%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP180-2 : 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 10:37:26 EDT 2022

% Result   : Unsatisfiable 205.27s 205.50s
% Output   : CNFRefutation 205.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :  112
%            Number of leaves      :  462
% Syntax   : Number of clauses     : 2141 (1107 unt;   0 nHn;1006 RR)
%            Number of literals    : 3623 (3622 equ;1484 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   : 4663 (  36 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(p11_1,hypothesis,
    inverse(identity) = identity ).

cnf(p11_2,hypothesis,
    inverse(inverse(X)) = X ).

cnf(p11_3,hypothesis,
    inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ).

cnf(prove_p11,negated_conjecture,
    multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != least_upper_bound(a,b) ).

cnf(refute_0_0,plain,
    multiply(inverse(X_67),least_upper_bound(X_116,multiply(X_67,X_68))) = least_upper_bound(multiply(inverse(X_67),X_116),multiply(inverse(X_67),multiply(X_67,X_68))),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_67))),bind(Y,$fot(X_116)),bind(Z,$fot(multiply(X_67,X_68)))]]) ).

cnf(refute_0_1,plain,
    multiply(multiply(inverse(X_67),X_67),X_68) = multiply(inverse(X_67),multiply(X_67,X_68)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_67))),bind(Y,$fot(X_67)),bind(Z,$fot(X_68))]]) ).

cnf(refute_0_2,plain,
    multiply(inverse(X_67),X_67) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_67))]]) ).

cnf(refute_0_3,plain,
    ( multiply(multiply(inverse(X_67),X_67),X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
    | multiply(inverse(X_67),X_67) != identity
    | multiply(identity,X_68) = multiply(inverse(X_67),multiply(X_67,X_68)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_67),X_67),X_68),multiply(inverse(X_67),multiply(X_67,X_68))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_4,plain,
    ( multiply(multiply(inverse(X_67),X_67),X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
    | multiply(identity,X_68) = multiply(inverse(X_67),multiply(X_67,X_68)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_67),X_67),identity) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    multiply(identity,X_68) = multiply(inverse(X_67),multiply(X_67,X_68)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_67),X_67),X_68),multiply(inverse(X_67),multiply(X_67,X_68))) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    multiply(identity,X_68) = X_68,
    inference(subst,[],[left_identity:[bind(X,$fot(X_68))]]) ).

cnf(refute_0_7,plain,
    ( multiply(identity,X_68) != X_68
    | multiply(identity,X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
    | X_68 = multiply(inverse(X_67),multiply(X_67,X_68)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_68),multiply(inverse(X_67),multiply(X_67,X_68))) ),[0],$fot(X_68)]]) ).

cnf(refute_0_8,plain,
    ( multiply(identity,X_68) != multiply(inverse(X_67),multiply(X_67,X_68))
    | X_68 = multiply(inverse(X_67),multiply(X_67,X_68)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_68),X_68) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    X_68 = multiply(inverse(X_67),multiply(X_67,X_68)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_68),multiply(inverse(X_67),multiply(X_67,X_68))) )],[refute_0_5,refute_0_8]) ).

cnf(refute_0_10,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_11,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_12,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( X_68 != multiply(inverse(X_67),multiply(X_67,X_68))
    | multiply(inverse(X_67),multiply(X_67,X_68)) = X_68 ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X_68)),bind(Y0,$fot(multiply(inverse(X_67),multiply(X_67,X_68))))]]) ).

cnf(refute_0_14,plain,
    multiply(inverse(X_67),multiply(X_67,X_68)) = X_68,
    inference(resolve,[$cnf( $equal(X_68,multiply(inverse(X_67),multiply(X_67,X_68))) )],[refute_0_9,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( multiply(inverse(X_67),multiply(X_67,X_68)) != X_68
    | multiply(inverse(X_67),least_upper_bound(X_116,multiply(X_67,X_68))) != least_upper_bound(multiply(inverse(X_67),X_116),multiply(inverse(X_67),multiply(X_67,X_68)))
    | multiply(inverse(X_67),least_upper_bound(X_116,multiply(X_67,X_68))) = least_upper_bound(multiply(inverse(X_67),X_116),X_68) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_67),least_upper_bound(X_116,multiply(X_67,X_68))),least_upper_bound(multiply(inverse(X_67),X_116),multiply(inverse(X_67),multiply(X_67,X_68)))) ),[1,1],$fot(X_68)]]) ).

cnf(refute_0_16,plain,
    ( multiply(inverse(X_67),least_upper_bound(X_116,multiply(X_67,X_68))) != least_upper_bound(multiply(inverse(X_67),X_116),multiply(inverse(X_67),multiply(X_67,X_68)))
    | multiply(inverse(X_67),least_upper_bound(X_116,multiply(X_67,X_68))) = least_upper_bound(multiply(inverse(X_67),X_116),X_68) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_67),multiply(X_67,X_68)),X_68) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    multiply(inverse(X_67),least_upper_bound(X_116,multiply(X_67,X_68))) = least_upper_bound(multiply(inverse(X_67),X_116),X_68),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_67),least_upper_bound(X_116,multiply(X_67,X_68))),least_upper_bound(multiply(inverse(X_67),X_116),multiply(inverse(X_67),multiply(X_67,X_68)))) )],[refute_0_0,refute_0_16]) ).

cnf(refute_0_18,plain,
    multiply(inverse(inverse(X_775)),least_upper_bound(identity,multiply(inverse(X_775),X_68))) = least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68),
    inference(subst,[],[refute_0_17:[bind(X_116,$fot(identity)),bind(X_67,$fot(inverse(X_775)))]]) ).

cnf(refute_0_19,plain,
    inverse(multiply(inverse(X),X_30)) = multiply(inverse(X_30),inverse(inverse(X))),
    inference(subst,[],[p11_3:[bind(X,$fot(inverse(X))),bind(Y,$fot(X_30))]]) ).

cnf(refute_0_20,plain,
    ( inverse(multiply(inverse(X),X_30)) != multiply(inverse(X_30),inverse(inverse(X)))
    | inverse(inverse(X)) != X
    | inverse(multiply(inverse(X),X_30)) = multiply(inverse(X_30),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),X_30)),multiply(inverse(X_30),inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).

cnf(refute_0_21,plain,
    ( inverse(multiply(inverse(X),X_30)) != multiply(inverse(X_30),inverse(inverse(X)))
    | inverse(multiply(inverse(X),X_30)) = multiply(inverse(X_30),X) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p11_2,refute_0_20]) ).

cnf(refute_0_22,plain,
    inverse(multiply(inverse(X),X_30)) = multiply(inverse(X_30),X),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),X_30)),multiply(inverse(X_30),inverse(inverse(X)))) )],[refute_0_19,refute_0_21]) ).

cnf(refute_0_23,plain,
    inverse(multiply(inverse(X),greatest_lower_bound(X_83,inverse(inverse(X))))) = multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X),
    inference(subst,[],[refute_0_22:[bind(X_30,$fot(greatest_lower_bound(X_83,inverse(inverse(X)))))]]) ).

cnf(refute_0_24,plain,
    multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))) = greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,inverse(X_79))),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_79)),bind(Y,$fot(X_80)),bind(Z,$fot(inverse(X_79)))]]) ).

cnf(refute_0_25,plain,
    multiply(inverse(inverse(X_1)),inverse(X_1)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_1)))]]) ).

cnf(refute_0_26,plain,
    inverse(inverse(X_1)) = X_1,
    inference(subst,[],[p11_2:[bind(X,$fot(X_1))]]) ).

cnf(refute_0_27,plain,
    ( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
    | inverse(inverse(X_1)) != X_1
    | multiply(X_1,inverse(X_1)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) ),[0,0],$fot(X_1)]]) ).

cnf(refute_0_28,plain,
    ( multiply(inverse(inverse(X_1)),inverse(X_1)) != identity
    | multiply(X_1,inverse(X_1)) = identity ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_1)),X_1) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    multiply(X_1,inverse(X_1)) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) )],[refute_0_25,refute_0_28]) ).

cnf(refute_0_30,plain,
    multiply(X_79,inverse(X_79)) = identity,
    inference(subst,[],[refute_0_29:[bind(X_1,$fot(X_79))]]) ).

cnf(refute_0_31,plain,
    ( multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))) != greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,inverse(X_79)))
    | multiply(X_79,inverse(X_79)) != identity
    | multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))) = greatest_lower_bound(multiply(X_79,X_80),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,inverse(X_79)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_32,plain,
    ( multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))) != greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,inverse(X_79)))
    | multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))) = greatest_lower_bound(multiply(X_79,X_80),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_79,inverse(X_79)),identity) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))) = greatest_lower_bound(multiply(X_79,X_80),identity),
    inference(resolve,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,inverse(X_79)))) )],[refute_0_24,refute_0_32]) ).

cnf(refute_0_34,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_12:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).

cnf(refute_0_35,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_34]) ).

cnf(refute_0_36,plain,
    greatest_lower_bound(multiply(X_79,X_80),identity) = greatest_lower_bound(identity,multiply(X_79,X_80)),
    inference(subst,[],[refute_0_35:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_79,X_80)))]]) ).

cnf(refute_0_37,plain,
    ( multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))) != greatest_lower_bound(multiply(X_79,X_80),identity)
    | greatest_lower_bound(multiply(X_79,X_80),identity) != greatest_lower_bound(identity,multiply(X_79,X_80))
    | multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))) = greatest_lower_bound(identity,multiply(X_79,X_80)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))),greatest_lower_bound(identity,multiply(X_79,X_80))) ),[0],$fot(greatest_lower_bound(multiply(X_79,X_80),identity))]]) ).

cnf(refute_0_38,plain,
    ( multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))) != greatest_lower_bound(multiply(X_79,X_80),identity)
    | multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))) = greatest_lower_bound(identity,multiply(X_79,X_80)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_80),identity),greatest_lower_bound(identity,multiply(X_79,X_80))) )],[refute_0_36,refute_0_37]) ).

cnf(refute_0_39,plain,
    multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))) = greatest_lower_bound(identity,multiply(X_79,X_80)),
    inference(resolve,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_80,inverse(X_79))),greatest_lower_bound(multiply(X_79,X_80),identity)) )],[refute_0_33,refute_0_38]) ).

cnf(refute_0_40,plain,
    multiply(inverse(X),greatest_lower_bound(X_83,inverse(inverse(X)))) = greatest_lower_bound(identity,multiply(inverse(X),X_83)),
    inference(subst,[],[refute_0_39:[bind(X_79,$fot(inverse(X))),bind(X_80,$fot(X_83))]]) ).

cnf(refute_0_41,plain,
    ( multiply(inverse(X),greatest_lower_bound(X_83,inverse(inverse(X)))) != greatest_lower_bound(identity,multiply(inverse(X),X_83))
    | inverse(multiply(inverse(X),greatest_lower_bound(X_83,inverse(inverse(X))))) != multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) = multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_83,inverse(inverse(X))))),multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X)) ),[0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X),X_83)))]]) ).

cnf(refute_0_42,plain,
    ( inverse(multiply(inverse(X),greatest_lower_bound(X_83,inverse(inverse(X))))) != multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) = multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X),greatest_lower_bound(X_83,inverse(inverse(X)))),greatest_lower_bound(identity,multiply(inverse(X),X_83))) )],[refute_0_40,refute_0_41]) ).

cnf(refute_0_43,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) = multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_83,inverse(inverse(X))))),multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X)) )],[refute_0_23,refute_0_42]) ).

cnf(refute_0_44,plain,
    greatest_lower_bound(X_83,inverse(inverse(X))) = greatest_lower_bound(X_83,inverse(inverse(X))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_83,inverse(inverse(X))))]]) ).

cnf(refute_0_45,plain,
    ( greatest_lower_bound(X_83,inverse(inverse(X))) != greatest_lower_bound(X_83,inverse(inverse(X)))
    | inverse(inverse(X)) != X
    | greatest_lower_bound(X_83,inverse(inverse(X))) = greatest_lower_bound(X_83,X) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_83,inverse(inverse(X))),greatest_lower_bound(X_83,inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).

cnf(refute_0_46,plain,
    ( inverse(inverse(X)) != X
    | greatest_lower_bound(X_83,inverse(inverse(X))) = greatest_lower_bound(X_83,X) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_83,inverse(inverse(X))),greatest_lower_bound(X_83,inverse(inverse(X)))) )],[refute_0_44,refute_0_45]) ).

cnf(refute_0_47,plain,
    greatest_lower_bound(X_83,inverse(inverse(X))) = greatest_lower_bound(X_83,X),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p11_2,refute_0_46]) ).

cnf(refute_0_48,plain,
    inverse(greatest_lower_bound(X_83,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))))]]) ).

cnf(refute_0_49,plain,
    ( greatest_lower_bound(X_83,inverse(inverse(X))) != greatest_lower_bound(X_83,X)
    | inverse(greatest_lower_bound(X_83,inverse(inverse(X)))) != inverse(greatest_lower_bound(X_83,inverse(inverse(X))))
    | inverse(greatest_lower_bound(X_83,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_83,X)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),inverse(greatest_lower_bound(X_83,inverse(inverse(X))))) ),[1,0],$fot(greatest_lower_bound(X_83,X))]]) ).

cnf(refute_0_50,plain,
    ( greatest_lower_bound(X_83,inverse(inverse(X))) != greatest_lower_bound(X_83,X)
    | inverse(greatest_lower_bound(X_83,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_83,X)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),inverse(greatest_lower_bound(X_83,inverse(inverse(X))))) )],[refute_0_48,refute_0_49]) ).

cnf(refute_0_51,plain,
    inverse(greatest_lower_bound(X_83,inverse(inverse(X)))) = inverse(greatest_lower_bound(X_83,X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_83,inverse(inverse(X))),greatest_lower_bound(X_83,X)) )],[refute_0_47,refute_0_50]) ).

cnf(refute_0_52,plain,
    multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X) = multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X))]]) ).

cnf(refute_0_53,plain,
    ( multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X) != multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X)
    | inverse(greatest_lower_bound(X_83,inverse(inverse(X)))) != inverse(greatest_lower_bound(X_83,X))
    | multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X) = multiply(inverse(greatest_lower_bound(X_83,X)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X),multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X)) ),[1,0],$fot(inverse(greatest_lower_bound(X_83,X)))]]) ).

cnf(refute_0_54,plain,
    ( inverse(greatest_lower_bound(X_83,inverse(inverse(X)))) != inverse(greatest_lower_bound(X_83,X))
    | multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X) = multiply(inverse(greatest_lower_bound(X_83,X)),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X),multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X)) )],[refute_0_52,refute_0_53]) ).

cnf(refute_0_55,plain,
    multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X) = multiply(inverse(greatest_lower_bound(X_83,X)),X),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),inverse(greatest_lower_bound(X_83,X))) )],[refute_0_51,refute_0_54]) ).

cnf(refute_0_56,plain,
    ( multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X) != multiply(inverse(greatest_lower_bound(X_83,X)),X)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) != multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) = multiply(inverse(greatest_lower_bound(X_83,X)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))),multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X)) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_83,X)),X))]]) ).

cnf(refute_0_57,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) != multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) = multiply(inverse(greatest_lower_bound(X_83,X)),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X),multiply(inverse(greatest_lower_bound(X_83,X)),X)) )],[refute_0_55,refute_0_56]) ).

cnf(refute_0_58,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) = multiply(inverse(greatest_lower_bound(X_83,X)),X),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))),multiply(inverse(greatest_lower_bound(X_83,inverse(inverse(X)))),X)) )],[refute_0_43,refute_0_57]) ).

cnf(refute_0_59,plain,
    multiply(least_upper_bound(X_121,X_122),inverse(X_122)) = least_upper_bound(multiply(X_121,inverse(X_122)),multiply(X_122,inverse(X_122))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_122))),bind(Y,$fot(X_121)),bind(Z,$fot(X_122))]]) ).

cnf(refute_0_60,plain,
    multiply(X_122,inverse(X_122)) = identity,
    inference(subst,[],[refute_0_29:[bind(X_1,$fot(X_122))]]) ).

cnf(refute_0_61,plain,
    ( multiply(X_122,inverse(X_122)) != identity
    | multiply(least_upper_bound(X_121,X_122),inverse(X_122)) != least_upper_bound(multiply(X_121,inverse(X_122)),multiply(X_122,inverse(X_122)))
    | multiply(least_upper_bound(X_121,X_122),inverse(X_122)) = least_upper_bound(multiply(X_121,inverse(X_122)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_121,X_122),inverse(X_122)),least_upper_bound(multiply(X_121,inverse(X_122)),multiply(X_122,inverse(X_122)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_62,plain,
    ( multiply(least_upper_bound(X_121,X_122),inverse(X_122)) != least_upper_bound(multiply(X_121,inverse(X_122)),multiply(X_122,inverse(X_122)))
    | multiply(least_upper_bound(X_121,X_122),inverse(X_122)) = least_upper_bound(multiply(X_121,inverse(X_122)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_122,inverse(X_122)),identity) )],[refute_0_60,refute_0_61]) ).

cnf(refute_0_63,plain,
    multiply(least_upper_bound(X_121,X_122),inverse(X_122)) = least_upper_bound(multiply(X_121,inverse(X_122)),identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,X_122),inverse(X_122)),least_upper_bound(multiply(X_121,inverse(X_122)),multiply(X_122,inverse(X_122)))) )],[refute_0_59,refute_0_62]) ).

cnf(refute_0_64,plain,
    least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_11,X_26),X_28)) = least_upper_bound(least_upper_bound(X_26,greatest_lower_bound(X_11,X_26)),X_28),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_26)),bind(Y,$fot(greatest_lower_bound(X_11,X_26))),bind(Z,$fot(X_28))]]) ).

cnf(refute_0_65,plain,
    least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) = X_10,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).

cnf(refute_0_66,plain,
    greatest_lower_bound(X_11,X_10) = greatest_lower_bound(X_10,X_11),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).

cnf(refute_0_67,plain,
    ( greatest_lower_bound(X_11,X_10) != greatest_lower_bound(X_10,X_11)
    | greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_11,X_10))),bind(Y0,$fot(greatest_lower_bound(X_10,X_11)))]]) ).

cnf(refute_0_68,plain,
    greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,X_10),greatest_lower_bound(X_10,X_11)) )],[refute_0_66,refute_0_67]) ).

cnf(refute_0_69,plain,
    ( greatest_lower_bound(X_10,X_11) != greatest_lower_bound(X_11,X_10)
    | least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
    | least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) ),[0,1],$fot(greatest_lower_bound(X_11,X_10))]]) ).

cnf(refute_0_70,plain,
    ( least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
    | least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,X_11),greatest_lower_bound(X_11,X_10)) )],[refute_0_68,refute_0_69]) ).

cnf(refute_0_71,plain,
    least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10,
    inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) )],[refute_0_65,refute_0_70]) ).

cnf(refute_0_72,plain,
    least_upper_bound(X_26,greatest_lower_bound(X_11,X_26)) = X_26,
    inference(subst,[],[refute_0_71:[bind(X_10,$fot(X_26))]]) ).

cnf(refute_0_73,plain,
    ( least_upper_bound(X_26,greatest_lower_bound(X_11,X_26)) != X_26
    | least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_11,X_26),X_28)) != least_upper_bound(least_upper_bound(X_26,greatest_lower_bound(X_11,X_26)),X_28)
    | least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_11,X_26),X_28)) = least_upper_bound(X_26,X_28) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_11,X_26),X_28)),least_upper_bound(least_upper_bound(X_26,greatest_lower_bound(X_11,X_26)),X_28)) ),[1,0],$fot(X_26)]]) ).

cnf(refute_0_74,plain,
    ( least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_11,X_26),X_28)) != least_upper_bound(least_upper_bound(X_26,greatest_lower_bound(X_11,X_26)),X_28)
    | least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_11,X_26),X_28)) = least_upper_bound(X_26,X_28) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,greatest_lower_bound(X_11,X_26)),X_26) )],[refute_0_72,refute_0_73]) ).

cnf(refute_0_75,plain,
    least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_11,X_26),X_28)) = least_upper_bound(X_26,X_28),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_11,X_26),X_28)),least_upper_bound(least_upper_bound(X_26,greatest_lower_bound(X_11,X_26)),X_28)) )],[refute_0_64,refute_0_74]) ).

cnf(refute_0_76,plain,
    least_upper_bound(multiply(X_11,X_113),least_upper_bound(greatest_lower_bound(X_11,multiply(X_11,X_113)),X_28)) = least_upper_bound(multiply(X_11,X_113),X_28),
    inference(subst,[],[refute_0_75:[bind(X_26,$fot(multiply(X_11,X_113)))]]) ).

cnf(refute_0_77,plain,
    multiply(X_79,greatest_lower_bound(X_80,identity)) = greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,identity)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_79)),bind(Y,$fot(X_80)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_78,plain,
    inverse(multiply(identity,X_30)) = multiply(inverse(X_30),inverse(identity)),
    inference(subst,[],[p11_3:[bind(X,$fot(identity)),bind(Y,$fot(X_30))]]) ).

cnf(refute_0_79,plain,
    ( inverse(multiply(identity,X_30)) != multiply(inverse(X_30),inverse(identity))
    | inverse(identity) != identity
    | inverse(multiply(identity,X_30)) = multiply(inverse(X_30),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_30)),multiply(inverse(X_30),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_80,plain,
    ( inverse(multiply(identity,X_30)) != multiply(inverse(X_30),inverse(identity))
    | inverse(multiply(identity,X_30)) = multiply(inverse(X_30),identity) ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p11_1,refute_0_79]) ).

cnf(refute_0_81,plain,
    inverse(multiply(identity,X_30)) = multiply(inverse(X_30),identity),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_30)),multiply(inverse(X_30),inverse(identity))) )],[refute_0_78,refute_0_80]) ).

cnf(refute_0_82,plain,
    multiply(identity,X_30) = X_30,
    inference(subst,[],[left_identity:[bind(X,$fot(X_30))]]) ).

cnf(refute_0_83,plain,
    inverse(multiply(identity,X_30)) = inverse(multiply(identity,X_30)),
    introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_30)))]]) ).

cnf(refute_0_84,plain,
    ( multiply(identity,X_30) != X_30
    | inverse(multiply(identity,X_30)) != inverse(multiply(identity,X_30))
    | inverse(multiply(identity,X_30)) = inverse(X_30) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_30)),inverse(multiply(identity,X_30))) ),[1,0],$fot(X_30)]]) ).

cnf(refute_0_85,plain,
    ( multiply(identity,X_30) != X_30
    | inverse(multiply(identity,X_30)) = inverse(X_30) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_30)),inverse(multiply(identity,X_30))) )],[refute_0_83,refute_0_84]) ).

cnf(refute_0_86,plain,
    inverse(multiply(identity,X_30)) = inverse(X_30),
    inference(resolve,[$cnf( $equal(multiply(identity,X_30),X_30) )],[refute_0_82,refute_0_85]) ).

cnf(refute_0_87,plain,
    ( inverse(multiply(identity,X_30)) != multiply(inverse(X_30),identity)
    | inverse(multiply(identity,X_30)) != inverse(X_30)
    | inverse(X_30) = multiply(inverse(X_30),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_30)),multiply(inverse(X_30),identity)) ),[0],$fot(inverse(X_30))]]) ).

cnf(refute_0_88,plain,
    ( inverse(multiply(identity,X_30)) != multiply(inverse(X_30),identity)
    | inverse(X_30) = multiply(inverse(X_30),identity) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_30)),inverse(X_30)) )],[refute_0_86,refute_0_87]) ).

cnf(refute_0_89,plain,
    inverse(X_30) = multiply(inverse(X_30),identity),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_30)),multiply(inverse(X_30),identity)) )],[refute_0_81,refute_0_88]) ).

cnf(refute_0_90,plain,
    inverse(inverse(X)) = multiply(inverse(inverse(X)),identity),
    inference(subst,[],[refute_0_89:[bind(X_30,$fot(inverse(X)))]]) ).

cnf(refute_0_91,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_92,plain,
    ( inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
    | inverse(inverse(X)) = multiply(X,identity) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p11_2,refute_0_91]) ).

cnf(refute_0_93,plain,
    inverse(inverse(X)) = multiply(X,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) )],[refute_0_90,refute_0_92]) ).

cnf(refute_0_94,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_95,plain,
    ( inverse(inverse(X)) != multiply(X,identity)
    | X = multiply(X,identity) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p11_2,refute_0_94]) ).

cnf(refute_0_96,plain,
    X = multiply(X,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) )],[refute_0_93,refute_0_95]) ).

cnf(refute_0_97,plain,
    X_79 = multiply(X_79,identity),
    inference(subst,[],[refute_0_96:[bind(X,$fot(X_79))]]) ).

cnf(refute_0_98,plain,
    ( X_79 != multiply(X_79,identity)
    | multiply(X_79,identity) = X_79 ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X_79)),bind(Y0,$fot(multiply(X_79,identity)))]]) ).

cnf(refute_0_99,plain,
    multiply(X_79,identity) = X_79,
    inference(resolve,[$cnf( $equal(X_79,multiply(X_79,identity)) )],[refute_0_97,refute_0_98]) ).

cnf(refute_0_100,plain,
    ( multiply(X_79,greatest_lower_bound(X_80,identity)) != greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,identity))
    | multiply(X_79,identity) != X_79
    | multiply(X_79,greatest_lower_bound(X_80,identity)) = greatest_lower_bound(multiply(X_79,X_80),X_79) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_80,identity)),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,identity))) ),[1,1],$fot(X_79)]]) ).

