))) )],[refute_0_2254,refute_0_2255]) ).

cnf(refute_0_2257,plain,
    ( multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))) != greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141)))
    | greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141))) != multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141))
    | multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))) = multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))),multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141))))]]) ).

cnf(refute_0_2258,plain,
    ( multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))) != greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141)))
    | multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))) = multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141))),multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141))) )],[refute_0_2256,refute_0_2257]) ).

cnf(refute_0_2259,plain,
    multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))) = multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))),greatest_lower_bound(identity,multiply(inverse(X_104),inverse(X_141)))) )],[refute_0_2253,refute_0_2258]) ).

cnf(refute_0_2260,plain,
    multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))) = greatest_lower_bound(identity,inverse(multiply(X_141,X_104))),
    inference(subst,[],[refute_0_986:[bind(X,$fot(X_141)),bind(X_112,$fot(X_104))]]) ).

cnf(refute_0_2261,plain,
    ( multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))) != multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141))
    | multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))) != greatest_lower_bound(identity,inverse(multiply(X_141,X_104)))
    | greatest_lower_bound(identity,inverse(multiply(X_141,X_104))) = multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))),multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141))) ),[0],$fot(greatest_lower_bound(identity,inverse(multiply(X_141,X_104))))]]) ).

cnf(refute_0_2262,plain,
    ( multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))) != multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141))
    | greatest_lower_bound(identity,inverse(multiply(X_141,X_104))) = multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))),greatest_lower_bound(identity,inverse(multiply(X_141,X_104)))) )],[refute_0_2260,refute_0_2261]) ).

cnf(refute_0_2263,plain,
    greatest_lower_bound(identity,inverse(multiply(X_141,X_104))) = multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_104),greatest_lower_bound(X_104,inverse(X_141))),multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141))) )],[refute_0_2259,refute_0_2262]) ).

cnf(refute_0_2264,plain,
    ( greatest_lower_bound(identity,inverse(multiply(X_141,X_104))) != multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141))
    | multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)) = greatest_lower_bound(identity,inverse(multiply(X_141,X_104))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(identity,inverse(multiply(X_141,X_104))))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141))))]]) ).

cnf(refute_0_2265,plain,
    multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141)) = greatest_lower_bound(identity,inverse(multiply(X_141,X_104))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_141,X_104))),multiply(greatest_lower_bound(inverse(X_104),X_141),inverse(X_141))) )],[refute_0_2263,refute_0_2264]) ).

cnf(refute_0_2266,plain,
    multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) = greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))),
    inference(subst,[],[refute_0_2265:[bind(X_104,$fot(greatest_lower_bound(inverse(X_135),identity))),bind(X_141,$fot(X_135))]]) ).

cnf(refute_0_2267,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) != greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))))
    | greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))) != identity
    | multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) = identity ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_2268,plain,
    ( greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))) != identity
    | multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) = identity ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)),greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity))))) )],[refute_0_2266,refute_0_2267]) ).

cnf(refute_0_2269,plain,
    multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) = identity,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_135,greatest_lower_bound(inverse(X_135),identity)))),identity) )],[refute_0_2252,refute_0_2268]) ).

cnf(refute_0_2270,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))
    | multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) != identity
    | identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))) ),[0],$fot(identity)]]) ).

cnf(refute_0_2271,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))
    | identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)),identity) )],[refute_0_2269,refute_0_2270]) ).

cnf(refute_0_2272,plain,
    inverse(inverse(X_135)) = X_135,
    inference(subst,[],[p12_2:[bind(X,$fot(X_135))]]) ).

cnf(refute_0_2273,plain,
    greatest_lower_bound(identity,inverse(inverse(X_135))) = greatest_lower_bound(identity,inverse(inverse(X_135))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(inverse(X_135))))]]) ).

cnf(refute_0_2274,plain,
    ( greatest_lower_bound(identity,inverse(inverse(X_135))) != greatest_lower_bound(identity,inverse(inverse(X_135)))
    | inverse(inverse(X_135)) != X_135
    | greatest_lower_bound(identity,inverse(inverse(X_135))) = greatest_lower_bound(identity,X_135) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_135))),greatest_lower_bound(identity,inverse(inverse(X_135)))) ),[1,1],$fot(X_135)]]) ).

cnf(refute_0_2275,plain,
    ( inverse(inverse(X_135)) != X_135
    | greatest_lower_bound(identity,inverse(inverse(X_135))) = greatest_lower_bound(identity,X_135) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_135))),greatest_lower_bound(identity,inverse(inverse(X_135)))) )],[refute_0_2273,refute_0_2274]) ).

cnf(refute_0_2276,plain,
    greatest_lower_bound(identity,inverse(inverse(X_135))) = greatest_lower_bound(identity,X_135),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_135)),X_135) )],[refute_0_2272,refute_0_2275]) ).

cnf(refute_0_2277,plain,
    inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))) = inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))]]) ).

cnf(refute_0_2278,plain,
    ( greatest_lower_bound(identity,inverse(inverse(X_135))) != greatest_lower_bound(identity,X_135)
    | inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))) != inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))
    | inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))) = inverse(greatest_lower_bound(identity,X_135)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))),inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) ),[1,0],$fot(greatest_lower_bound(identity,X_135))]]) ).

cnf(refute_0_2279,plain,
    ( greatest_lower_bound(identity,inverse(inverse(X_135))) != greatest_lower_bound(identity,X_135)
    | inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))) = inverse(greatest_lower_bound(identity,X_135)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))),inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) )],[refute_0_2277,refute_0_2278]) ).

cnf(refute_0_2280,plain,
    inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))) = inverse(greatest_lower_bound(identity,X_135)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(inverse(X_135))),greatest_lower_bound(identity,X_135)) )],[refute_0_2276,refute_0_2279]) ).

cnf(refute_0_2281,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))))]]) ).

cnf(refute_0_2282,plain,
    ( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))
    | inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))) != inverse(greatest_lower_bound(identity,X_135))
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_135))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,X_135)))]]) ).

cnf(refute_0_2283,plain,
    ( inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))) != inverse(greatest_lower_bound(identity,X_135))
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_135))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))) )],[refute_0_2281,refute_0_2282]) ).

cnf(refute_0_2284,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_135))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))),inverse(greatest_lower_bound(identity,X_135))) )],[refute_0_2280,refute_0_2283]) ).

cnf(refute_0_2285,plain,
    ( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_135)))
    | identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))
    | identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_135))) ),
    introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))) ),[1],$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_135))))]]) ).

cnf(refute_0_2286,plain,
    ( identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))
    | identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_135))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135))))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_135)))) )],[refute_0_2284,refute_0_2285]) ).

cnf(refute_0_2287,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))
    | identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_135))) ),
    inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))) )],[refute_0_2271,refute_0_2286]) ).

cnf(refute_0_2288,plain,
    identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_135))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(inverse(X_135),identity)),X_135),inverse(X_135)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(inverse(X_135)))))) )],[refute_0_2202,refute_0_2287]) ).

cnf(refute_0_2289,plain,
    identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221))),
    inference(subst,[],[refute_0_2288:[bind(X_135,$fot(X_221))]]) ).

cnf(refute_0_2290,plain,
    ( identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221)))
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221))) = identity ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221)))))]]) ).

cnf(refute_0_2291,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221))) = identity,
    inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221)))) )],[refute_0_2289,refute_0_2290]) ).

cnf(refute_0_2292,plain,
    ( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221))) != identity
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221)))) != inverse(greatest_lower_bound(identity,X_221))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),identity) = inverse(greatest_lower_bound(identity,X_221)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221)))),inverse(greatest_lower_bound(identity,X_221))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_2293,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221)))) != inverse(greatest_lower_bound(identity,X_221))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),identity) = inverse(greatest_lower_bound(identity,X_221)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221))),identity) )],[refute_0_2291,refute_0_2292]) ).

cnf(refute_0_2294,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),identity) = inverse(greatest_lower_bound(identity,X_221)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_221)))),inverse(greatest_lower_bound(identity,X_221))) )],[refute_0_2182,refute_0_2293]) ).

cnf(refute_0_2295,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_221))),
    inference(subst,[],[refute_0_256:[bind(X,$fot(identity)),bind(Y,$fot(inverse(greatest_lower_bound(identity,X_221))))]]) ).

cnf(refute_0_2296,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),identity) != inverse(greatest_lower_bound(identity,X_221))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_221)))
    | least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_221))) = inverse(greatest_lower_bound(identity,X_221)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),identity),inverse(greatest_lower_bound(identity,X_221))) ),[0],$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_221))))]]) ).

cnf(refute_0_2297,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),identity) != inverse(greatest_lower_bound(identity,X_221))
    | least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_221))) = inverse(greatest_lower_bound(identity,X_221)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_221)))) )],[refute_0_2295,refute_0_2296]) ).

cnf(refute_0_2298,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_221))) = inverse(greatest_lower_bound(identity,X_221)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_221)),identity),inverse(greatest_lower_bound(identity,X_221))) )],[refute_0_2294,refute_0_2297]) ).

cnf(refute_0_2299,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))) = inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),
    inference(subst,[],[refute_0_2298:[bind(X_221,$fot(multiply(X_118,X_349)))]]) ).

cnf(refute_0_2300,plain,
    multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118) = multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118))]]) ).

cnf(refute_0_2301,plain,
    ( multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118) != multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118)
    | least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))) != inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))
    | multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118) = multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118),multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118)) ),[1,0],$fot(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))))]]) ).

cnf(refute_0_2302,plain,
    ( least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))) != inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))
    | multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118) = multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118),multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118)) )],[refute_0_2300,refute_0_2301]) ).

cnf(refute_0_2303,plain,
    multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118) = multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))) )],[refute_0_2299,refute_0_2302]) ).

cnf(refute_0_2304,plain,
    ( multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118) != inverse(greatest_lower_bound(X_349,inverse(X_118)))
    | multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118) != multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118)
    | multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118) = inverse(greatest_lower_bound(X_349,inverse(X_118))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118))),bind(Z0,$fot(inverse(greatest_lower_bound(X_349,inverse(X_118)))))]]) ).

cnf(refute_0_2305,plain,
    ( multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118) != inverse(greatest_lower_bound(X_349,inverse(X_118)))
    | multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118) = inverse(greatest_lower_bound(X_349,inverse(X_118))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118),multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118)) )],[refute_0_2303,refute_0_2304]) ).

cnf(refute_0_2306,plain,
    multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118) = inverse(greatest_lower_bound(X_349,inverse(X_118))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),X_118),inverse(greatest_lower_bound(X_349,inverse(X_118)))) )],[refute_0_2178,refute_0_2305]) ).

cnf(refute_0_2307,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) = multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118),
    inference(subst,[],[refute_0_687:[bind(X_122,$fot(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))))),bind(X_15,$fot(X_118))]]) ).

cnf(refute_0_2308,plain,
    ( multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118) != inverse(greatest_lower_bound(X_349,inverse(X_118)))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) != multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118)
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) = inverse(greatest_lower_bound(X_349,inverse(X_118))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118))),bind(Z0,$fot(inverse(greatest_lower_bound(X_349,inverse(X_118)))))]]) ).

cnf(refute_0_2309,plain,
    ( multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118) != inverse(greatest_lower_bound(X_349,inverse(X_118)))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) = inverse(greatest_lower_bound(X_349,inverse(X_118))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118),multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118)) )],[refute_0_2307,refute_0_2308]) ).

cnf(refute_0_2310,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) = inverse(greatest_lower_bound(X_349,inverse(X_118))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(X_118,X_349)))),X_118),inverse(greatest_lower_bound(X_349,inverse(X_118)))) )],[refute_0_2306,refute_0_2309]) ).

cnf(refute_0_2311,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) != inverse(greatest_lower_bound(X_349,inverse(X_118)))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) != least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118))))
    | inverse(greatest_lower_bound(X_349,inverse(X_118))) = least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118),least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118))))) ),[0],$fot(inverse(greatest_lower_bound(X_349,inverse(X_118))))]]) ).

cnf(refute_0_2312,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118) != least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118))))
    | inverse(greatest_lower_bound(X_349,inverse(X_118))) = least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118),inverse(greatest_lower_bound(X_349,inverse(X_118)))) )],[refute_0_2310,refute_0_2311]) ).

cnf(refute_0_2313,plain,
    inverse(greatest_lower_bound(X_349,inverse(X_118))) = least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_118,X_349))),identity),X_118),least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118))))) )],[refute_0_2181,refute_0_2312]) ).

cnf(refute_0_2314,plain,
    ( inverse(greatest_lower_bound(X_349,inverse(X_118))) != least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118))))
    | least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118)))) = inverse(greatest_lower_bound(X_349,inverse(X_118))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(X_349,inverse(X_118))))),bind(Y0,$fot(least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118))))))]]) ).

cnf(refute_0_2315,plain,
    least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118)))) = inverse(greatest_lower_bound(X_349,inverse(X_118))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_349,inverse(X_118))),least_upper_bound(X_118,inverse(greatest_lower_bound(X_349,inverse(X_118))))) )],[refute_0_2313,refute_0_2314]) ).

cnf(refute_0_2316,plain,
    least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))) = inverse(greatest_lower_bound(inverse(b),inverse(c))),
    inference(subst,[],[refute_0_2315:[bind(X_118,$fot(c)),bind(X_349,$fot(inverse(b)))]]) ).

cnf(refute_0_2317,plain,
    least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(X_238,c))) = least_upper_bound(X_238,c),
    inference(subst,[],[refute_0_281:[bind(X_8,$fot(least_upper_bound(X_238,c))),bind(X_9,$fot(b))]]) ).

cnf(refute_0_2318,plain,
    greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(X_201,least_upper_bound(a,c))),X_216)) = greatest_lower_bound(greatest_lower_bound(X_201,b),X_216),
    inference(subst,[],[refute_0_1630:[bind(Y,$fot(greatest_lower_bound(X_201,least_upper_bound(a,c)))),bind(X_38,$fot(greatest_lower_bound(X_201,b))),bind(X_40,$fot(X_216))]]) ).

cnf(refute_0_2319,plain,
    least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c)))) = greatest_lower_bound(X_47,least_upper_bound(a,c)),
    inference(subst,[],[refute_0_281:[bind(X_8,$fot(greatest_lower_bound(X_47,least_upper_bound(a,c)))),bind(X_9,$fot(b))]]) ).

cnf(refute_0_2320,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b),
    inference(subst,[],[refute_0_83:[bind(Y,$fot(b)),bind(X_30,$fot(greatest_lower_bound(least_upper_bound(a,c),X_41)))]]) ).

cnf(refute_0_2321,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41)) = greatest_lower_bound(b,X_41),
    inference(subst,[],[refute_0_228:[bind(X_40,$fot(X_41))]]) ).

cnf(refute_0_2322,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41)) != greatest_lower_bound(b,X_41)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)) ),[0,1],$fot(greatest_lower_bound(b,X_41))]]) ).

cnf(refute_0_2323,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41)),greatest_lower_bound(b,X_41)) )],[refute_0_2321,refute_0_2322]) ).

cnf(refute_0_2324,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)) )],[refute_0_2320,refute_0_2323]) ).

cnf(refute_0_2325,plain,
    greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)) = greatest_lower_bound(X_41,least_upper_bound(a,c)),
    inference(subst,[],[refute_0_83:[bind(Y,$fot(least_upper_bound(a,c))),bind(X_30,$fot(X_41))]]) ).

cnf(refute_0_2326,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))) = greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))))]]) ).

cnf(refute_0_2327,plain,
    ( greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)) != greatest_lower_bound(X_41,least_upper_bound(a,c))
    | greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))) != greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)))
    | greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))) = greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))),greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)))) ),[1,1],$fot(greatest_lower_bound(X_41,least_upper_bound(a,c)))]]) ).

cnf(refute_0_2328,plain,
    ( greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)) != greatest_lower_bound(X_41,least_upper_bound(a,c))
    | greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))) = greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))),greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)))) )],[refute_0_2326,refute_0_2327]) ).

cnf(refute_0_2329,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))) = greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)),greatest_lower_bound(X_41,least_upper_bound(a,c))) )],[refute_0_2325,refute_0_2328]) ).

cnf(refute_0_2330,plain,
    greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),X_41)) = greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))),
    inference(subst,[],[refute_0_400:[bind(X_38,$fot(b)),bind(X_39,$fot(greatest_lower_bound(least_upper_bound(a,c),X_41))),bind(X_40,$fot(X_41))]]) ).

cnf(refute_0_2331,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) = greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),X_41)),
    inference(subst,[],[refute_0_375:[bind(Y,$fot(b)),bind(X_38,$fot(greatest_lower_bound(least_upper_bound(a,c),X_41))),bind(X_40,$fot(X_41))]]) ).