cnf(refute_0_101,plain,
    ( multiply(X_79,greatest_lower_bound(X_80,identity)) != greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,identity))
    | multiply(X_79,greatest_lower_bound(X_80,identity)) = greatest_lower_bound(multiply(X_79,X_80),X_79) ),
    inference(resolve,[$cnf( $equal(multiply(X_79,identity),X_79) )],[refute_0_99,refute_0_100]) ).

cnf(refute_0_102,plain,
    multiply(X_79,greatest_lower_bound(X_80,identity)) = greatest_lower_bound(multiply(X_79,X_80),X_79),
    inference(resolve,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_80,identity)),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,identity))) )],[refute_0_77,refute_0_101]) ).

cnf(refute_0_103,plain,
    greatest_lower_bound(multiply(X_79,X_80),X_79) = greatest_lower_bound(X_79,multiply(X_79,X_80)),
    inference(subst,[],[refute_0_35:[bind(X,$fot(X_79)),bind(Y,$fot(multiply(X_79,X_80)))]]) ).

cnf(refute_0_104,plain,
    ( multiply(X_79,greatest_lower_bound(X_80,identity)) != greatest_lower_bound(multiply(X_79,X_80),X_79)
    | greatest_lower_bound(multiply(X_79,X_80),X_79) != greatest_lower_bound(X_79,multiply(X_79,X_80))
    | multiply(X_79,greatest_lower_bound(X_80,identity)) = greatest_lower_bound(X_79,multiply(X_79,X_80)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_79,greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_79,multiply(X_79,X_80))) ),[0],$fot(greatest_lower_bound(multiply(X_79,X_80),X_79))]]) ).

cnf(refute_0_105,plain,
    ( multiply(X_79,greatest_lower_bound(X_80,identity)) != greatest_lower_bound(multiply(X_79,X_80),X_79)
    | multiply(X_79,greatest_lower_bound(X_80,identity)) = greatest_lower_bound(X_79,multiply(X_79,X_80)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_80),X_79),greatest_lower_bound(X_79,multiply(X_79,X_80))) )],[refute_0_103,refute_0_104]) ).

cnf(refute_0_106,plain,
    multiply(X_79,greatest_lower_bound(X_80,identity)) = greatest_lower_bound(X_79,multiply(X_79,X_80)),
    inference(resolve,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_80,identity)),greatest_lower_bound(multiply(X_79,X_80),X_79)) )],[refute_0_102,refute_0_105]) ).

cnf(refute_0_107,plain,
    multiply(X_11,greatest_lower_bound(X_113,identity)) = greatest_lower_bound(X_11,multiply(X_11,X_113)),
    inference(subst,[],[refute_0_106:[bind(X_79,$fot(X_11)),bind(X_80,$fot(X_113))]]) ).

cnf(refute_0_108,plain,
    ( multiply(X_11,greatest_lower_bound(X_113,identity)) != greatest_lower_bound(X_11,multiply(X_11,X_113))
    | greatest_lower_bound(X_11,multiply(X_11,X_113)) = multiply(X_11,greatest_lower_bound(X_113,identity)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_11,greatest_lower_bound(X_113,identity)))),bind(Y0,$fot(greatest_lower_bound(X_11,multiply(X_11,X_113))))]]) ).

cnf(refute_0_109,plain,
    greatest_lower_bound(X_11,multiply(X_11,X_113)) = multiply(X_11,greatest_lower_bound(X_113,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_11,greatest_lower_bound(X_113,identity)),greatest_lower_bound(X_11,multiply(X_11,X_113))) )],[refute_0_107,refute_0_108]) ).

cnf(refute_0_110,plain,
    ( greatest_lower_bound(X_11,multiply(X_11,X_113)) != multiply(X_11,greatest_lower_bound(X_113,identity))
    | least_upper_bound(multiply(X_11,X_113),least_upper_bound(greatest_lower_bound(X_11,multiply(X_11,X_113)),X_28)) != least_upper_bound(multiply(X_11,X_113),X_28)
    | least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)) = least_upper_bound(multiply(X_11,X_113),X_28) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_11,X_113),least_upper_bound(greatest_lower_bound(X_11,multiply(X_11,X_113)),X_28)),least_upper_bound(multiply(X_11,X_113),X_28)) ),[0,1,0],$fot(multiply(X_11,greatest_lower_bound(X_113,identity)))]]) ).

cnf(refute_0_111,plain,
    ( least_upper_bound(multiply(X_11,X_113),least_upper_bound(greatest_lower_bound(X_11,multiply(X_11,X_113)),X_28)) != least_upper_bound(multiply(X_11,X_113),X_28)
    | least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)) = least_upper_bound(multiply(X_11,X_113),X_28) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,multiply(X_11,X_113)),multiply(X_11,greatest_lower_bound(X_113,identity))) )],[refute_0_109,refute_0_110]) ).

cnf(refute_0_112,plain,
    least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)) = least_upper_bound(multiply(X_11,X_113),X_28),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_11,X_113),least_upper_bound(greatest_lower_bound(X_11,multiply(X_11,X_113)),X_28)),least_upper_bound(multiply(X_11,X_113),X_28)) )],[refute_0_76,refute_0_111]) ).

cnf(refute_0_113,plain,
    least_upper_bound(X_113,greatest_lower_bound(X_113,identity)) = X_113,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_113)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_114,plain,
    multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))) = multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))),
    introduced(tautology,[refl,[$fot(multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))))]]) ).

cnf(refute_0_115,plain,
    ( multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))) != multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))
    | least_upper_bound(X_113,greatest_lower_bound(X_113,identity)) != X_113
    | multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))) = multiply(X_11,X_113) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))),multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))) ),[1,1],$fot(X_113)]]) ).

cnf(refute_0_116,plain,
    ( least_upper_bound(X_113,greatest_lower_bound(X_113,identity)) != X_113
    | multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))) = multiply(X_11,X_113) ),
    inference(resolve,[$cnf( $equal(multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))),multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))) )],[refute_0_114,refute_0_115]) ).

cnf(refute_0_117,plain,
    multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))) = multiply(X_11,X_113),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_113,greatest_lower_bound(X_113,identity)),X_113) )],[refute_0_113,refute_0_116]) ).

cnf(refute_0_118,plain,
    least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))) = least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))))]]) ).

cnf(refute_0_119,plain,
    ( multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))) != multiply(X_11,X_113)
    | least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))) != least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))))
    | least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))) = least_upper_bound(X_28,multiply(X_11,X_113)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))),least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))))) ),[1,1],$fot(multiply(X_11,X_113))]]) ).

cnf(refute_0_120,plain,
    ( multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))) != multiply(X_11,X_113)
    | least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))) = least_upper_bound(X_28,multiply(X_11,X_113)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))),least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))))) )],[refute_0_118,refute_0_119]) ).

cnf(refute_0_121,plain,
    least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))) = least_upper_bound(X_28,multiply(X_11,X_113)),
    inference(resolve,[$cnf( $equal(multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))),multiply(X_11,X_113)) )],[refute_0_117,refute_0_120]) ).

cnf(refute_0_122,plain,
    least_upper_bound(X,least_upper_bound(X_26,X_27)) = least_upper_bound(least_upper_bound(X_26,X_27),X),
    inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_26,X_27)))]]) ).

cnf(refute_0_123,plain,
    least_upper_bound(X_26,least_upper_bound(X_27,X)) = least_upper_bound(least_upper_bound(X_26,X_27),X),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(X))]]) ).

cnf(refute_0_124,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_27,X)) != least_upper_bound(least_upper_bound(X_26,X_27),X)
    | least_upper_bound(least_upper_bound(X_26,X_27),X) = least_upper_bound(X_26,least_upper_bound(X_27,X)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_26,least_upper_bound(X_27,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_26,X_27),X)))]]) ).

cnf(refute_0_125,plain,
    least_upper_bound(least_upper_bound(X_26,X_27),X) = least_upper_bound(X_26,least_upper_bound(X_27,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_27,X)),least_upper_bound(least_upper_bound(X_26,X_27),X)) )],[refute_0_123,refute_0_124]) ).

cnf(refute_0_126,plain,
    ( least_upper_bound(X,least_upper_bound(X_26,X_27)) != least_upper_bound(least_upper_bound(X_26,X_27),X)
    | least_upper_bound(least_upper_bound(X_26,X_27),X) != least_upper_bound(X_26,least_upper_bound(X_27,X))
    | least_upper_bound(X,least_upper_bound(X_26,X_27)) = least_upper_bound(X_26,least_upper_bound(X_27,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_26,X_27)),least_upper_bound(X_26,least_upper_bound(X_27,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_26,X_27),X))]]) ).

cnf(refute_0_127,plain,
    ( least_upper_bound(X,least_upper_bound(X_26,X_27)) != least_upper_bound(least_upper_bound(X_26,X_27),X)
    | least_upper_bound(X,least_upper_bound(X_26,X_27)) = least_upper_bound(X_26,least_upper_bound(X_27,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_26,X_27),X),least_upper_bound(X_26,least_upper_bound(X_27,X))) )],[refute_0_125,refute_0_126]) ).

cnf(refute_0_128,plain,
    least_upper_bound(X,least_upper_bound(X_26,X_27)) = least_upper_bound(X_26,least_upper_bound(X_27,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_26,X_27)),least_upper_bound(least_upper_bound(X_26,X_27),X)) )],[refute_0_122,refute_0_127]) ).

cnf(refute_0_129,plain,
    least_upper_bound(X,least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117))) = least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X)),
    inference(subst,[],[refute_0_128:[bind(X_26,$fot(multiply(X_115,X_116))),bind(X_27,$fot(multiply(X_115,X_117)))]]) ).

cnf(refute_0_130,plain,
    multiply(X_115,least_upper_bound(X_116,X_117)) = least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_115)),bind(Y,$fot(X_116)),bind(Z,$fot(X_117))]]) ).

cnf(refute_0_131,plain,
    ( multiply(X_115,least_upper_bound(X_116,X_117)) != least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117))
    | least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117)) = multiply(X_115,least_upper_bound(X_116,X_117)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_115,least_upper_bound(X_116,X_117)))),bind(Y0,$fot(least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117))))]]) ).

cnf(refute_0_132,plain,
    least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117)) = multiply(X_115,least_upper_bound(X_116,X_117)),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(X_116,X_117)),least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117))) )],[refute_0_130,refute_0_131]) ).

cnf(refute_0_133,plain,
    ( least_upper_bound(X,least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117))) != least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X))
    | least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117)) != multiply(X_115,least_upper_bound(X_116,X_117))
    | least_upper_bound(X,multiply(X_115,least_upper_bound(X_116,X_117))) = least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117))),least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X))) ),[0,1],$fot(multiply(X_115,least_upper_bound(X_116,X_117)))]]) ).

cnf(refute_0_134,plain,
    ( least_upper_bound(X,least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117))) != least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X))
    | least_upper_bound(X,multiply(X_115,least_upper_bound(X_116,X_117))) = least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117)),multiply(X_115,least_upper_bound(X_116,X_117))) )],[refute_0_132,refute_0_133]) ).

cnf(refute_0_135,plain,
    least_upper_bound(X,multiply(X_115,least_upper_bound(X_116,X_117))) = least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_115,X_116),multiply(X_115,X_117))),least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X))) )],[refute_0_129,refute_0_134]) ).

cnf(refute_0_136,plain,
    ( least_upper_bound(X,multiply(X_115,least_upper_bound(X_116,X_117))) != least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X))
    | least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X)) = least_upper_bound(X,multiply(X_115,least_upper_bound(X_116,X_117))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,multiply(X_115,least_upper_bound(X_116,X_117))))),bind(Y0,$fot(least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X))))]]) ).

cnf(refute_0_137,plain,
    least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X)) = least_upper_bound(X,multiply(X_115,least_upper_bound(X_116,X_117))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(X_115,least_upper_bound(X_116,X_117))),least_upper_bound(multiply(X_115,X_116),least_upper_bound(multiply(X_115,X_117),X))) )],[refute_0_135,refute_0_136]) ).

cnf(refute_0_138,plain,
    least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)) = least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))),
    inference(subst,[],[refute_0_137:[bind(X,$fot(X_28)),bind(X_115,$fot(X_11)),bind(X_116,$fot(X_113)),bind(X_117,$fot(greatest_lower_bound(X_113,identity)))]]) ).

cnf(refute_0_139,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_140,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_12,refute_0_139]) ).

cnf(refute_0_141,plain,
    ( least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))) != least_upper_bound(X_28,multiply(X_11,X_113))
    | least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)) != least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))))
    | least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)) = least_upper_bound(X_28,multiply(X_11,X_113)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)))),bind(Y0,$fot(least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))))),bind(Z0,$fot(least_upper_bound(X_28,multiply(X_11,X_113))))]]) ).

cnf(refute_0_142,plain,
    ( least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))) != least_upper_bound(X_28,multiply(X_11,X_113))
    | least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)) = least_upper_bound(X_28,multiply(X_11,X_113)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)),least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity))))) )],[refute_0_138,refute_0_141]) ).

cnf(refute_0_143,plain,
    least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)) = least_upper_bound(X_28,multiply(X_11,X_113)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_28,multiply(X_11,least_upper_bound(X_113,greatest_lower_bound(X_113,identity)))),least_upper_bound(X_28,multiply(X_11,X_113))) )],[refute_0_121,refute_0_142]) ).

cnf(refute_0_144,plain,
    ( least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)) != least_upper_bound(X_28,multiply(X_11,X_113))
    | least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)) != least_upper_bound(multiply(X_11,X_113),X_28)
    | least_upper_bound(X_28,multiply(X_11,X_113)) = least_upper_bound(multiply(X_11,X_113),X_28) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)),least_upper_bound(multiply(X_11,X_113),X_28)) ),[0],$fot(least_upper_bound(X_28,multiply(X_11,X_113)))]]) ).

cnf(refute_0_145,plain,
    ( least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)) != least_upper_bound(multiply(X_11,X_113),X_28)
    | least_upper_bound(X_28,multiply(X_11,X_113)) = least_upper_bound(multiply(X_11,X_113),X_28) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)),least_upper_bound(X_28,multiply(X_11,X_113))) )],[refute_0_143,refute_0_144]) ).

cnf(refute_0_146,plain,
    least_upper_bound(X_28,multiply(X_11,X_113)) = least_upper_bound(multiply(X_11,X_113),X_28),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_11,X_113),least_upper_bound(multiply(X_11,greatest_lower_bound(X_113,identity)),X_28)),least_upper_bound(multiply(X_11,X_113),X_28)) )],[refute_0_112,refute_0_145]) ).

cnf(refute_0_147,plain,
    ( least_upper_bound(X_28,multiply(X_11,X_113)) != least_upper_bound(multiply(X_11,X_113),X_28)
    | least_upper_bound(multiply(X_11,X_113),X_28) = least_upper_bound(X_28,multiply(X_11,X_113)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_28,multiply(X_11,X_113)))),bind(Y0,$fot(least_upper_bound(multiply(X_11,X_113),X_28)))]]) ).

cnf(refute_0_148,plain,
    least_upper_bound(multiply(X_11,X_113),X_28) = least_upper_bound(X_28,multiply(X_11,X_113)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_28,multiply(X_11,X_113)),least_upper_bound(multiply(X_11,X_113),X_28)) )],[refute_0_146,refute_0_147]) ).

cnf(refute_0_149,plain,
    least_upper_bound(multiply(X_121,inverse(X_122)),identity) = least_upper_bound(identity,multiply(X_121,inverse(X_122))),
    inference(subst,[],[refute_0_148:[bind(X_11,$fot(X_121)),bind(X_113,$fot(inverse(X_122))),bind(X_28,$fot(identity))]]) ).

cnf(refute_0_150,plain,
    ( multiply(least_upper_bound(X_121,X_122),inverse(X_122)) != least_upper_bound(multiply(X_121,inverse(X_122)),identity)
    | least_upper_bound(multiply(X_121,inverse(X_122)),identity) != least_upper_bound(identity,multiply(X_121,inverse(X_122)))
    | multiply(least_upper_bound(X_121,X_122),inverse(X_122)) = least_upper_bound(identity,multiply(X_121,inverse(X_122))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_121,X_122),inverse(X_122)),least_upper_bound(identity,multiply(X_121,inverse(X_122)))) ),[0],$fot(least_upper_bound(multiply(X_121,inverse(X_122)),identity))]]) ).

cnf(refute_0_151,plain,
    ( multiply(least_upper_bound(X_121,X_122),inverse(X_122)) != least_upper_bound(multiply(X_121,inverse(X_122)),identity)
    | multiply(least_upper_bound(X_121,X_122),inverse(X_122)) = least_upper_bound(identity,multiply(X_121,inverse(X_122))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_121,inverse(X_122)),identity),least_upper_bound(identity,multiply(X_121,inverse(X_122)))) )],[refute_0_149,refute_0_150]) ).

cnf(refute_0_152,plain,
    multiply(least_upper_bound(X_121,X_122),inverse(X_122)) = least_upper_bound(identity,multiply(X_121,inverse(X_122))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,X_122),inverse(X_122)),least_upper_bound(multiply(X_121,inverse(X_122)),identity)) )],[refute_0_63,refute_0_151]) ).

cnf(refute_0_153,plain,
    multiply(least_upper_bound(identity,X_126),inverse(X_126)) = least_upper_bound(identity,multiply(identity,inverse(X_126))),
    inference(subst,[],[refute_0_152:[bind(X_121,$fot(identity)),bind(X_122,$fot(X_126))]]) ).

cnf(refute_0_154,plain,
    multiply(identity,inverse(X_126)) = inverse(X_126),
    inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_126)))]]) ).

cnf(refute_0_155,plain,
    ( multiply(identity,inverse(X_126)) != inverse(X_126)
    | multiply(least_upper_bound(identity,X_126),inverse(X_126)) != least_upper_bound(identity,multiply(identity,inverse(X_126)))
    | multiply(least_upper_bound(identity,X_126),inverse(X_126)) = least_upper_bound(identity,inverse(X_126)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_126),inverse(X_126)),least_upper_bound(identity,multiply(identity,inverse(X_126)))) ),[1,1],$fot(inverse(X_126))]]) ).

cnf(refute_0_156,plain,
    ( multiply(least_upper_bound(identity,X_126),inverse(X_126)) != least_upper_bound(identity,multiply(identity,inverse(X_126)))
    | multiply(least_upper_bound(identity,X_126),inverse(X_126)) = least_upper_bound(identity,inverse(X_126)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_126)),inverse(X_126)) )],[refute_0_154,refute_0_155]) ).

cnf(refute_0_157,plain,
    multiply(least_upper_bound(identity,X_126),inverse(X_126)) = least_upper_bound(identity,inverse(X_126)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_126),inverse(X_126)),least_upper_bound(identity,multiply(identity,inverse(X_126)))) )],[refute_0_153,refute_0_156]) ).

cnf(refute_0_158,plain,
    multiply(multiply(X_66,inverse(X_66)),X_68) = multiply(X_66,multiply(inverse(X_66),X_68)),
    inference(subst,[],[associativity:[bind(X,$fot(X_66)),bind(Y,$fot(inverse(X_66))),bind(Z,$fot(X_68))]]) ).

cnf(refute_0_159,plain,
    multiply(X_66,inverse(X_66)) = identity,
    inference(subst,[],[refute_0_29:[bind(X_1,$fot(X_66))]]) ).

cnf(refute_0_160,plain,
    ( multiply(X_66,inverse(X_66)) != identity
    | multiply(multiply(X_66,inverse(X_66)),X_68) != multiply(X_66,multiply(inverse(X_66),X_68))
    | multiply(identity,X_68) = multiply(X_66,multiply(inverse(X_66),X_68)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_66,inverse(X_66)),X_68),multiply(X_66,multiply(inverse(X_66),X_68))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_161,plain,
    ( multiply(multiply(X_66,inverse(X_66)),X_68) != multiply(X_66,multiply(inverse(X_66),X_68))
    | multiply(identity,X_68) = multiply(X_66,multiply(inverse(X_66),X_68)) ),
    inference(resolve,[$cnf( $equal(multiply(X_66,inverse(X_66)),identity) )],[refute_0_159,refute_0_160]) ).

cnf(refute_0_162,plain,
    multiply(identity,X_68) = multiply(X_66,multiply(inverse(X_66),X_68)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_66,inverse(X_66)),X_68),multiply(X_66,multiply(inverse(X_66),X_68))) )],[refute_0_158,refute_0_161]) ).

cnf(refute_0_163,plain,
    ( multiply(identity,X_68) != X_68
    | multiply(identity,X_68) != multiply(X_66,multiply(inverse(X_66),X_68))
    | X_68 = multiply(X_66,multiply(inverse(X_66),X_68)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_68),multiply(X_66,multiply(inverse(X_66),X_68))) ),[0],$fot(X_68)]]) ).

cnf(refute_0_164,plain,
    ( multiply(identity,X_68) != multiply(X_66,multiply(inverse(X_66),X_68))
    | X_68 = multiply(X_66,multiply(inverse(X_66),X_68)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_68),X_68) )],[refute_0_6,refute_0_163]) ).

cnf(refute_0_165,plain,
    X_68 = multiply(X_66,multiply(inverse(X_66),X_68)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_68),multiply(X_66,multiply(inverse(X_66),X_68))) )],[refute_0_162,refute_0_164]) ).

cnf(refute_0_166,plain,
    inverse(X) = multiply(X_69,multiply(inverse(X_69),inverse(X))),
    inference(subst,[],[refute_0_165:[bind(X_66,$fot(X_69)),bind(X_68,$fot(inverse(X)))]]) ).

cnf(refute_0_167,plain,
    inverse(multiply(X,X_69)) = multiply(inverse(X_69),inverse(X)),
    inference(subst,[],[p11_3:[bind(Y,$fot(X_69))]]) ).

cnf(refute_0_168,plain,
    ( inverse(multiply(X,X_69)) != multiply(inverse(X_69),inverse(X))
    | multiply(inverse(X_69),inverse(X)) = inverse(multiply(X,X_69)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(multiply(X,X_69)))),bind(Y0,$fot(multiply(inverse(X_69),inverse(X))))]]) ).

cnf(refute_0_169,plain,
    multiply(inverse(X_69),inverse(X)) = inverse(multiply(X,X_69)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,X_69)),multiply(inverse(X_69),inverse(X))) )],[refute_0_167,refute_0_168]) ).

cnf(refute_0_170,plain,
    ( multiply(inverse(X_69),inverse(X)) != inverse(multiply(X,X_69))
    | inverse(X) != multiply(X_69,multiply(inverse(X_69),inverse(X)))
    | inverse(X) = multiply(X_69,inverse(multiply(X,X_69))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(X_69,multiply(inverse(X_69),inverse(X)))) ),[1,1],$fot(inverse(multiply(X,X_69)))]]) ).

cnf(refute_0_171,plain,
    ( inverse(X) != multiply(X_69,multiply(inverse(X_69),inverse(X)))
    | inverse(X) = multiply(X_69,inverse(multiply(X,X_69))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_69),inverse(X)),inverse(multiply(X,X_69))) )],[refute_0_169,refute_0_170]) ).

cnf(refute_0_172,plain,
    inverse(X) = multiply(X_69,inverse(multiply(X,X_69))),
    inference(resolve,[$cnf( $equal(inverse(X),multiply(X_69,multiply(inverse(X_69),inverse(X)))) )],[refute_0_166,refute_0_171]) ).

cnf(refute_0_173,plain,
    inverse(X) = multiply(least_upper_bound(X_119,inverse(X)),inverse(multiply(X,least_upper_bound(X_119,inverse(X))))),
    inference(subst,[],[refute_0_172:[bind(X_69,$fot(least_upper_bound(X_119,inverse(X))))]]) ).

cnf(refute_0_174,plain,
    multiply(X_115,least_upper_bound(X_116,inverse(X_115))) = least_upper_bound(multiply(X_115,X_116),multiply(X_115,inverse(X_115))),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_115)),bind(Y,$fot(X_116)),bind(Z,$fot(inverse(X_115)))]]) ).

cnf(refute_0_175,plain,
    multiply(X_115,inverse(X_115)) = identity,
    inference(subst,[],[refute_0_29:[bind(X_1,$fot(X_115))]]) ).

cnf(refute_0_176,plain,
    ( multiply(X_115,inverse(X_115)) != identity
    | multiply(X_115,least_upper_bound(X_116,inverse(X_115))) != least_upper_bound(multiply(X_115,X_116),multiply(X_115,inverse(X_115)))
    | multiply(X_115,least_upper_bound(X_116,inverse(X_115))) = least_upper_bound(multiply(X_115,X_116),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_115,least_upper_bound(X_116,inverse(X_115))),least_upper_bound(multiply(X_115,X_116),multiply(X_115,inverse(X_115)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_177,plain,
    ( multiply(X_115,least_upper_bound(X_116,inverse(X_115))) != least_upper_bound(multiply(X_115,X_116),multiply(X_115,inverse(X_115)))
    | multiply(X_115,least_upper_bound(X_116,inverse(X_115))) = least_upper_bound(multiply(X_115,X_116),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_115,inverse(X_115)),identity) )],[refute_0_175,refute_0_176]) ).

cnf(refute_0_178,plain,
    multiply(X_115,least_upper_bound(X_116,inverse(X_115))) = least_upper_bound(multiply(X_115,X_116),identity),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(X_116,inverse(X_115))),least_upper_bound(multiply(X_115,X_116),multiply(X_115,inverse(X_115)))) )],[refute_0_174,refute_0_177]) ).

cnf(refute_0_179,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_12:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).

cnf(refute_0_180,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_179]) ).

cnf(refute_0_181,plain,
    least_upper_bound(multiply(X_115,X_116),identity) = least_upper_bound(identity,multiply(X_115,X_116)),
    inference(subst,[],[refute_0_180:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_115,X_116)))]]) ).

cnf(refute_0_182,plain,
    ( multiply(X_115,least_upper_bound(X_116,inverse(X_115))) != least_upper_bound(multiply(X_115,X_116),identity)
    | least_upper_bound(multiply(X_115,X_116),identity) != least_upper_bound(identity,multiply(X_115,X_116))
    | multiply(X_115,least_upper_bound(X_116,inverse(X_115))) = least_upper_bound(identity,multiply(X_115,X_116)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_115,least_upper_bound(X_116,inverse(X_115))),least_upper_bound(identity,multiply(X_115,X_116))) ),[0],$fot(least_upper_bound(multiply(X_115,X_116),identity))]]) ).

cnf(refute_0_183,plain,
    ( multiply(X_115,least_upper_bound(X_116,inverse(X_115))) != least_upper_bound(multiply(X_115,X_116),identity)
    | multiply(X_115,least_upper_bound(X_116,inverse(X_115))) = least_upper_bound(identity,multiply(X_115,X_116)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_115,X_116),identity),least_upper_bound(identity,multiply(X_115,X_116))) )],[refute_0_181,refute_0_182]) ).

cnf(refute_0_184,plain,
    multiply(X_115,least_upper_bound(X_116,inverse(X_115))) = least_upper_bound(identity,multiply(X_115,X_116)),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(X_116,inverse(X_115))),least_upper_bound(multiply(X_115,X_116),identity)) )],[refute_0_178,refute_0_183]) ).

cnf(refute_0_185,plain,
    multiply(X,least_upper_bound(X_119,inverse(X))) = least_upper_bound(identity,multiply(X,X_119)),
    inference(subst,[],[refute_0_184:[bind(X_115,$fot(X)),bind(X_116,$fot(X_119))]]) ).

cnf(refute_0_186,plain,
    ( multiply(X,least_upper_bound(X_119,inverse(X))) != least_upper_bound(identity,multiply(X,X_119))
    | inverse(X) != multiply(least_upper_bound(X_119,inverse(X)),inverse(multiply(X,least_upper_bound(X_119,inverse(X)))))
    | inverse(X) = multiply(least_upper_bound(X_119,inverse(X)),inverse(least_upper_bound(identity,multiply(X,X_119)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(least_upper_bound(X_119,inverse(X)),inverse(multiply(X,least_upper_bound(X_119,inverse(X)))))) ),[1,1,0],$fot(least_upper_bound(identity,multiply(X,X_119)))]]) ).

cnf(refute_0_187,plain,
    ( inverse(X) != multiply(least_upper_bound(X_119,inverse(X)),inverse(multiply(X,least_upper_bound(X_119,inverse(X)))))
    | inverse(X) = multiply(least_upper_bound(X_119,inverse(X)),inverse(least_upper_bound(identity,multiply(X,X_119)))) ),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_119,inverse(X))),least_upper_bound(identity,multiply(X,X_119))) )],[refute_0_185,refute_0_186]) ).

cnf(refute_0_188,plain,
    inverse(X) = multiply(least_upper_bound(X_119,inverse(X)),inverse(least_upper_bound(identity,multiply(X,X_119)))),
    inference(resolve,[$cnf( $equal(inverse(X),multiply(least_upper_bound(X_119,inverse(X)),inverse(multiply(X,least_upper_bound(X_119,inverse(X)))))) )],[refute_0_173,refute_0_187]) ).

cnf(refute_0_189,plain,
    inverse(greatest_lower_bound(identity,X_86)) = multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86))))))),
    inference(subst,[],[refute_0_188:[bind(X,$fot(greatest_lower_bound(identity,X_86))),bind(X_119,$fot(inverse(greatest_lower_bound(identity,inverse(X_86)))))]]) ).

cnf(refute_0_190,plain,
    inverse(inverse(X_86)) = multiply(greatest_lower_bound(identity,X_86),inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86)))),
    inference(subst,[],[refute_0_172:[bind(X,$fot(inverse(X_86))),bind(X_69,$fot(greatest_lower_bound(identity,X_86)))]]) ).

cnf(refute_0_191,plain,
    multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(multiply(inverse(X_81),X_80),multiply(inverse(X_81),X_81)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_81))),bind(Y,$fot(X_80)),bind(Z,$fot(X_81))]]) ).

cnf(refute_0_192,plain,
    multiply(inverse(X_81),X_81) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_81))]]) ).

cnf(refute_0_193,plain,
    ( multiply(inverse(X_81),X_81) != identity
    | multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)) != greatest_lower_bound(multiply(inverse(X_81),X_80),multiply(inverse(X_81),X_81))
    | multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(multiply(inverse(X_81),X_80),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)),greatest_lower_bound(multiply(inverse(X_81),X_80),multiply(inverse(X_81),X_81))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_194,plain,
    ( multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)) != greatest_lower_bound(multiply(inverse(X_81),X_80),multiply(inverse(X_81),X_81))
    | multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(multiply(inverse(X_81),X_80),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_81),X_81),identity) )],[refute_0_192,refute_0_193]) ).

cnf(refute_0_195,plain,
    multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(multiply(inverse(X_81),X_80),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)),greatest_lower_bound(multiply(inverse(X_81),X_80),multiply(inverse(X_81),X_81))) )],[refute_0_191,refute_0_194]) ).

cnf(refute_0_196,plain,
    greatest_lower_bound(multiply(inverse(X_81),X_80),identity) = greatest_lower_bound(identity,multiply(inverse(X_81),X_80)),
    inference(subst,[],[refute_0_35:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_81),X_80)))]]) ).

cnf(refute_0_197,plain,
    ( multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)) != greatest_lower_bound(multiply(inverse(X_81),X_80),identity)
    | greatest_lower_bound(multiply(inverse(X_81),X_80),identity) != greatest_lower_bound(identity,multiply(inverse(X_81),X_80))
    | multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(identity,multiply(inverse(X_81),X_80)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)),greatest_lower_bound(identity,multiply(inverse(X_81),X_80))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_81),X_80),identity))]]) ).

cnf(refute_0_198,plain,
    ( multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)) != greatest_lower_bound(multiply(inverse(X_81),X_80),identity)
    | multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(identity,multiply(inverse(X_81),X_80)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_81),X_80),identity),greatest_lower_bound(identity,multiply(inverse(X_81),X_80))) )],[refute_0_196,refute_0_197]) ).

cnf(refute_0_199,plain,
    multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(identity,multiply(inverse(X_81),X_80)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_81),greatest_lower_bound(X_80,X_81)),greatest_lower_bound(multiply(inverse(X_81),X_80),identity)) )],[refute_0_195,refute_0_198]) ).

cnf(refute_0_200,plain,
    multiply(inverse(X_85),greatest_lower_bound(identity,X_85)) = greatest_lower_bound(identity,multiply(inverse(X_85),identity)),
    inference(subst,[],[refute_0_199:[bind(X_80,$fot(identity)),bind(X_81,$fot(X_85))]]) ).

cnf(refute_0_201,plain,
    inverse(X_85) = multiply(inverse(X_85),identity),
    inference(subst,[],[refute_0_96:[bind(X,$fot(inverse(X_85)))]]) ).

cnf(refute_0_202,plain,
    ( inverse(X_85) != multiply(inverse(X_85),identity)
    | multiply(inverse(X_85),identity) = inverse(X_85) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X_85))),bind(Y0,$fot(multiply(inverse(X_85),identity)))]]) ).

cnf(refute_0_203,plain,
    multiply(inverse(X_85),identity) = inverse(X_85),
    inference(resolve,[$cnf( $equal(inverse(X_85),multiply(inverse(X_85),identity)) )],[refute_0_201,refute_0_202]) ).

cnf(refute_0_204,plain,
    ( multiply(inverse(X_85),greatest_lower_bound(identity,X_85)) != greatest_lower_bound(identity,multiply(inverse(X_85),identity))
    | multiply(inverse(X_85),identity) != inverse(X_85)
    | multiply(inverse(X_85),greatest_lower_bound(identity,X_85)) = greatest_lower_bound(identity,inverse(X_85)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_85),greatest_lower_bound(identity,X_85)),greatest_lower_bound(identity,multiply(inverse(X_85),identity))) ),[1,1],$fot(inverse(X_85))]]) ).

cnf(refute_0_205,plain,
    ( multiply(inverse(X_85),greatest_lower_bound(identity,X_85)) != greatest_lower_bound(identity,multiply(inverse(X_85),identity))
    | multiply(inverse(X_85),greatest_lower_bound(identity,X_85)) = greatest_lower_bound(identity,inverse(X_85)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_85),identity),inverse(X_85)) )],[refute_0_203,refute_0_204]) ).

cnf(refute_0_206,plain,
    multiply(inverse(X_85),greatest_lower_bound(identity,X_85)) = greatest_lower_bound(identity,inverse(X_85)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_85),greatest_lower_bound(identity,X_85)),greatest_lower_bound(identity,multiply(inverse(X_85),identity))) )],[refute_0_200,refute_0_205]) ).

cnf(refute_0_207,plain,
    multiply(inverse(X_86),greatest_lower_bound(identity,X_86)) = greatest_lower_bound(identity,inverse(X_86)),
    inference(subst,[],[refute_0_206:[bind(X_85,$fot(X_86))]]) ).

cnf(refute_0_208,plain,
    ( multiply(inverse(X_86),greatest_lower_bound(identity,X_86)) != greatest_lower_bound(identity,inverse(X_86))
    | inverse(inverse(X_86)) != multiply(greatest_lower_bound(identity,X_86),inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))))
    | inverse(inverse(X_86)) = multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_86)),multiply(greatest_lower_bound(identity,X_86),inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))))) ),[1,1,0],$fot(greatest_lower_bound(identity,inverse(X_86)))]]) ).

cnf(refute_0_209,plain,
    ( inverse(inverse(X_86)) != multiply(greatest_lower_bound(identity,X_86),inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))))
    | inverse(inverse(X_86)) = multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_86),greatest_lower_bound(identity,X_86)),greatest_lower_bound(identity,inverse(X_86))) )],[refute_0_207,refute_0_208]) ).

cnf(refute_0_210,plain,
    inverse(inverse(X_86)) = multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_86)),multiply(greatest_lower_bound(identity,X_86),inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))))) )],[refute_0_190,refute_0_209]) ).

cnf(refute_0_211,plain,
    inverse(inverse(X_86)) = X_86,
    inference(subst,[],[p11_2:[bind(X,$fot(X_86))]]) ).

cnf(refute_0_212,plain,
    ( inverse(inverse(X_86)) != X_86
    | inverse(inverse(X_86)) != multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86))))
    | X_86 = multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_86)),multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86))))) ),[0],$fot(X_86)]]) ).

cnf(refute_0_213,plain,
    ( inverse(inverse(X_86)) != multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86))))
    | X_86 = multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_86)),X_86) )],[refute_0_211,refute_0_212]) ).

cnf(refute_0_214,plain,
    X_86 = multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_86)),multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86))))) )],[refute_0_210,refute_0_213]) ).

cnf(refute_0_215,plain,
    ( X_86 != multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86))))
    | multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))) = X_86 ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X_86)),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86))))))]]) ).

cnf(refute_0_216,plain,
    multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))) = X_86,
    inference(resolve,[$cnf( $equal(X_86,multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86))))) )],[refute_0_214,refute_0_215]) ).

cnf(refute_0_217,plain,
    ( multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))) != X_86
    | inverse(greatest_lower_bound(identity,X_86)) != multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))))))
    | inverse(greatest_lower_bound(identity,X_86)) = multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_86)),multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))))))) ),[1,1,0,1],$fot(X_86)]]) ).

cnf(refute_0_218,plain,
    ( inverse(greatest_lower_bound(identity,X_86)) != multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))))))
    | inverse(greatest_lower_bound(identity,X_86)) = multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))),X_86) )],[refute_0_216,refute_0_217]) ).

cnf(refute_0_219,plain,
    inverse(greatest_lower_bound(identity,X_86)) = multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_86)),multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_86),inverse(greatest_lower_bound(identity,inverse(X_86)))))))) )],[refute_0_189,refute_0_218]) ).

cnf(refute_0_220,plain,
    ( inverse(multiply(X,Y)) != multiply(inverse(Y),inverse(X))
    | multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(inverse(Y),inverse(X))))]]) ).

cnf(refute_0_221,plain,
    multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))) )],[p11_3,refute_0_220]) ).

cnf(refute_0_222,plain,
    multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86))) = inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))),
    inference(subst,[],[refute_0_221:[bind(X,$fot(least_upper_bound(identity,X_86))),bind(Y,$fot(greatest_lower_bound(identity,X_86)))]]) ).

cnf(refute_0_223,plain,
    multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))) = multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))))]]) ).

cnf(refute_0_224,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86))) != inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))
    | multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))) != multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86))))
    | multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))),multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86))))) ),[1,1],$fot(inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))]]) ).

cnf(refute_0_225,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86))) != inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))
    | multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))),multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86))))) )],[refute_0_223,refute_0_224]) ).

cnf(refute_0_226,plain,
    multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86))),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) )],[refute_0_222,refute_0_225]) ).

cnf(refute_0_227,plain,
    multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))),
    inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(X_86,identity))),bind(Y,$fot(inverse(greatest_lower_bound(identity,X_86)))),bind(Z,$fot(inverse(least_upper_bound(identity,X_86))))]]) ).

cnf(refute_0_228,plain,
    ( multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) != multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86))))
    | multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))) != multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))
    | multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))))),bind(Y0,$fot(multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))))),bind(Z0,$fot(multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))))]]) ).

cnf(refute_0_229,plain,
    ( multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))) != multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))
    | multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))),multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86))))) )],[refute_0_227,refute_0_228]) ).

cnf(refute_0_230,plain,
    multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(least_upper_bound(identity,X_86)))),multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))) )],[refute_0_226,refute_0_229]) ).

cnf(refute_0_231,plain,
    multiply(X_115,least_upper_bound(X_116,identity)) = least_upper_bound(multiply(X_115,X_116),multiply(X_115,identity)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_115)),bind(Y,$fot(X_116)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_232,plain,
    X_115 = multiply(X_115,identity),
    inference(subst,[],[refute_0_96:[bind(X,$fot(X_115))]]) ).

cnf(refute_0_233,plain,
    ( X_115 != multiply(X_115,identity)
    | multiply(X_115,identity) = X_115 ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X_115)),bind(Y0,$fot(multiply(X_115,identity)))]]) ).

cnf(refute_0_234,plain,
    multiply(X_115,identity) = X_115,
    inference(resolve,[$cnf( $equal(X_115,multiply(X_115,identity)) )],[refute_0_232,refute_0_233]) ).

cnf(refute_0_235,plain,
    ( multiply(X_115,identity) != X_115
    | multiply(X_115,least_upper_bound(X_116,identity)) != least_upper_bound(multiply(X_115,X_116),multiply(X_115,identity))
    | multiply(X_115,least_upper_bound(X_116,identity)) = least_upper_bound(multiply(X_115,X_116),X_115) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_115,least_upper_bound(X_116,identity)),least_upper_bound(multiply(X_115,X_116),multiply(X_115,identity))) ),[1,1],$fot(X_115)]]) ).

cnf(refute_0_236,plain,
    ( multiply(X_115,least_upper_bound(X_116,identity)) != least_upper_bound(multiply(X_115,X_116),multiply(X_115,identity))
    | multiply(X_115,least_upper_bound(X_116,identity)) = least_upper_bound(multiply(X_115,X_116),X_115) ),
    inference(resolve,[$cnf( $equal(multiply(X_115,identity),X_115) )],[refute_0_234,refute_0_235]) ).

cnf(refute_0_237,plain,
    multiply(X_115,least_upper_bound(X_116,identity)) = least_upper_bound(multiply(X_115,X_116),X_115),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(X_116,identity)),least_upper_bound(multiply(X_115,X_116),multiply(X_115,identity))) )],[refute_0_231,refute_0_236]) ).

cnf(refute_0_238,plain,
    least_upper_bound(multiply(X_115,X_116),X_115) = least_upper_bound(X_115,multiply(X_115,X_116)),
    inference(subst,[],[refute_0_180:[bind(X,$fot(X_115)),bind(Y,$fot(multiply(X_115,X_116)))]]) ).

cnf(refute_0_239,plain,
    ( multiply(X_115,least_upper_bound(X_116,identity)) != least_upper_bound(multiply(X_115,X_116),X_115)
    | least_upper_bound(multiply(X_115,X_116),X_115) != least_upper_bound(X_115,multiply(X_115,X_116))
    | multiply(X_115,least_upper_bound(X_116,identity)) = least_upper_bound(X_115,multiply(X_115,X_116)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_115,least_upper_bound(X_116,identity)),least_upper_bound(X_115,multiply(X_115,X_116))) ),[0],$fot(least_upper_bound(multiply(X_115,X_116),X_115))]]) ).

cnf(refute_0_240,plain,
    ( multiply(X_115,least_upper_bound(X_116,identity)) != least_upper_bound(multiply(X_115,X_116),X_115)
    | multiply(X_115,least_upper_bound(X_116,identity)) = least_upper_bound(X_115,multiply(X_115,X_116)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_115,X_116),X_115),least_upper_bound(X_115,multiply(X_115,X_116))) )],[refute_0_238,refute_0_239]) ).

cnf(refute_0_241,plain,
    multiply(X_115,least_upper_bound(X_116,identity)) = least_upper_bound(X_115,multiply(X_115,X_116)),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(X_116,identity)),least_upper_bound(multiply(X_115,X_116),X_115)) )],[refute_0_237,refute_0_240]) ).

cnf(refute_0_242,plain,
    multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),multiply(inverse(greatest_lower_bound(identity,X_116)),X_116)),
    inference(subst,[],[refute_0_241:[bind(X_115,$fot(inverse(greatest_lower_bound(identity,X_116))))]]) ).

cnf(refute_0_243,plain,
    inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))) = multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))),
    inference(subst,[],[p11_3:[bind(X,$fot(inverse(X_86))),bind(Y,$fot(greatest_lower_bound(identity,X_86)))]]) ).

cnf(refute_0_244,plain,
    ( multiply(inverse(X_86),greatest_lower_bound(identity,X_86)) != greatest_lower_bound(identity,inverse(X_86))
    | inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))) != multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86)))
    | inverse(greatest_lower_bound(identity,inverse(X_86))) = multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86)))) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_86)))]]) ).

cnf(refute_0_245,plain,
    ( inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))) != multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86)))
    | inverse(greatest_lower_bound(identity,inverse(X_86))) = multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_86),greatest_lower_bound(identity,X_86)),greatest_lower_bound(identity,inverse(X_86))) )],[refute_0_207,refute_0_244]) ).

cnf(refute_0_246,plain,
    inverse(greatest_lower_bound(identity,inverse(X_86))) = multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86)))) )],[refute_0_243,refute_0_245]) ).

cnf(refute_0_247,plain,
    inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))) = multiply(inverse(greatest_lower_bound(identity,X_86)),X_86),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_86)),bind(X_30,$fot(greatest_lower_bound(identity,X_86)))]]) ).

cnf(refute_0_248,plain,
    multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))) = inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))),
    inference(subst,[],[refute_0_221:[bind(X,$fot(inverse(X_86))),bind(Y,$fot(greatest_lower_bound(identity,X_86)))]]) ).

cnf(refute_0_249,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))) != inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86)))
    | inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))) != multiply(inverse(greatest_lower_bound(identity,X_86)),X_86)
    | multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))) = multiply(inverse(greatest_lower_bound(identity,X_86)),X_86) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))))),bind(Y0,$fot(inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,X_86)),X_86)))]]) ).

cnf(refute_0_250,plain,
    ( inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))) != multiply(inverse(greatest_lower_bound(identity,X_86)),X_86)
    | multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))) = multiply(inverse(greatest_lower_bound(identity,X_86)),X_86) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))),inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86)))) )],[refute_0_248,refute_0_249]) ).

cnf(refute_0_251,plain,
    multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))) = multiply(inverse(greatest_lower_bound(identity,X_86)),X_86),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_86),greatest_lower_bound(identity,X_86))),multiply(inverse(greatest_lower_bound(identity,X_86)),X_86)) )],[refute_0_247,refute_0_250]) ).

cnf(refute_0_252,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))) != multiply(inverse(greatest_lower_bound(identity,X_86)),X_86)
    | inverse(greatest_lower_bound(identity,inverse(X_86))) != multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86)))
    | inverse(greatest_lower_bound(identity,inverse(X_86))) = multiply(inverse(greatest_lower_bound(identity,X_86)),X_86) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_86))),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(identity,X_86)),X_86))]]) ).

cnf(refute_0_253,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_86))) != multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86)))
    | inverse(greatest_lower_bound(identity,inverse(X_86))) = multiply(inverse(greatest_lower_bound(identity,X_86)),X_86) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86))),multiply(inverse(greatest_lower_bound(identity,X_86)),X_86)) )],[refute_0_251,refute_0_252]) ).

cnf(refute_0_254,plain,
    inverse(greatest_lower_bound(identity,inverse(X_86))) = multiply(inverse(greatest_lower_bound(identity,X_86)),X_86),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_86))),multiply(inverse(greatest_lower_bound(identity,X_86)),inverse(inverse(X_86)))) )],[refute_0_246,refute_0_253]) ).

cnf(refute_0_255,plain,
    inverse(greatest_lower_bound(identity,inverse(X_116))) = multiply(inverse(greatest_lower_bound(identity,X_116)),X_116),
    inference(subst,[],[refute_0_254:[bind(X_86,$fot(X_116))]]) ).

cnf(refute_0_256,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_116))) != multiply(inverse(greatest_lower_bound(identity,X_116)),X_116)
    | multiply(inverse(greatest_lower_bound(identity,X_116)),X_116) = inverse(greatest_lower_bound(identity,inverse(X_116))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_116))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_116)),X_116)))]]) ).

cnf(refute_0_257,plain,
    multiply(inverse(greatest_lower_bound(identity,X_116)),X_116) = inverse(greatest_lower_bound(identity,inverse(X_116))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_116))),multiply(inverse(greatest_lower_bound(identity,X_116)),X_116)) )],[refute_0_255,refute_0_256]) ).

cnf(refute_0_258,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_116)),X_116) != inverse(greatest_lower_bound(identity,inverse(X_116)))
    | multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),multiply(inverse(greatest_lower_bound(identity,X_116)),X_116))
    | multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)),least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),multiply(inverse(greatest_lower_bound(identity,X_116)),X_116))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_116))))]]) ).

cnf(refute_0_259,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),multiply(inverse(greatest_lower_bound(identity,X_116)),X_116))
    | multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_116)),X_116),inverse(greatest_lower_bound(identity,inverse(X_116)))) )],[refute_0_257,refute_0_258]) ).

cnf(refute_0_260,plain,
    multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)),least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),multiply(inverse(greatest_lower_bound(identity,X_116)),X_116))) )],[refute_0_242,refute_0_259]) ).

cnf(refute_0_261,plain,
    multiply(least_upper_bound(X_121,identity),X_120) = least_upper_bound(multiply(X_121,X_120),multiply(identity,X_120)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_120)),bind(Y,$fot(X_121)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_262,plain,
    multiply(identity,X_120) = X_120,
    inference(subst,[],[left_identity:[bind(X,$fot(X_120))]]) ).

cnf(refute_0_263,plain,
    ( multiply(identity,X_120) != X_120
    | multiply(least_upper_bound(X_121,identity),X_120) != least_upper_bound(multiply(X_121,X_120),multiply(identity,X_120))
    | multiply(least_upper_bound(X_121,identity),X_120) = least_upper_bound(multiply(X_121,X_120),X_120) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_121,identity),X_120),least_upper_bound(multiply(X_121,X_120),multiply(identity,X_120))) ),[1,1],$fot(X_120)]]) ).

cnf(refute_0_264,plain,
    ( multiply(least_upper_bound(X_121,identity),X_120) != least_upper_bound(multiply(X_121,X_120),multiply(identity,X_120))
    | multiply(least_upper_bound(X_121,identity),X_120) = least_upper_bound(multiply(X_121,X_120),X_120) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_120),X_120) )],[refute_0_262,refute_0_263]) ).

cnf(refute_0_265,plain,
    multiply(least_upper_bound(X_121,identity),X_120) = least_upper_bound(multiply(X_121,X_120),X_120),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,identity),X_120),least_upper_bound(multiply(X_121,X_120),multiply(identity,X_120))) )],[refute_0_261,refute_0_264]) ).

cnf(refute_0_266,plain,
    least_upper_bound(multiply(X_121,X_120),X_120) = least_upper_bound(X_120,multiply(X_121,X_120)),
    inference(subst,[],[refute_0_148:[bind(X_11,$fot(X_121)),bind(X_113,$fot(X_120)),bind(X_28,$fot(X_120))]]) ).