cnf(refute_0_2332,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),X_41)) != greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) != greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),X_41))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) = greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),X_41)))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)))))]]) ).

cnf(refute_0_2333,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),X_41)) != greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) = greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)),greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),X_41))) )],[refute_0_2331,refute_0_2332]) ).

cnf(refute_0_2334,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) = greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),X_41)),greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)))) )],[refute_0_2330,refute_0_2333]) ).

cnf(refute_0_2335,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))) != greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) != greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) = greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c)))))]]) ).

cnf(refute_0_2336,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))) != greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) = greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)),greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41)))) )],[refute_0_2334,refute_0_2335]) ).

cnf(refute_0_2337,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) = greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_41,greatest_lower_bound(least_upper_bound(a,c),X_41))),greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c)))) )],[refute_0_2329,refute_0_2336]) ).

cnf(refute_0_2338,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) != greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)) ),[0],$fot(greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))))]]) ).

cnf(refute_0_2339,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)),greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c)))) )],[refute_0_2337,refute_0_2338]) ).

cnf(refute_0_2340,plain,
    greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41)),
    inference(subst,[],[refute_0_348:[bind(X,$fot(b)),bind(X_38,$fot(least_upper_bound(a,c))),bind(X_39,$fot(X_41))]]) ).

cnf(refute_0_2341,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41)) != greatest_lower_bound(b,X_41)
    | greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)) != greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41))
    | greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)) = greatest_lower_bound(b,X_41) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41)))),bind(Z0,$fot(greatest_lower_bound(b,X_41)))]]) ).

cnf(refute_0_2342,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41)) != greatest_lower_bound(b,X_41)
    | greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)) = greatest_lower_bound(b,X_41) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41))) )],[refute_0_2340,refute_0_2341]) ).

cnf(refute_0_2343,plain,
    greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)) = greatest_lower_bound(b,X_41),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_41)),greatest_lower_bound(b,X_41)) )],[refute_0_2321,refute_0_2342]) ).

cnf(refute_0_2344,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(least_upper_bound(a,c))),bind(Y,$fot(X_41)),bind(Z,$fot(b))]]) ).

cnf(refute_0_2345,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b) != greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b))
    | greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)) != greatest_lower_bound(b,X_41)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b) = greatest_lower_bound(b,X_41) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)))),bind(Z0,$fot(greatest_lower_bound(b,X_41)))]]) ).

cnf(refute_0_2346,plain,
    ( greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)) != greatest_lower_bound(b,X_41)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b) = greatest_lower_bound(b,X_41) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b))) )],[refute_0_2344,refute_0_2345]) ).

cnf(refute_0_2347,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b) = greatest_lower_bound(b,X_41),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_41,b)),greatest_lower_bound(b,X_41)) )],[refute_0_2343,refute_0_2346]) ).

cnf(refute_0_2348,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b) != greatest_lower_bound(b,X_41)
    | greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) = greatest_lower_bound(b,X_41) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))),greatest_lower_bound(b,X_41)) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b))]]) ).

cnf(refute_0_2349,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) = greatest_lower_bound(b,X_41) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b),greatest_lower_bound(b,X_41)) )],[refute_0_2347,refute_0_2348]) ).

cnf(refute_0_2350,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) = greatest_lower_bound(b,X_41) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)) )],[refute_0_2339,refute_0_2349]) ).

cnf(refute_0_2351,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_41,least_upper_bound(a,c))) = greatest_lower_bound(b,X_41),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),greatest_lower_bound(b,X_41)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_41),b)) )],[refute_0_2324,refute_0_2350]) ).

cnf(refute_0_2352,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c))) = greatest_lower_bound(b,X_47),
    inference(subst,[],[refute_0_2351:[bind(X_41,$fot(X_47))]]) ).

cnf(refute_0_2353,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c))) != greatest_lower_bound(b,X_47)
    | least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c)))) != greatest_lower_bound(X_47,least_upper_bound(a,c))
    | least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,X_47)) = greatest_lower_bound(X_47,least_upper_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c)))),greatest_lower_bound(X_47,least_upper_bound(a,c))) ),[0,1],$fot(greatest_lower_bound(b,X_47))]]) ).

cnf(refute_0_2354,plain,
    ( least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c)))) != greatest_lower_bound(X_47,least_upper_bound(a,c))
    | least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,X_47)) = greatest_lower_bound(X_47,least_upper_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c))),greatest_lower_bound(b,X_47)) )],[refute_0_2352,refute_0_2353]) ).

cnf(refute_0_2355,plain,
    least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,X_47)) = greatest_lower_bound(X_47,least_upper_bound(a,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c)))),greatest_lower_bound(X_47,least_upper_bound(a,c))) )],[refute_0_2319,refute_0_2354]) ).

cnf(refute_0_2356,plain,
    least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,X_47)) = least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(X_47,least_upper_bound(a,c))),
    inference(subst,[],[refute_0_256:[bind(X,$fot(greatest_lower_bound(b,X_47))),bind(Y,$fot(greatest_lower_bound(X_47,least_upper_bound(a,c))))]]) ).

cnf(refute_0_2357,plain,
    ( least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,X_47)) != greatest_lower_bound(X_47,least_upper_bound(a,c))
    | least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,X_47)) != least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(X_47,least_upper_bound(a,c)))
    | least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(X_47,least_upper_bound(a,c))) = greatest_lower_bound(X_47,least_upper_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,X_47)),greatest_lower_bound(X_47,least_upper_bound(a,c))) ),[0],$fot(least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(X_47,least_upper_bound(a,c))))]]) ).

cnf(refute_0_2358,plain,
    ( least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,X_47)) != greatest_lower_bound(X_47,least_upper_bound(a,c))
    | least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(X_47,least_upper_bound(a,c))) = greatest_lower_bound(X_47,least_upper_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,X_47)),least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(X_47,least_upper_bound(a,c)))) )],[refute_0_2356,refute_0_2357]) ).

cnf(refute_0_2359,plain,
    least_upper_bound(greatest_lower_bound(b,X_47),greatest_lower_bound(X_47,least_upper_bound(a,c))) = greatest_lower_bound(X_47,least_upper_bound(a,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),greatest_lower_bound(b,X_47)),greatest_lower_bound(X_47,least_upper_bound(a,c))) )],[refute_0_2355,refute_0_2358]) ).

cnf(refute_0_2360,plain,
    least_upper_bound(greatest_lower_bound(b,X_201),greatest_lower_bound(X_201,least_upper_bound(a,c))) = greatest_lower_bound(X_201,least_upper_bound(a,c)),
    inference(subst,[],[refute_0_2359:[bind(X_47,$fot(X_201))]]) ).

cnf(refute_0_2361,plain,
    greatest_lower_bound(X_201,b) = greatest_lower_bound(b,X_201),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_201)),bind(Y,$fot(b))]]) ).

cnf(refute_0_2362,plain,
    ( greatest_lower_bound(X_201,b) != greatest_lower_bound(b,X_201)
    | greatest_lower_bound(b,X_201) = greatest_lower_bound(X_201,b) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_201,b))),bind(Y0,$fot(greatest_lower_bound(b,X_201)))]]) ).

cnf(refute_0_2363,plain,
    greatest_lower_bound(b,X_201) = greatest_lower_bound(X_201,b),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_201,b),greatest_lower_bound(b,X_201)) )],[refute_0_2361,refute_0_2362]) ).

cnf(refute_0_2364,plain,
    ( greatest_lower_bound(b,X_201) != greatest_lower_bound(X_201,b)
    | least_upper_bound(greatest_lower_bound(b,X_201),greatest_lower_bound(X_201,least_upper_bound(a,c))) != greatest_lower_bound(X_201,least_upper_bound(a,c))
    | least_upper_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(X_201,least_upper_bound(a,c))) = greatest_lower_bound(X_201,least_upper_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_201),greatest_lower_bound(X_201,least_upper_bound(a,c))),greatest_lower_bound(X_201,least_upper_bound(a,c))) ),[0,0],$fot(greatest_lower_bound(X_201,b))]]) ).

cnf(refute_0_2365,plain,
    ( least_upper_bound(greatest_lower_bound(b,X_201),greatest_lower_bound(X_201,least_upper_bound(a,c))) != greatest_lower_bound(X_201,least_upper_bound(a,c))
    | least_upper_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(X_201,least_upper_bound(a,c))) = greatest_lower_bound(X_201,least_upper_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,X_201),greatest_lower_bound(X_201,b)) )],[refute_0_2363,refute_0_2364]) ).

cnf(refute_0_2366,plain,
    least_upper_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(X_201,least_upper_bound(a,c))) = greatest_lower_bound(X_201,least_upper_bound(a,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,X_201),greatest_lower_bound(X_201,least_upper_bound(a,c))),greatest_lower_bound(X_201,least_upper_bound(a,c))) )],[refute_0_2360,refute_0_2365]) ).

cnf(refute_0_2367,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(X_201,least_upper_bound(a,c))),X_216)) != greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)
    | least_upper_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(X_201,least_upper_bound(a,c))) != greatest_lower_bound(X_201,least_upper_bound(a,c))
    | greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(greatest_lower_bound(X_201,b),X_216) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(X_201,least_upper_bound(a,c))),X_216)),greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)) ),[0,1,0],$fot(greatest_lower_bound(X_201,least_upper_bound(a,c)))]]) ).

cnf(refute_0_2368,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(X_201,least_upper_bound(a,c))),X_216)) != greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)
    | greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(greatest_lower_bound(X_201,b),X_216) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(X_201,least_upper_bound(a,c))),greatest_lower_bound(X_201,least_upper_bound(a,c))) )],[refute_0_2366,refute_0_2367]) ).

cnf(refute_0_2369,plain,
    greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(greatest_lower_bound(X_201,b),X_216),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(X_201,least_upper_bound(a,c))),X_216)),greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)) )],[refute_0_2318,refute_0_2368]) ).

cnf(refute_0_2370,plain,
    greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)),
    inference(subst,[],[refute_0_357:[bind(Y,$fot(X_216)),bind(X_38,$fot(b)),bind(X_39,$fot(X_201))]]) ).

cnf(refute_0_2371,plain,
    greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) = greatest_lower_bound(greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c))),Z),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(greatest_lower_bound(X_47,least_upper_bound(a,c))))]]) ).

cnf(refute_0_2372,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c))) != greatest_lower_bound(b,X_47)
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) != greatest_lower_bound(greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c))),Z)
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) = greatest_lower_bound(greatest_lower_bound(b,X_47),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)),greatest_lower_bound(greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c))),Z)) ),[1,0],$fot(greatest_lower_bound(b,X_47))]]) ).

cnf(refute_0_2373,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) != greatest_lower_bound(greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c))),Z)
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) = greatest_lower_bound(greatest_lower_bound(b,X_47),Z) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c))),greatest_lower_bound(b,X_47)) )],[refute_0_2352,refute_0_2372]) ).

cnf(refute_0_2374,plain,
    greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) = greatest_lower_bound(greatest_lower_bound(b,X_47),Z),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)),greatest_lower_bound(greatest_lower_bound(b,greatest_lower_bound(X_47,least_upper_bound(a,c))),Z)) )],[refute_0_2371,refute_0_2373]) ).

cnf(refute_0_2375,plain,
    greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z) = greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_47)),bind(Y,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_2376,plain,
    greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) = greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)))]]) ).

cnf(refute_0_2377,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) != greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z))
    | greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z) != greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) = greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)),greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z))) ),[1,1],$fot(greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z)))]]) ).

cnf(refute_0_2378,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z) != greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) = greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)),greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z))) )],[refute_0_2376,refute_0_2377]) ).

cnf(refute_0_2379,plain,
    greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) = greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z),greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))) )],[refute_0_2375,refute_0_2378]) ).

cnf(refute_0_2380,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) != greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z)))
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) != greatest_lower_bound(greatest_lower_bound(b,X_47),Z)
    | greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(greatest_lower_bound(b,X_47),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)),greatest_lower_bound(greatest_lower_bound(b,X_47),Z)) ),[0],$fot(greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))))]]) ).

cnf(refute_0_2381,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) != greatest_lower_bound(greatest_lower_bound(b,X_47),Z)
    | greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(greatest_lower_bound(b,X_47),Z) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)),greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z)))) )],[refute_0_2379,refute_0_2380]) ).

cnf(refute_0_2382,plain,
    greatest_lower_bound(greatest_lower_bound(b,X_47),Z) = greatest_lower_bound(b,greatest_lower_bound(X_47,Z)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(b)),bind(Y,$fot(X_47))]]) ).

cnf(refute_0_2383,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))) != greatest_lower_bound(greatest_lower_bound(b,X_47),Z)
    | greatest_lower_bound(greatest_lower_bound(b,X_47),Z) != greatest_lower_bound(b,greatest_lower_bound(X_47,Z))
    | greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(b,greatest_lower_bound(X_47,Z)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))),greatest_lower_bound(b,greatest_lower_bound(X_47,Z))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(b,X_47),Z))]]) ).

cnf(refute_0_2384,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))) != greatest_lower_bound(greatest_lower_bound(b,X_47),Z)
    | greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(b,greatest_lower_bound(X_47,Z)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_47),Z),greatest_lower_bound(b,greatest_lower_bound(X_47,Z))) )],[refute_0_2382,refute_0_2383]) ).

cnf(refute_0_2385,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)) != greatest_lower_bound(greatest_lower_bound(b,X_47),Z)
    | greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(b,greatest_lower_bound(X_47,Z)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))),greatest_lower_bound(greatest_lower_bound(b,X_47),Z)) )],[refute_0_2381,refute_0_2384]) ).

cnf(refute_0_2386,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_47,greatest_lower_bound(least_upper_bound(a,c),Z))) = greatest_lower_bound(b,greatest_lower_bound(X_47,Z)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_47,least_upper_bound(a,c)),Z)),greatest_lower_bound(greatest_lower_bound(b,X_47),Z)) )],[refute_0_2374,refute_0_2385]) ).

cnf(refute_0_2387,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216))) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)),
    inference(subst,[],[refute_0_2386:[bind(Z,$fot(X_216)),bind(X_47,$fot(X_201))]]) ).

cnf(refute_0_2388,plain,
    greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216) = greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_201)),bind(Y,$fot(least_upper_bound(a,c))),bind(Z,$fot(X_216))]]) ).

cnf(refute_0_2389,plain,
    greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)))]]) ).

cnf(refute_0_2390,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) != greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))
    | greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216) != greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216))
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(b,greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)),greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) ),[1,1],$fot(greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216)))]]) ).

cnf(refute_0_2391,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216) != greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216))
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(b,greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)),greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) )],[refute_0_2389,refute_0_2390]) ).

cnf(refute_0_2392,plain,
    greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(b,greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216),greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216))) )],[refute_0_2388,refute_0_2391]) ).

cnf(refute_0_2393,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216))) != greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) != greatest_lower_bound(b,greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216)))
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216))))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))))]]) ).

cnf(refute_0_2394,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216))) != greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)),greatest_lower_bound(b,greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216)))) )],[refute_0_2392,refute_0_2393]) ).

cnf(refute_0_2395,plain,
    greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_201,greatest_lower_bound(least_upper_bound(a,c),X_216))),greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))) )],[refute_0_2387,refute_0_2394]) ).

cnf(refute_0_2396,plain,
    greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) = greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))))]]) ).

cnf(refute_0_2397,plain,
    ( greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) != greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)))
    | greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) != greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))
    | greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) = greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))),greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)))) ),[1,1],$fot(greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)))]]) ).

cnf(refute_0_2398,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) != greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))
    | greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) = greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))),greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)))) )],[refute_0_2396,refute_0_2397]) ).

cnf(refute_0_2399,plain,
    greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) = greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)),greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))) )],[refute_0_2395,refute_0_2398]) ).

cnf(refute_0_2400,plain,
    ( greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))) != greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))
    | greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) != greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)))
    | greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))))),bind(Y0,$fot(greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))))]]) ).

cnf(refute_0_2401,plain,
    ( greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))) != greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))
    | greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))),greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)))) )],[refute_0_2399,refute_0_2400]) ).

cnf(refute_0_2402,plain,
    greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))),greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))) )],[refute_0_2370,refute_0_2401]) ).

cnf(refute_0_2403,plain,
    greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_201)),bind(Y,$fot(b)),bind(Z,$fot(greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)))]]) ).