cnf(refute_0_267,plain,
    ( multiply(least_upper_bound(X_121,identity),X_120) != least_upper_bound(multiply(X_121,X_120),X_120)
    | least_upper_bound(multiply(X_121,X_120),X_120) != least_upper_bound(X_120,multiply(X_121,X_120))
    | multiply(least_upper_bound(X_121,identity),X_120) = least_upper_bound(X_120,multiply(X_121,X_120)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_121,identity),X_120),least_upper_bound(X_120,multiply(X_121,X_120))) ),[0],$fot(least_upper_bound(multiply(X_121,X_120),X_120))]]) ).

cnf(refute_0_268,plain,
    ( multiply(least_upper_bound(X_121,identity),X_120) != least_upper_bound(multiply(X_121,X_120),X_120)
    | multiply(least_upper_bound(X_121,identity),X_120) = least_upper_bound(X_120,multiply(X_121,X_120)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_121,X_120),X_120),least_upper_bound(X_120,multiply(X_121,X_120))) )],[refute_0_266,refute_0_267]) ).

cnf(refute_0_269,plain,
    multiply(least_upper_bound(X_121,identity),X_120) = least_upper_bound(X_120,multiply(X_121,X_120)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,identity),X_120),least_upper_bound(multiply(X_121,X_120),X_120)) )],[refute_0_265,refute_0_268]) ).

cnf(refute_0_270,plain,
    multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),multiply(X_121,inverse(greatest_lower_bound(identity,X_121)))),
    inference(subst,[],[refute_0_269:[bind(X_120,$fot(inverse(greatest_lower_bound(identity,X_121))))]]) ).

cnf(refute_0_271,plain,
    inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))) = multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))),
    inference(subst,[],[p11_3:[bind(X,$fot(greatest_lower_bound(identity,X_92))),bind(Y,$fot(inverse(X_92)))]]) ).

cnf(refute_0_272,plain,
    multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) = greatest_lower_bound(multiply(X_88,inverse(X_89)),multiply(X_89,inverse(X_89))),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_89))),bind(Y,$fot(X_88)),bind(Z,$fot(X_89))]]) ).

cnf(refute_0_273,plain,
    multiply(X_89,inverse(X_89)) = identity,
    inference(subst,[],[refute_0_29:[bind(X_1,$fot(X_89))]]) ).

cnf(refute_0_274,plain,
    ( multiply(X_89,inverse(X_89)) != identity
    | multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) != greatest_lower_bound(multiply(X_88,inverse(X_89)),multiply(X_89,inverse(X_89)))
    | multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) = greatest_lower_bound(multiply(X_88,inverse(X_89)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)),greatest_lower_bound(multiply(X_88,inverse(X_89)),multiply(X_89,inverse(X_89)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_275,plain,
    ( multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) != greatest_lower_bound(multiply(X_88,inverse(X_89)),multiply(X_89,inverse(X_89)))
    | multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) = greatest_lower_bound(multiply(X_88,inverse(X_89)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_89,inverse(X_89)),identity) )],[refute_0_273,refute_0_274]) ).

cnf(refute_0_276,plain,
    multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) = greatest_lower_bound(multiply(X_88,inverse(X_89)),identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)),greatest_lower_bound(multiply(X_88,inverse(X_89)),multiply(X_89,inverse(X_89)))) )],[refute_0_272,refute_0_275]) ).

cnf(refute_0_277,plain,
    greatest_lower_bound(multiply(X_88,inverse(X_89)),identity) = greatest_lower_bound(identity,multiply(X_88,inverse(X_89))),
    inference(subst,[],[refute_0_35:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_88,inverse(X_89))))]]) ).

cnf(refute_0_278,plain,
    ( multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) != greatest_lower_bound(multiply(X_88,inverse(X_89)),identity)
    | greatest_lower_bound(multiply(X_88,inverse(X_89)),identity) != greatest_lower_bound(identity,multiply(X_88,inverse(X_89)))
    | multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) = greatest_lower_bound(identity,multiply(X_88,inverse(X_89))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)),greatest_lower_bound(identity,multiply(X_88,inverse(X_89)))) ),[0],$fot(greatest_lower_bound(multiply(X_88,inverse(X_89)),identity))]]) ).

cnf(refute_0_279,plain,
    ( multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) != greatest_lower_bound(multiply(X_88,inverse(X_89)),identity)
    | multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) = greatest_lower_bound(identity,multiply(X_88,inverse(X_89))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,inverse(X_89)),identity),greatest_lower_bound(identity,multiply(X_88,inverse(X_89)))) )],[refute_0_277,refute_0_278]) ).

cnf(refute_0_280,plain,
    multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) = greatest_lower_bound(identity,multiply(X_88,inverse(X_89))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)),greatest_lower_bound(multiply(X_88,inverse(X_89)),identity)) )],[refute_0_276,refute_0_279]) ).

cnf(refute_0_281,plain,
    multiply(greatest_lower_bound(identity,X_91),inverse(X_91)) = greatest_lower_bound(identity,multiply(identity,inverse(X_91))),
    inference(subst,[],[refute_0_280:[bind(X_88,$fot(identity)),bind(X_89,$fot(X_91))]]) ).

cnf(refute_0_282,plain,
    multiply(identity,inverse(X_91)) = inverse(X_91),
    inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_91)))]]) ).

cnf(refute_0_283,plain,
    ( multiply(greatest_lower_bound(identity,X_91),inverse(X_91)) != greatest_lower_bound(identity,multiply(identity,inverse(X_91)))
    | multiply(identity,inverse(X_91)) != inverse(X_91)
    | multiply(greatest_lower_bound(identity,X_91),inverse(X_91)) = greatest_lower_bound(identity,inverse(X_91)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_91),inverse(X_91)),greatest_lower_bound(identity,multiply(identity,inverse(X_91)))) ),[1,1],$fot(inverse(X_91))]]) ).

cnf(refute_0_284,plain,
    ( multiply(greatest_lower_bound(identity,X_91),inverse(X_91)) != greatest_lower_bound(identity,multiply(identity,inverse(X_91)))
    | multiply(greatest_lower_bound(identity,X_91),inverse(X_91)) = greatest_lower_bound(identity,inverse(X_91)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_91)),inverse(X_91)) )],[refute_0_282,refute_0_283]) ).

cnf(refute_0_285,plain,
    multiply(greatest_lower_bound(identity,X_91),inverse(X_91)) = greatest_lower_bound(identity,inverse(X_91)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_91),inverse(X_91)),greatest_lower_bound(identity,multiply(identity,inverse(X_91)))) )],[refute_0_281,refute_0_284]) ).

cnf(refute_0_286,plain,
    multiply(greatest_lower_bound(identity,X_92),inverse(X_92)) = greatest_lower_bound(identity,inverse(X_92)),
    inference(subst,[],[refute_0_285:[bind(X_91,$fot(X_92))]]) ).

cnf(refute_0_287,plain,
    ( multiply(greatest_lower_bound(identity,X_92),inverse(X_92)) != greatest_lower_bound(identity,inverse(X_92))
    | inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))) != multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92)))
    | inverse(greatest_lower_bound(identity,inverse(X_92))) = multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))),multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92)))) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_92)))]]) ).

cnf(refute_0_288,plain,
    ( inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))) != multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92)))
    | inverse(greatest_lower_bound(identity,inverse(X_92))) = multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_92),inverse(X_92)),greatest_lower_bound(identity,inverse(X_92))) )],[refute_0_286,refute_0_287]) ).

cnf(refute_0_289,plain,
    inverse(greatest_lower_bound(identity,inverse(X_92))) = multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))),multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92)))) )],[refute_0_271,refute_0_288]) ).

cnf(refute_0_290,plain,
    inverse(multiply(X_29,inverse(X))) = multiply(inverse(inverse(X)),inverse(X_29)),
    inference(subst,[],[p11_3:[bind(X,$fot(X_29)),bind(Y,$fot(inverse(X)))]]) ).

cnf(refute_0_291,plain,
    ( inverse(multiply(X_29,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_29))
    | inverse(inverse(X)) != X
    | inverse(multiply(X_29,inverse(X))) = multiply(X,inverse(X_29)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_29,inverse(X))),multiply(inverse(inverse(X)),inverse(X_29))) ),[1,0],$fot(X)]]) ).

cnf(refute_0_292,plain,
    ( inverse(multiply(X_29,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_29))
    | inverse(multiply(X_29,inverse(X))) = multiply(X,inverse(X_29)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p11_2,refute_0_291]) ).

cnf(refute_0_293,plain,
    inverse(multiply(X_29,inverse(X))) = multiply(X,inverse(X_29)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_29,inverse(X))),multiply(inverse(inverse(X)),inverse(X_29))) )],[refute_0_290,refute_0_292]) ).

cnf(refute_0_294,plain,
    inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))) = multiply(X_92,inverse(greatest_lower_bound(identity,X_92))),
    inference(subst,[],[refute_0_293:[bind(X,$fot(X_92)),bind(X_29,$fot(greatest_lower_bound(identity,X_92)))]]) ).

cnf(refute_0_295,plain,
    multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))) = inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))),
    inference(subst,[],[refute_0_221:[bind(X,$fot(greatest_lower_bound(identity,X_92))),bind(Y,$fot(inverse(X_92)))]]) ).

cnf(refute_0_296,plain,
    ( multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))) != inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92)))
    | inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))) != multiply(X_92,inverse(greatest_lower_bound(identity,X_92)))
    | multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))) = multiply(X_92,inverse(greatest_lower_bound(identity,X_92))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))))),bind(Z0,$fot(multiply(X_92,inverse(greatest_lower_bound(identity,X_92)))))]]) ).

cnf(refute_0_297,plain,
    ( inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))) != multiply(X_92,inverse(greatest_lower_bound(identity,X_92)))
    | multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))) = multiply(X_92,inverse(greatest_lower_bound(identity,X_92))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))),inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92)))) )],[refute_0_295,refute_0_296]) ).

cnf(refute_0_298,plain,
    multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))) = multiply(X_92,inverse(greatest_lower_bound(identity,X_92))),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))),multiply(X_92,inverse(greatest_lower_bound(identity,X_92)))) )],[refute_0_294,refute_0_297]) ).

cnf(refute_0_299,plain,
    ( multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))) != multiply(X_92,inverse(greatest_lower_bound(identity,X_92)))
    | inverse(greatest_lower_bound(identity,inverse(X_92))) != multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92)))
    | inverse(greatest_lower_bound(identity,inverse(X_92))) = multiply(X_92,inverse(greatest_lower_bound(identity,X_92))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_92))),multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92)))) ),[1],$fot(multiply(X_92,inverse(greatest_lower_bound(identity,X_92))))]]) ).

cnf(refute_0_300,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_92))) != multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92)))
    | inverse(greatest_lower_bound(identity,inverse(X_92))) = multiply(X_92,inverse(greatest_lower_bound(identity,X_92))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92))),multiply(X_92,inverse(greatest_lower_bound(identity,X_92)))) )],[refute_0_298,refute_0_299]) ).

cnf(refute_0_301,plain,
    inverse(greatest_lower_bound(identity,inverse(X_92))) = multiply(X_92,inverse(greatest_lower_bound(identity,X_92))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_92))),multiply(inverse(inverse(X_92)),inverse(greatest_lower_bound(identity,X_92)))) )],[refute_0_289,refute_0_300]) ).

cnf(refute_0_302,plain,
    inverse(greatest_lower_bound(identity,inverse(X_121))) = multiply(X_121,inverse(greatest_lower_bound(identity,X_121))),
    inference(subst,[],[refute_0_301:[bind(X_92,$fot(X_121))]]) ).

cnf(refute_0_303,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_121))) != multiply(X_121,inverse(greatest_lower_bound(identity,X_121)))
    | multiply(X_121,inverse(greatest_lower_bound(identity,X_121))) = inverse(greatest_lower_bound(identity,inverse(X_121))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_121))))),bind(Y0,$fot(multiply(X_121,inverse(greatest_lower_bound(identity,X_121)))))]]) ).

cnf(refute_0_304,plain,
    multiply(X_121,inverse(greatest_lower_bound(identity,X_121))) = inverse(greatest_lower_bound(identity,inverse(X_121))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_121))),multiply(X_121,inverse(greatest_lower_bound(identity,X_121)))) )],[refute_0_302,refute_0_303]) ).

cnf(refute_0_305,plain,
    ( multiply(X_121,inverse(greatest_lower_bound(identity,X_121))) != inverse(greatest_lower_bound(identity,inverse(X_121)))
    | multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),multiply(X_121,inverse(greatest_lower_bound(identity,X_121))))
    | multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),inverse(greatest_lower_bound(identity,inverse(X_121)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))),least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),multiply(X_121,inverse(greatest_lower_bound(identity,X_121))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_121))))]]) ).

cnf(refute_0_306,plain,
    ( multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),multiply(X_121,inverse(greatest_lower_bound(identity,X_121))))
    | multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),inverse(greatest_lower_bound(identity,inverse(X_121)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_121,inverse(greatest_lower_bound(identity,X_121))),inverse(greatest_lower_bound(identity,inverse(X_121)))) )],[refute_0_304,refute_0_305]) ).

cnf(refute_0_307,plain,
    multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),inverse(greatest_lower_bound(identity,inverse(X_121)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))),least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),multiply(X_121,inverse(greatest_lower_bound(identity,X_121))))) )],[refute_0_270,refute_0_306]) ).

cnf(refute_0_308,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116))))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116)))) = multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116))))))]]) ).

cnf(refute_0_309,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116)))) = multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)),least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116))))) )],[refute_0_260,refute_0_308]) ).

cnf(refute_0_310,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),inverse(greatest_lower_bound(identity,inverse(X_121)))) = multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity)),
    inference(subst,[],[refute_0_309:[bind(X_116,$fot(X_121))]]) ).

cnf(refute_0_311,plain,
    ( multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),inverse(greatest_lower_bound(identity,inverse(X_121))))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),inverse(greatest_lower_bound(identity,inverse(X_121)))) != multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity))
    | multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) = multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))),multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),inverse(greatest_lower_bound(identity,inverse(X_121)))))]]) ).

cnf(refute_0_312,plain,
    ( multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),inverse(greatest_lower_bound(identity,inverse(X_121))))
    | multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) = multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),inverse(greatest_lower_bound(identity,inverse(X_121)))),multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity))) )],[refute_0_310,refute_0_311]) ).

cnf(refute_0_313,plain,
    multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) = multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))),least_upper_bound(inverse(greatest_lower_bound(identity,X_121)),inverse(greatest_lower_bound(identity,inverse(X_121))))) )],[refute_0_307,refute_0_312]) ).

cnf(refute_0_314,plain,
    ( multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) != multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity))
    | multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity)) = multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity))))]]) ).

cnf(refute_0_315,plain,
    multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity)) = multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,identity),inverse(greatest_lower_bound(identity,X_121))),multiply(inverse(greatest_lower_bound(identity,X_121)),least_upper_bound(X_121,identity))) )],[refute_0_313,refute_0_314]) ).

cnf(refute_0_316,plain,
    multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) = multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116))),
    inference(subst,[],[refute_0_315:[bind(X_121,$fot(X_116))]]) ).

cnf(refute_0_317,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) != multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116)))
    | multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116))))
    | multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)),least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116))))) ),[0],$fot(multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116))))]]) ).

cnf(refute_0_318,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116))))
    | multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)),multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116)))) )],[refute_0_316,refute_0_317]) ).

cnf(refute_0_319,plain,
    multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_116)),least_upper_bound(X_116,identity)),least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116))))) )],[refute_0_260,refute_0_318]) ).

cnf(refute_0_320,plain,
    ( multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116))))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116)))) = multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116))))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116))))))]]) ).

cnf(refute_0_321,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116)))) = multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_116,identity),inverse(greatest_lower_bound(identity,X_116))),least_upper_bound(inverse(greatest_lower_bound(identity,X_116)),inverse(greatest_lower_bound(identity,inverse(X_116))))) )],[refute_0_319,refute_0_320]) ).

cnf(refute_0_322,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))) = multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),
    inference(subst,[],[refute_0_321:[bind(X_116,$fot(X_86))]]) ).

cnf(refute_0_323,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))))]]) ).

cnf(refute_0_324,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))) != multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86)))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))) != multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86)))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))) = multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))),multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86)))) ),[1,0],$fot(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))))]]) ).

cnf(refute_0_325,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))) != multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86)))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))) = multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))),multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86)))) )],[refute_0_323,refute_0_324]) ).

cnf(refute_0_326,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))) = multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86)))) )],[refute_0_322,refute_0_325]) ).

cnf(refute_0_327,plain,
    ( multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) != multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))) != multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86)))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))))),bind(Y0,$fot(multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))))),bind(Z0,$fot(multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))))]]) ).

cnf(refute_0_328,plain,
    ( multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) != multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))),multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86)))) )],[refute_0_326,refute_0_327]) ).

cnf(refute_0_329,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_86,identity),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))),multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))) )],[refute_0_230,refute_0_328]) ).

cnf(refute_0_330,plain,
    greatest_lower_bound(X_14,least_upper_bound(X_14,X_15)) = X_14,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_14)),bind(Y,$fot(X_15))]]) ).

cnf(refute_0_331,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_332,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_12:[bind(X0,$fot(least_upper_bound(X_15,X_14))),bind(Y0,$fot(least_upper_bound(X_14,X_15)))]]) ).

cnf(refute_0_333,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_331,refute_0_332]) ).

cnf(refute_0_334,plain,
    ( greatest_lower_bound(X_14,least_upper_bound(X_14,X_15)) != X_14
    | least_upper_bound(X_14,X_15) != least_upper_bound(X_15,X_14)
    | greatest_lower_bound(X_14,least_upper_bound(X_15,X_14)) = X_14 ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_14,least_upper_bound(X_14,X_15)),X_14) ),[0,1],$fot(least_upper_bound(X_15,X_14))]]) ).

cnf(refute_0_335,plain,
    ( greatest_lower_bound(X_14,least_upper_bound(X_14,X_15)) != X_14
    | greatest_lower_bound(X_14,least_upper_bound(X_15,X_14)) = X_14 ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,X_15),least_upper_bound(X_15,X_14)) )],[refute_0_333,refute_0_334]) ).

cnf(refute_0_336,plain,
    greatest_lower_bound(X_14,least_upper_bound(X_15,X_14)) = X_14,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_14,least_upper_bound(X_14,X_15)),X_14) )],[refute_0_330,refute_0_335]) ).

cnf(refute_0_337,plain,
    greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))) = greatest_lower_bound(X_17,Y),
    inference(subst,[],[refute_0_336:[bind(X_14,$fot(greatest_lower_bound(X_17,Y))),bind(X_15,$fot(X_17))]]) ).

cnf(refute_0_338,plain,
    least_upper_bound(X_17,greatest_lower_bound(X_17,Y)) = X_17,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_17))]]) ).

cnf(refute_0_339,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))) != greatest_lower_bound(X_17,Y)
    | least_upper_bound(X_17,greatest_lower_bound(X_17,Y)) != X_17
    | greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))),greatest_lower_bound(X_17,Y)) ),[0,1],$fot(X_17)]]) ).

cnf(refute_0_340,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))) != greatest_lower_bound(X_17,Y)
    | greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_17,greatest_lower_bound(X_17,Y)),X_17) )],[refute_0_338,refute_0_339]) ).

cnf(refute_0_341,plain,
    greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))),greatest_lower_bound(X_17,Y)) )],[refute_0_337,refute_0_340]) ).

cnf(refute_0_342,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_12:[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_343,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_342]) ).

cnf(refute_0_344,plain,
    greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)),
    inference(subst,[],[refute_0_343:[bind(X,$fot(X_17)),bind(Z,$fot(X_17))]]) ).

cnf(refute_0_345,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) != greatest_lower_bound(X_17,Y)
    | greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) != greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17))
    | greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)) = greatest_lower_bound(X_17,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17),greatest_lower_bound(X_17,Y)) ),[0],$fot(greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)))]]) ).

cnf(refute_0_346,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) != greatest_lower_bound(X_17,Y)
    | greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)) = greatest_lower_bound(X_17,Y) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17),greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17))) )],[refute_0_344,refute_0_345]) ).

cnf(refute_0_347,plain,
    greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)) = greatest_lower_bound(X_17,Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17),greatest_lower_bound(X_17,Y)) )],[refute_0_341,refute_0_346]) ).

cnf(refute_0_348,plain,
    greatest_lower_bound(X_19,greatest_lower_bound(X_18,X_19)) = greatest_lower_bound(X_19,X_18),
    inference(subst,[],[refute_0_347:[bind(Y,$fot(X_18)),bind(X_17,$fot(X_19))]]) ).

cnf(refute_0_349,plain,
    greatest_lower_bound(X_19,X_18) = greatest_lower_bound(X_18,X_19),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_19)),bind(Y,$fot(X_18))]]) ).

cnf(refute_0_350,plain,
    ( greatest_lower_bound(X_19,X_18) != greatest_lower_bound(X_18,X_19)
    | greatest_lower_bound(X_18,X_19) = greatest_lower_bound(X_19,X_18) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_19,X_18))),bind(Y0,$fot(greatest_lower_bound(X_18,X_19)))]]) ).

cnf(refute_0_351,plain,
    greatest_lower_bound(X_18,X_19) = greatest_lower_bound(X_19,X_18),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,X_18),greatest_lower_bound(X_18,X_19)) )],[refute_0_349,refute_0_350]) ).

cnf(refute_0_352,plain,
    ( greatest_lower_bound(X_18,X_19) != greatest_lower_bound(X_19,X_18)
    | greatest_lower_bound(X_19,greatest_lower_bound(X_18,X_19)) != greatest_lower_bound(X_19,X_18)
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_18)) = greatest_lower_bound(X_19,X_18) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_18,X_19)),greatest_lower_bound(X_19,X_18)) ),[0,1],$fot(greatest_lower_bound(X_19,X_18))]]) ).

cnf(refute_0_353,plain,
    ( greatest_lower_bound(X_19,greatest_lower_bound(X_18,X_19)) != greatest_lower_bound(X_19,X_18)
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_18)) = greatest_lower_bound(X_19,X_18) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,X_19),greatest_lower_bound(X_19,X_18)) )],[refute_0_351,refute_0_352]) ).

cnf(refute_0_354,plain,
    greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_18)) = greatest_lower_bound(X_19,X_18),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_18,X_19)),greatest_lower_bound(X_19,X_18)) )],[refute_0_348,refute_0_353]) ).

cnf(refute_0_355,plain,
    greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87)),
    inference(subst,[],[refute_0_354:[bind(X_18,$fot(multiply(X_89,X_87))),bind(X_19,$fot(multiply(X_88,X_87)))]]) ).

cnf(refute_0_356,plain,
    multiply(greatest_lower_bound(X_88,X_89),X_87) = greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_87)),bind(Y,$fot(X_88)),bind(Z,$fot(X_89))]]) ).

cnf(refute_0_357,plain,
    ( multiply(greatest_lower_bound(X_88,X_89),X_87) != greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))
    | greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87)) = multiply(greatest_lower_bound(X_88,X_89),X_87) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_88,X_89),X_87))),bind(Y0,$fot(greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))))]]) ).

cnf(refute_0_358,plain,
    greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87)) = multiply(greatest_lower_bound(X_88,X_89),X_87),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,X_89),X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) )],[refute_0_356,refute_0_357]) ).

cnf(refute_0_359,plain,
    ( greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87)) != multiply(greatest_lower_bound(X_88,X_89),X_87)
    | greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) != greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))
    | greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = multiply(greatest_lower_bound(X_88,X_89),X_87) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) ),[1],$fot(multiply(greatest_lower_bound(X_88,X_89),X_87))]]) ).

cnf(refute_0_360,plain,
    ( greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) != greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))
    | greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = multiply(greatest_lower_bound(X_88,X_89),X_87) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87)),multiply(greatest_lower_bound(X_88,X_89),X_87)) )],[refute_0_358,refute_0_359]) ).

cnf(refute_0_361,plain,
    greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = multiply(greatest_lower_bound(X_88,X_89),X_87),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) )],[refute_0_355,refute_0_360]) ).

cnf(refute_0_362,plain,
    greatest_lower_bound(X_88,X_88) = X_88,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_88))]]) ).

cnf(refute_0_363,plain,
    greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)) = greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)))]]) ).

cnf(refute_0_364,plain,
    ( greatest_lower_bound(X_88,X_88) != X_88
    | greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)) != greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88))
    | greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)) = greatest_lower_bound(X_89,X_88) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88))) ),[1,1],$fot(X_88)]]) ).

cnf(refute_0_365,plain,
    ( greatest_lower_bound(X_88,X_88) != X_88
    | greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)) = greatest_lower_bound(X_89,X_88) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88))) )],[refute_0_363,refute_0_364]) ).

cnf(refute_0_366,plain,
    greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)) = greatest_lower_bound(X_89,X_88),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_88,X_88),X_88) )],[refute_0_362,refute_0_365]) ).

cnf(refute_0_367,plain,
    multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87) = multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87))]]) ).

cnf(refute_0_368,plain,
    ( multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87) != multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87)
    | greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)) != greatest_lower_bound(X_89,X_88)
    | multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87) = multiply(greatest_lower_bound(X_89,X_88),X_87) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87),multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87)) ),[1,0],$fot(greatest_lower_bound(X_89,X_88))]]) ).

cnf(refute_0_369,plain,
    ( greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)) != greatest_lower_bound(X_89,X_88)
    | multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87) = multiply(greatest_lower_bound(X_89,X_88),X_87) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87),multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87)) )],[refute_0_367,refute_0_368]) ).

cnf(refute_0_370,plain,
    multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87) = multiply(greatest_lower_bound(X_89,X_88),X_87),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),greatest_lower_bound(X_89,X_88)) )],[refute_0_366,refute_0_369]) ).

cnf(refute_0_371,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_12:[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_372,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_371]) ).

cnf(refute_0_373,plain,
    greatest_lower_bound(multiply(X_89,X_87),multiply(greatest_lower_bound(X_88,X_88),X_87)) = multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87),
    inference(subst,[],[refute_0_372:[bind(X,$fot(X_87)),bind(Y,$fot(X_89)),bind(Z,$fot(greatest_lower_bound(X_88,X_88)))]]) ).

cnf(refute_0_374,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)) = greatest_lower_bound(greatest_lower_bound(X_33,X_34),X),
    inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_33,X_34)))]]) ).

cnf(refute_0_375,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_34,X)) = greatest_lower_bound(greatest_lower_bound(X_33,X_34),X),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_33)),bind(Y,$fot(X_34)),bind(Z,$fot(X))]]) ).

cnf(refute_0_376,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_34,X)) != greatest_lower_bound(greatest_lower_bound(X_33,X_34),X)
    | greatest_lower_bound(greatest_lower_bound(X_33,X_34),X) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,X)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_33,greatest_lower_bound(X_34,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_33,X_34),X)))]]) ).

cnf(refute_0_377,plain,
    greatest_lower_bound(greatest_lower_bound(X_33,X_34),X) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_34,X)),greatest_lower_bound(greatest_lower_bound(X_33,X_34),X)) )],[refute_0_375,refute_0_376]) ).

cnf(refute_0_378,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)) != greatest_lower_bound(greatest_lower_bound(X_33,X_34),X)
    | greatest_lower_bound(greatest_lower_bound(X_33,X_34),X) != greatest_lower_bound(X_33,greatest_lower_bound(X_34,X))
    | greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)),greatest_lower_bound(X_33,greatest_lower_bound(X_34,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_33,X_34),X))]]) ).

cnf(refute_0_379,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)) != greatest_lower_bound(greatest_lower_bound(X_33,X_34),X)
    | greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_33,X_34),X),greatest_lower_bound(X_33,greatest_lower_bound(X_34,X))) )],[refute_0_377,refute_0_378]) ).

cnf(refute_0_380,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)),greatest_lower_bound(greatest_lower_bound(X_33,X_34),X)) )],[refute_0_374,refute_0_379]) ).

cnf(refute_0_381,plain,
    greatest_lower_bound(X,greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X)),
    inference(subst,[],[refute_0_380:[bind(X_33,$fot(multiply(X_88,X_87))),bind(X_34,$fot(multiply(X_89,X_87)))]]) ).

cnf(refute_0_382,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) != greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X))
    | greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87)) != multiply(greatest_lower_bound(X_88,X_89),X_87)
    | greatest_lower_bound(X,multiply(greatest_lower_bound(X_88,X_89),X_87)) = greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))),greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X))) ),[0,1],$fot(multiply(greatest_lower_bound(X_88,X_89),X_87))]]) ).

cnf(refute_0_383,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) != greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X))
    | greatest_lower_bound(X,multiply(greatest_lower_bound(X_88,X_89),X_87)) = greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87)),multiply(greatest_lower_bound(X_88,X_89),X_87)) )],[refute_0_358,refute_0_382]) ).

cnf(refute_0_384,plain,
    greatest_lower_bound(X,multiply(greatest_lower_bound(X_88,X_89),X_87)) = greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))),greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X))) )],[refute_0_381,refute_0_383]) ).

cnf(refute_0_385,plain,
    ( greatest_lower_bound(X,multiply(greatest_lower_bound(X_88,X_89),X_87)) != greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X))
    | greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_88,X_89),X_87)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X,multiply(greatest_lower_bound(X_88,X_89),X_87)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X))))]]) ).

cnf(refute_0_386,plain,
    greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_88,X_89),X_87)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,multiply(greatest_lower_bound(X_88,X_89),X_87)),greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_89,X_87),X))) )],[refute_0_384,refute_0_385]) ).

cnf(refute_0_387,plain,
    greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = greatest_lower_bound(multiply(X_89,X_87),multiply(greatest_lower_bound(X_88,X_88),X_87)),
    inference(subst,[],[refute_0_386:[bind(X,$fot(multiply(X_89,X_87))),bind(X_89,$fot(X_88))]]) ).

cnf(refute_0_388,plain,
    ( greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) != greatest_lower_bound(multiply(X_89,X_87),multiply(greatest_lower_bound(X_88,X_88),X_87))
    | greatest_lower_bound(multiply(X_89,X_87),multiply(greatest_lower_bound(X_88,X_88),X_87)) != multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87)
    | greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_89,X_87),multiply(greatest_lower_bound(X_88,X_88),X_87)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87)))]]) ).

cnf(refute_0_389,plain,
    ( greatest_lower_bound(multiply(X_89,X_87),multiply(greatest_lower_bound(X_88,X_88),X_87)) != multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87)
    | greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))),greatest_lower_bound(multiply(X_89,X_87),multiply(greatest_lower_bound(X_88,X_88),X_87))) )],[refute_0_387,refute_0_388]) ).

cnf(refute_0_390,plain,
    greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_89,X_87),multiply(greatest_lower_bound(X_88,X_88),X_87)),multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87)) )],[refute_0_373,refute_0_389]) ).

cnf(refute_0_391,plain,
    ( multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87) != multiply(greatest_lower_bound(X_89,X_88),X_87)
    | greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) != multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87)
    | greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = multiply(greatest_lower_bound(X_89,X_88),X_87) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87))),bind(Z0,$fot(multiply(greatest_lower_bound(X_89,X_88),X_87)))]]) ).

cnf(refute_0_392,plain,
    ( multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87) != multiply(greatest_lower_bound(X_89,X_88),X_87)
    | greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = multiply(greatest_lower_bound(X_89,X_88),X_87) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))),multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87)) )],[refute_0_390,refute_0_391]) ).

cnf(refute_0_393,plain,
    greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) = multiply(greatest_lower_bound(X_89,X_88),X_87),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_89,greatest_lower_bound(X_88,X_88)),X_87),multiply(greatest_lower_bound(X_89,X_88),X_87)) )],[refute_0_370,refute_0_392]) ).

cnf(refute_0_394,plain,
    ( greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) != multiply(greatest_lower_bound(X_88,X_89),X_87)
    | greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) != multiply(greatest_lower_bound(X_89,X_88),X_87)
    | multiply(greatest_lower_bound(X_89,X_88),X_87) = multiply(greatest_lower_bound(X_88,X_89),X_87) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))),multiply(greatest_lower_bound(X_88,X_89),X_87)) ),[0],$fot(multiply(greatest_lower_bound(X_89,X_88),X_87))]]) ).

cnf(refute_0_395,plain,
    ( greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))) != multiply(greatest_lower_bound(X_88,X_89),X_87)
    | multiply(greatest_lower_bound(X_89,X_88),X_87) = multiply(greatest_lower_bound(X_88,X_89),X_87) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))),multiply(greatest_lower_bound(X_89,X_88),X_87)) )],[refute_0_393,refute_0_394]) ).

cnf(refute_0_396,plain,
    multiply(greatest_lower_bound(X_89,X_88),X_87) = multiply(greatest_lower_bound(X_88,X_89),X_87),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(X_89,X_87))),multiply(greatest_lower_bound(X_88,X_89),X_87)) )],[refute_0_361,refute_0_395]) ).

cnf(refute_0_397,plain,
    multiply(greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)),X_170) = multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170),
    inference(subst,[],[refute_0_396:[bind(X_87,$fot(X_170)),bind(X_88,$fot(least_upper_bound(X_15,X_23))),bind(X_89,$fot(least_upper_bound(X_23,X_15)))]]) ).

cnf(refute_0_398,plain,
    greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,least_upper_bound(X_23,X_15))) = least_upper_bound(X_23,X_15),
    inference(subst,[],[refute_0_336:[bind(X_14,$fot(least_upper_bound(X_23,X_15)))]]) ).

cnf(refute_0_399,plain,
    least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))) = least_upper_bound(X_11,X_15),
    inference(subst,[],[refute_0_71:[bind(X_10,$fot(least_upper_bound(X_11,X_15)))]]) ).

cnf(refute_0_400,plain,
    greatest_lower_bound(X_11,least_upper_bound(X_11,X_15)) = X_11,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_11)),bind(Y,$fot(X_15))]]) ).

cnf(refute_0_401,plain,
    ( greatest_lower_bound(X_11,least_upper_bound(X_11,X_15)) != X_11
    | least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))) != least_upper_bound(X_11,X_15)
    | least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,X_15) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))),least_upper_bound(X_11,X_15)) ),[0,1],$fot(X_11)]]) ).

cnf(refute_0_402,plain,
    ( least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))) != least_upper_bound(X_11,X_15)
    | least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,X_15) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,least_upper_bound(X_11,X_15)),X_11) )],[refute_0_400,refute_0_401]) ).

cnf(refute_0_403,plain,
    least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,X_15),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))),least_upper_bound(X_11,X_15)) )],[refute_0_399,refute_0_402]) ).

cnf(refute_0_404,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_12:[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_405,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_404]) ).

cnf(refute_0_406,plain,
    least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,least_upper_bound(X_15,X_11)),
    inference(subst,[],[refute_0_405:[bind(X,$fot(X_11)),bind(Y,$fot(X_15)),bind(Z,$fot(X_11))]]) ).

cnf(refute_0_407,plain,
    ( least_upper_bound(least_upper_bound(X_11,X_15),X_11) != least_upper_bound(X_11,X_15)
    | least_upper_bound(least_upper_bound(X_11,X_15),X_11) != least_upper_bound(X_11,least_upper_bound(X_15,X_11))
    | least_upper_bound(X_11,least_upper_bound(X_15,X_11)) = least_upper_bound(X_11,X_15) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),X_11),least_upper_bound(X_11,X_15)) ),[0],$fot(least_upper_bound(X_11,least_upper_bound(X_15,X_11)))]]) ).

cnf(refute_0_408,plain,
    ( least_upper_bound(least_upper_bound(X_11,X_15),X_11) != least_upper_bound(X_11,X_15)
    | least_upper_bound(X_11,least_upper_bound(X_15,X_11)) = least_upper_bound(X_11,X_15) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),X_11),least_upper_bound(X_11,least_upper_bound(X_15,X_11))) )],[refute_0_406,refute_0_407]) ).

cnf(refute_0_409,plain,
    least_upper_bound(X_11,least_upper_bound(X_15,X_11)) = least_upper_bound(X_11,X_15),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),X_11),least_upper_bound(X_11,X_15)) )],[refute_0_403,refute_0_408]) ).

cnf(refute_0_410,plain,
    least_upper_bound(X_15,least_upper_bound(X_23,X_15)) = least_upper_bound(X_15,X_23),
    inference(subst,[],[refute_0_409:[bind(X_11,$fot(X_15)),bind(X_15,$fot(X_23))]]) ).

cnf(refute_0_411,plain,
    ( greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,least_upper_bound(X_23,X_15))) != least_upper_bound(X_23,X_15)
    | least_upper_bound(X_15,least_upper_bound(X_23,X_15)) != least_upper_bound(X_15,X_23)
    | greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)) = least_upper_bound(X_23,X_15) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,least_upper_bound(X_23,X_15))),least_upper_bound(X_23,X_15)) ),[0,1],$fot(least_upper_bound(X_15,X_23))]]) ).

cnf(refute_0_412,plain,
    ( greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,least_upper_bound(X_23,X_15))) != least_upper_bound(X_23,X_15)
    | greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)) = least_upper_bound(X_23,X_15) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_23,X_15)),least_upper_bound(X_15,X_23)) )],[refute_0_410,refute_0_411]) ).

cnf(refute_0_413,plain,
    greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)) = least_upper_bound(X_23,X_15),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,least_upper_bound(X_23,X_15))),least_upper_bound(X_23,X_15)) )],[refute_0_398,refute_0_412]) ).

cnf(refute_0_414,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)),X_170) != multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170)
    | greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)) != least_upper_bound(X_23,X_15)
    | multiply(least_upper_bound(X_23,X_15),X_170) = multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)),X_170),multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170)) ),[0,0],$fot(least_upper_bound(X_23,X_15))]]) ).

cnf(refute_0_415,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)),X_170) != multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170)
    | multiply(least_upper_bound(X_23,X_15),X_170) = multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)),least_upper_bound(X_23,X_15)) )],[refute_0_413,refute_0_414]) ).

cnf(refute_0_416,plain,
    multiply(least_upper_bound(X_23,X_15),X_170) = multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)),X_170),multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170)) )],[refute_0_397,refute_0_415]) ).

cnf(refute_0_417,plain,
    greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)) = least_upper_bound(X_15,X_23),
    inference(subst,[],[refute_0_413:[bind(X_15,$fot(X_23)),bind(X_23,$fot(X_15))]]) ).

cnf(refute_0_418,plain,
    multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170) = multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170))]]) ).

cnf(refute_0_419,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170) != multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170)
    | greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)) != least_upper_bound(X_15,X_23)
    | multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170) = multiply(least_upper_bound(X_15,X_23),X_170) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170),multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170)) ),[1,0],$fot(least_upper_bound(X_15,X_23))]]) ).

cnf(refute_0_420,plain,
    ( greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)) != least_upper_bound(X_15,X_23)
    | multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170) = multiply(least_upper_bound(X_15,X_23),X_170) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170),multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170)) )],[refute_0_418,refute_0_419]) ).

cnf(refute_0_421,plain,
    multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170) = multiply(least_upper_bound(X_15,X_23),X_170),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),least_upper_bound(X_15,X_23)) )],[refute_0_417,refute_0_420]) ).

cnf(refute_0_422,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170) != multiply(least_upper_bound(X_15,X_23),X_170)
    | multiply(least_upper_bound(X_23,X_15),X_170) != multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170)
    | multiply(least_upper_bound(X_23,X_15),X_170) = multiply(least_upper_bound(X_15,X_23),X_170) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_23,X_15),X_170),multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170)) ),[1],$fot(multiply(least_upper_bound(X_15,X_23),X_170))]]) ).

cnf(refute_0_423,plain,
    ( multiply(least_upper_bound(X_23,X_15),X_170) != multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170)
    | multiply(least_upper_bound(X_23,X_15),X_170) = multiply(least_upper_bound(X_15,X_23),X_170) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170),multiply(least_upper_bound(X_15,X_23),X_170)) )],[refute_0_421,refute_0_422]) ).

cnf(refute_0_424,plain,
    multiply(least_upper_bound(X_23,X_15),X_170) = multiply(least_upper_bound(X_15,X_23),X_170),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_23,X_15),X_170),multiply(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),X_170)) )],[refute_0_416,refute_0_423]) ).

cnf(refute_0_425,plain,
    ( multiply(least_upper_bound(X_23,X_15),X_170) != multiply(least_upper_bound(X_15,X_23),X_170)
    | multiply(least_upper_bound(X_15,X_23),X_170) = multiply(least_upper_bound(X_23,X_15),X_170) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_23,X_15),X_170))),bind(Y0,$fot(multiply(least_upper_bound(X_15,X_23),X_170)))]]) ).

cnf(refute_0_426,plain,
    multiply(least_upper_bound(X_15,X_23),X_170) = multiply(least_upper_bound(X_23,X_15),X_170),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_23,X_15),X_170),multiply(least_upper_bound(X_15,X_23),X_170)) )],[refute_0_424,refute_0_425]) ).

cnf(refute_0_427,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))),
    inference(subst,[],[refute_0_426:[bind(X_15,$fot(inverse(greatest_lower_bound(identity,inverse(X_86))))),bind(X_170,$fot(inverse(least_upper_bound(identity,X_86)))),bind(X_23,$fot(inverse(greatest_lower_bound(identity,X_86))))]]) ).

cnf(refute_0_428,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))) != multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) != multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86)))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))))),bind(Y0,$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))))),bind(Z0,$fot(multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))))]]) ).

cnf(refute_0_429,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))) != multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))),multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86)))) )],[refute_0_427,refute_0_428]) ).

cnf(refute_0_430,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X_86)),inverse(greatest_lower_bound(identity,inverse(X_86)))),inverse(least_upper_bound(identity,X_86))),multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))) )],[refute_0_329,refute_0_429]) ).

cnf(refute_0_431,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))) != multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))
    | inverse(greatest_lower_bound(identity,X_86)) != multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86)))
    | inverse(greatest_lower_bound(identity,X_86)) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_86)),multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86)))) ),[1],$fot(multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))))]]) ).

cnf(refute_0_432,plain,
    ( inverse(greatest_lower_bound(identity,X_86)) != multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86)))
    | inverse(greatest_lower_bound(identity,X_86)) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86))),multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))) )],[refute_0_430,refute_0_431]) ).

cnf(refute_0_433,plain,
    inverse(greatest_lower_bound(identity,X_86)) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_86)),multiply(least_upper_bound(inverse(greatest_lower_bound(identity,inverse(X_86))),inverse(greatest_lower_bound(identity,X_86))),inverse(least_upper_bound(identity,X_86)))) )],[refute_0_219,refute_0_432]) ).

cnf(refute_0_434,plain,
    multiply(least_upper_bound(X_121,X_122),inverse(X_121)) = least_upper_bound(multiply(X_121,inverse(X_121)),multiply(X_122,inverse(X_121))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_121))),bind(Y,$fot(X_121)),bind(Z,$fot(X_122))]]) ).

cnf(refute_0_435,plain,
    multiply(X_121,inverse(X_121)) = identity,
    inference(subst,[],[refute_0_29:[bind(X_1,$fot(X_121))]]) ).

cnf(refute_0_436,plain,
    ( multiply(X_121,inverse(X_121)) != identity
    | multiply(least_upper_bound(X_121,X_122),inverse(X_121)) != least_upper_bound(multiply(X_121,inverse(X_121)),multiply(X_122,inverse(X_121)))
    | multiply(least_upper_bound(X_121,X_122),inverse(X_121)) = least_upper_bound(identity,multiply(X_122,inverse(X_121))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_121,X_122),inverse(X_121)),least_upper_bound(multiply(X_121,inverse(X_121)),multiply(X_122,inverse(X_121)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_437,plain,
    ( multiply(least_upper_bound(X_121,X_122),inverse(X_121)) != least_upper_bound(multiply(X_121,inverse(X_121)),multiply(X_122,inverse(X_121)))
    | multiply(least_upper_bound(X_121,X_122),inverse(X_121)) = least_upper_bound(identity,multiply(X_122,inverse(X_121))) ),
    inference(resolve,[$cnf( $equal(multiply(X_121,inverse(X_121)),identity) )],[refute_0_435,refute_0_436]) ).

cnf(refute_0_438,plain,
    multiply(least_upper_bound(X_121,X_122),inverse(X_121)) = least_upper_bound(identity,multiply(X_122,inverse(X_121))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,X_122),inverse(X_121)),least_upper_bound(multiply(X_121,inverse(X_121)),multiply(X_122,inverse(X_121)))) )],[refute_0_434,refute_0_437]) ).

cnf(refute_0_439,plain,
    multiply(least_upper_bound(X_127,identity),inverse(X_127)) = least_upper_bound(identity,multiply(identity,inverse(X_127))),
    inference(subst,[],[refute_0_438:[bind(X_121,$fot(X_127)),bind(X_122,$fot(identity))]]) ).

cnf(refute_0_440,plain,
    multiply(identity,inverse(X_127)) = inverse(X_127),
    inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_127)))]]) ).

cnf(refute_0_441,plain,
    ( multiply(identity,inverse(X_127)) != inverse(X_127)
    | multiply(least_upper_bound(X_127,identity),inverse(X_127)) != least_upper_bound(identity,multiply(identity,inverse(X_127)))
    | multiply(least_upper_bound(X_127,identity),inverse(X_127)) = least_upper_bound(identity,inverse(X_127)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_127,identity),inverse(X_127)),least_upper_bound(identity,multiply(identity,inverse(X_127)))) ),[1,1],$fot(inverse(X_127))]]) ).

cnf(refute_0_442,plain,
    ( multiply(least_upper_bound(X_127,identity),inverse(X_127)) != least_upper_bound(identity,multiply(identity,inverse(X_127)))
    | multiply(least_upper_bound(X_127,identity),inverse(X_127)) = least_upper_bound(identity,inverse(X_127)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_127)),inverse(X_127)) )],[refute_0_440,refute_0_441]) ).

cnf(refute_0_443,plain,
    multiply(least_upper_bound(X_127,identity),inverse(X_127)) = least_upper_bound(identity,inverse(X_127)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_127,identity),inverse(X_127)),least_upper_bound(identity,multiply(identity,inverse(X_127)))) )],[refute_0_439,refute_0_442]) ).

cnf(refute_0_444,plain,
    multiply(least_upper_bound(X_86,identity),inverse(X_86)) = least_upper_bound(identity,inverse(X_86)),
    inference(subst,[],[refute_0_443:[bind(X_127,$fot(X_86))]]) ).

cnf(refute_0_445,plain,
    multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169))))),
    inference(subst,[],[refute_0_269:[bind(X_120,$fot(inverse(least_upper_bound(identity,inverse(X_169))))),bind(X_121,$fot(least_upper_bound(X_169,identity)))]]) ).

cnf(refute_0_446,plain,
    inverse(inverse(X_144)) = multiply(least_upper_bound(X_144,identity),inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity)))),
    inference(subst,[],[refute_0_172:[bind(X,$fot(inverse(X_144))),bind(X_69,$fot(least_upper_bound(X_144,identity)))]]) ).

cnf(refute_0_447,plain,
    multiply(inverse(X_143),least_upper_bound(X_143,identity)) = least_upper_bound(inverse(X_143),multiply(inverse(X_143),X_143)),
    inference(subst,[],[refute_0_241:[bind(X_115,$fot(inverse(X_143))),bind(X_116,$fot(X_143))]]) ).

cnf(refute_0_448,plain,
    multiply(inverse(X_143),X_143) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_143))]]) ).

cnf(refute_0_449,plain,
    ( multiply(inverse(X_143),X_143) != identity
    | multiply(inverse(X_143),least_upper_bound(X_143,identity)) != least_upper_bound(inverse(X_143),multiply(inverse(X_143),X_143))
    | multiply(inverse(X_143),least_upper_bound(X_143,identity)) = least_upper_bound(inverse(X_143),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_143),least_upper_bound(X_143,identity)),least_upper_bound(inverse(X_143),multiply(inverse(X_143),X_143))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_450,plain,
    ( multiply(inverse(X_143),least_upper_bound(X_143,identity)) != least_upper_bound(inverse(X_143),multiply(inverse(X_143),X_143))
    | multiply(inverse(X_143),least_upper_bound(X_143,identity)) = least_upper_bound(inverse(X_143),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_143),X_143),identity) )],[refute_0_448,refute_0_449]) ).

cnf(refute_0_451,plain,
    multiply(inverse(X_143),least_upper_bound(X_143,identity)) = least_upper_bound(inverse(X_143),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_143),least_upper_bound(X_143,identity)),least_upper_bound(inverse(X_143),multiply(inverse(X_143),X_143))) )],[refute_0_447,refute_0_450]) ).

cnf(refute_0_452,plain,
    least_upper_bound(inverse(X_143),identity) = least_upper_bound(identity,inverse(X_143)),
    inference(subst,[],[refute_0_180:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_143)))]]) ).

cnf(refute_0_453,plain,
    ( multiply(inverse(X_143),least_upper_bound(X_143,identity)) != least_upper_bound(inverse(X_143),identity)
    | least_upper_bound(inverse(X_143),identity) != least_upper_bound(identity,inverse(X_143))
    | multiply(inverse(X_143),least_upper_bound(X_143,identity)) = least_upper_bound(identity,inverse(X_143)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_143),least_upper_bound(X_143,identity)),least_upper_bound(identity,inverse(X_143))) ),[0],$fot(least_upper_bound(inverse(X_143),identity))]]) ).

cnf(refute_0_454,plain,
    ( multiply(inverse(X_143),least_upper_bound(X_143,identity)) != least_upper_bound(inverse(X_143),identity)
    | multiply(inverse(X_143),least_upper_bound(X_143,identity)) = least_upper_bound(identity,inverse(X_143)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_143),identity),least_upper_bound(identity,inverse(X_143))) )],[refute_0_452,refute_0_453]) ).

cnf(refute_0_455,plain,
    multiply(inverse(X_143),least_upper_bound(X_143,identity)) = least_upper_bound(identity,inverse(X_143)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_143),least_upper_bound(X_143,identity)),least_upper_bound(inverse(X_143),identity)) )],[refute_0_451,refute_0_454]) ).

cnf(refute_0_456,plain,
    multiply(inverse(X_144),least_upper_bound(X_144,identity)) = least_upper_bound(identity,inverse(X_144)),
    inference(subst,[],[refute_0_455:[bind(X_143,$fot(X_144))]]) ).