cnf(refute_0_2404,plain,
    ( greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) != greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))
    | greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) != greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)))
    | greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)))),bind(Y0,$fot(greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))))]]) ).

cnf(refute_0_2405,plain,
    ( greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))) != greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))
    | greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)),greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)))) )],[refute_0_2403,refute_0_2404]) ).

cnf(refute_0_2406,plain,
    greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_201,greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216))),greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))) )],[refute_0_2402,refute_0_2405]) ).

cnf(refute_0_2407,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) != greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))
    | greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) != greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)
    | greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) = greatest_lower_bound(greatest_lower_bound(X_201,b),X_216) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)),greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)) ),[0],$fot(greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)))]]) ).

cnf(refute_0_2408,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) != greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)
    | greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) = greatest_lower_bound(greatest_lower_bound(X_201,b),X_216) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)),greatest_lower_bound(b,greatest_lower_bound(X_201,X_216))) )],[refute_0_2406,refute_0_2407]) ).

cnf(refute_0_2409,plain,
    greatest_lower_bound(greatest_lower_bound(X_201,b),X_216) = greatest_lower_bound(X_201,greatest_lower_bound(b,X_216)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_201)),bind(Y,$fot(b)),bind(Z,$fot(X_216))]]) ).

cnf(refute_0_2410,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) != greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)
    | greatest_lower_bound(greatest_lower_bound(X_201,b),X_216) != greatest_lower_bound(X_201,greatest_lower_bound(b,X_216))
    | greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) = greatest_lower_bound(X_201,greatest_lower_bound(b,X_216)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)),greatest_lower_bound(X_201,greatest_lower_bound(b,X_216))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_201,b),X_216))]]) ).

cnf(refute_0_2411,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) != greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)
    | greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) = greatest_lower_bound(X_201,greatest_lower_bound(b,X_216)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_201,b),X_216),greatest_lower_bound(X_201,greatest_lower_bound(b,X_216))) )],[refute_0_2409,refute_0_2410]) ).

cnf(refute_0_2412,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)) != greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)
    | greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) = greatest_lower_bound(X_201,greatest_lower_bound(b,X_216)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)),greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)) )],[refute_0_2408,refute_0_2411]) ).

cnf(refute_0_2413,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) = greatest_lower_bound(X_201,greatest_lower_bound(b,X_216)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_201,b),greatest_lower_bound(greatest_lower_bound(X_201,least_upper_bound(a,c)),X_216)),greatest_lower_bound(greatest_lower_bound(X_201,b),X_216)) )],[refute_0_2369,refute_0_2412]) ).

cnf(refute_0_2414,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236)))) = greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))),
    inference(subst,[],[refute_0_2413:[bind(X_201,$fot(least_upper_bound(X_236,c))),bind(X_216,$fot(least_upper_bound(a,least_upper_bound(c,X_236))))]]) ).

cnf(refute_0_2415,plain,
    greatest_lower_bound(least_upper_bound(b,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)),
    inference(subst,[],[refute_0_1737:[bind(X_34,$fot(least_upper_bound(c,X_57)))]]) ).

cnf(refute_0_2416,plain,
    least_upper_bound(b,least_upper_bound(c,X_57)) = least_upper_bound(a,least_upper_bound(c,X_57)),
    inference(subst,[],[refute_0_1639:[bind(X_16,$fot(X_57))]]) ).

cnf(refute_0_2417,plain,
    ( greatest_lower_bound(least_upper_bound(b,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))
    | least_upper_bound(b,least_upper_bound(c,X_57)) != least_upper_bound(a,least_upper_bound(c,X_57))
    | greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))) ),[0,0],$fot(least_upper_bound(a,least_upper_bound(c,X_57)))]]) ).

cnf(refute_0_2418,plain,
    ( greatest_lower_bound(least_upper_bound(b,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))
    | greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_57)),least_upper_bound(a,least_upper_bound(c,X_57))) )],[refute_0_2416,refute_0_2417]) ).

cnf(refute_0_2419,plain,
    greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))) )],[refute_0_2415,refute_0_2418]) ).

cnf(refute_0_2420,plain,
    greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(X_57,c)) = greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))),
    inference(subst,[],[refute_0_46:[bind(X,$fot(least_upper_bound(X_57,c))),bind(Y,$fot(least_upper_bound(a,least_upper_bound(c,X_57))))]]) ).

cnf(refute_0_2421,plain,
    least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)) = least_upper_bound(X_55,least_upper_bound(X_56,greatest_lower_bound(X_9,X_56))),
    inference(subst,[],[refute_0_588:[bind(X,$fot(greatest_lower_bound(X_9,X_56))),bind(X_14,$fot(X_55)),bind(X_15,$fot(X_56))]]) ).

cnf(refute_0_2422,plain,
    least_upper_bound(X_56,greatest_lower_bound(X_9,X_56)) = X_56,
    inference(subst,[],[refute_0_281:[bind(X_8,$fot(X_56))]]) ).

cnf(refute_0_2423,plain,
    ( least_upper_bound(X_56,greatest_lower_bound(X_9,X_56)) != X_56
    | least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)) != least_upper_bound(X_55,least_upper_bound(X_56,greatest_lower_bound(X_9,X_56)))
    | least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)) = least_upper_bound(X_55,X_56) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)),least_upper_bound(X_55,least_upper_bound(X_56,greatest_lower_bound(X_9,X_56)))) ),[1,1],$fot(X_56)]]) ).

cnf(refute_0_2424,plain,
    ( least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)) != least_upper_bound(X_55,least_upper_bound(X_56,greatest_lower_bound(X_9,X_56)))
    | least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)) = least_upper_bound(X_55,X_56) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_56,greatest_lower_bound(X_9,X_56)),X_56) )],[refute_0_2422,refute_0_2423]) ).

cnf(refute_0_2425,plain,
    least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)) = least_upper_bound(X_55,X_56),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)),least_upper_bound(X_55,least_upper_bound(X_56,greatest_lower_bound(X_9,X_56)))) )],[refute_0_2421,refute_0_2424]) ).

cnf(refute_0_2426,plain,
    least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)) = least_upper_bound(X_56,least_upper_bound(X_55,greatest_lower_bound(X_9,X_56))),
    inference(subst,[],[refute_0_1055:[bind(X_54,$fot(X_56)),bind(X_55,$fot(greatest_lower_bound(X_9,X_56))),bind(X_56,$fot(X_55))]]) ).

cnf(refute_0_2427,plain,
    ( least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)) != least_upper_bound(X_55,X_56)
    | least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)) != least_upper_bound(X_56,least_upper_bound(X_55,greatest_lower_bound(X_9,X_56)))
    | least_upper_bound(X_56,least_upper_bound(X_55,greatest_lower_bound(X_9,X_56))) = least_upper_bound(X_55,X_56) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)),least_upper_bound(X_55,X_56)) ),[0],$fot(least_upper_bound(X_56,least_upper_bound(X_55,greatest_lower_bound(X_9,X_56))))]]) ).

cnf(refute_0_2428,plain,
    ( least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)) != least_upper_bound(X_55,X_56)
    | least_upper_bound(X_56,least_upper_bound(X_55,greatest_lower_bound(X_9,X_56))) = least_upper_bound(X_55,X_56) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)),least_upper_bound(X_56,least_upper_bound(X_55,greatest_lower_bound(X_9,X_56)))) )],[refute_0_2426,refute_0_2427]) ).

cnf(refute_0_2429,plain,
    least_upper_bound(X_56,least_upper_bound(X_55,greatest_lower_bound(X_9,X_56))) = least_upper_bound(X_55,X_56),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_9,X_56),least_upper_bound(X_55,X_56)),least_upper_bound(X_55,X_56)) )],[refute_0_2425,refute_0_2428]) ).

cnf(refute_0_2430,plain,
    least_upper_bound(c,least_upper_bound(X_57,greatest_lower_bound(a,c))) = least_upper_bound(X_57,c),
    inference(subst,[],[refute_0_2429:[bind(X_55,$fot(X_57)),bind(X_56,$fot(c)),bind(X_9,$fot(a))]]) ).

cnf(refute_0_2431,plain,
    least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)) = least_upper_bound(c,least_upper_bound(X_57,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_237:[bind(X,$fot(c)),bind(Y,$fot(X_57)),bind(Z,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2432,plain,
    ( least_upper_bound(c,least_upper_bound(X_57,greatest_lower_bound(a,c))) != least_upper_bound(X_57,c)
    | least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)) != least_upper_bound(c,least_upper_bound(X_57,greatest_lower_bound(a,c)))
    | least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)) = least_upper_bound(X_57,c) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(X_57,greatest_lower_bound(a,c))))),bind(Z0,$fot(least_upper_bound(X_57,c)))]]) ).

cnf(refute_0_2433,plain,
    ( least_upper_bound(c,least_upper_bound(X_57,greatest_lower_bound(a,c))) != least_upper_bound(X_57,c)
    | least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)) = least_upper_bound(X_57,c) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)),least_upper_bound(c,least_upper_bound(X_57,greatest_lower_bound(a,c)))) )],[refute_0_2431,refute_0_2432]) ).

cnf(refute_0_2434,plain,
    least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)) = least_upper_bound(X_57,c),
    inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(X_57,greatest_lower_bound(a,c))),least_upper_bound(X_57,c)) )],[refute_0_2430,refute_0_2433]) ).

cnf(refute_0_2435,plain,
    greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2436,plain,
    ( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) != greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)))
    | least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)) != least_upper_bound(X_57,c)
    | greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(X_57,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)))) ),[1,1],$fot(least_upper_bound(X_57,c))]]) ).

cnf(refute_0_2437,plain,
    ( least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)) != least_upper_bound(X_57,c)
    | greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(X_57,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)))) )],[refute_0_2435,refute_0_2436]) ).

cnf(refute_0_2438,plain,
    greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(X_57,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c)),least_upper_bound(X_57,c)) )],[refute_0_2434,refute_0_2437]) ).

cnf(refute_0_2439,plain,
    ( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(X_57,c)) != greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57)))
    | greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) != greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(X_57,c))
    | greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(X_57,c)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57)))))]]) ).

cnf(refute_0_2440,plain,
    ( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(X_57,c)) != greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57)))
    | greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))),greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(X_57,c))) )],[refute_0_2438,refute_0_2439]) ).

cnf(refute_0_2441,plain,
    greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(X_57,c)),greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57)))) )],[refute_0_2420,refute_0_2440]) ).

cnf(refute_0_2442,plain,
    ( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) != greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57)))
    | greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))
    | greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))))]]) ).

cnf(refute_0_2443,plain,
    ( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))
    | greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))),greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57)))) )],[refute_0_2441,refute_0_2442]) ).

cnf(refute_0_2444,plain,
    least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,c),X_57)) = least_upper_bound(c,X_57),
    inference(subst,[],[refute_0_1123:[bind(X,$fot(c)),bind(Z,$fot(X_57)),bind(X_27,$fot(a))]]) ).

cnf(refute_0_2445,plain,
    least_upper_bound(X_54,X_56) = least_upper_bound(X_56,X_54),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_54)),bind(Y,$fot(X_56))]]) ).

cnf(refute_0_2446,plain,
    ( least_upper_bound(X_54,X_56) != least_upper_bound(X_56,X_54)
    | least_upper_bound(X_56,X_54) = least_upper_bound(X_54,X_56) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_54,X_56))),bind(Y0,$fot(least_upper_bound(X_56,X_54)))]]) ).

cnf(refute_0_2447,plain,
    least_upper_bound(X_56,X_54) = least_upper_bound(X_54,X_56),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_54,X_56),least_upper_bound(X_56,X_54)) )],[refute_0_2445,refute_0_2446]) ).

cnf(refute_0_2448,plain,
    ( least_upper_bound(X_54,least_upper_bound(X_55,X_56)) != least_upper_bound(X_55,least_upper_bound(X_56,X_54))
    | least_upper_bound(X_56,X_54) != least_upper_bound(X_54,X_56)
    | least_upper_bound(X_54,least_upper_bound(X_55,X_56)) = least_upper_bound(X_55,least_upper_bound(X_54,X_56)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_54,least_upper_bound(X_55,X_56)),least_upper_bound(X_55,least_upper_bound(X_56,X_54))) ),[1,1],$fot(least_upper_bound(X_54,X_56))]]) ).

cnf(refute_0_2449,plain,
    ( least_upper_bound(X_54,least_upper_bound(X_55,X_56)) != least_upper_bound(X_55,least_upper_bound(X_56,X_54))
    | least_upper_bound(X_54,least_upper_bound(X_55,X_56)) = least_upper_bound(X_55,least_upper_bound(X_54,X_56)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_56,X_54),least_upper_bound(X_54,X_56)) )],[refute_0_2447,refute_0_2448]) ).

cnf(refute_0_2450,plain,
    least_upper_bound(X_54,least_upper_bound(X_55,X_56)) = least_upper_bound(X_55,least_upper_bound(X_54,X_56)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_54,least_upper_bound(X_55,X_56)),least_upper_bound(X_55,least_upper_bound(X_56,X_54))) )],[refute_0_1047,refute_0_2449]) ).

cnf(refute_0_2451,plain,
    ( least_upper_bound(X_54,least_upper_bound(X_55,X_56)) != least_upper_bound(X_55,least_upper_bound(X_54,X_56))
    | least_upper_bound(X_55,least_upper_bound(X_54,X_56)) = least_upper_bound(X_54,least_upper_bound(X_55,X_56)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_54,least_upper_bound(X_55,X_56)))),bind(Y0,$fot(least_upper_bound(X_55,least_upper_bound(X_54,X_56))))]]) ).

cnf(refute_0_2452,plain,
    least_upper_bound(X_55,least_upper_bound(X_54,X_56)) = least_upper_bound(X_54,least_upper_bound(X_55,X_56)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_54,least_upper_bound(X_55,X_56)),least_upper_bound(X_55,least_upper_bound(X_54,X_56))) )],[refute_0_2450,refute_0_2451]) ).

cnf(refute_0_2453,plain,
    least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)) = least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,c),X_57)),
    inference(subst,[],[refute_0_2452:[bind(X_54,$fot(c)),bind(X_55,$fot(greatest_lower_bound(a,c))),bind(X_56,$fot(X_57))]]) ).

cnf(refute_0_2454,plain,
    ( least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,c),X_57)) != least_upper_bound(c,X_57)
    | least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)) != least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,c),X_57))
    | least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)) = least_upper_bound(c,X_57) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)))),bind(Y0,$fot(least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,c),X_57)))),bind(Z0,$fot(least_upper_bound(c,X_57)))]]) ).

cnf(refute_0_2455,plain,
    ( least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,c),X_57)) != least_upper_bound(c,X_57)
    | least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)) = least_upper_bound(c,X_57) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)),least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,c),X_57))) )],[refute_0_2453,refute_0_2454]) ).

cnf(refute_0_2456,plain,
    least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)) = least_upper_bound(c,X_57),
    inference(resolve,[$cnf( $equal(least_upper_bound(c,least_upper_bound(greatest_lower_bound(a,c),X_57)),least_upper_bound(c,X_57)) )],[refute_0_2444,refute_0_2455]) ).

cnf(refute_0_2457,plain,
    ( greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))) != least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))
    | least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)) != least_upper_bound(c,X_57)
    | greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))) = least_upper_bound(c,X_57) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))),least_upper_bound(c,X_57)) ),[0],$fot(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)))]]) ).

cnf(refute_0_2458,plain,
    ( greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))) != least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))
    | greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))) = least_upper_bound(c,X_57) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57)),least_upper_bound(c,X_57)) )],[refute_0_2456,refute_0_2457]) ).

cnf(refute_0_2459,plain,
    ( greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))
    | greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))) = least_upper_bound(c,X_57) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))),least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))) )],[refute_0_2443,refute_0_2458]) ).

cnf(refute_0_2460,plain,
    greatest_lower_bound(least_upper_bound(X_57,c),least_upper_bound(a,least_upper_bound(c,X_57))) = least_upper_bound(c,X_57),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_57)),least_upper_bound(least_upper_bound(c,X_57),greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(c,X_57))) )],[refute_0_2419,refute_0_2459]) ).

cnf(refute_0_2461,plain,
    greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236))) = least_upper_bound(c,X_236),
    inference(subst,[],[refute_0_2460:[bind(X_57,$fot(X_236))]]) ).

cnf(refute_0_2462,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236)))) != greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236))))
    | greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236))) != least_upper_bound(c,X_236)
    | greatest_lower_bound(b,least_upper_bound(c,X_236)) = greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236)))),greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236))))) ),[0,1],$fot(least_upper_bound(c,X_236))]]) ).

cnf(refute_0_2463,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236)))) != greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236))))
    | greatest_lower_bound(b,least_upper_bound(c,X_236)) = greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236))),least_upper_bound(c,X_236)) )],[refute_0_2461,refute_0_2462]) ).

cnf(refute_0_2464,plain,
    greatest_lower_bound(b,least_upper_bound(c,X_236)) = greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236)))),greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236))))) )],[refute_0_2414,refute_0_2463]) ).

cnf(refute_0_2465,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b),
    inference(subst,[],[refute_0_83:[bind(Y,$fot(b)),bind(X_30,$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))]]) ).

cnf(refute_0_2466,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_43)),Z)) = greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43))),Z),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(least_upper_bound(a,least_upper_bound(c,X_43))))]]) ).

cnf(refute_0_2467,plain,
    b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43))),
    inference(subst,[],[refute_0_246:[bind(Y,$fot(X_43))]]) ).

cnf(refute_0_2468,plain,
    ( b != greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43)))
    | greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43))) = b ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(b)),bind(Y0,$fot(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43)))))]]) ).

cnf(refute_0_2469,plain,
    greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43))) = b,
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43)))) )],[refute_0_2467,refute_0_2468]) ).

cnf(refute_0_2470,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_43)),Z)) != greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43))),Z)
    | greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43))) != b
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_43)),Z)) = greatest_lower_bound(b,Z) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_43)),Z)),greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43))),Z)) ),[1,0],$fot(b)]]) ).

cnf(refute_0_2471,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_43)),Z)) != greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43))),Z)
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_43)),Z)) = greatest_lower_bound(b,Z) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43))),b) )],[refute_0_2469,refute_0_2470]) ).

cnf(refute_0_2472,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_43)),Z)) = greatest_lower_bound(b,Z),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_43)),Z)),greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_43))),Z)) )],[refute_0_2466,refute_0_2471]) ).

cnf(refute_0_2473,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)) = greatest_lower_bound(b,X_196),
    inference(subst,[],[refute_0_2472:[bind(Z,$fot(X_196)),bind(X_43,$fot(X_197))]]) ).

cnf(refute_0_2474,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)) != greatest_lower_bound(b,X_196)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)) ),[0,1],$fot(greatest_lower_bound(b,X_196))]]) ).

cnf(refute_0_2475,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)),greatest_lower_bound(b,X_196)) )],[refute_0_2473,refute_0_2474]) ).

cnf(refute_0_2476,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)) )],[refute_0_2465,refute_0_2475]) ).

cnf(refute_0_2477,plain,
    greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)) = greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197))),
    inference(subst,[],[refute_0_83:[bind(Y,$fot(least_upper_bound(a,least_upper_bound(c,X_197)))),bind(X_30,$fot(X_196))]]) ).

cnf(refute_0_2478,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) = greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))))]]) ).

cnf(refute_0_2479,plain,
    ( greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)) != greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))
    | greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) != greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))
    | greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) = greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))),greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))) ),[1,1],$fot(greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197))))]]) ).

cnf(refute_0_2480,plain,
    ( greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)) != greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))
    | greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) = greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))),greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))) )],[refute_0_2478,refute_0_2479]) ).

cnf(refute_0_2481,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) = greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)),greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) )],[refute_0_2477,refute_0_2480]) ).

cnf(refute_0_2482,plain,
    greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))) = greatest_lower_bound(X_38,X_39),
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(greatest_lower_bound(X_38,X_39)))]]) ).

cnf(refute_0_2483,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))))]]) ).

cnf(refute_0_2484,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))))]]) ).

cnf(refute_0_2485,plain,
    greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))),greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))) )],[refute_0_2483,refute_0_2484]) ).

cnf(refute_0_2486,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))) != greatest_lower_bound(X_38,X_39)
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))) != greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))))
    | greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))) = greatest_lower_bound(X_38,X_39) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))),greatest_lower_bound(X_38,X_39)) ),[0],$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))))]]) ).

cnf(refute_0_2487,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))) != greatest_lower_bound(X_38,X_39)
    | greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))) = greatest_lower_bound(X_38,X_39) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))),greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))))) )],[refute_0_2485,refute_0_2486]) ).

cnf(refute_0_2488,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_39,least_upper_bound(X_13,greatest_lower_bound(X_38,X_39)))) = greatest_lower_bound(X_38,X_39),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_38,X_39),least_upper_bound(X_13,greatest_lower_bound(X_38,X_39))),greatest_lower_bound(X_38,X_39)) )],[refute_0_2482,refute_0_2487]) ).

cnf(refute_0_2489,plain,
    greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),least_upper_bound(X_178,greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))))) = greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178)),
    inference(subst,[],[refute_0_2488:[bind(X_13,$fot(X_178)),bind(X_38,$fot(X_179)),bind(X_39,$fot(greatest_lower_bound(X_39,X_178)))]]) ).

cnf(refute_0_2490,plain,
    least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8)) = X_8,
    inference(subst,[],[refute_0_281:[bind(X_9,$fot(greatest_lower_bound(X_38,X_39)))]]) ).

cnf(refute_0_2491,plain,
    greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8)) = greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_38)),bind(Y,$fot(X_39)),bind(Z,$fot(X_8))]]) ).

cnf(refute_0_2492,plain,
    ( greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8)) != greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8)
    | greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8)))]]) ).

cnf(refute_0_2493,plain,
    greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8) = greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8)),greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8)) )],[refute_0_2491,refute_0_2492]) ).

cnf(refute_0_2494,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8) != greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8))
    | least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8)) != X_8
    | least_upper_bound(X_8,greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8))) = X_8 ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8)),X_8) ),[0,1],$fot(greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8)))]]) ).

cnf(refute_0_2495,plain,
    ( least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8)) != X_8
    | least_upper_bound(X_8,greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8))) = X_8 ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8),greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8))) )],[refute_0_2493,refute_0_2494]) ).

cnf(refute_0_2496,plain,
    least_upper_bound(X_8,greatest_lower_bound(X_38,greatest_lower_bound(X_39,X_8))) = X_8,
    inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_38,X_39),X_8)),X_8) )],[refute_0_2490,refute_0_2495]) ).

cnf(refute_0_2497,plain,
    least_upper_bound(X_178,greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))) = X_178,
    inference(subst,[],[refute_0_2496:[bind(X_38,$fot(X_179)),bind(X_8,$fot(X_178))]]) ).

cnf(refute_0_2498,plain,
    ( greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),least_upper_bound(X_178,greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))))) != greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))
    | least_upper_bound(X_178,greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))) != X_178
    | greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)) = greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),least_upper_bound(X_178,greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))))),greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))) ),[0,1,1],$fot(X_178)]]) ).

cnf(refute_0_2499,plain,
    ( greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),least_upper_bound(X_178,greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))))) != greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))
    | greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)) = greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_178,greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))),X_178) )],[refute_0_2497,refute_0_2498]) ).

cnf(refute_0_2500,plain,
    greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)) = greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),least_upper_bound(X_178,greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))))),greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))) )],[refute_0_2489,refute_0_2499]) ).

cnf(refute_0_2501,plain,
    greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178)) = greatest_lower_bound(X_178,X_39),
    inference(subst,[],[refute_0_83:[bind(Y,$fot(X_39)),bind(X_30,$fot(X_178))]]) ).

cnf(refute_0_2502,plain,
    greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))) = greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))))]]) ).

cnf(refute_0_2503,plain,
    ( greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178)) != greatest_lower_bound(X_178,X_39)
    | greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))) != greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178)))
    | greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))) = greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))),greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178)))) ),[1,1],$fot(greatest_lower_bound(X_178,X_39))]]) ).

cnf(refute_0_2504,plain,
    ( greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178)) != greatest_lower_bound(X_178,X_39)
    | greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))) = greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))),greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178)))) )],[refute_0_2502,refute_0_2503]) ).

cnf(refute_0_2505,plain,
    greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))) = greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178)),greatest_lower_bound(X_178,X_39)) )],[refute_0_2501,refute_0_2504]) ).

cnf(refute_0_2506,plain,
    greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),least_upper_bound(X_13,greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)))) = greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))))]]) ).

cnf(refute_0_2507,plain,
    least_upper_bound(X_13,greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))) = X_13,
    inference(subst,[],[refute_0_2496:[bind(X_38,$fot(X_72)),bind(X_39,$fot(X_73)),bind(X_8,$fot(X_13))]]) ).

cnf(refute_0_2508,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),least_upper_bound(X_13,greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)))) != greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))
    | least_upper_bound(X_13,greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))) != X_13
    | greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) = greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),least_upper_bound(X_13,greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)))),greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))) ),[0,1],$fot(X_13)]]) ).

cnf(refute_0_2509,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),least_upper_bound(X_13,greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)))) != greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))
    | greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) = greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_13,greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))),X_13) )],[refute_0_2507,refute_0_2508]) ).

cnf(refute_0_2510,plain,
    greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) = greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),least_upper_bound(X_13,greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)))),greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))) )],[refute_0_2506,refute_0_2509]) ).

cnf(refute_0_2511,plain,
    greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)) = greatest_lower_bound(X_13,X_73),
    inference(subst,[],[refute_0_83:[bind(Y,$fot(X_73)),bind(X_30,$fot(X_13))]]) ).

cnf(refute_0_2512,plain,
    greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))))]]) ).

cnf(refute_0_2513,plain,
    ( greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)) != greatest_lower_bound(X_13,X_73)
    | greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))) != greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)))
    | greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))),greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)))) ),[1,1],$fot(greatest_lower_bound(X_13,X_73))]]) ).

cnf(refute_0_2514,plain,
    ( greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)) != greatest_lower_bound(X_13,X_73)
    | greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))),greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)))) )],[refute_0_2512,refute_0_2513]) ).

cnf(refute_0_2515,plain,
    greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)),greatest_lower_bound(X_13,X_73)) )],[refute_0_2511,refute_0_2514]) ).

cnf(refute_0_2516,plain,
    greatest_lower_bound(X_72,greatest_lower_bound(greatest_lower_bound(X_73,X_13),X_13)) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))),
    inference(subst,[],[refute_0_400:[bind(X_38,$fot(X_72)),bind(X_39,$fot(greatest_lower_bound(X_73,X_13))),bind(X_40,$fot(X_13))]]) ).

cnf(refute_0_2517,plain,
    greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) = greatest_lower_bound(X_72,greatest_lower_bound(greatest_lower_bound(X_73,X_13),X_13)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_72)),bind(Y,$fot(greatest_lower_bound(X_73,X_13))),bind(Z,$fot(X_13))]]) ).

cnf(refute_0_2518,plain,
    ( greatest_lower_bound(X_72,greatest_lower_bound(greatest_lower_bound(X_73,X_13),X_13)) != greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)))
    | greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) != greatest_lower_bound(X_72,greatest_lower_bound(greatest_lower_bound(X_73,X_13),X_13))
    | greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13))),bind(Y0,$fot(greatest_lower_bound(X_72,greatest_lower_bound(greatest_lower_bound(X_73,X_13),X_13)))),bind(Z0,$fot(greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)))))]]) ).

cnf(refute_0_2519,plain,
    ( greatest_lower_bound(X_72,greatest_lower_bound(greatest_lower_bound(X_73,X_13),X_13)) != greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)))
    | greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13),greatest_lower_bound(X_72,greatest_lower_bound(greatest_lower_bound(X_73,X_13),X_13))) )],[refute_0_2517,refute_0_2518]) ).

cnf(refute_0_2520,plain,
    greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_72,greatest_lower_bound(greatest_lower_bound(X_73,X_13),X_13)),greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)))) )],[refute_0_2516,refute_0_2519]) ).

cnf(refute_0_2521,plain,
    ( greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))) != greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73))
    | greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) != greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)))
    | greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13))),bind(Y0,$fot(greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))))),bind(Z0,$fot(greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73))))]]) ).

cnf(refute_0_2522,plain,
    ( greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))) != greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73))
    | greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13),greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13)))) )],[refute_0_2520,refute_0_2521]) ).

cnf(refute_0_2523,plain,
    greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_72,greatest_lower_bound(X_13,greatest_lower_bound(X_73,X_13))),greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73))) )],[refute_0_2515,refute_0_2522]) ).

cnf(refute_0_2524,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) != greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73))
    | greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) != greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))
    | greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)) = greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13),greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))) ),[0],$fot(greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)))]]) ).

cnf(refute_0_2525,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13) != greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))
    | greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)) = greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13),greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73))) )],[refute_0_2523,refute_0_2524]) ).

cnf(refute_0_2526,plain,
    greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)) = greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)),X_13),greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))) )],[refute_0_2510,refute_0_2525]) ).

cnf(refute_0_2527,plain,
    ( greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)) != greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))
    | greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)))),bind(Y0,$fot(greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))))]]) ).

cnf(refute_0_2528,plain,
    greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13)) = greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_72,greatest_lower_bound(X_13,X_73)),greatest_lower_bound(X_72,greatest_lower_bound(X_73,X_13))) )],[refute_0_2526,refute_0_2527]) ).

cnf(refute_0_2529,plain,
    greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)) = greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))),
    inference(subst,[],[refute_0_2528:[bind(X_13,$fot(X_178)),bind(X_72,$fot(X_179)),bind(X_73,$fot(greatest_lower_bound(X_39,X_178)))]]) ).

cnf(refute_0_2530,plain,
    ( greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))) != greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39))
    | greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)) != greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178)))
    | greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)) = greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)))),bind(Y0,$fot(greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))))),bind(Z0,$fot(greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39))))]]) ).

cnf(refute_0_2531,plain,
    ( greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))) != greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39))
    | greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)) = greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)),greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178)))) )],[refute_0_2529,refute_0_2530]) ).

cnf(refute_0_2532,plain,
    greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)) = greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_179,greatest_lower_bound(X_178,greatest_lower_bound(X_39,X_178))),greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39))) )],[refute_0_2505,refute_0_2531]) ).

cnf(refute_0_2533,plain,
    ( greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)) != greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39))
    | greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)) != greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))
    | greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)) = greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)),greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))) ),[0],$fot(greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)))]]) ).

cnf(refute_0_2534,plain,
    ( greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)) != greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))
    | greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)) = greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)),greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39))) )],[refute_0_2532,refute_0_2533]) ).

cnf(refute_0_2535,plain,
    greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)) = greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_179,greatest_lower_bound(greatest_lower_bound(X_39,X_178),X_178)),greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))) )],[refute_0_2500,refute_0_2534]) ).

cnf(refute_0_2536,plain,
    ( greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)) != greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))
    | greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178)) = greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)))),bind(Y0,$fot(greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))))]]) ).

cnf(refute_0_2537,plain,
    greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178)) = greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_179,greatest_lower_bound(X_178,X_39)),greatest_lower_bound(X_179,greatest_lower_bound(X_39,X_178))) )],[refute_0_2535,refute_0_2536]) ).

cnf(refute_0_2538,plain,
    greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),X_196)) = greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))),
    inference(subst,[],[refute_0_2537:[bind(X_178,$fot(X_196)),bind(X_179,$fot(b)),bind(X_39,$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))]]) ).

cnf(refute_0_2539,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) = greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),X_196)),
    inference(subst,[],[refute_0_375:[bind(Y,$fot(b)),bind(X_38,$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))),bind(X_40,$fot(X_196))]]) ).

cnf(refute_0_2540,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),X_196)) != greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) != greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),X_196))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) = greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),X_196)))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))))]]) ).

cnf(refute_0_2541,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),X_196)) != greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) = greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)),greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),X_196))) )],[refute_0_2539,refute_0_2540]) ).

cnf(refute_0_2542,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) = greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),X_196)),greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))) )],[refute_0_2538,refute_0_2541]) ).

cnf(refute_0_2543,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) != greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197))))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) != greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) = greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197))))))]]) ).

cnf(refute_0_2544,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) != greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197))))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) = greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)),greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))) )],[refute_0_2542,refute_0_2543]) ).

cnf(refute_0_2545,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) = greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_196,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))),greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197))))) )],[refute_0_2481,refute_0_2544]) ).

cnf(refute_0_2546,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) != greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197))))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)) ),[0],$fot(greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))))]]) ).

cnf(refute_0_2547,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)),greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197))))) )],[refute_0_2545,refute_0_2546]) ).