cnf(refute_0_457,plain,
    ( multiply(inverse(X_144),least_upper_bound(X_144,identity)) != least_upper_bound(identity,inverse(X_144))
    | inverse(inverse(X_144)) != multiply(least_upper_bound(X_144,identity),inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))))
    | inverse(inverse(X_144)) = multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_144)),multiply(least_upper_bound(X_144,identity),inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))))) ),[1,1,0],$fot(least_upper_bound(identity,inverse(X_144)))]]) ).

cnf(refute_0_458,plain,
    ( inverse(inverse(X_144)) != multiply(least_upper_bound(X_144,identity),inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))))
    | inverse(inverse(X_144)) = multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_144),least_upper_bound(X_144,identity)),least_upper_bound(identity,inverse(X_144))) )],[refute_0_456,refute_0_457]) ).

cnf(refute_0_459,plain,
    inverse(inverse(X_144)) = multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_144)),multiply(least_upper_bound(X_144,identity),inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))))) )],[refute_0_446,refute_0_458]) ).

cnf(refute_0_460,plain,
    inverse(inverse(X_144)) = X_144,
    inference(subst,[],[p11_2:[bind(X,$fot(X_144))]]) ).

cnf(refute_0_461,plain,
    ( inverse(inverse(X_144)) != X_144
    | inverse(inverse(X_144)) != multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144))))
    | X_144 = multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_144)),multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144))))) ),[0],$fot(X_144)]]) ).

cnf(refute_0_462,plain,
    ( inverse(inverse(X_144)) != multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144))))
    | X_144 = multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_144)),X_144) )],[refute_0_460,refute_0_461]) ).

cnf(refute_0_463,plain,
    X_144 = multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_144)),multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144))))) )],[refute_0_459,refute_0_462]) ).

cnf(refute_0_464,plain,
    X_169 = multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169)))),
    inference(subst,[],[refute_0_463:[bind(X_144,$fot(X_169))]]) ).

cnf(refute_0_465,plain,
    ( X_169 != multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169))))
    | multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169)))) = X_169 ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X_169)),bind(Y0,$fot(multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169))))))]]) ).

cnf(refute_0_466,plain,
    multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169)))) = X_169,
    inference(resolve,[$cnf( $equal(X_169,multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169))))) )],[refute_0_464,refute_0_465]) ).

cnf(refute_0_467,plain,
    ( multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169)))) != X_169
    | multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169)))))
    | multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169)))))) ),[1,1],$fot(X_169)]]) ).

cnf(refute_0_468,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169)))))
    | multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169)))),X_169) )],[refute_0_466,refute_0_467]) ).

cnf(refute_0_469,plain,
    multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),multiply(least_upper_bound(X_169,identity),inverse(least_upper_bound(identity,inverse(X_169)))))) )],[refute_0_445,refute_0_468]) ).

cnf(refute_0_470,plain,
    least_upper_bound(identity,least_upper_bound(X_169,identity)) = least_upper_bound(identity,X_169),
    inference(subst,[],[refute_0_409:[bind(X_11,$fot(identity)),bind(X_15,$fot(X_169))]]) ).

cnf(refute_0_471,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))))]]) ).

cnf(refute_0_472,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))) != multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169))))
    | least_upper_bound(identity,least_upper_bound(X_169,identity)) != least_upper_bound(identity,X_169)
    | multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))),multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169))))) ),[1,0],$fot(least_upper_bound(identity,X_169))]]) ).

cnf(refute_0_473,plain,
    ( least_upper_bound(identity,least_upper_bound(X_169,identity)) != least_upper_bound(identity,X_169)
    | multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))),multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169))))) )],[refute_0_471,refute_0_472]) ).

cnf(refute_0_474,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_169,identity)),least_upper_bound(identity,X_169)) )],[refute_0_470,refute_0_473]) ).

cnf(refute_0_475,plain,
    least_upper_bound(X_22,least_upper_bound(X_23,X_22)) = least_upper_bound(X_22,X_23),
    inference(subst,[],[refute_0_409:[bind(X_11,$fot(X_22)),bind(X_15,$fot(X_23))]]) ).

cnf(refute_0_476,plain,
    least_upper_bound(X_22,X_23) = least_upper_bound(X_23,X_22),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_22)),bind(Y,$fot(X_23))]]) ).

cnf(refute_0_477,plain,
    ( least_upper_bound(X_22,X_23) != least_upper_bound(X_23,X_22)
    | least_upper_bound(X_23,X_22) = least_upper_bound(X_22,X_23) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_22,X_23))),bind(Y0,$fot(least_upper_bound(X_23,X_22)))]]) ).

cnf(refute_0_478,plain,
    least_upper_bound(X_23,X_22) = least_upper_bound(X_22,X_23),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,X_23),least_upper_bound(X_23,X_22)) )],[refute_0_476,refute_0_477]) ).

cnf(refute_0_479,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_23,X_22)) != least_upper_bound(X_22,X_23)
    | least_upper_bound(X_23,X_22) != least_upper_bound(X_22,X_23)
    | least_upper_bound(X_22,least_upper_bound(X_22,X_23)) = least_upper_bound(X_22,X_23) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,X_22)),least_upper_bound(X_22,X_23)) ),[0,1],$fot(least_upper_bound(X_22,X_23))]]) ).

cnf(refute_0_480,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_23,X_22)) != least_upper_bound(X_22,X_23)
    | least_upper_bound(X_22,least_upper_bound(X_22,X_23)) = least_upper_bound(X_22,X_23) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_23,X_22),least_upper_bound(X_22,X_23)) )],[refute_0_478,refute_0_479]) ).

cnf(refute_0_481,plain,
    least_upper_bound(X_22,least_upper_bound(X_22,X_23)) = least_upper_bound(X_22,X_23),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,X_22)),least_upper_bound(X_22,X_23)) )],[refute_0_475,refute_0_480]) ).

cnf(refute_0_482,plain,
    least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) = least_upper_bound(X_22,multiply(X_148,X_22)),
    inference(subst,[],[refute_0_481:[bind(X_23,$fot(multiply(X_148,X_22)))]]) ).

cnf(refute_0_483,plain,
    multiply(least_upper_bound(X_148,identity),X_22) = least_upper_bound(X_22,multiply(X_148,X_22)),
    inference(subst,[],[refute_0_269:[bind(X_120,$fot(X_22)),bind(X_121,$fot(X_148))]]) ).

cnf(refute_0_484,plain,
    ( multiply(least_upper_bound(X_148,identity),X_22) != least_upper_bound(X_22,multiply(X_148,X_22))
    | least_upper_bound(X_22,multiply(X_148,X_22)) = multiply(least_upper_bound(X_148,identity),X_22) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_148,identity),X_22))),bind(Y0,$fot(least_upper_bound(X_22,multiply(X_148,X_22))))]]) ).

cnf(refute_0_485,plain,
    least_upper_bound(X_22,multiply(X_148,X_22)) = multiply(least_upper_bound(X_148,identity),X_22),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_148,identity),X_22),least_upper_bound(X_22,multiply(X_148,X_22))) )],[refute_0_483,refute_0_484]) ).

cnf(refute_0_486,plain,
    ( least_upper_bound(X_22,multiply(X_148,X_22)) != multiply(least_upper_bound(X_148,identity),X_22)
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) != least_upper_bound(X_22,multiply(X_148,X_22))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) = multiply(least_upper_bound(X_148,identity),X_22) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))),least_upper_bound(X_22,multiply(X_148,X_22))) ),[1],$fot(multiply(least_upper_bound(X_148,identity),X_22))]]) ).

cnf(refute_0_487,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) != least_upper_bound(X_22,multiply(X_148,X_22))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) = multiply(least_upper_bound(X_148,identity),X_22) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,multiply(X_148,X_22)),multiply(least_upper_bound(X_148,identity),X_22)) )],[refute_0_485,refute_0_486]) ).

cnf(refute_0_488,plain,
    least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) = multiply(least_upper_bound(X_148,identity),X_22),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))),least_upper_bound(X_22,multiply(X_148,X_22))) )],[refute_0_482,refute_0_487]) ).

cnf(refute_0_489,plain,
    least_upper_bound(identity,least_upper_bound(X_148,identity)) = least_upper_bound(identity,X_148),
    inference(subst,[],[refute_0_409:[bind(X_11,$fot(identity)),bind(X_15,$fot(X_148))]]) ).

cnf(refute_0_490,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22) = multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22))]]) ).

cnf(refute_0_491,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22) != multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)
    | least_upper_bound(identity,least_upper_bound(X_148,identity)) != least_upper_bound(identity,X_148)
    | multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22) = multiply(least_upper_bound(identity,X_148),X_22) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22),multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)) ),[1,0],$fot(least_upper_bound(identity,X_148))]]) ).

cnf(refute_0_492,plain,
    ( least_upper_bound(identity,least_upper_bound(X_148,identity)) != least_upper_bound(identity,X_148)
    | multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22) = multiply(least_upper_bound(identity,X_148),X_22) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22),multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)) )],[refute_0_490,refute_0_491]) ).

cnf(refute_0_493,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22) = multiply(least_upper_bound(identity,X_148),X_22),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_148,identity)),least_upper_bound(identity,X_148)) )],[refute_0_489,refute_0_492]) ).

cnf(refute_0_494,plain,
    greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
    inference(subst,[],[refute_0_413:[bind(X_15,$fot(multiply(Y,X))),bind(X_23,$fot(multiply(Z,X)))]]) ).

cnf(refute_0_495,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_12:[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_496,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_495]) ).

cnf(refute_0_497,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) != least_upper_bound(multiply(Z,X),multiply(Y,X))
    | least_upper_bound(multiply(Y,X),multiply(Z,X)) != multiply(least_upper_bound(Y,Z),X)
    | greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) ),[0,1],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).

cnf(refute_0_498,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) != least_upper_bound(multiply(Z,X),multiply(Y,X))
    | greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(Z,X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_496,refute_0_497]) ).

cnf(refute_0_499,plain,
    greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_494,refute_0_498]) ).

cnf(refute_0_500,plain,
    greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) = least_upper_bound(Y,Z),
    inference(subst,[],[refute_0_413:[bind(X_15,$fot(Z)),bind(X_23,$fot(Y))]]) ).

cnf(refute_0_501,plain,
    multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))]]) ).

cnf(refute_0_502,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
    | greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
    | multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) ),[1,0],$fot(least_upper_bound(Y,Z))]]) ).

cnf(refute_0_503,plain,
    ( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
    | multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_501,refute_0_502]) ).

cnf(refute_0_504,plain,
    multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_500,refute_0_503]) ).

cnf(refute_0_505,plain,
    greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
    inference(subst,[],[refute_0_372:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).

cnf(refute_0_506,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
    | greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
    | greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)))),bind(Y0,$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).

cnf(refute_0_507,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
    | greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_505,refute_0_506]) ).

cnf(refute_0_508,plain,
    greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_504,refute_0_507]) ).

cnf(refute_0_509,plain,
    least_upper_bound(multiply(Z,X),multiply(Y,X)) = multiply(least_upper_bound(Z,Y),X),
    inference(subst,[],[refute_0_496:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_510,plain,
    greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).

cnf(refute_0_511,plain,
    ( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
    | least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
    | greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) ),[1,1],$fot(multiply(least_upper_bound(Z,Y),X))]]) ).

cnf(refute_0_512,plain,
    ( least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
    | greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_510,refute_0_511]) ).

cnf(refute_0_513,plain,
    greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_509,refute_0_512]) ).

cnf(refute_0_514,plain,
    ( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
    | greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))
    | greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).

cnf(refute_0_515,plain,
    ( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
    | greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))) )],[refute_0_513,refute_0_514]) ).

cnf(refute_0_516,plain,
    greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_508,refute_0_515]) ).

cnf(refute_0_517,plain,
    greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
    inference(subst,[],[refute_0_35:[bind(X,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y,$fot(least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).

cnf(refute_0_518,plain,
    ( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
    | greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
    | greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).

cnf(refute_0_519,plain,
    ( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
    | greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_517,refute_0_518]) ).

cnf(refute_0_520,plain,
    greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_516,refute_0_519]) ).

cnf(refute_0_521,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != multiply(least_upper_bound(Y,Z),X)
    | greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
    | multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) ),[0],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).

cnf(refute_0_522,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
    | multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_520,refute_0_521]) ).

cnf(refute_0_523,plain,
    ( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
    | least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
    | multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),[0],$fot(least_upper_bound(multiply(Z,X),multiply(Y,X)))]]) ).

cnf(refute_0_524,plain,
    ( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
    | multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_509,refute_0_523]) ).

cnf(refute_0_525,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
    | multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_522,refute_0_524]) ).

cnf(refute_0_526,plain,
    multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_499,refute_0_525]) ).

cnf(refute_0_527,plain,
    ( multiply(least_upper_bound(Y,Z),X) != multiply(least_upper_bound(Z,Y),X)
    | multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(multiply(least_upper_bound(Z,Y),X)))]]) ).

cnf(refute_0_528,plain,
    multiply(least_upper_bound(Z,Y),X) = multiply(least_upper_bound(Y,Z),X),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_526,refute_0_527]) ).

cnf(refute_0_529,plain,
    multiply(least_upper_bound(least_upper_bound(X_148,identity),identity),X_22) = multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22),
    inference(subst,[],[refute_0_528:[bind(X,$fot(X_22)),bind(Y,$fot(identity)),bind(Z,$fot(least_upper_bound(X_148,identity)))]]) ).

cnf(refute_0_530,plain,
    ( multiply(least_upper_bound(X_121,identity),X_120) != least_upper_bound(X_120,multiply(X_121,X_120))
    | least_upper_bound(X_120,multiply(X_121,X_120)) = multiply(least_upper_bound(X_121,identity),X_120) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_121,identity),X_120))),bind(Y0,$fot(least_upper_bound(X_120,multiply(X_121,X_120))))]]) ).

cnf(refute_0_531,plain,
    least_upper_bound(X_120,multiply(X_121,X_120)) = multiply(least_upper_bound(X_121,identity),X_120),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,identity),X_120),least_upper_bound(X_120,multiply(X_121,X_120))) )],[refute_0_269,refute_0_530]) ).

cnf(refute_0_532,plain,
    least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)) = multiply(least_upper_bound(least_upper_bound(X_148,identity),identity),X_22),
    inference(subst,[],[refute_0_531:[bind(X_120,$fot(X_22)),bind(X_121,$fot(least_upper_bound(X_148,identity)))]]) ).

cnf(refute_0_533,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_148,identity),identity),X_22) != multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)
    | least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)) != multiply(least_upper_bound(least_upper_bound(X_148,identity),identity),X_22)
    | least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)) = multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_148,identity),identity),X_22))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)))]]) ).

cnf(refute_0_534,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_148,identity),identity),X_22) != multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)
    | least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)) = multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)),multiply(least_upper_bound(least_upper_bound(X_148,identity),identity),X_22)) )],[refute_0_532,refute_0_533]) ).

cnf(refute_0_535,plain,
    least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)) = multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_148,identity),identity),X_22),multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)) )],[refute_0_529,refute_0_534]) ).

cnf(refute_0_536,plain,
    least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) = least_upper_bound(least_upper_bound(X_26,least_upper_bound(X_15,X_26)),X_28),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_26)),bind(Y,$fot(least_upper_bound(X_15,X_26))),bind(Z,$fot(X_28))]]) ).

cnf(refute_0_537,plain,
    least_upper_bound(X_26,least_upper_bound(X_15,X_26)) = least_upper_bound(X_26,X_15),
    inference(subst,[],[refute_0_409:[bind(X_11,$fot(X_26))]]) ).

cnf(refute_0_538,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_15,X_26)) != least_upper_bound(X_26,X_15)
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) != least_upper_bound(least_upper_bound(X_26,least_upper_bound(X_15,X_26)),X_28)
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) = least_upper_bound(least_upper_bound(X_26,X_15),X_28) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)),least_upper_bound(least_upper_bound(X_26,least_upper_bound(X_15,X_26)),X_28)) ),[1,0],$fot(least_upper_bound(X_26,X_15))]]) ).

cnf(refute_0_539,plain,
    ( least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) != least_upper_bound(least_upper_bound(X_26,least_upper_bound(X_15,X_26)),X_28)
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) = least_upper_bound(least_upper_bound(X_26,X_15),X_28) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_15,X_26)),least_upper_bound(X_26,X_15)) )],[refute_0_537,refute_0_538]) ).

cnf(refute_0_540,plain,
    least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) = least_upper_bound(least_upper_bound(X_26,X_15),X_28),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)),least_upper_bound(least_upper_bound(X_26,least_upper_bound(X_15,X_26)),X_28)) )],[refute_0_536,refute_0_539]) ).

cnf(refute_0_541,plain,
    least_upper_bound(X_26,least_upper_bound(X_27,least_upper_bound(X_15,X_27))) = least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(least_upper_bound(X_15,X_27)))]]) ).

cnf(refute_0_542,plain,
    least_upper_bound(X_27,least_upper_bound(X_15,X_27)) = least_upper_bound(X_27,X_15),
    inference(subst,[],[refute_0_409:[bind(X_11,$fot(X_27))]]) ).

cnf(refute_0_543,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_27,least_upper_bound(X_15,X_27))) != least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27))
    | least_upper_bound(X_27,least_upper_bound(X_15,X_27)) != least_upper_bound(X_27,X_15)
    | least_upper_bound(X_26,least_upper_bound(X_27,X_15)) = least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_27,least_upper_bound(X_15,X_27))),least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27))) ),[0,1],$fot(least_upper_bound(X_27,X_15))]]) ).

cnf(refute_0_544,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_27,least_upper_bound(X_15,X_27))) != least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27))
    | least_upper_bound(X_26,least_upper_bound(X_27,X_15)) = least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(X_15,X_27)),least_upper_bound(X_27,X_15)) )],[refute_0_542,refute_0_543]) ).

cnf(refute_0_545,plain,
    least_upper_bound(X_26,least_upper_bound(X_27,X_15)) = least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_27,least_upper_bound(X_15,X_27))),least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27))) )],[refute_0_541,refute_0_544]) ).

cnf(refute_0_546,plain,
    least_upper_bound(least_upper_bound(X_26,X_27),X_15) = least_upper_bound(X_26,least_upper_bound(X_27,X_15)),
    inference(subst,[],[refute_0_405:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(X_15))]]) ).

cnf(refute_0_547,plain,
    least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)) = least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)))]]) ).

cnf(refute_0_548,plain,
    ( least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)) != least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15))
    | least_upper_bound(least_upper_bound(X_26,X_27),X_15) != least_upper_bound(X_26,least_upper_bound(X_27,X_15))
    | least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)),least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15))) ),[1,1],$fot(least_upper_bound(X_26,least_upper_bound(X_27,X_15)))]]) ).

cnf(refute_0_549,plain,
    ( least_upper_bound(least_upper_bound(X_26,X_27),X_15) != least_upper_bound(X_26,least_upper_bound(X_27,X_15))
    | least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)),least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15))) )],[refute_0_547,refute_0_548]) ).

cnf(refute_0_550,plain,
    least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_26,X_27),X_15),least_upper_bound(X_26,least_upper_bound(X_27,X_15))) )],[refute_0_546,refute_0_549]) ).

cnf(refute_0_551,plain,
    ( least_upper_bound(X,least_upper_bound(X_26,X_27)) != least_upper_bound(X_26,least_upper_bound(X_27,X))
    | least_upper_bound(X_26,least_upper_bound(X_27,X)) = least_upper_bound(X,least_upper_bound(X_26,X_27)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_26,X_27)))),bind(Y0,$fot(least_upper_bound(X_26,least_upper_bound(X_27,X))))]]) ).

cnf(refute_0_552,plain,
    least_upper_bound(X_26,least_upper_bound(X_27,X)) = least_upper_bound(X,least_upper_bound(X_26,X_27)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_26,X_27)),least_upper_bound(X_26,least_upper_bound(X_27,X))) )],[refute_0_128,refute_0_551]) ).

cnf(refute_0_553,plain,
    least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)) = least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)),
    inference(subst,[],[refute_0_552:[bind(X,$fot(X_27)),bind(X_26,$fot(least_upper_bound(X_26,X_27))),bind(X_27,$fot(X_15))]]) ).

cnf(refute_0_554,plain,
    ( least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15)))
    | least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)) != least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15))
    | least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)))),bind(Y0,$fot(least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)))),bind(Z0,$fot(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15)))))]]) ).

cnf(refute_0_555,plain,
    ( least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15)))
    | least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)),least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15))) )],[refute_0_553,refute_0_554]) ).

cnf(refute_0_556,plain,
    least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(least_upper_bound(X_26,X_27),X_15)),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15)))) )],[refute_0_550,refute_0_555]) ).

cnf(refute_0_557,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_27,X_15)) != least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27))
    | least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15)))
    | least_upper_bound(X_26,least_upper_bound(X_27,X_15)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_26,least_upper_bound(X_27,X_15)),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)))]]) ).

cnf(refute_0_558,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_27,X_15)) != least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27))
    | least_upper_bound(X_26,least_upper_bound(X_27,X_15)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27)),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15)))) )],[refute_0_556,refute_0_557]) ).

cnf(refute_0_559,plain,
    least_upper_bound(X_26,least_upper_bound(X_27,X_15)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_27,X_15)),least_upper_bound(least_upper_bound(X_26,X_27),least_upper_bound(X_15,X_27))) )],[refute_0_545,refute_0_558]) ).

cnf(refute_0_560,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_27,X_15)) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15)))
    | least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15))) = least_upper_bound(X_26,least_upper_bound(X_27,X_15)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_26,least_upper_bound(X_27,X_15)))),bind(Y0,$fot(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15)))))]]) ).

cnf(refute_0_561,plain,
    least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15))) = least_upper_bound(X_26,least_upper_bound(X_27,X_15)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_27,X_15)),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_27,X_15)))) )],[refute_0_559,refute_0_560]) ).

cnf(refute_0_562,plain,
    least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(X_26,X_28))) = least_upper_bound(X_15,least_upper_bound(X_26,X_28)),
    inference(subst,[],[refute_0_561:[bind(X_15,$fot(X_28)),bind(X_26,$fot(X_15)),bind(X_27,$fot(X_26))]]) ).

cnf(refute_0_563,plain,
    least_upper_bound(least_upper_bound(X_15,X_26),X_28) = least_upper_bound(X_15,least_upper_bound(X_26,X_28)),
    inference(subst,[],[refute_0_405:[bind(X,$fot(X_15)),bind(Y,$fot(X_26)),bind(Z,$fot(X_28))]]) ).

cnf(refute_0_564,plain,
    least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) = least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)))]]) ).

cnf(refute_0_565,plain,
    ( least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) != least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28))
    | least_upper_bound(least_upper_bound(X_15,X_26),X_28) != least_upper_bound(X_15,least_upper_bound(X_26,X_28))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) = least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(X_26,X_28))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28))) ),[1,1],$fot(least_upper_bound(X_15,least_upper_bound(X_26,X_28)))]]) ).

cnf(refute_0_566,plain,
    ( least_upper_bound(least_upper_bound(X_15,X_26),X_28) != least_upper_bound(X_15,least_upper_bound(X_26,X_28))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) = least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(X_26,X_28))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28))) )],[refute_0_564,refute_0_565]) ).

cnf(refute_0_567,plain,
    least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) = least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(X_26,X_28))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,X_26),X_28),least_upper_bound(X_15,least_upper_bound(X_26,X_28))) )],[refute_0_563,refute_0_566]) ).

cnf(refute_0_568,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(X_26,X_28))) != least_upper_bound(X_15,least_upper_bound(X_26,X_28))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) != least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(X_26,X_28)))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) = least_upper_bound(X_15,least_upper_bound(X_26,X_28)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)))),bind(Y0,$fot(least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(X_26,X_28))))),bind(Z0,$fot(least_upper_bound(X_15,least_upper_bound(X_26,X_28))))]]) ).

cnf(refute_0_569,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(X_26,X_28))) != least_upper_bound(X_15,least_upper_bound(X_26,X_28))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) = least_upper_bound(X_15,least_upper_bound(X_26,X_28)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)),least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(X_26,X_28)))) )],[refute_0_567,refute_0_568]) ).

cnf(refute_0_570,plain,
    least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) = least_upper_bound(X_15,least_upper_bound(X_26,X_28)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(X_26,X_28))),least_upper_bound(X_15,least_upper_bound(X_26,X_28))) )],[refute_0_562,refute_0_569]) ).

cnf(refute_0_571,plain,
    ( least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) != least_upper_bound(X_15,least_upper_bound(X_26,X_28))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) != least_upper_bound(least_upper_bound(X_26,X_15),X_28)
    | least_upper_bound(X_15,least_upper_bound(X_26,X_28)) = least_upper_bound(least_upper_bound(X_26,X_15),X_28) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)),least_upper_bound(least_upper_bound(X_26,X_15),X_28)) ),[0],$fot(least_upper_bound(X_15,least_upper_bound(X_26,X_28)))]]) ).

cnf(refute_0_572,plain,
    ( least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) != least_upper_bound(least_upper_bound(X_26,X_15),X_28)
    | least_upper_bound(X_15,least_upper_bound(X_26,X_28)) = least_upper_bound(least_upper_bound(X_26,X_15),X_28) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)),least_upper_bound(X_15,least_upper_bound(X_26,X_28))) )],[refute_0_570,refute_0_571]) ).