cnf(refute_0_2548,plain,
    greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177))) = greatest_lower_bound(b,X_177),
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(greatest_lower_bound(b,X_177))),bind(X_13,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2549,plain,
    greatest_lower_bound(least_upper_bound(b,greatest_lower_bound(b,Y)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y)),
    inference(subst,[],[refute_0_1730:[bind(X_16,$fot(greatest_lower_bound(b,Y)))]]) ).

cnf(refute_0_2550,plain,
    least_upper_bound(b,greatest_lower_bound(b,Y)) = b,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(b))]]) ).

cnf(refute_0_2551,plain,
    ( greatest_lower_bound(least_upper_bound(b,greatest_lower_bound(b,Y)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))
    | least_upper_bound(b,greatest_lower_bound(b,Y)) != b
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,greatest_lower_bound(b,Y)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))) ),[0,0],$fot(b)]]) ).

cnf(refute_0_2552,plain,
    ( greatest_lower_bound(least_upper_bound(b,greatest_lower_bound(b,Y)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,Y)),b) )],[refute_0_2550,refute_0_2551]) ).

cnf(refute_0_2553,plain,
    greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,greatest_lower_bound(b,Y)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,Y))) )],[refute_0_2549,refute_0_2552]) ).

cnf(refute_0_2554,plain,
    greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76)),
    inference(subst,[],[refute_0_2553:[bind(Y,$fot(X_76))]]) ).

cnf(refute_0_2555,plain,
    greatest_lower_bound(X_76,b) = greatest_lower_bound(b,X_76),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_76)),bind(Y,$fot(b))]]) ).

cnf(refute_0_2556,plain,
    ( greatest_lower_bound(X_76,b) != greatest_lower_bound(b,X_76)
    | greatest_lower_bound(b,X_76) = greatest_lower_bound(X_76,b) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X_76,b))),bind(Y0,$fot(greatest_lower_bound(b,X_76)))]]) ).

cnf(refute_0_2557,plain,
    greatest_lower_bound(b,X_76) = greatest_lower_bound(X_76,b),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_76,b),greatest_lower_bound(b,X_76)) )],[refute_0_2555,refute_0_2556]) ).

cnf(refute_0_2558,plain,
    ( greatest_lower_bound(b,X_76) != greatest_lower_bound(X_76,b)
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))) ),[0,1,1],$fot(greatest_lower_bound(X_76,b))]]) ).

cnf(refute_0_2559,plain,
    ( greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,X_76),greatest_lower_bound(X_76,b)) )],[refute_0_2557,refute_0_2558]) ).

cnf(refute_0_2560,plain,
    greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))) )],[refute_0_2554,refute_0_2559]) ).

cnf(refute_0_2561,plain,
    greatest_lower_bound(least_upper_bound(b,greatest_lower_bound(X_9,b)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b)),
    inference(subst,[],[refute_0_1730:[bind(X_16,$fot(greatest_lower_bound(X_9,b)))]]) ).

cnf(refute_0_2562,plain,
    least_upper_bound(b,greatest_lower_bound(X_9,b)) = b,
    inference(subst,[],[refute_0_281:[bind(X_8,$fot(b))]]) ).

cnf(refute_0_2563,plain,
    ( greatest_lower_bound(least_upper_bound(b,greatest_lower_bound(X_9,b)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))
    | least_upper_bound(b,greatest_lower_bound(X_9,b)) != b
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,greatest_lower_bound(X_9,b)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))) ),[0,0],$fot(b)]]) ).

cnf(refute_0_2564,plain,
    ( greatest_lower_bound(least_upper_bound(b,greatest_lower_bound(X_9,b)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(X_9,b)),b) )],[refute_0_2562,refute_0_2563]) ).

cnf(refute_0_2565,plain,
    greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,greatest_lower_bound(X_9,b)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_9,b))) )],[refute_0_2561,refute_0_2564]) ).

cnf(refute_0_2566,plain,
    greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b)),
    inference(subst,[],[refute_0_2565:[bind(X_9,$fot(X_76))]]) ).

cnf(refute_0_2567,plain,
    ( greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))
    | greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))
    | least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b)) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))) ),[0],$fot(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b)))]]) ).

cnf(refute_0_2568,plain,
    ( greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))
    | least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b)) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))) )],[refute_0_2566,refute_0_2567]) ).

cnf(refute_0_2569,plain,
    least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b)) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_76,b))),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_76))) )],[refute_0_2560,refute_0_2568]) ).

cnf(refute_0_2570,plain,
    least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177)),
    inference(subst,[],[refute_0_2569:[bind(X_76,$fot(X_177))]]) ).

cnf(refute_0_2571,plain,
    ( least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177))
    | least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177)) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177))))]]) ).

cnf(refute_0_2572,plain,
    least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177)) = least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177))) )],[refute_0_2570,refute_0_2571]) ).

cnf(refute_0_2573,plain,
    ( greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177))) != greatest_lower_bound(b,X_177)
    | least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177)) != least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))
    | greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))) = greatest_lower_bound(b,X_177) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177))),greatest_lower_bound(b,X_177)) ),[0,1],$fot(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))]]) ).

cnf(refute_0_2574,plain,
    ( greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177))) != greatest_lower_bound(b,X_177)
    | greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))) = greatest_lower_bound(b,X_177) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177)),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))) )],[refute_0_2572,refute_0_2573]) ).

cnf(refute_0_2575,plain,
    greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))) = greatest_lower_bound(b,X_177),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X_177))),greatest_lower_bound(b,X_177)) )],[refute_0_2548,refute_0_2574]) ).

cnf(refute_0_2576,plain,
    greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))) = greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))),
    inference(subst,[],[refute_0_79:[bind(X,$fot(b)),bind(Y,$fot(X_177)),bind(Z,$fot(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))))]]) ).

cnf(refute_0_2577,plain,
    ( greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))) != greatest_lower_bound(b,X_177)
    | greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))) != greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))))
    | greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))) = greatest_lower_bound(b,X_177) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))),greatest_lower_bound(b,X_177)) ),[0],$fot(greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))))]]) ).

cnf(refute_0_2578,plain,
    ( greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))) != greatest_lower_bound(b,X_177)
    | greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))) = greatest_lower_bound(b,X_177) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))),greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))))) )],[refute_0_2576,refute_0_2577]) ).

cnf(refute_0_2579,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))) = greatest_lower_bound(b,X_177),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(b,X_177),least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b))),greatest_lower_bound(b,X_177)) )],[refute_0_2575,refute_0_2578]) ).

cnf(refute_0_2580,plain,
    greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) = greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y),
    inference(subst,[],[refute_0_83:[bind(X_30,$fot(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))]]) ).

cnf(refute_0_2581,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) = greatest_lower_bound(Y,X_180),
    inference(subst,[],[refute_0_2488:[bind(X_13,$fot(X_178)),bind(X_38,$fot(Y)),bind(X_39,$fot(X_180))]]) ).

cnf(refute_0_2582,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) != greatest_lower_bound(Y,X_180)
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) != greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) = greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))),greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)) ),[0,1],$fot(greatest_lower_bound(Y,X_180))]]) ).

cnf(refute_0_2583,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) != greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) = greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))),greatest_lower_bound(Y,X_180)) )],[refute_0_2581,refute_0_2582]) ).

cnf(refute_0_2584,plain,
    greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) = greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))),greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)) )],[refute_0_2580,refute_0_2583]) ).

cnf(refute_0_2585,plain,
    greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) = greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),
    inference(subst,[],[refute_0_319:[bind(X_31,$fot(least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))),bind(X_32,$fot(X_180))]]) ).

cnf(refute_0_2586,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) = greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))))]]) ).

cnf(refute_0_2587,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) != greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))
    | greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) != greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))
    | greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) = greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))),greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))) ),[1,1],$fot(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))]]) ).

cnf(refute_0_2588,plain,
    ( greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) != greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))
    | greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) = greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))),greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))) )],[refute_0_2586,refute_0_2587]) ).

cnf(refute_0_2589,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) = greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))),greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) )],[refute_0_2585,refute_0_2588]) ).

cnf(refute_0_2590,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) != greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))
    | greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) != greatest_lower_bound(Y,X_180)
    | greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) = greatest_lower_bound(Y,X_180) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))),bind(Z0,$fot(greatest_lower_bound(Y,X_180)))]]) ).

cnf(refute_0_2591,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) != greatest_lower_bound(Y,X_180)
    | greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) = greatest_lower_bound(Y,X_180) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))),greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) )],[refute_0_2589,refute_0_2590]) ).

cnf(refute_0_2592,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) = greatest_lower_bound(Y,X_180),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))),greatest_lower_bound(Y,X_180)) )],[refute_0_2581,refute_0_2591]) ).

cnf(refute_0_2593,plain,
    greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),X_180)) = greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))),
    inference(subst,[],[refute_0_2528:[bind(X_13,$fot(X_180)),bind(X_72,$fot(Y)),bind(X_73,$fot(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))]]) ).

cnf(refute_0_2594,plain,
    greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) = greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),X_180)),
    inference(subst,[],[refute_0_375:[bind(X_38,$fot(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))),bind(X_40,$fot(X_180))]]) ).

cnf(refute_0_2595,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),X_180)) != greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) != greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),X_180))
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) = greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),X_180)))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))))]]) ).

cnf(refute_0_2596,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),X_180)) != greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) = greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)),greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),X_180))) )],[refute_0_2594,refute_0_2595]) ).

cnf(refute_0_2597,plain,
    greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) = greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),X_180)),greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))) )],[refute_0_2593,refute_0_2596]) ).

cnf(refute_0_2598,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) != greatest_lower_bound(Y,X_180)
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) != greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) = greatest_lower_bound(Y,X_180) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))))),bind(Z0,$fot(greatest_lower_bound(Y,X_180)))]]) ).

cnf(refute_0_2599,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) != greatest_lower_bound(Y,X_180)
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) = greatest_lower_bound(Y,X_180) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)),greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))))) )],[refute_0_2597,refute_0_2598]) ).

cnf(refute_0_2600,plain,
    greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) = greatest_lower_bound(Y,X_180),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_180,greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))),greatest_lower_bound(Y,X_180)) )],[refute_0_2592,refute_0_2599]) ).

cnf(refute_0_2601,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) != greatest_lower_bound(Y,X_180)
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) != greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)
    | greatest_lower_bound(Y,X_180) = greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)),greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)) ),[0],$fot(greatest_lower_bound(Y,X_180))]]) ).

cnf(refute_0_2602,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) != greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)
    | greatest_lower_bound(Y,X_180) = greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)),greatest_lower_bound(Y,X_180)) )],[refute_0_2600,refute_0_2601]) ).

cnf(refute_0_2603,plain,
    greatest_lower_bound(X_180,greatest_lower_bound(least_upper_bound(X_178,greatest_lower_bound(Y,X_180)),Y)) = greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))),
    inference(subst,[],[refute_0_2528:[bind(X_13,$fot(Y)),bind(X_72,$fot(X_180)),bind(X_73,$fot(least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))]]) ).

cnf(refute_0_2604,plain,
    greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y) = greatest_lower_bound(X_180,greatest_lower_bound(least_upper_bound(X_178,greatest_lower_bound(Y,X_180)),Y)),
    inference(subst,[],[refute_0_79:[bind(X,$fot(X_180)),bind(Y,$fot(least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))),bind(Z,$fot(Y))]]) ).

cnf(refute_0_2605,plain,
    ( greatest_lower_bound(X_180,greatest_lower_bound(least_upper_bound(X_178,greatest_lower_bound(Y,X_180)),Y)) != greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y) != greatest_lower_bound(X_180,greatest_lower_bound(least_upper_bound(X_178,greatest_lower_bound(Y,X_180)),Y))
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y) = greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y))),bind(Y0,$fot(greatest_lower_bound(X_180,greatest_lower_bound(least_upper_bound(X_178,greatest_lower_bound(Y,X_180)),Y)))),bind(Z0,$fot(greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))))]]) ).

cnf(refute_0_2606,plain,
    ( greatest_lower_bound(X_180,greatest_lower_bound(least_upper_bound(X_178,greatest_lower_bound(Y,X_180)),Y)) != greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y) = greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y),greatest_lower_bound(X_180,greatest_lower_bound(least_upper_bound(X_178,greatest_lower_bound(Y,X_180)),Y))) )],[refute_0_2604,refute_0_2605]) ).

cnf(refute_0_2607,plain,
    greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y) = greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_180,greatest_lower_bound(least_upper_bound(X_178,greatest_lower_bound(Y,X_180)),Y)),greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) )],[refute_0_2603,refute_0_2606]) ).

cnf(refute_0_2608,plain,
    ( greatest_lower_bound(Y,X_180) != greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)
    | greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y) != greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))
    | greatest_lower_bound(Y,X_180) = greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(Y,X_180),greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y))]]) ).

cnf(refute_0_2609,plain,
    ( greatest_lower_bound(Y,X_180) != greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)
    | greatest_lower_bound(Y,X_180) = greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y),greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) )],[refute_0_2607,refute_0_2608]) ).

cnf(refute_0_2610,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)) != greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)
    | greatest_lower_bound(Y,X_180) = greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,X_180),greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)) )],[refute_0_2602,refute_0_2609]) ).

cnf(refute_0_2611,plain,
    greatest_lower_bound(Y,X_180) = greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),greatest_lower_bound(Y,X_180)),greatest_lower_bound(greatest_lower_bound(X_180,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))),Y)) )],[refute_0_2584,refute_0_2610]) ).

cnf(refute_0_2612,plain,
    ( greatest_lower_bound(Y,X_180) != greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))
    | greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) = greatest_lower_bound(Y,X_180) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(Y,X_180))),bind(Y0,$fot(greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))))]]) ).

cnf(refute_0_2613,plain,
    greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180)))) = greatest_lower_bound(Y,X_180),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,X_180),greatest_lower_bound(X_180,greatest_lower_bound(Y,least_upper_bound(X_178,greatest_lower_bound(Y,X_180))))) )],[refute_0_2611,refute_0_2612]) ).

cnf(refute_0_2614,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))) = greatest_lower_bound(X_177,b),
    inference(subst,[],[refute_0_2613:[bind(Y,$fot(X_177)),bind(X_178,$fot(greatest_lower_bound(a,c))),bind(X_180,$fot(b))]]) ).

cnf(refute_0_2615,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))) != greatest_lower_bound(X_177,b)
    | greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))) != greatest_lower_bound(b,X_177)
    | greatest_lower_bound(X_177,b) = greatest_lower_bound(b,X_177) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))),greatest_lower_bound(b,X_177)) ),[0],$fot(greatest_lower_bound(X_177,b))]]) ).

cnf(refute_0_2616,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))) != greatest_lower_bound(b,X_177)
    | greatest_lower_bound(X_177,b) = greatest_lower_bound(b,X_177) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))),greatest_lower_bound(X_177,b)) )],[refute_0_2614,refute_0_2615]) ).

cnf(refute_0_2617,plain,
    greatest_lower_bound(X_177,b) = greatest_lower_bound(b,X_177),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_177,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(X_177,b)))),greatest_lower_bound(b,X_177)) )],[refute_0_2579,refute_0_2616]) ).

cnf(refute_0_2618,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)),
    inference(subst,[],[refute_0_2617:[bind(X_177,$fot(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))]]) ).

cnf(refute_0_2619,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)) != greatest_lower_bound(b,X_196)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b) != greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b) = greatest_lower_bound(b,X_196) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)))),bind(Z0,$fot(greatest_lower_bound(b,X_196)))]]) ).

cnf(refute_0_2620,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)) != greatest_lower_bound(b,X_196)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b) = greatest_lower_bound(b,X_196) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196))) )],[refute_0_2618,refute_0_2619]) ).

cnf(refute_0_2621,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b) = greatest_lower_bound(b,X_196),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196)),greatest_lower_bound(b,X_196)) )],[refute_0_2473,refute_0_2620]) ).

cnf(refute_0_2622,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b) != greatest_lower_bound(b,X_196)
    | greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) = greatest_lower_bound(b,X_196) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))),greatest_lower_bound(b,X_196)) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b))]]) ).

cnf(refute_0_2623,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) = greatest_lower_bound(b,X_196) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b),greatest_lower_bound(b,X_196)) )],[refute_0_2621,refute_0_2622]) ).

cnf(refute_0_2624,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) = greatest_lower_bound(b,X_196) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)) )],[refute_0_2547,refute_0_2623]) ).

cnf(refute_0_2625,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_196,least_upper_bound(a,least_upper_bound(c,X_197)))) = greatest_lower_bound(b,X_196),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),greatest_lower_bound(b,X_196)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X_197)),X_196),b)) )],[refute_0_2476,refute_0_2624]) ).

cnf(refute_0_2626,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236)))) = greatest_lower_bound(b,least_upper_bound(X_236,c)),
    inference(subst,[],[refute_0_2625:[bind(X_196,$fot(least_upper_bound(X_236,c))),bind(X_197,$fot(X_236))]]) ).

cnf(refute_0_2627,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) != greatest_lower_bound(X_201,greatest_lower_bound(b,X_216))
    | greatest_lower_bound(X_201,greatest_lower_bound(b,X_216)) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)))),bind(Y0,$fot(greatest_lower_bound(X_201,greatest_lower_bound(b,X_216))))]]) ).

cnf(refute_0_2628,plain,
    greatest_lower_bound(X_201,greatest_lower_bound(b,X_216)) = greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_201,X_216)),greatest_lower_bound(X_201,greatest_lower_bound(b,X_216))) )],[refute_0_2413,refute_0_2627]) ).

cnf(refute_0_2629,plain,
    greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236)))),
    inference(subst,[],[refute_0_2628:[bind(X_201,$fot(least_upper_bound(X_236,c))),bind(X_216,$fot(least_upper_bound(a,least_upper_bound(c,X_236))))]]) ).

cnf(refute_0_2630,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236)))) != greatest_lower_bound(b,least_upper_bound(X_236,c))
    | greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))) != greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236))))
    | greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))) = greatest_lower_bound(b,least_upper_bound(X_236,c)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236)))))),bind(Z0,$fot(greatest_lower_bound(b,least_upper_bound(X_236,c))))]]) ).

cnf(refute_0_2631,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236)))) != greatest_lower_bound(b,least_upper_bound(X_236,c))
    | greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))) = greatest_lower_bound(b,least_upper_bound(X_236,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236))))) )],[refute_0_2629,refute_0_2630]) ).

cnf(refute_0_2632,plain,
    greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))) = greatest_lower_bound(b,least_upper_bound(X_236,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(X_236,c),least_upper_bound(a,least_upper_bound(c,X_236)))),greatest_lower_bound(b,least_upper_bound(X_236,c))) )],[refute_0_2626,refute_0_2631]) ).

cnf(refute_0_2633,plain,
    ( greatest_lower_bound(b,least_upper_bound(c,X_236)) != greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236))))
    | greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))) != greatest_lower_bound(b,least_upper_bound(X_236,c))
    | greatest_lower_bound(b,least_upper_bound(c,X_236)) = greatest_lower_bound(b,least_upper_bound(X_236,c)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,least_upper_bound(c,X_236)),greatest_lower_bound(b,least_upper_bound(X_236,c))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))))]]) ).

cnf(refute_0_2634,plain,
    ( greatest_lower_bound(b,least_upper_bound(c,X_236)) != greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236))))
    | greatest_lower_bound(b,least_upper_bound(c,X_236)) = greatest_lower_bound(b,least_upper_bound(X_236,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236)))),greatest_lower_bound(b,least_upper_bound(X_236,c))) )],[refute_0_2632,refute_0_2633]) ).

cnf(refute_0_2635,plain,
    greatest_lower_bound(b,least_upper_bound(c,X_236)) = greatest_lower_bound(b,least_upper_bound(X_236,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(c,X_236)),greatest_lower_bound(least_upper_bound(X_236,c),greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X_236))))) )],[refute_0_2464,refute_0_2634]) ).

cnf(refute_0_2636,plain,
    greatest_lower_bound(b,least_upper_bound(c,X_238)) = greatest_lower_bound(b,least_upper_bound(X_238,c)),
    inference(subst,[],[refute_0_2635:[bind(X_236,$fot(X_238))]]) ).

cnf(refute_0_2637,plain,
    ( greatest_lower_bound(b,least_upper_bound(c,X_238)) != greatest_lower_bound(b,least_upper_bound(X_238,c))
    | greatest_lower_bound(b,least_upper_bound(X_238,c)) = greatest_lower_bound(b,least_upper_bound(c,X_238)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(b,least_upper_bound(c,X_238)))),bind(Y0,$fot(greatest_lower_bound(b,least_upper_bound(X_238,c))))]]) ).

cnf(refute_0_2638,plain,
    greatest_lower_bound(b,least_upper_bound(X_238,c)) = greatest_lower_bound(b,least_upper_bound(c,X_238)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(c,X_238)),greatest_lower_bound(b,least_upper_bound(X_238,c))) )],[refute_0_2636,refute_0_2637]) ).

cnf(refute_0_2639,plain,
    ( greatest_lower_bound(b,least_upper_bound(X_238,c)) != greatest_lower_bound(b,least_upper_bound(c,X_238))
    | least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(X_238,c))) != least_upper_bound(X_238,c)
    | least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(c,X_238))) = least_upper_bound(X_238,c) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(X_238,c))),least_upper_bound(X_238,c)) ),[0,1],$fot(greatest_lower_bound(b,least_upper_bound(c,X_238)))]]) ).

cnf(refute_0_2640,plain,
    ( least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(X_238,c))) != least_upper_bound(X_238,c)
    | least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(c,X_238))) = least_upper_bound(X_238,c) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(X_238,c)),greatest_lower_bound(b,least_upper_bound(c,X_238))) )],[refute_0_2638,refute_0_2639]) ).

cnf(refute_0_2641,plain,
    least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(c,X_238))) = least_upper_bound(X_238,c),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(X_238,c))),least_upper_bound(X_238,c)) )],[refute_0_2317,refute_0_2640]) ).

cnf(refute_0_2642,plain,
    least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(c,X_238))) = least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))),
    inference(subst,[],[refute_0_237:[bind(X,$fot(X_238)),bind(Y,$fot(c)),bind(Z,$fot(greatest_lower_bound(b,least_upper_bound(c,X_238))))]]) ).

cnf(refute_0_2643,plain,
    ( least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(c,X_238))) != least_upper_bound(X_238,c)
    | least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(c,X_238))) != least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238))))
    | least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))) = least_upper_bound(X_238,c) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(c,X_238))),least_upper_bound(X_238,c)) ),[0],$fot(least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))))]]) ).

cnf(refute_0_2644,plain,
    ( least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(c,X_238))) != least_upper_bound(X_238,c)
    | least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))) = least_upper_bound(X_238,c) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(c,X_238))),least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238))))) )],[refute_0_2642,refute_0_2643]) ).

cnf(refute_0_2645,plain,
    least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))) = least_upper_bound(X_238,c),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_238,c),greatest_lower_bound(b,least_upper_bound(c,X_238))),least_upper_bound(X_238,c)) )],[refute_0_2641,refute_0_2644]) ).

cnf(refute_0_2646,plain,
    least_upper_bound(X_15,X_14) = least_upper_bound(X_14,X_15),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_15)),bind(Y,$fot(X_14))]]) ).

cnf(refute_0_2647,plain,
    ( least_upper_bound(X_15,X_14) != least_upper_bound(X_14,X_15)
    | least_upper_bound(X_14,X_15) = least_upper_bound(X_15,X_14) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_15,X_14))),bind(Y0,$fot(least_upper_bound(X_14,X_15)))]]) ).

cnf(refute_0_2648,plain,
    least_upper_bound(X_14,X_15) = least_upper_bound(X_15,X_14),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,X_14),least_upper_bound(X_14,X_15)) )],[refute_0_2646,refute_0_2647]) ).

cnf(refute_0_2649,plain,
    ( least_upper_bound(X_14,X_15) != least_upper_bound(X_15,X_14)
    | least_upper_bound(X_14,least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(X_14,X_15),X_16)
    | least_upper_bound(X_14,least_upper_bound(X_15,X_16)) = least_upper_bound(least_upper_bound(X_15,X_14),X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(X_15,X_16)),least_upper_bound(least_upper_bound(X_14,X_15),X_16)) ),[1,0],$fot(least_upper_bound(X_15,X_14))]]) ).

cnf(refute_0_2650,plain,
    ( least_upper_bound(X_14,least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(X_14,X_15),X_16)
    | least_upper_bound(X_14,least_upper_bound(X_15,X_16)) = least_upper_bound(least_upper_bound(X_15,X_14),X_16) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,X_15),least_upper_bound(X_15,X_14)) )],[refute_0_2648,refute_0_2649]) ).

cnf(refute_0_2651,plain,
    least_upper_bound(X_14,least_upper_bound(X_15,X_16)) = least_upper_bound(least_upper_bound(X_15,X_14),X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(X_15,X_16)),least_upper_bound(least_upper_bound(X_14,X_15),X_16)) )],[refute_0_568,refute_0_2650]) ).

cnf(refute_0_2652,plain,
    least_upper_bound(least_upper_bound(X_15,X_14),X_16) = least_upper_bound(X_15,least_upper_bound(X_14,X_16)),
    inference(subst,[],[refute_0_237:[bind(X,$fot(X_15)),bind(Y,$fot(X_14)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_2653,plain,
    ( least_upper_bound(X_14,least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(X_15,X_14),X_16)
    | least_upper_bound(least_upper_bound(X_15,X_14),X_16) != least_upper_bound(X_15,least_upper_bound(X_14,X_16))
    | least_upper_bound(X_14,least_upper_bound(X_15,X_16)) = least_upper_bound(X_15,least_upper_bound(X_14,X_16)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_14,least_upper_bound(X_15,X_16)),least_upper_bound(X_15,least_upper_bound(X_14,X_16))) ),[0],$fot(least_upper_bound(least_upper_bound(X_15,X_14),X_16))]]) ).

cnf(refute_0_2654,plain,
    ( least_upper_bound(X_14,least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(X_15,X_14),X_16)
    | least_upper_bound(X_14,least_upper_bound(X_15,X_16)) = least_upper_bound(X_15,least_upper_bound(X_14,X_16)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,X_14),X_16),least_upper_bound(X_15,least_upper_bound(X_14,X_16))) )],[refute_0_2652,refute_0_2653]) ).

cnf(refute_0_2655,plain,
    least_upper_bound(X_14,least_upper_bound(X_15,X_16)) = least_upper_bound(X_15,least_upper_bound(X_14,X_16)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(X_15,X_16)),least_upper_bound(least_upper_bound(X_15,X_14),X_16)) )],[refute_0_2651,refute_0_2654]) ).

cnf(refute_0_2656,plain,
    least_upper_bound(X_14,least_upper_bound(X_15,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))) = least_upper_bound(X_15,least_upper_bound(X_14,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))),
    inference(subst,[],[refute_0_2655:[bind(X_16,$fot(greatest_lower_bound(X_399,least_upper_bound(X_15,X_14))))]]) ).

cnf(refute_0_2657,plain,
    least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(X_27,least_upper_bound(X,Y)))) = least_upper_bound(least_upper_bound(X,Y),greatest_lower_bound(X_27,least_upper_bound(X,Y))),
    inference(subst,[],[associativity_of_lub:[bind(Z,$fot(greatest_lower_bound(X_27,least_upper_bound(X,Y))))]]) ).

cnf(refute_0_2658,plain,
    least_upper_bound(least_upper_bound(X,Y),greatest_lower_bound(X_27,least_upper_bound(X,Y))) = least_upper_bound(X,Y),
    inference(subst,[],[refute_0_281:[bind(X_8,$fot(least_upper_bound(X,Y))),bind(X_9,$fot(X_27))]]) ).

cnf(refute_0_2659,plain,
    ( least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(X_27,least_upper_bound(X,Y)))) != least_upper_bound(least_upper_bound(X,Y),greatest_lower_bound(X_27,least_upper_bound(X,Y)))
    | least_upper_bound(least_upper_bound(X,Y),greatest_lower_bound(X_27,least_upper_bound(X,Y))) != least_upper_bound(X,Y)
    | least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(X_27,least_upper_bound(X,Y)))) = least_upper_bound(X,Y) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(X_27,least_upper_bound(X,Y)))),least_upper_bound(X,Y)) ),[0],$fot(least_upper_bound(least_upper_bound(X,Y),greatest_lower_bound(X_27,least_upper_bound(X,Y))))]]) ).

cnf(refute_0_2660,plain,
    ( least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(X_27,least_upper_bound(X,Y)))) != least_upper_bound(least_upper_bound(X,Y),greatest_lower_bound(X_27,least_upper_bound(X,Y)))
    | least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(X_27,least_upper_bound(X,Y)))) = least_upper_bound(X,Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),greatest_lower_bound(X_27,least_upper_bound(X,Y))),least_upper_bound(X,Y)) )],[refute_0_2658,refute_0_2659]) ).

cnf(refute_0_2661,plain,
    least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(X_27,least_upper_bound(X,Y)))) = least_upper_bound(X,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(X_27,least_upper_bound(X,Y)))),least_upper_bound(least_upper_bound(X,Y),greatest_lower_bound(X_27,least_upper_bound(X,Y)))) )],[refute_0_2657,refute_0_2660]) ).

cnf(refute_0_2662,plain,
    least_upper_bound(X_15,least_upper_bound(X_14,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))) = least_upper_bound(X_15,X_14),
    inference(subst,[],[refute_0_2661:[bind(X,$fot(X_15)),bind(Y,$fot(X_14)),bind(X_27,$fot(X_399))]]) ).

cnf(refute_0_2663,plain,
    ( least_upper_bound(X_14,least_upper_bound(X_15,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))) != least_upper_bound(X_15,least_upper_bound(X_14,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14))))
    | least_upper_bound(X_15,least_upper_bound(X_14,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))) != least_upper_bound(X_15,X_14)
    | least_upper_bound(X_14,least_upper_bound(X_15,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))) = least_upper_bound(X_15,X_14) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_14,least_upper_bound(X_15,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))),least_upper_bound(X_15,X_14)) ),[0],$fot(least_upper_bound(X_15,least_upper_bound(X_14,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))))]]) ).

cnf(refute_0_2664,plain,
    ( least_upper_bound(X_14,least_upper_bound(X_15,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))) != least_upper_bound(X_15,least_upper_bound(X_14,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14))))
    | least_upper_bound(X_14,least_upper_bound(X_15,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))) = least_upper_bound(X_15,X_14) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_14,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))),least_upper_bound(X_15,X_14)) )],[refute_0_2662,refute_0_2663]) ).

cnf(refute_0_2665,plain,
    least_upper_bound(X_14,least_upper_bound(X_15,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))) = least_upper_bound(X_15,X_14),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(X_15,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14)))),least_upper_bound(X_15,least_upper_bound(X_14,greatest_lower_bound(X_399,least_upper_bound(X_15,X_14))))) )],[refute_0_2656,refute_0_2664]) ).

cnf(refute_0_2666,plain,
    least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))) = least_upper_bound(c,X_238),
    inference(subst,[],[refute_0_2665:[bind(X_14,$fot(X_238)),bind(X_15,$fot(c)),bind(X_399,$fot(b))]]) ).

cnf(refute_0_2667,plain,
    ( least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))) != least_upper_bound(X_238,c)
    | least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))) != least_upper_bound(c,X_238)
    | least_upper_bound(c,X_238) = least_upper_bound(X_238,c) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))),least_upper_bound(X_238,c)) ),[0],$fot(least_upper_bound(c,X_238))]]) ).

cnf(refute_0_2668,plain,
    ( least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))) != least_upper_bound(X_238,c)
    | least_upper_bound(c,X_238) = least_upper_bound(X_238,c) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))),least_upper_bound(c,X_238)) )],[refute_0_2666,refute_0_2667]) ).

cnf(refute_0_2669,plain,
    least_upper_bound(c,X_238) = least_upper_bound(X_238,c),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_238,least_upper_bound(c,greatest_lower_bound(b,least_upper_bound(c,X_238)))),least_upper_bound(X_238,c)) )],[refute_0_2645,refute_0_2668]) ).

cnf(refute_0_2670,plain,
    ( least_upper_bound(c,X_238) != least_upper_bound(X_238,c)
    | least_upper_bound(X_238,c) = least_upper_bound(c,X_238) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(c,X_238))),bind(Y0,$fot(least_upper_bound(X_238,c)))]]) ).

cnf(refute_0_2671,plain,
    least_upper_bound(X_238,c) = least_upper_bound(c,X_238),
    inference(resolve,[$cnf( $equal(least_upper_bound(c,X_238),least_upper_bound(X_238,c)) )],[refute_0_2669,refute_0_2670]) ).

cnf(refute_0_2672,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c) = least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))),
    inference(subst,[],[refute_0_2671:[bind(X_238,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_2673,plain,
    ( least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c) != least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c))),bind(Y0,$fot(least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))),bind(Z0,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_2674,plain,
    ( least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c),least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_2672,refute_0_2673]) ).

cnf(refute_0_2675,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c) = inverse(greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_2316,refute_0_2674]) ).

cnf(refute_0_2676,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),Z)) = least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z),
    inference(subst,[],[refute_0_1123:[bind(X,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))),bind(X_27,$fot(a))]]) ).