cnf(refute_0_573,plain,
    least_upper_bound(least_upper_bound(X_26,X_15),X_28) = least_upper_bound(X_26,least_upper_bound(X_15,X_28)),
    inference(subst,[],[refute_0_405:[bind(X,$fot(X_26)),bind(Y,$fot(X_15)),bind(Z,$fot(X_28))]]) ).

cnf(refute_0_574,plain,
    ( least_upper_bound(X_15,least_upper_bound(X_26,X_28)) != least_upper_bound(least_upper_bound(X_26,X_15),X_28)
    | least_upper_bound(least_upper_bound(X_26,X_15),X_28) != least_upper_bound(X_26,least_upper_bound(X_15,X_28))
    | least_upper_bound(X_15,least_upper_bound(X_26,X_28)) = least_upper_bound(X_26,least_upper_bound(X_15,X_28)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_15,least_upper_bound(X_26,X_28)),least_upper_bound(X_26,least_upper_bound(X_15,X_28))) ),[0],$fot(least_upper_bound(least_upper_bound(X_26,X_15),X_28))]]) ).

cnf(refute_0_575,plain,
    ( least_upper_bound(X_15,least_upper_bound(X_26,X_28)) != least_upper_bound(least_upper_bound(X_26,X_15),X_28)
    | least_upper_bound(X_15,least_upper_bound(X_26,X_28)) = least_upper_bound(X_26,least_upper_bound(X_15,X_28)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_26,X_15),X_28),least_upper_bound(X_26,least_upper_bound(X_15,X_28))) )],[refute_0_573,refute_0_574]) ).

cnf(refute_0_576,plain,
    ( least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)) != least_upper_bound(least_upper_bound(X_26,X_15),X_28)
    | least_upper_bound(X_15,least_upper_bound(X_26,X_28)) = least_upper_bound(X_26,least_upper_bound(X_15,X_28)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_26,X_28)),least_upper_bound(least_upper_bound(X_26,X_15),X_28)) )],[refute_0_572,refute_0_575]) ).

cnf(refute_0_577,plain,
    least_upper_bound(X_15,least_upper_bound(X_26,X_28)) = least_upper_bound(X_26,least_upper_bound(X_15,X_28)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_15,X_26),X_28)),least_upper_bound(least_upper_bound(X_26,X_15),X_28)) )],[refute_0_540,refute_0_576]) ).

cnf(refute_0_578,plain,
    least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_148,X_15))) = least_upper_bound(X_26,least_upper_bound(X_15,multiply(X_148,X_15))),
    inference(subst,[],[refute_0_577:[bind(X_28,$fot(multiply(X_148,X_15)))]]) ).

cnf(refute_0_579,plain,
    multiply(least_upper_bound(X_148,identity),X_15) = least_upper_bound(X_15,multiply(X_148,X_15)),
    inference(subst,[],[refute_0_269:[bind(X_120,$fot(X_15)),bind(X_121,$fot(X_148))]]) ).

cnf(refute_0_580,plain,
    ( multiply(least_upper_bound(X_148,identity),X_15) != least_upper_bound(X_15,multiply(X_148,X_15))
    | least_upper_bound(X_15,multiply(X_148,X_15)) = multiply(least_upper_bound(X_148,identity),X_15) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_148,identity),X_15))),bind(Y0,$fot(least_upper_bound(X_15,multiply(X_148,X_15))))]]) ).

cnf(refute_0_581,plain,
    least_upper_bound(X_15,multiply(X_148,X_15)) = multiply(least_upper_bound(X_148,identity),X_15),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_148,identity),X_15),least_upper_bound(X_15,multiply(X_148,X_15))) )],[refute_0_579,refute_0_580]) ).

cnf(refute_0_582,plain,
    ( least_upper_bound(X_15,multiply(X_148,X_15)) != multiply(least_upper_bound(X_148,identity),X_15)
    | least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_148,X_15))) != least_upper_bound(X_26,least_upper_bound(X_15,multiply(X_148,X_15)))
    | least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_148,X_15))) = least_upper_bound(X_26,multiply(least_upper_bound(X_148,identity),X_15)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_148,X_15))),least_upper_bound(X_26,least_upper_bound(X_15,multiply(X_148,X_15)))) ),[1,1],$fot(multiply(least_upper_bound(X_148,identity),X_15))]]) ).

cnf(refute_0_583,plain,
    ( least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_148,X_15))) != least_upper_bound(X_26,least_upper_bound(X_15,multiply(X_148,X_15)))
    | least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_148,X_15))) = least_upper_bound(X_26,multiply(least_upper_bound(X_148,identity),X_15)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_148,X_15)),multiply(least_upper_bound(X_148,identity),X_15)) )],[refute_0_581,refute_0_582]) ).

cnf(refute_0_584,plain,
    least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_148,X_15))) = least_upper_bound(X_26,multiply(least_upper_bound(X_148,identity),X_15)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_148,X_15))),least_upper_bound(X_26,least_upper_bound(X_15,multiply(X_148,X_15)))) )],[refute_0_578,refute_0_583]) ).

cnf(refute_0_585,plain,
    least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) = least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)),
    inference(subst,[],[refute_0_584:[bind(X_15,$fot(X_22)),bind(X_26,$fot(X_22))]]) ).

cnf(refute_0_586,plain,
    ( least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)) != multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) != least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) = multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))))),bind(Y0,$fot(least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)))]]) ).

cnf(refute_0_587,plain,
    ( least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)) != multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) = multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))),least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22))) )],[refute_0_585,refute_0_586]) ).

cnf(refute_0_588,plain,
    least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) = multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,multiply(least_upper_bound(X_148,identity),X_22)),multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)) )],[refute_0_535,refute_0_587]) ).

cnf(refute_0_589,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22) != multiply(least_upper_bound(identity,X_148),X_22)
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) != multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) = multiply(least_upper_bound(identity,X_148),X_22) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_148),X_22)))]]) ).

cnf(refute_0_590,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22) != multiply(least_upper_bound(identity,X_148),X_22)
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) = multiply(least_upper_bound(identity,X_148),X_22) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))),multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22)) )],[refute_0_588,refute_0_589]) ).

cnf(refute_0_591,plain,
    least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) = multiply(least_upper_bound(identity,X_148),X_22),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_148,identity)),X_22),multiply(least_upper_bound(identity,X_148),X_22)) )],[refute_0_493,refute_0_590]) ).

cnf(refute_0_592,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) != multiply(least_upper_bound(X_148,identity),X_22)
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) != multiply(least_upper_bound(identity,X_148),X_22)
    | multiply(least_upper_bound(identity,X_148),X_22) = multiply(least_upper_bound(X_148,identity),X_22) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))),multiply(least_upper_bound(X_148,identity),X_22)) ),[0],$fot(multiply(least_upper_bound(identity,X_148),X_22))]]) ).

cnf(refute_0_593,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))) != multiply(least_upper_bound(X_148,identity),X_22)
    | multiply(least_upper_bound(identity,X_148),X_22) = multiply(least_upper_bound(X_148,identity),X_22) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))),multiply(least_upper_bound(identity,X_148),X_22)) )],[refute_0_591,refute_0_592]) ).

cnf(refute_0_594,plain,
    multiply(least_upper_bound(identity,X_148),X_22) = multiply(least_upper_bound(X_148,identity),X_22),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_148,X_22))),multiply(least_upper_bound(X_148,identity),X_22)) )],[refute_0_488,refute_0_593]) ).

cnf(refute_0_595,plain,
    ( multiply(least_upper_bound(identity,X_148),X_22) != multiply(least_upper_bound(X_148,identity),X_22)
    | multiply(least_upper_bound(X_148,identity),X_22) = multiply(least_upper_bound(identity,X_148),X_22) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(identity,X_148),X_22))),bind(Y0,$fot(multiply(least_upper_bound(X_148,identity),X_22)))]]) ).

cnf(refute_0_596,plain,
    multiply(least_upper_bound(X_148,identity),X_22) = multiply(least_upper_bound(identity,X_148),X_22),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_148),X_22),multiply(least_upper_bound(X_148,identity),X_22)) )],[refute_0_594,refute_0_595]) ).

cnf(refute_0_597,plain,
    multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))),
    inference(subst,[],[refute_0_596:[bind(X_148,$fot(least_upper_bound(X_169,identity))),bind(X_22,$fot(inverse(least_upper_bound(identity,inverse(X_169)))))]]) ).

cnf(refute_0_598,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))) != multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169))))
    | multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) != multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169))))
    | multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169))))))]]) ).

cnf(refute_0_599,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))) != multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169))))
    | multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))),multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169))))) )],[refute_0_597,refute_0_598]) ).

cnf(refute_0_600,plain,
    multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_169,identity)),inverse(least_upper_bound(identity,inverse(X_169)))),multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169))))) )],[refute_0_474,refute_0_599]) ).

cnf(refute_0_601,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) != multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169))))
    | multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169)
    | multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169)) ),[0],$fot(multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))))]]) ).

cnf(refute_0_602,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169)
    | multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))),multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169))))) )],[refute_0_600,refute_0_601]) ).

cnf(refute_0_603,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159))),
    inference(subst,[],[refute_0_241:[bind(X_115,$fot(inverse(least_upper_bound(identity,inverse(X_159))))),bind(X_116,$fot(least_upper_bound(identity,X_159)))]]) ).

cnf(refute_0_604,plain,
    inverse(multiply(inverse(X),multiply(inverse(inverse(X)),X_70))) = multiply(inverse(multiply(inverse(inverse(X)),X_70)),X),
    inference(subst,[],[refute_0_22:[bind(X_30,$fot(multiply(inverse(inverse(X)),X_70)))]]) ).

cnf(refute_0_605,plain,
    X_70 = multiply(inverse(X),multiply(inverse(inverse(X)),X_70)),
    inference(subst,[],[refute_0_165:[bind(X_66,$fot(inverse(X))),bind(X_68,$fot(X_70))]]) ).

cnf(refute_0_606,plain,
    ( X_70 != multiply(inverse(X),multiply(inverse(inverse(X)),X_70))
    | multiply(inverse(X),multiply(inverse(inverse(X)),X_70)) = X_70 ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X_70)),bind(Y0,$fot(multiply(inverse(X),multiply(inverse(inverse(X)),X_70))))]]) ).

cnf(refute_0_607,plain,
    multiply(inverse(X),multiply(inverse(inverse(X)),X_70)) = X_70,
    inference(resolve,[$cnf( $equal(X_70,multiply(inverse(X),multiply(inverse(inverse(X)),X_70))) )],[refute_0_605,refute_0_606]) ).

cnf(refute_0_608,plain,
    ( multiply(inverse(X),multiply(inverse(inverse(X)),X_70)) != X_70
    | inverse(multiply(inverse(X),multiply(inverse(inverse(X)),X_70))) != multiply(inverse(multiply(inverse(inverse(X)),X_70)),X)
    | inverse(X_70) = multiply(inverse(multiply(inverse(inverse(X)),X_70)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),multiply(inverse(inverse(X)),X_70))),multiply(inverse(multiply(inverse(inverse(X)),X_70)),X)) ),[0,0],$fot(X_70)]]) ).

cnf(refute_0_609,plain,
    ( inverse(multiply(inverse(X),multiply(inverse(inverse(X)),X_70))) != multiply(inverse(multiply(inverse(inverse(X)),X_70)),X)
    | inverse(X_70) = multiply(inverse(multiply(inverse(inverse(X)),X_70)),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X),multiply(inverse(inverse(X)),X_70)),X_70) )],[refute_0_607,refute_0_608]) ).

cnf(refute_0_610,plain,
    inverse(X_70) = multiply(inverse(multiply(inverse(inverse(X)),X_70)),X),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),multiply(inverse(inverse(X)),X_70))),multiply(inverse(multiply(inverse(inverse(X)),X_70)),X)) )],[refute_0_604,refute_0_609]) ).

cnf(refute_0_611,plain,
    multiply(inverse(X_70),inverse(X)) = inverse(multiply(X,X_70)),
    inference(subst,[],[refute_0_221:[bind(Y,$fot(X_70))]]) ).

cnf(refute_0_612,plain,
    inverse(multiply(inverse(inverse(X)),X_70)) = multiply(inverse(X_70),inverse(X)),
    inference(subst,[],[refute_0_22:[bind(X,$fot(inverse(X))),bind(X_30,$fot(X_70))]]) ).

cnf(refute_0_613,plain,
    ( multiply(inverse(X_70),inverse(X)) != inverse(multiply(X,X_70))
    | inverse(multiply(inverse(inverse(X)),X_70)) != multiply(inverse(X_70),inverse(X))
    | inverse(multiply(inverse(inverse(X)),X_70)) = inverse(multiply(X,X_70)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(inverse(multiply(inverse(inverse(X)),X_70)))),bind(Y0,$fot(multiply(inverse(X_70),inverse(X)))),bind(Z0,$fot(inverse(multiply(X,X_70))))]]) ).

cnf(refute_0_614,plain,
    ( multiply(inverse(X_70),inverse(X)) != inverse(multiply(X,X_70))
    | inverse(multiply(inverse(inverse(X)),X_70)) = inverse(multiply(X,X_70)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(inverse(X)),X_70)),multiply(inverse(X_70),inverse(X))) )],[refute_0_612,refute_0_613]) ).

cnf(refute_0_615,plain,
    inverse(multiply(inverse(inverse(X)),X_70)) = inverse(multiply(X,X_70)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_70),inverse(X)),inverse(multiply(X,X_70))) )],[refute_0_611,refute_0_614]) ).

cnf(refute_0_616,plain,
    multiply(inverse(multiply(inverse(inverse(X)),X_70)),X) = multiply(inverse(multiply(inverse(inverse(X)),X_70)),X),
    introduced(tautology,[refl,[$fot(multiply(inverse(multiply(inverse(inverse(X)),X_70)),X))]]) ).

cnf(refute_0_617,plain,
    ( multiply(inverse(multiply(inverse(inverse(X)),X_70)),X) != multiply(inverse(multiply(inverse(inverse(X)),X_70)),X)
    | inverse(multiply(inverse(inverse(X)),X_70)) != inverse(multiply(X,X_70))
    | multiply(inverse(multiply(inverse(inverse(X)),X_70)),X) = multiply(inverse(multiply(X,X_70)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(X)),X_70)),X),multiply(inverse(multiply(inverse(inverse(X)),X_70)),X)) ),[1,0],$fot(inverse(multiply(X,X_70)))]]) ).

cnf(refute_0_618,plain,
    ( inverse(multiply(inverse(inverse(X)),X_70)) != inverse(multiply(X,X_70))
    | multiply(inverse(multiply(inverse(inverse(X)),X_70)),X) = multiply(inverse(multiply(X,X_70)),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(X)),X_70)),X),multiply(inverse(multiply(inverse(inverse(X)),X_70)),X)) )],[refute_0_616,refute_0_617]) ).

cnf(refute_0_619,plain,
    multiply(inverse(multiply(inverse(inverse(X)),X_70)),X) = multiply(inverse(multiply(X,X_70)),X),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(inverse(X)),X_70)),inverse(multiply(X,X_70))) )],[refute_0_615,refute_0_618]) ).

cnf(refute_0_620,plain,
    ( multiply(inverse(multiply(inverse(inverse(X)),X_70)),X) != multiply(inverse(multiply(X,X_70)),X)
    | inverse(X_70) != multiply(inverse(multiply(inverse(inverse(X)),X_70)),X)
    | inverse(X_70) = multiply(inverse(multiply(X,X_70)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(X_70),multiply(inverse(multiply(inverse(inverse(X)),X_70)),X)) ),[1],$fot(multiply(inverse(multiply(X,X_70)),X))]]) ).

cnf(refute_0_621,plain,
    ( inverse(X_70) != multiply(inverse(multiply(inverse(inverse(X)),X_70)),X)
    | inverse(X_70) = multiply(inverse(multiply(X,X_70)),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(inverse(X)),X_70)),X),multiply(inverse(multiply(X,X_70)),X)) )],[refute_0_619,refute_0_620]) ).

cnf(refute_0_622,plain,
    inverse(X_70) = multiply(inverse(multiply(X,X_70)),X),
    inference(resolve,[$cnf( $equal(inverse(X_70),multiply(inverse(multiply(inverse(inverse(X)),X_70)),X)) )],[refute_0_610,refute_0_621]) ).

cnf(refute_0_623,plain,
    inverse(inverse(X_158)) = multiply(inverse(multiply(least_upper_bound(identity,X_158),inverse(X_158))),least_upper_bound(identity,X_158)),
    inference(subst,[],[refute_0_622:[bind(X,$fot(least_upper_bound(identity,X_158))),bind(X_70,$fot(inverse(X_158)))]]) ).

cnf(refute_0_624,plain,
    multiply(least_upper_bound(identity,X_158),inverse(X_158)) = least_upper_bound(identity,inverse(X_158)),
    inference(subst,[],[refute_0_157:[bind(X_126,$fot(X_158))]]) ).

cnf(refute_0_625,plain,
    ( multiply(least_upper_bound(identity,X_158),inverse(X_158)) != least_upper_bound(identity,inverse(X_158))
    | inverse(inverse(X_158)) != multiply(inverse(multiply(least_upper_bound(identity,X_158),inverse(X_158))),least_upper_bound(identity,X_158))
    | inverse(inverse(X_158)) = multiply(inverse(least_upper_bound(identity,inverse(X_158))),least_upper_bound(identity,X_158)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_158)),multiply(inverse(multiply(least_upper_bound(identity,X_158),inverse(X_158))),least_upper_bound(identity,X_158))) ),[1,0,0],$fot(least_upper_bound(identity,inverse(X_158)))]]) ).

cnf(refute_0_626,plain,
    ( inverse(inverse(X_158)) != multiply(inverse(multiply(least_upper_bound(identity,X_158),inverse(X_158))),least_upper_bound(identity,X_158))
    | inverse(inverse(X_158)) = multiply(inverse(least_upper_bound(identity,inverse(X_158))),least_upper_bound(identity,X_158)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_158),inverse(X_158)),least_upper_bound(identity,inverse(X_158))) )],[refute_0_624,refute_0_625]) ).

cnf(refute_0_627,plain,
    inverse(inverse(X_158)) = multiply(inverse(least_upper_bound(identity,inverse(X_158))),least_upper_bound(identity,X_158)),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_158)),multiply(inverse(multiply(least_upper_bound(identity,X_158),inverse(X_158))),least_upper_bound(identity,X_158))) )],[refute_0_623,refute_0_626]) ).

cnf(refute_0_628,plain,
    inverse(inverse(X_158)) = X_158,
    inference(subst,[],[p11_2:[bind(X,$fot(X_158))]]) ).

cnf(refute_0_629,plain,
    ( inverse(inverse(X_158)) != X_158
    | inverse(inverse(X_158)) != multiply(inverse(least_upper_bound(identity,inverse(X_158))),least_upper_bound(identity,X_158))
    | X_158 = multiply(inverse(least_upper_bound(identity,inverse(X_158))),least_upper_bound(identity,X_158)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_158)),multiply(inverse(least_upper_bound(identity,inverse(X_158))),least_upper_bound(identity,X_158))) ),[0],$fot(X_158)]]) ).

cnf(refute_0_630,plain,
    ( inverse(inverse(X_158)) != multiply(inverse(least_upper_bound(identity,inverse(X_158))),least_upper_bound(identity,X_158))
    | X_158 = multiply(inverse(least_upper_bound(identity,inverse(X_158))),least_upper_bound(identity,X_158)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_158)),X_158) )],[refute_0_628,refute_0_629]) ).

cnf(refute_0_631,plain,
    X_158 = multiply(inverse(least_upper_bound(identity,inverse(X_158))),least_upper_bound(identity,X_158)),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_158)),multiply(inverse(least_upper_bound(identity,inverse(X_158))),least_upper_bound(identity,X_158))) )],[refute_0_627,refute_0_630]) ).

cnf(refute_0_632,plain,
    X_159 = multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)),
    inference(subst,[],[refute_0_631:[bind(X_158,$fot(X_159))]]) ).

cnf(refute_0_633,plain,
    ( X_159 != multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159))
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)) = X_159 ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X_159)),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159))))]]) ).

cnf(refute_0_634,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)) = X_159,
    inference(resolve,[$cnf( $equal(X_159,multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159))) )],[refute_0_632,refute_0_633]) ).

cnf(refute_0_635,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)) != X_159
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)))
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)))) ),[1,1],$fot(X_159)]]) ).

cnf(refute_0_636,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)))
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)),X_159) )],[refute_0_634,refute_0_635]) ).

cnf(refute_0_637,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)))) )],[refute_0_603,refute_0_636]) ).

cnf(refute_0_638,plain,
    least_upper_bound(identity,least_upper_bound(identity,X_159)) = least_upper_bound(identity,X_159),
    inference(subst,[],[refute_0_481:[bind(X_22,$fot(identity)),bind(X_23,$fot(X_159))]]) ).

cnf(refute_0_639,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))) = multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))),
    introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))))]]) ).

cnf(refute_0_640,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))) != multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159)))
    | least_upper_bound(identity,least_upper_bound(identity,X_159)) != least_upper_bound(identity,X_159)
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))) = multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))),multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159)))) ),[1,1],$fot(least_upper_bound(identity,X_159))]]) ).

cnf(refute_0_641,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,X_159)) != least_upper_bound(identity,X_159)
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))) = multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))),multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159)))) )],[refute_0_639,refute_0_640]) ).

cnf(refute_0_642,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))) = multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,X_159)),least_upper_bound(identity,X_159)) )],[refute_0_638,refute_0_641]) ).

cnf(refute_0_643,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)) != X_159
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))) != multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159))
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))) = X_159 ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)))),bind(Z0,$fot(X_159))]]) ).

cnf(refute_0_644,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)) != X_159
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))) = X_159 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))),multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159))) )],[refute_0_642,refute_0_643]) ).

cnf(refute_0_645,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))) = X_159,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,X_159)),X_159) )],[refute_0_634,refute_0_644]) ).

cnf(refute_0_646,plain,
    greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81)),
    inference(subst,[],[refute_0_354:[bind(X_18,$fot(multiply(X_79,X_81))),bind(X_19,$fot(multiply(X_79,X_80)))]]) ).

cnf(refute_0_647,plain,
    multiply(X_79,greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_79)),bind(Y,$fot(X_80)),bind(Z,$fot(X_81))]]) ).

cnf(refute_0_648,plain,
    ( multiply(X_79,greatest_lower_bound(X_80,X_81)) != greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))
    | greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81)) = multiply(X_79,greatest_lower_bound(X_80,X_81)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_79,greatest_lower_bound(X_80,X_81)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))))]]) ).

cnf(refute_0_649,plain,
    greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81)) = multiply(X_79,greatest_lower_bound(X_80,X_81)),
    inference(resolve,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_80,X_81)),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) )],[refute_0_647,refute_0_648]) ).

cnf(refute_0_650,plain,
    ( greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81)) != multiply(X_79,greatest_lower_bound(X_80,X_81))
    | greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) != greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))
    | greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = multiply(X_79,greatest_lower_bound(X_80,X_81)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) ),[1],$fot(multiply(X_79,greatest_lower_bound(X_80,X_81)))]]) ).

cnf(refute_0_651,plain,
    ( greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) != greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))
    | greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = multiply(X_79,greatest_lower_bound(X_80,X_81)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81)),multiply(X_79,greatest_lower_bound(X_80,X_81))) )],[refute_0_649,refute_0_650]) ).

cnf(refute_0_652,plain,
    greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = multiply(X_79,greatest_lower_bound(X_80,X_81)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) )],[refute_0_646,refute_0_651]) ).

cnf(refute_0_653,plain,
    greatest_lower_bound(X_80,X_80) = X_80,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_80))]]) ).

cnf(refute_0_654,plain,
    greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)) = greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)))]]) ).

cnf(refute_0_655,plain,
    ( greatest_lower_bound(X_80,X_80) != X_80
    | greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)) != greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))
    | greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)) = greatest_lower_bound(X_81,X_80) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)),greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))) ),[1,1],$fot(X_80)]]) ).

cnf(refute_0_656,plain,
    ( greatest_lower_bound(X_80,X_80) != X_80
    | greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)) = greatest_lower_bound(X_81,X_80) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)),greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))) )],[refute_0_654,refute_0_655]) ).

cnf(refute_0_657,plain,
    greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)) = greatest_lower_bound(X_81,X_80),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_80,X_80),X_80) )],[refute_0_653,refute_0_656]) ).

cnf(refute_0_658,plain,
    multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))) = multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))),
    introduced(tautology,[refl,[$fot(multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))))]]) ).

cnf(refute_0_659,plain,
    ( multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))) != multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)))
    | greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)) != greatest_lower_bound(X_81,X_80)
    | multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))) = multiply(X_79,greatest_lower_bound(X_81,X_80)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))),multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)))) ),[1,1],$fot(greatest_lower_bound(X_81,X_80))]]) ).

cnf(refute_0_660,plain,
    ( greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)) != greatest_lower_bound(X_81,X_80)
    | multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))) = multiply(X_79,greatest_lower_bound(X_81,X_80)) ),
    inference(resolve,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))),multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)))) )],[refute_0_658,refute_0_659]) ).

cnf(refute_0_661,plain,
    multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))) = multiply(X_79,greatest_lower_bound(X_81,X_80)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)),greatest_lower_bound(X_81,X_80)) )],[refute_0_657,refute_0_660]) ).