cnf(refute_0_2677,plain,
    ( greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) != b
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),Z)) != least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,Z)) = least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),Z)),least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)) ),[0,1,0],$fot(b)]]) ).

cnf(refute_0_2678,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),Z)) != least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,Z)) = least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),b) )],[refute_0_1714,refute_0_2677]) ).

cnf(refute_0_2679,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,Z)) = least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),Z)),least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)) )],[refute_0_2676,refute_0_2678]) ).

cnf(refute_0_2680,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,Z)) = least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)),
    inference(subst,[],[refute_0_2159:[bind(Y,$fot(Z)),bind(X_171,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))),bind(X_172,$fot(b))]]) ).

cnf(refute_0_2681,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,Z)) != least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,Z)) != least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)
    | least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)) = least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,Z)),least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)) ),[0],$fot(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)))]]) ).

cnf(refute_0_2682,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,Z)) != least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)
    | least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)) = least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,Z)),least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z))) )],[refute_0_2680,refute_0_2681]) ).

cnf(refute_0_2683,plain,
    least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)) = least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,Z)),least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),Z)) )],[refute_0_2679,refute_0_2682]) ).

cnf(refute_0_2684,plain,
    least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)) = least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c),
    inference(subst,[],[refute_0_2683:[bind(Z,$fot(c))]]) ).

cnf(refute_0_2685,plain,
    ( least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)) != least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c))),bind(Z0,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_2686,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)),least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)) )],[refute_0_2684,refute_0_2685]) ).

cnf(refute_0_2687,plain,
    least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)) = inverse(greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c),inverse(greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_2675,refute_0_2686]) ).

cnf(refute_0_2688,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)) = least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)),
    inference(subst,[],[refute_0_2159:[bind(Y,$fot(c)),bind(X_171,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))),bind(X_172,$fot(b))]]) ).

cnf(refute_0_2689,plain,
    ( least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)) != least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)))),bind(Z0,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_2690,plain,
    ( least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)),least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c))) )],[refute_0_2688,refute_0_2689]) ).

cnf(refute_0_2691,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)) = inverse(greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),c)),inverse(greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_2687,refute_0_2690]) ).

cnf(refute_0_2692,plain,
    least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(least_upper_bound(X_427,greatest_lower_bound(a,c)),least_upper_bound(X,least_upper_bound(b,X_427))))) = least_upper_bound(X,least_upper_bound(b,X_427)),
    inference(subst,[],[refute_0_2661:[bind(Y,$fot(least_upper_bound(b,X_427))),bind(X_27,$fot(least_upper_bound(X_427,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2693,plain,
    greatest_lower_bound(X_29,least_upper_bound(least_upper_bound(X,Y),X_29)) = X_29,
    inference(subst,[],[refute_0_72:[bind(X_12,$fot(X_29)),bind(X_13,$fot(least_upper_bound(X,Y)))]]) ).

cnf(refute_0_2694,plain,
    least_upper_bound(X,least_upper_bound(Y,X_29)) = least_upper_bound(least_upper_bound(X,Y),X_29),
    inference(subst,[],[associativity_of_lub:[bind(Z,$fot(X_29))]]) ).

cnf(refute_0_2695,plain,
    ( least_upper_bound(X,least_upper_bound(Y,X_29)) != least_upper_bound(least_upper_bound(X,Y),X_29)
    | least_upper_bound(least_upper_bound(X,Y),X_29) = least_upper_bound(X,least_upper_bound(Y,X_29)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,X_29)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),X_29)))]]) ).

cnf(refute_0_2696,plain,
    least_upper_bound(least_upper_bound(X,Y),X_29) = least_upper_bound(X,least_upper_bound(Y,X_29)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_29)),least_upper_bound(least_upper_bound(X,Y),X_29)) )],[refute_0_2694,refute_0_2695]) ).

cnf(refute_0_2697,plain,
    ( greatest_lower_bound(X_29,least_upper_bound(least_upper_bound(X,Y),X_29)) != X_29
    | least_upper_bound(least_upper_bound(X,Y),X_29) != least_upper_bound(X,least_upper_bound(Y,X_29))
    | greatest_lower_bound(X_29,least_upper_bound(X,least_upper_bound(Y,X_29))) = X_29 ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_29,least_upper_bound(least_upper_bound(X,Y),X_29)),X_29) ),[0,1],$fot(least_upper_bound(X,least_upper_bound(Y,X_29)))]]) ).

cnf(refute_0_2698,plain,
    ( greatest_lower_bound(X_29,least_upper_bound(least_upper_bound(X,Y),X_29)) != X_29
    | greatest_lower_bound(X_29,least_upper_bound(X,least_upper_bound(Y,X_29))) = X_29 ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),X_29),least_upper_bound(X,least_upper_bound(Y,X_29))) )],[refute_0_2696,refute_0_2697]) ).

cnf(refute_0_2699,plain,
    greatest_lower_bound(X_29,least_upper_bound(X,least_upper_bound(Y,X_29))) = X_29,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_29,least_upper_bound(least_upper_bound(X,Y),X_29)),X_29) )],[refute_0_2693,refute_0_2698]) ).

cnf(refute_0_2700,plain,
    greatest_lower_bound(least_upper_bound(X_25,greatest_lower_bound(a,c)),least_upper_bound(X_48,least_upper_bound(b,least_upper_bound(X_25,greatest_lower_bound(a,c))))) = least_upper_bound(X_25,greatest_lower_bound(a,c)),
    inference(subst,[],[refute_0_2699:[bind(X,$fot(X_48)),bind(Y,$fot(b)),bind(X_29,$fot(least_upper_bound(X_25,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2701,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_25)) = least_upper_bound(b,X_25),
    inference(subst,[],[refute_0_1723:[bind(X_16,$fot(X_25))]]) ).

cnf(refute_0_2702,plain,
    least_upper_bound(X_25,greatest_lower_bound(a,c)) = least_upper_bound(greatest_lower_bound(a,c),X_25),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_25)),bind(Y,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2703,plain,
    ( least_upper_bound(X_25,greatest_lower_bound(a,c)) != least_upper_bound(greatest_lower_bound(a,c),X_25)
    | least_upper_bound(greatest_lower_bound(a,c),X_25) = least_upper_bound(X_25,greatest_lower_bound(a,c)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_25,greatest_lower_bound(a,c)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,c),X_25)))]]) ).

cnf(refute_0_2704,plain,
    least_upper_bound(greatest_lower_bound(a,c),X_25) = least_upper_bound(X_25,greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_25,greatest_lower_bound(a,c)),least_upper_bound(greatest_lower_bound(a,c),X_25)) )],[refute_0_2702,refute_0_2703]) ).

cnf(refute_0_2705,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_25)) != least_upper_bound(b,X_25)
    | least_upper_bound(greatest_lower_bound(a,c),X_25) != least_upper_bound(X_25,greatest_lower_bound(a,c))
    | least_upper_bound(b,least_upper_bound(X_25,greatest_lower_bound(a,c))) = least_upper_bound(b,X_25) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_25)),least_upper_bound(b,X_25)) ),[0,1],$fot(least_upper_bound(X_25,greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2706,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_25)) != least_upper_bound(b,X_25)
    | least_upper_bound(b,least_upper_bound(X_25,greatest_lower_bound(a,c))) = least_upper_bound(b,X_25) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),X_25),least_upper_bound(X_25,greatest_lower_bound(a,c))) )],[refute_0_2704,refute_0_2705]) ).

cnf(refute_0_2707,plain,
    least_upper_bound(b,least_upper_bound(X_25,greatest_lower_bound(a,c))) = least_upper_bound(b,X_25),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_25)),least_upper_bound(b,X_25)) )],[refute_0_2701,refute_0_2706]) ).

cnf(refute_0_2708,plain,
    ( greatest_lower_bound(least_upper_bound(X_25,greatest_lower_bound(a,c)),least_upper_bound(X_48,least_upper_bound(b,least_upper_bound(X_25,greatest_lower_bound(a,c))))) != least_upper_bound(X_25,greatest_lower_bound(a,c))
    | least_upper_bound(b,least_upper_bound(X_25,greatest_lower_bound(a,c))) != least_upper_bound(b,X_25)
    | greatest_lower_bound(least_upper_bound(X_25,greatest_lower_bound(a,c)),least_upper_bound(X_48,least_upper_bound(b,X_25))) = least_upper_bound(X_25,greatest_lower_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_25,greatest_lower_bound(a,c)),least_upper_bound(X_48,least_upper_bound(b,least_upper_bound(X_25,greatest_lower_bound(a,c))))),least_upper_bound(X_25,greatest_lower_bound(a,c))) ),[0,1,1],$fot(least_upper_bound(b,X_25))]]) ).

cnf(refute_0_2709,plain,
    ( greatest_lower_bound(least_upper_bound(X_25,greatest_lower_bound(a,c)),least_upper_bound(X_48,least_upper_bound(b,least_upper_bound(X_25,greatest_lower_bound(a,c))))) != least_upper_bound(X_25,greatest_lower_bound(a,c))
    | greatest_lower_bound(least_upper_bound(X_25,greatest_lower_bound(a,c)),least_upper_bound(X_48,least_upper_bound(b,X_25))) = least_upper_bound(X_25,greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(X_25,greatest_lower_bound(a,c))),least_upper_bound(b,X_25)) )],[refute_0_2707,refute_0_2708]) ).

cnf(refute_0_2710,plain,
    greatest_lower_bound(least_upper_bound(X_25,greatest_lower_bound(a,c)),least_upper_bound(X_48,least_upper_bound(b,X_25))) = least_upper_bound(X_25,greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_25,greatest_lower_bound(a,c)),least_upper_bound(X_48,least_upper_bound(b,least_upper_bound(X_25,greatest_lower_bound(a,c))))),least_upper_bound(X_25,greatest_lower_bound(a,c))) )],[refute_0_2700,refute_0_2709]) ).

cnf(refute_0_2711,plain,
    greatest_lower_bound(least_upper_bound(X_427,greatest_lower_bound(a,c)),least_upper_bound(X,least_upper_bound(b,X_427))) = least_upper_bound(X_427,greatest_lower_bound(a,c)),
    inference(subst,[],[refute_0_2710:[bind(X_25,$fot(X_427)),bind(X_48,$fot(X))]]) ).

cnf(refute_0_2712,plain,
    ( greatest_lower_bound(least_upper_bound(X_427,greatest_lower_bound(a,c)),least_upper_bound(X,least_upper_bound(b,X_427))) != least_upper_bound(X_427,greatest_lower_bound(a,c))
    | least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(least_upper_bound(X_427,greatest_lower_bound(a,c)),least_upper_bound(X,least_upper_bound(b,X_427))))) != least_upper_bound(X,least_upper_bound(b,X_427))
    | least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))) = least_upper_bound(X,least_upper_bound(b,X_427)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(least_upper_bound(X_427,greatest_lower_bound(a,c)),least_upper_bound(X,least_upper_bound(b,X_427))))),least_upper_bound(X,least_upper_bound(b,X_427))) ),[0,1,1],$fot(least_upper_bound(X_427,greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2713,plain,
    ( least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(least_upper_bound(X_427,greatest_lower_bound(a,c)),least_upper_bound(X,least_upper_bound(b,X_427))))) != least_upper_bound(X,least_upper_bound(b,X_427))
    | least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))) = least_upper_bound(X,least_upper_bound(b,X_427)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_427,greatest_lower_bound(a,c)),least_upper_bound(X,least_upper_bound(b,X_427))),least_upper_bound(X_427,greatest_lower_bound(a,c))) )],[refute_0_2711,refute_0_2712]) ).

cnf(refute_0_2714,plain,
    least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))) = least_upper_bound(X,least_upper_bound(b,X_427)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(least_upper_bound(X_427,greatest_lower_bound(a,c)),least_upper_bound(X,least_upper_bound(b,X_427))))),least_upper_bound(X,least_upper_bound(b,X_427))) )],[refute_0_2692,refute_0_2713]) ).

cnf(refute_0_2715,plain,
    least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))) = least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2716,plain,
    ( least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))) != least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))
    | least_upper_bound(b,greatest_lower_bound(a,c)) != b
    | least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))) = least_upper_bound(X_427,b) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))),least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))) ),[1,1],$fot(b)]]) ).

cnf(refute_0_2717,plain,
    ( least_upper_bound(b,greatest_lower_bound(a,c)) != b
    | least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))) = least_upper_bound(X_427,b) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))),least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))) )],[refute_0_2715,refute_0_2716]) ).

cnf(refute_0_2718,plain,
    least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))) = least_upper_bound(X_427,b),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,c)),b) )],[refute_0_1021,refute_0_2717]) ).

cnf(refute_0_2719,plain,
    least_upper_bound(X_427,least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_427))) = least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_1045:[bind(X_15,$fot(X_427)),bind(X_55,$fot(b)),bind(X_56,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2720,plain,
    least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342)),
    inference(subst,[],[associativity_of_lub:[bind(Z,$fot(least_upper_bound(X_341,X_342)))]]) ).

cnf(refute_0_2721,plain,
    least_upper_bound(Y,least_upper_bound(X_341,X_342)) = least_upper_bound(X_341,least_upper_bound(Y,X_342)),
    inference(subst,[],[refute_0_2655:[bind(X_14,$fot(Y)),bind(X_15,$fot(X_341)),bind(X_16,$fot(X_342))]]) ).

cnf(refute_0_2722,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342))
    | least_upper_bound(Y,least_upper_bound(X_341,X_342)) != least_upper_bound(X_341,least_upper_bound(Y,X_342))
    | least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342))) ),[0,1],$fot(least_upper_bound(X_341,least_upper_bound(Y,X_342)))]]) ).

cnf(refute_0_2723,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342))
    | least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_341,X_342)),least_upper_bound(X_341,least_upper_bound(Y,X_342))) )],[refute_0_2721,refute_0_2722]) ).

cnf(refute_0_2724,plain,
    least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342))) )],[refute_0_2720,refute_0_2723]) ).

cnf(refute_0_2725,plain,
    least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342)) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342))),
    inference(subst,[],[refute_0_237:[bind(Z,$fot(least_upper_bound(X_341,X_342)))]]) ).

cnf(refute_0_2726,plain,
    ( least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342)) != least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342)))
    | least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342)))) ),[0],$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342)))]]) ).

cnf(refute_0_2727,plain,
    ( least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342))
    | least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342)),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342)))) )],[refute_0_2725,refute_0_2726]) ).

cnf(refute_0_2728,plain,
    least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))) = least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_341,X_342))) )],[refute_0_2724,refute_0_2727]) ).

cnf(refute_0_2729,plain,
    ( least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))) != least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342)))
    | least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342))) = least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))))),bind(Y0,$fot(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342)))))]]) ).

cnf(refute_0_2730,plain,
    least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342))) = least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_341,least_upper_bound(Y,X_342))),least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_341,X_342)))) )],[refute_0_2728,refute_0_2729]) ).

cnf(refute_0_2731,plain,
    least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))) = least_upper_bound(X_427,least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_427))),
    inference(subst,[],[refute_0_2730:[bind(X,$fot(X_427)),bind(Y,$fot(greatest_lower_bound(a,c))),bind(X_341,$fot(b)),bind(X_342,$fot(X_427))]]) ).

cnf(refute_0_2732,plain,
    ( least_upper_bound(X_427,least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_427))) != least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))
    | least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))) != least_upper_bound(X_427,least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_427)))
    | least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))) = least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))))),bind(Y0,$fot(least_upper_bound(X_427,least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_427))))),bind(Z0,$fot(least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2733,plain,
    ( least_upper_bound(X_427,least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_427))) != least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))
    | least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))) = least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))),least_upper_bound(X_427,least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_427)))) )],[refute_0_2731,refute_0_2732]) ).

cnf(refute_0_2734,plain,
    least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))) = least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_427,least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_427))),least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))) )],[refute_0_2719,refute_0_2733]) ).

cnf(refute_0_2735,plain,
    least_upper_bound(least_upper_bound(X_341,X_342),Y) = least_upper_bound(Y,least_upper_bound(X_341,X_342)),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(least_upper_bound(X_341,X_342)))]]) ).

cnf(refute_0_2736,plain,
    ( least_upper_bound(Y,least_upper_bound(X_341,X_342)) != least_upper_bound(X_341,least_upper_bound(Y,X_342))
    | least_upper_bound(least_upper_bound(X_341,X_342),Y) != least_upper_bound(Y,least_upper_bound(X_341,X_342))
    | least_upper_bound(least_upper_bound(X_341,X_342),Y) = least_upper_bound(X_341,least_upper_bound(Y,X_342)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_341,X_342),Y),least_upper_bound(Y,least_upper_bound(X_341,X_342))) ),[1],$fot(least_upper_bound(X_341,least_upper_bound(Y,X_342)))]]) ).

cnf(refute_0_2737,plain,
    ( least_upper_bound(least_upper_bound(X_341,X_342),Y) != least_upper_bound(Y,least_upper_bound(X_341,X_342))
    | least_upper_bound(least_upper_bound(X_341,X_342),Y) = least_upper_bound(X_341,least_upper_bound(Y,X_342)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_341,X_342)),least_upper_bound(X_341,least_upper_bound(Y,X_342))) )],[refute_0_2721,refute_0_2736]) ).

cnf(refute_0_2738,plain,
    least_upper_bound(least_upper_bound(X_341,X_342),Y) = least_upper_bound(X_341,least_upper_bound(Y,X_342)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_341,X_342),Y),least_upper_bound(Y,least_upper_bound(X_341,X_342))) )],[refute_0_2735,refute_0_2737]) ).

cnf(refute_0_2739,plain,
    least_upper_bound(least_upper_bound(X_341,X_342),Y) = least_upper_bound(X_341,least_upper_bound(X_342,Y)),
    inference(subst,[],[refute_0_237:[bind(X,$fot(X_341)),bind(Y,$fot(X_342)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_2740,plain,
    ( least_upper_bound(least_upper_bound(X_341,X_342),Y) != least_upper_bound(X_341,least_upper_bound(Y,X_342))
    | least_upper_bound(least_upper_bound(X_341,X_342),Y) != least_upper_bound(X_341,least_upper_bound(X_342,Y))
    | least_upper_bound(X_341,least_upper_bound(X_342,Y)) = least_upper_bound(X_341,least_upper_bound(Y,X_342)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_341,X_342),Y),least_upper_bound(X_341,least_upper_bound(Y,X_342))) ),[0],$fot(least_upper_bound(X_341,least_upper_bound(X_342,Y)))]]) ).

cnf(refute_0_2741,plain,
    ( least_upper_bound(least_upper_bound(X_341,X_342),Y) != least_upper_bound(X_341,least_upper_bound(Y,X_342))
    | least_upper_bound(X_341,least_upper_bound(X_342,Y)) = least_upper_bound(X_341,least_upper_bound(Y,X_342)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_341,X_342),Y),least_upper_bound(X_341,least_upper_bound(X_342,Y))) )],[refute_0_2739,refute_0_2740]) ).

cnf(refute_0_2742,plain,
    least_upper_bound(X_341,least_upper_bound(X_342,Y)) = least_upper_bound(X_341,least_upper_bound(Y,X_342)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_341,X_342),Y),least_upper_bound(X_341,least_upper_bound(Y,X_342))) )],[refute_0_2738,refute_0_2741]) ).

cnf(refute_0_2743,plain,
    ( least_upper_bound(X_341,least_upper_bound(X_342,Y)) != least_upper_bound(X_341,least_upper_bound(Y,X_342))
    | least_upper_bound(X_341,least_upper_bound(Y,X_342)) = least_upper_bound(X_341,least_upper_bound(X_342,Y)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(least_upper_bound(X_341,least_upper_bound(X_342,Y)))),bind(Y0,$fot(least_upper_bound(X_341,least_upper_bound(Y,X_342))))]]) ).

cnf(refute_0_2744,plain,
    least_upper_bound(X_341,least_upper_bound(Y,X_342)) = least_upper_bound(X_341,least_upper_bound(X_342,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_341,least_upper_bound(X_342,Y)),least_upper_bound(X_341,least_upper_bound(Y,X_342))) )],[refute_0_2742,refute_0_2743]) ).

cnf(refute_0_2745,plain,
    least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))) = least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))),
    inference(subst,[],[refute_0_2744:[bind(Y,$fot(least_upper_bound(b,X_427))),bind(X_341,$fot(X_427)),bind(X_342,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2746,plain,
    ( least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))) != least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))
    | least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))) != least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427)))
    | least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))) = least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))))),bind(Y0,$fot(least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))))),bind(Z0,$fot(least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2747,plain,
    ( least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))) != least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))
    | least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))) = least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))),least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427)))) )],[refute_0_2745,refute_0_2746]) ).

cnf(refute_0_2748,plain,
    least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))) = least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_427,least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X_427))),least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))) )],[refute_0_2734,refute_0_2747]) ).

cnf(refute_0_2749,plain,
    ( least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))) != least_upper_bound(X_427,b)
    | least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))) != least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))
    | least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))) = least_upper_bound(X_427,b) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))))),bind(Y0,$fot(least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))))),bind(Z0,$fot(least_upper_bound(X_427,b)))]]) ).

cnf(refute_0_2750,plain,
    ( least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))) != least_upper_bound(X_427,b)
    | least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))) = least_upper_bound(X_427,b) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))),least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c)))) )],[refute_0_2748,refute_0_2749]) ).

cnf(refute_0_2751,plain,
    least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))) = least_upper_bound(X_427,b),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_427,least_upper_bound(b,greatest_lower_bound(a,c))),least_upper_bound(X_427,b)) )],[refute_0_2718,refute_0_2750]) ).

cnf(refute_0_2752,plain,
    least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))) = least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2753,plain,
    ( least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))) != least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))))
    | least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))) != least_upper_bound(X_427,b)
    | least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))) = least_upper_bound(X,least_upper_bound(X_427,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))),least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))))) ),[1,1],$fot(least_upper_bound(X_427,b))]]) ).

cnf(refute_0_2754,plain,
    ( least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))) != least_upper_bound(X_427,b)
    | least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))) = least_upper_bound(X,least_upper_bound(X_427,b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))),least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))))) )],[refute_0_2752,refute_0_2753]) ).

cnf(refute_0_2755,plain,
    least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))) = least_upper_bound(X,least_upper_bound(X_427,b)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))),least_upper_bound(X_427,b)) )],[refute_0_2751,refute_0_2754]) ).

cnf(refute_0_2756,plain,
    least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))) = least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_2730:[bind(Y,$fot(least_upper_bound(b,X_427))),bind(X_341,$fot(X_427)),bind(X_342,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2757,plain,
    ( least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))) != least_upper_bound(X,least_upper_bound(X_427,b))
    | least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))) != least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))))
    | least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))) = least_upper_bound(X,least_upper_bound(X_427,b)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))))),bind(Y0,$fot(least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))))),bind(Z0,$fot(least_upper_bound(X,least_upper_bound(X_427,b))))]]) ).

cnf(refute_0_2758,plain,
    ( least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))) != least_upper_bound(X,least_upper_bound(X_427,b))
    | least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))) = least_upper_bound(X,least_upper_bound(X_427,b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))),least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c))))) )],[refute_0_2756,refute_0_2757]) ).

cnf(refute_0_2759,plain,
    least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))) = least_upper_bound(X,least_upper_bound(X_427,b)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_427,least_upper_bound(least_upper_bound(b,X_427),greatest_lower_bound(a,c)))),least_upper_bound(X,least_upper_bound(X_427,b))) )],[refute_0_2755,refute_0_2758]) ).

cnf(refute_0_2760,plain,
    ( least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))) != least_upper_bound(X,least_upper_bound(X_427,b))
    | least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))) != least_upper_bound(X,least_upper_bound(b,X_427))
    | least_upper_bound(X,least_upper_bound(X_427,b)) = least_upper_bound(X,least_upper_bound(b,X_427)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))),least_upper_bound(X,least_upper_bound(b,X_427))) ),[0],$fot(least_upper_bound(X,least_upper_bound(X_427,b)))]]) ).

cnf(refute_0_2761,plain,
    ( least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))) != least_upper_bound(X,least_upper_bound(b,X_427))
    | least_upper_bound(X,least_upper_bound(X_427,b)) = least_upper_bound(X,least_upper_bound(b,X_427)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))),least_upper_bound(X,least_upper_bound(X_427,b))) )],[refute_0_2759,refute_0_2760]) ).

cnf(refute_0_2762,plain,
    least_upper_bound(X,least_upper_bound(X_427,b)) = least_upper_bound(X,least_upper_bound(b,X_427)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(b,X_427),least_upper_bound(X_427,greatest_lower_bound(a,c)))),least_upper_bound(X,least_upper_bound(b,X_427))) )],[refute_0_2714,refute_0_2761]) ).

cnf(refute_0_2763,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)) = least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)),
    inference(subst,[],[refute_0_2762:[bind(X,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))),bind(X_427,$fot(c))]]) ).

cnf(refute_0_2764,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)) != least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)))),bind(Z0,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_2765,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)),least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c))) )],[refute_0_2763,refute_0_2764]) ).

cnf(refute_0_2766,plain,
    least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)) = inverse(greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(b,c)),inverse(greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_2691,refute_0_2765]) ).

cnf(refute_0_2767,plain,
    least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) = least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)),
    inference(subst,[],[refute_0_2683:[bind(Z,$fot(least_upper_bound(c,b)))]]) ).

cnf(refute_0_2768,plain,
    ( least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) != least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))
    | least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)))),bind(Z0,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_2769,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))),least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) )],[refute_0_2767,refute_0_2768]) ).

cnf(refute_0_2770,plain,
    least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) = inverse(greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b)),inverse(greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_2766,refute_0_2769]) ).

cnf(refute_0_2771,plain,
    ( least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))
    | inverse(greatest_lower_bound(inverse(b),inverse(c))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))),least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) ),[0],$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))]]) ).

cnf(refute_0_2772,plain,
    ( least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))
    | inverse(greatest_lower_bound(inverse(b),inverse(c))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))),inverse(greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_2770,refute_0_2771]) ).

cnf(refute_0_2773,plain,
    least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))) = least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_2774,plain,
    ( least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))
    | least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))) = least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))),least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) ),[1,1],$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))]]) ).

cnf(refute_0_2775,plain,
    ( least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))) = least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))),least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) )],[refute_0_2773,refute_0_2774]) ).

cnf(refute_0_2776,plain,
    least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))) = least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_2316,refute_0_2775]) ).

cnf(refute_0_2777,plain,
    ( inverse(greatest_lower_bound(inverse(b),inverse(c))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))
    | least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))) != least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | inverse(greatest_lower_bound(inverse(b),inverse(c))) = least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) ),[0],$fot(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_2778,plain,
    ( inverse(greatest_lower_bound(inverse(b),inverse(c))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))
    | inverse(greatest_lower_bound(inverse(b),inverse(c))) = least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c))))),least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_2776,refute_0_2777]) ).

cnf(refute_0_2779,plain,
    ( least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))) != least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))
    | inverse(greatest_lower_bound(inverse(b),inverse(c))) = least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) )],[refute_0_2772,refute_0_2778]) ).

cnf(refute_0_2780,plain,
    inverse(greatest_lower_bound(inverse(b),inverse(c))) = least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(c,b))),least_upper_bound(a,least_upper_bound(c,inverse(greatest_lower_bound(inverse(b),inverse(c)))))) )],[refute_0_2174,refute_0_2779]) ).

cnf(refute_0_2781,plain,
    ( inverse(greatest_lower_bound(inverse(b),inverse(c))) != least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))
    | least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) = inverse(greatest_lower_bound(inverse(b),inverse(c))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))),bind(Y0,$fot(least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))))]]) ).

cnf(refute_0_2782,plain,
    least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) = inverse(greatest_lower_bound(inverse(b),inverse(c))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(b),inverse(c))),least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) )],[refute_0_2780,refute_0_2781]) ).

cnf(refute_0_2783,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),X_40)) != greatest_lower_bound(a,X_40)
    | least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) != inverse(greatest_lower_bound(inverse(b),inverse(c)))
    | greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X_40)) = greatest_lower_bound(a,X_40) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),X_40)),greatest_lower_bound(a,X_40)) ),[0,1,0],$fot(inverse(greatest_lower_bound(inverse(b),inverse(c))))]]) ).

cnf(refute_0_2784,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),X_40)) != greatest_lower_bound(a,X_40)
    | greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X_40)) = greatest_lower_bound(a,X_40) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),inverse(greatest_lower_bound(inverse(b),inverse(c)))) )],[refute_0_2782,refute_0_2783]) ).

cnf(refute_0_2785,plain,
    greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X_40)) = greatest_lower_bound(a,X_40),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),X_40)),greatest_lower_bound(a,X_40)) )],[refute_0_1631,refute_0_2784]) ).

cnf(refute_0_2786,plain,
    greatest_lower_bound(X,greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) = greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X)),
    inference(subst,[],[refute_0_346:[bind(X_38,$fot(a)),bind(X_39,$fot(inverse(greatest_lower_bound(inverse(b),inverse(c)))))]]) ).

cnf(refute_0_2787,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) != greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X))
    | greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))) != b
    | greatest_lower_bound(X,b) = greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X))) ),[0,1],$fot(b)]]) ).

cnf(refute_0_2788,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))) != greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X))
    | greatest_lower_bound(X,b) = greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c)))),b) )],[refute_0_1714,refute_0_2787]) ).

cnf(refute_0_2789,plain,
    greatest_lower_bound(X,b) = greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(a,inverse(greatest_lower_bound(inverse(b),inverse(c))))),greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X))) )],[refute_0_2786,refute_0_2788]) ).

cnf(refute_0_2790,plain,
    ( greatest_lower_bound(X,b) != greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X))
    | greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X)) = greatest_lower_bound(X,b) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(greatest_lower_bound(X,b))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X))))]]) ).

cnf(refute_0_2791,plain,
    greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X)) = greatest_lower_bound(X,b),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,b),greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X))) )],[refute_0_2789,refute_0_2790]) ).

cnf(refute_0_2792,plain,
    greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X_40)) = greatest_lower_bound(X_40,b),
    inference(subst,[],[refute_0_2791:[bind(X,$fot(X_40))]]) ).

cnf(refute_0_2793,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X_40)) != greatest_lower_bound(X_40,b)
    | greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X_40)) != greatest_lower_bound(a,X_40)
    | greatest_lower_bound(X_40,b) = greatest_lower_bound(a,X_40) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X_40)),greatest_lower_bound(a,X_40)) ),[0],$fot(greatest_lower_bound(X_40,b))]]) ).

cnf(refute_0_2794,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X_40)) != greatest_lower_bound(a,X_40)
    | greatest_lower_bound(X_40,b) = greatest_lower_bound(a,X_40) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X_40)),greatest_lower_bound(X_40,b)) )],[refute_0_2792,refute_0_2793]) ).

cnf(refute_0_2795,plain,
    greatest_lower_bound(X_40,b) = greatest_lower_bound(a,X_40),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(inverse(greatest_lower_bound(inverse(b),inverse(c))),X_40)),greatest_lower_bound(a,X_40)) )],[refute_0_2785,refute_0_2794]) ).

cnf(refute_0_2796,plain,
    greatest_lower_bound(a,b) = greatest_lower_bound(a,a),
    inference(subst,[],[refute_0_2795:[bind(X_40,$fot(a))]]) ).

cnf(refute_0_2797,plain,
    ( greatest_lower_bound(a,a) != a
    | greatest_lower_bound(a,b) != greatest_lower_bound(a,a)
    | greatest_lower_bound(a,b) = a ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(greatest_lower_bound(a,b))),bind(Y0,$fot(greatest_lower_bound(a,a))),bind(Z0,$fot(a))]]) ).

cnf(refute_0_2798,plain,
    ( greatest_lower_bound(a,a) != a
    | greatest_lower_bound(a,b) = a ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),greatest_lower_bound(a,a)) )],[refute_0_2796,refute_0_2797]) ).

cnf(refute_0_2799,plain,
    greatest_lower_bound(a,b) = a,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,a),a) )],[refute_0_1625,refute_0_2798]) ).

cnf(refute_0_2800,plain,
    ( b != greatest_lower_bound(a,b)
    | greatest_lower_bound(a,b) != a
    | b = a ),
    introduced(tautology,[equality,[$cnf( ~ $equal(b,a) ),[0],$fot(greatest_lower_bound(a,b))]]) ).

cnf(refute_0_2801,plain,
    ( b != greatest_lower_bound(a,b)
    | b = a ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),a) )],[refute_0_2799,refute_0_2800]) ).

cnf(refute_0_2802,plain,
    b = a,
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(a,b)) )],[refute_0_1624,refute_0_2801]) ).

cnf(refute_0_2803,plain,
    ( b != a
    | a = b ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(b)),bind(Y0,$fot(a))]]) ).

cnf(refute_0_2804,plain,
    b != a,
    inference(resolve,[$cnf( $equal(a,b) )],[refute_0_2803,prove_p12]) ).

cnf(refute_0_2805,plain,
    $false,
    inference(resolve,[$cnf( $equal(b,a) )],[refute_0_2802,refute_0_2804]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : GRP181-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.14  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n019.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue Jun 14 07:37:54 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 41.82/42.05  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.82/42.05  
% 41.82/42.05  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 42.12/42.32  
%------------------------------------------------------------------------------