cnf(refute_0_662,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_12:[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_663,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_662]) ).

cnf(refute_0_664,plain,
    greatest_lower_bound(multiply(X_79,X_81),multiply(X_79,greatest_lower_bound(X_80,X_80))) = multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))),
    inference(subst,[],[refute_0_663:[bind(X,$fot(X_79)),bind(Y,$fot(X_81)),bind(Z,$fot(greatest_lower_bound(X_80,X_80)))]]) ).

cnf(refute_0_665,plain,
    greatest_lower_bound(X,greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X)),
    inference(subst,[],[refute_0_380:[bind(X_33,$fot(multiply(X_79,X_80))),bind(X_34,$fot(multiply(X_79,X_81)))]]) ).

cnf(refute_0_666,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) != greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X))
    | greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81)) != multiply(X_79,greatest_lower_bound(X_80,X_81))
    | greatest_lower_bound(X,multiply(X_79,greatest_lower_bound(X_80,X_81))) = greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))),greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X))) ),[0,1],$fot(multiply(X_79,greatest_lower_bound(X_80,X_81)))]]) ).

cnf(refute_0_667,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) != greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X))
    | greatest_lower_bound(X,multiply(X_79,greatest_lower_bound(X_80,X_81))) = greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81)),multiply(X_79,greatest_lower_bound(X_80,X_81))) )],[refute_0_649,refute_0_666]) ).

cnf(refute_0_668,plain,
    greatest_lower_bound(X,multiply(X_79,greatest_lower_bound(X_80,X_81))) = greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))),greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X))) )],[refute_0_665,refute_0_667]) ).

cnf(refute_0_669,plain,
    ( greatest_lower_bound(X,multiply(X_79,greatest_lower_bound(X_80,X_81))) != greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X))
    | greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X)) = greatest_lower_bound(X,multiply(X_79,greatest_lower_bound(X_80,X_81))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X,multiply(X_79,greatest_lower_bound(X_80,X_81))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X))))]]) ).

cnf(refute_0_670,plain,
    greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X)) = greatest_lower_bound(X,multiply(X_79,greatest_lower_bound(X_80,X_81))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,multiply(X_79,greatest_lower_bound(X_80,X_81))),greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_81),X))) )],[refute_0_668,refute_0_669]) ).

cnf(refute_0_671,plain,
    greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = greatest_lower_bound(multiply(X_79,X_81),multiply(X_79,greatest_lower_bound(X_80,X_80))),
    inference(subst,[],[refute_0_670:[bind(X,$fot(multiply(X_79,X_81))),bind(X_81,$fot(X_80))]]) ).

cnf(refute_0_672,plain,
    ( greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) != greatest_lower_bound(multiply(X_79,X_81),multiply(X_79,greatest_lower_bound(X_80,X_80)))
    | greatest_lower_bound(multiply(X_79,X_81),multiply(X_79,greatest_lower_bound(X_80,X_80))) != multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)))
    | greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_79,X_81),multiply(X_79,greatest_lower_bound(X_80,X_80))))),bind(Z0,$fot(multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)))))]]) ).

cnf(refute_0_673,plain,
    ( greatest_lower_bound(multiply(X_79,X_81),multiply(X_79,greatest_lower_bound(X_80,X_80))) != multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)))
    | greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))),greatest_lower_bound(multiply(X_79,X_81),multiply(X_79,greatest_lower_bound(X_80,X_80)))) )],[refute_0_671,refute_0_672]) ).

cnf(refute_0_674,plain,
    greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_81),multiply(X_79,greatest_lower_bound(X_80,X_80))),multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)))) )],[refute_0_664,refute_0_673]) ).

cnf(refute_0_675,plain,
    ( multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))) != multiply(X_79,greatest_lower_bound(X_81,X_80))
    | greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) != multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)))
    | greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = multiply(X_79,greatest_lower_bound(X_81,X_80)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))))),bind(Y0,$fot(multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))))),bind(Z0,$fot(multiply(X_79,greatest_lower_bound(X_81,X_80))))]]) ).

cnf(refute_0_676,plain,
    ( multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))) != multiply(X_79,greatest_lower_bound(X_81,X_80))
    | greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = multiply(X_79,greatest_lower_bound(X_81,X_80)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))),multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80)))) )],[refute_0_674,refute_0_675]) ).

cnf(refute_0_677,plain,
    greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) = multiply(X_79,greatest_lower_bound(X_81,X_80)),
    inference(resolve,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_81,greatest_lower_bound(X_80,X_80))),multiply(X_79,greatest_lower_bound(X_81,X_80))) )],[refute_0_661,refute_0_676]) ).

cnf(refute_0_678,plain,
    ( greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) != multiply(X_79,greatest_lower_bound(X_80,X_81))
    | greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) != multiply(X_79,greatest_lower_bound(X_81,X_80))
    | multiply(X_79,greatest_lower_bound(X_81,X_80)) = multiply(X_79,greatest_lower_bound(X_80,X_81)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))),multiply(X_79,greatest_lower_bound(X_80,X_81))) ),[0],$fot(multiply(X_79,greatest_lower_bound(X_81,X_80)))]]) ).

cnf(refute_0_679,plain,
    ( greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))) != multiply(X_79,greatest_lower_bound(X_80,X_81))
    | multiply(X_79,greatest_lower_bound(X_81,X_80)) = multiply(X_79,greatest_lower_bound(X_80,X_81)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))),multiply(X_79,greatest_lower_bound(X_81,X_80))) )],[refute_0_677,refute_0_678]) ).

cnf(refute_0_680,plain,
    multiply(X_79,greatest_lower_bound(X_81,X_80)) = multiply(X_79,greatest_lower_bound(X_80,X_81)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_79,X_80),greatest_lower_bound(multiply(X_79,X_80),multiply(X_79,X_81))),multiply(X_79,greatest_lower_bound(X_80,X_81))) )],[refute_0_652,refute_0_679]) ).

cnf(refute_0_681,plain,
    multiply(X_152,greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23))) = multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),
    inference(subst,[],[refute_0_680:[bind(X_79,$fot(X_152)),bind(X_80,$fot(least_upper_bound(X_15,X_23))),bind(X_81,$fot(least_upper_bound(X_23,X_15)))]]) ).

cnf(refute_0_682,plain,
    ( multiply(X_152,greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23))) != multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))
    | greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)) != least_upper_bound(X_23,X_15)
    | multiply(X_152,least_upper_bound(X_23,X_15)) = multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_152,greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23))),multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) ),[0,1],$fot(least_upper_bound(X_23,X_15))]]) ).

cnf(refute_0_683,plain,
    ( multiply(X_152,greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23))) != multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))
    | multiply(X_152,least_upper_bound(X_23,X_15)) = multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)),least_upper_bound(X_23,X_15)) )],[refute_0_413,refute_0_682]) ).

cnf(refute_0_684,plain,
    multiply(X_152,least_upper_bound(X_23,X_15)) = multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),
    inference(resolve,[$cnf( $equal(multiply(X_152,greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23))),multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) )],[refute_0_681,refute_0_683]) ).

cnf(refute_0_685,plain,
    multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) = multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),
    introduced(tautology,[refl,[$fot(multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))))]]) ).

cnf(refute_0_686,plain,
    ( multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) != multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))
    | greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)) != least_upper_bound(X_15,X_23)
    | multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) = multiply(X_152,least_upper_bound(X_15,X_23)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) ),[1,1],$fot(least_upper_bound(X_15,X_23))]]) ).

cnf(refute_0_687,plain,
    ( greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)) != least_upper_bound(X_15,X_23)
    | multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) = multiply(X_152,least_upper_bound(X_15,X_23)) ),
    inference(resolve,[$cnf( $equal(multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) )],[refute_0_685,refute_0_686]) ).

cnf(refute_0_688,plain,
    multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) = multiply(X_152,least_upper_bound(X_15,X_23)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),least_upper_bound(X_15,X_23)) )],[refute_0_417,refute_0_687]) ).

cnf(refute_0_689,plain,
    ( multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) != multiply(X_152,least_upper_bound(X_15,X_23))
    | multiply(X_152,least_upper_bound(X_23,X_15)) != multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))
    | multiply(X_152,least_upper_bound(X_23,X_15)) = multiply(X_152,least_upper_bound(X_15,X_23)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_152,least_upper_bound(X_23,X_15)),multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) ),[1],$fot(multiply(X_152,least_upper_bound(X_15,X_23)))]]) ).

cnf(refute_0_690,plain,
    ( multiply(X_152,least_upper_bound(X_23,X_15)) != multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))
    | multiply(X_152,least_upper_bound(X_23,X_15)) = multiply(X_152,least_upper_bound(X_15,X_23)) ),
    inference(resolve,[$cnf( $equal(multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),multiply(X_152,least_upper_bound(X_15,X_23))) )],[refute_0_688,refute_0_689]) ).

cnf(refute_0_691,plain,
    multiply(X_152,least_upper_bound(X_23,X_15)) = multiply(X_152,least_upper_bound(X_15,X_23)),
    inference(resolve,[$cnf( $equal(multiply(X_152,least_upper_bound(X_23,X_15)),multiply(X_152,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) )],[refute_0_684,refute_0_690]) ).

cnf(refute_0_692,plain,
    ( multiply(X_152,least_upper_bound(X_23,X_15)) != multiply(X_152,least_upper_bound(X_15,X_23))
    | multiply(X_152,least_upper_bound(X_15,X_23)) = multiply(X_152,least_upper_bound(X_23,X_15)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_152,least_upper_bound(X_23,X_15)))),bind(Y0,$fot(multiply(X_152,least_upper_bound(X_15,X_23))))]]) ).

cnf(refute_0_693,plain,
    multiply(X_152,least_upper_bound(X_15,X_23)) = multiply(X_152,least_upper_bound(X_23,X_15)),
    inference(resolve,[$cnf( $equal(multiply(X_152,least_upper_bound(X_23,X_15)),multiply(X_152,least_upper_bound(X_15,X_23))) )],[refute_0_691,refute_0_692]) ).

cnf(refute_0_694,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) = multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))),
    inference(subst,[],[refute_0_693:[bind(X_15,$fot(least_upper_bound(identity,X_159))),bind(X_152,$fot(inverse(least_upper_bound(identity,inverse(X_159))))),bind(X_23,$fot(identity))]]) ).

cnf(refute_0_695,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))) != X_159
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) != multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159)))
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) = X_159 ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))))),bind(Z0,$fot(X_159))]]) ).

cnf(refute_0_696,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))) != X_159
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) = X_159 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)),multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159)))) )],[refute_0_694,refute_0_695]) ).

cnf(refute_0_697,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) = X_159,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(identity,least_upper_bound(identity,X_159))),X_159) )],[refute_0_645,refute_0_696]) ).

cnf(refute_0_698,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) != X_159
    | multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159)
    | X_159 = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159)) ),[0],$fot(X_159)]]) ).

cnf(refute_0_699,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159)
    | X_159 = least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)),X_159) )],[refute_0_697,refute_0_698]) ).

cnf(refute_0_700,plain,
    least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159) = least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159)))),
    inference(subst,[],[refute_0_180:[bind(X,$fot(X_159)),bind(Y,$fot(inverse(least_upper_bound(identity,inverse(X_159)))))]]) ).

cnf(refute_0_701,plain,
    ( X_159 != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159)
    | least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159) != least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159))))
    | X_159 = least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_159,least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159))))) ),[0],$fot(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159))]]) ).

cnf(refute_0_702,plain,
    ( X_159 != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159)
    | X_159 = least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159),least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159))))) )],[refute_0_700,refute_0_701]) ).

cnf(refute_0_703,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159)
    | X_159 = least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159)))) ),
    inference(resolve,[$cnf( $equal(X_159,least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159)) )],[refute_0_699,refute_0_702]) ).

cnf(refute_0_704,plain,
    X_159 = least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_159))),least_upper_bound(least_upper_bound(identity,X_159),identity)),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_159))),X_159)) )],[refute_0_637,refute_0_703]) ).

cnf(refute_0_705,plain,
    ( X_159 != least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159))))
    | least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159)))) = X_159 ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X_159)),bind(Y0,$fot(least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159))))))]]) ).

cnf(refute_0_706,plain,
    least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159)))) = X_159,
    inference(resolve,[$cnf( $equal(X_159,least_upper_bound(X_159,inverse(least_upper_bound(identity,inverse(X_159))))) )],[refute_0_704,refute_0_705]) ).

cnf(refute_0_707,plain,
    least_upper_bound(X_169,inverse(least_upper_bound(identity,inverse(X_169)))) = X_169,
    inference(subst,[],[refute_0_706:[bind(X_159,$fot(X_169))]]) ).

cnf(refute_0_708,plain,
    least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169) = least_upper_bound(X_169,inverse(least_upper_bound(identity,inverse(X_169)))),
    inference(subst,[],[refute_0_180:[bind(X,$fot(X_169)),bind(Y,$fot(inverse(least_upper_bound(identity,inverse(X_169)))))]]) ).

cnf(refute_0_709,plain,
    ( least_upper_bound(X_169,inverse(least_upper_bound(identity,inverse(X_169)))) != X_169
    | least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169) != least_upper_bound(X_169,inverse(least_upper_bound(identity,inverse(X_169))))
    | least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169) = X_169 ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169))),bind(Y0,$fot(least_upper_bound(X_169,inverse(least_upper_bound(identity,inverse(X_169)))))),bind(Z0,$fot(X_169))]]) ).

cnf(refute_0_710,plain,
    ( least_upper_bound(X_169,inverse(least_upper_bound(identity,inverse(X_169)))) != X_169
    | least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169) = X_169 ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169),least_upper_bound(X_169,inverse(least_upper_bound(identity,inverse(X_169))))) )],[refute_0_708,refute_0_709]) ).

cnf(refute_0_711,plain,
    least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169) = X_169,
    inference(resolve,[$cnf( $equal(least_upper_bound(X_169,inverse(least_upper_bound(identity,inverse(X_169)))),X_169) )],[refute_0_707,refute_0_710]) ).

cnf(refute_0_712,plain,
    ( multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169)
    | least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169) != X_169
    | multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) = X_169 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))),X_169) ),[0],$fot(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169))]]) ).

cnf(refute_0_713,plain,
    ( multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169)
    | multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) = X_169 ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169),X_169) )],[refute_0_711,refute_0_712]) ).

cnf(refute_0_714,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))) != least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169)
    | multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) = X_169 ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169)) )],[refute_0_602,refute_0_713]) ).

cnf(refute_0_715,plain,
    multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) = X_169,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_169,identity),identity),inverse(least_upper_bound(identity,inverse(X_169)))),least_upper_bound(inverse(least_upper_bound(identity,inverse(X_169))),X_169)) )],[refute_0_469,refute_0_714]) ).

cnf(refute_0_716,plain,
    multiply(greatest_lower_bound(inverse(X_87),X_89),X_87) = greatest_lower_bound(multiply(inverse(X_87),X_87),multiply(X_89,X_87)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_87)),bind(Y,$fot(inverse(X_87))),bind(Z,$fot(X_89))]]) ).

cnf(refute_0_717,plain,
    multiply(inverse(X_87),X_87) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_87))]]) ).

cnf(refute_0_718,plain,
    ( multiply(greatest_lower_bound(inverse(X_87),X_89),X_87) != greatest_lower_bound(multiply(inverse(X_87),X_87),multiply(X_89,X_87))
    | multiply(inverse(X_87),X_87) != identity
    | multiply(greatest_lower_bound(inverse(X_87),X_89),X_87) = greatest_lower_bound(identity,multiply(X_89,X_87)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_87),X_89),X_87),greatest_lower_bound(multiply(inverse(X_87),X_87),multiply(X_89,X_87))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_719,plain,
    ( multiply(greatest_lower_bound(inverse(X_87),X_89),X_87) != greatest_lower_bound(multiply(inverse(X_87),X_87),multiply(X_89,X_87))
    | multiply(greatest_lower_bound(inverse(X_87),X_89),X_87) = greatest_lower_bound(identity,multiply(X_89,X_87)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_87),X_87),identity) )],[refute_0_717,refute_0_718]) ).

cnf(refute_0_720,plain,
    multiply(greatest_lower_bound(inverse(X_87),X_89),X_87) = greatest_lower_bound(identity,multiply(X_89,X_87)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_87),X_89),X_87),greatest_lower_bound(multiply(inverse(X_87),X_87),multiply(X_89,X_87))) )],[refute_0_716,refute_0_719]) ).

cnf(refute_0_721,plain,
    multiply(greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80)),X_162) = greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)),
    inference(subst,[],[refute_0_720:[bind(X_87,$fot(X_162)),bind(X_89,$fot(multiply(inverse(X_162),X_80)))]]) ).

cnf(refute_0_722,plain,
    multiply(inverse(X_162),greatest_lower_bound(X_80,identity)) = greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80)),
    inference(subst,[],[refute_0_106:[bind(X_79,$fot(inverse(X_162)))]]) ).

cnf(refute_0_723,plain,
    ( multiply(inverse(X_162),greatest_lower_bound(X_80,identity)) != greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80))
    | greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80)) = multiply(inverse(X_162),greatest_lower_bound(X_80,identity)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80))))]]) ).

cnf(refute_0_724,plain,
    greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80)) = multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80))) )],[refute_0_722,refute_0_723]) ).

cnf(refute_0_725,plain,
    ( multiply(greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80)),X_162) != greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))
    | greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80)) != multiply(inverse(X_162),greatest_lower_bound(X_80,identity))
    | multiply(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),X_162) = greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80)),X_162),greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))) ),[0,0],$fot(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)))]]) ).

cnf(refute_0_726,plain,
    ( multiply(greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80)),X_162) != greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))
    | multiply(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),X_162) = greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80)),multiply(inverse(X_162),greatest_lower_bound(X_80,identity))) )],[refute_0_724,refute_0_725]) ).

cnf(refute_0_727,plain,
    multiply(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),X_162) = greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_162),multiply(inverse(X_162),X_80)),X_162),greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))) )],[refute_0_721,refute_0_726]) ).

cnf(refute_0_728,plain,
    multiply(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),X_162) = multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_162))),bind(Y,$fot(greatest_lower_bound(X_80,identity))),bind(Z,$fot(X_162))]]) ).

cnf(refute_0_729,plain,
    ( multiply(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),X_162) != multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162))
    | multiply(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),X_162) != greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))
    | multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)) = greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),X_162),greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))) ),[0],$fot(multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)))]]) ).

cnf(refute_0_730,plain,
    ( multiply(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),X_162) != greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))
    | multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)) = greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),X_162),multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162))) )],[refute_0_728,refute_0_729]) ).

cnf(refute_0_731,plain,
    multiply(multiply(inverse(X_162),X_80),X_162) = multiply(inverse(X_162),multiply(X_80,X_162)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_162))),bind(Y,$fot(X_80)),bind(Z,$fot(X_162))]]) ).

cnf(refute_0_732,plain,
    greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)) = greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)))]]) ).

cnf(refute_0_733,plain,
    ( multiply(multiply(inverse(X_162),X_80),X_162) != multiply(inverse(X_162),multiply(X_80,X_162))
    | greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)) != greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))
    | greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)) = greatest_lower_bound(identity,multiply(inverse(X_162),multiply(X_80,X_162))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)),greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))) ),[1,1],$fot(multiply(inverse(X_162),multiply(X_80,X_162)))]]) ).

cnf(refute_0_734,plain,
    ( multiply(multiply(inverse(X_162),X_80),X_162) != multiply(inverse(X_162),multiply(X_80,X_162))
    | greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)) = greatest_lower_bound(identity,multiply(inverse(X_162),multiply(X_80,X_162))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)),greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))) )],[refute_0_732,refute_0_733]) ).

cnf(refute_0_735,plain,
    greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)) = greatest_lower_bound(identity,multiply(inverse(X_162),multiply(X_80,X_162))),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_162),X_80),X_162),multiply(inverse(X_162),multiply(X_80,X_162))) )],[refute_0_731,refute_0_734]) ).

cnf(refute_0_736,plain,
    ( multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)) != greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))
    | greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)) != greatest_lower_bound(identity,multiply(inverse(X_162),multiply(X_80,X_162)))
    | multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)) = greatest_lower_bound(identity,multiply(inverse(X_162),multiply(X_80,X_162))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)),greatest_lower_bound(identity,multiply(inverse(X_162),multiply(X_80,X_162)))) ),[0],$fot(greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)))]]) ).

cnf(refute_0_737,plain,
    ( multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)) != greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))
    | multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)) = greatest_lower_bound(identity,multiply(inverse(X_162),multiply(X_80,X_162))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162)),greatest_lower_bound(identity,multiply(inverse(X_162),multiply(X_80,X_162)))) )],[refute_0_735,refute_0_736]) ).

cnf(refute_0_738,plain,
    ( multiply(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),X_162) != greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))
    | multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)) = greatest_lower_bound(identity,multiply(inverse(X_162),multiply(X_80,X_162))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)),greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))) )],[refute_0_730,refute_0_737]) ).

cnf(refute_0_739,plain,
    multiply(inverse(X_162),multiply(greatest_lower_bound(X_80,identity),X_162)) = greatest_lower_bound(identity,multiply(inverse(X_162),multiply(X_80,X_162))),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_162),greatest_lower_bound(X_80,identity)),X_162),greatest_lower_bound(identity,multiply(multiply(inverse(X_162),X_80),X_162))) )],[refute_0_727,refute_0_738]) ).

cnf(refute_0_740,plain,
    multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(X_561,inverse(least_upper_bound(X_561,identity))))),
    inference(subst,[],[refute_0_739:[bind(X_162,$fot(inverse(least_upper_bound(X_561,identity)))),bind(X_80,$fot(X_561))]]) ).

cnf(refute_0_741,plain,
    inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))) = multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))),
    inference(subst,[],[p11_3:[bind(X,$fot(least_upper_bound(X_129,identity))),bind(Y,$fot(inverse(X_129)))]]) ).

cnf(refute_0_742,plain,
    multiply(least_upper_bound(X_129,identity),inverse(X_129)) = least_upper_bound(identity,inverse(X_129)),
    inference(subst,[],[refute_0_443:[bind(X_127,$fot(X_129))]]) ).

cnf(refute_0_743,plain,
    ( multiply(least_upper_bound(X_129,identity),inverse(X_129)) != least_upper_bound(identity,inverse(X_129))
    | inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))) != multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity)))
    | inverse(least_upper_bound(identity,inverse(X_129))) = multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))),multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity)))) ),[0,0],$fot(least_upper_bound(identity,inverse(X_129)))]]) ).

cnf(refute_0_744,plain,
    ( inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))) != multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity)))
    | inverse(least_upper_bound(identity,inverse(X_129))) = multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_129,identity),inverse(X_129)),least_upper_bound(identity,inverse(X_129))) )],[refute_0_742,refute_0_743]) ).

cnf(refute_0_745,plain,
    inverse(least_upper_bound(identity,inverse(X_129))) = multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))),multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity)))) )],[refute_0_741,refute_0_744]) ).

cnf(refute_0_746,plain,
    inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))) = multiply(X_129,inverse(least_upper_bound(X_129,identity))),
    inference(subst,[],[refute_0_293:[bind(X,$fot(X_129)),bind(X_29,$fot(least_upper_bound(X_129,identity)))]]) ).

cnf(refute_0_747,plain,
    multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))) = inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))),
    inference(subst,[],[refute_0_221:[bind(X,$fot(least_upper_bound(X_129,identity))),bind(Y,$fot(inverse(X_129)))]]) ).

cnf(refute_0_748,plain,
    ( multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))) != inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129)))
    | inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))) != multiply(X_129,inverse(least_upper_bound(X_129,identity)))
    | multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))) = multiply(X_129,inverse(least_upper_bound(X_129,identity))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))))),bind(Z0,$fot(multiply(X_129,inverse(least_upper_bound(X_129,identity)))))]]) ).

cnf(refute_0_749,plain,
    ( inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))) != multiply(X_129,inverse(least_upper_bound(X_129,identity)))
    | multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))) = multiply(X_129,inverse(least_upper_bound(X_129,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))),inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129)))) )],[refute_0_747,refute_0_748]) ).

cnf(refute_0_750,plain,
    multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))) = multiply(X_129,inverse(least_upper_bound(X_129,identity))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))),multiply(X_129,inverse(least_upper_bound(X_129,identity)))) )],[refute_0_746,refute_0_749]) ).

cnf(refute_0_751,plain,
    ( multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))) != multiply(X_129,inverse(least_upper_bound(X_129,identity)))
    | inverse(least_upper_bound(identity,inverse(X_129))) != multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity)))
    | inverse(least_upper_bound(identity,inverse(X_129))) = multiply(X_129,inverse(least_upper_bound(X_129,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_129))),multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity)))) ),[1],$fot(multiply(X_129,inverse(least_upper_bound(X_129,identity))))]]) ).

cnf(refute_0_752,plain,
    ( inverse(least_upper_bound(identity,inverse(X_129))) != multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity)))
    | inverse(least_upper_bound(identity,inverse(X_129))) = multiply(X_129,inverse(least_upper_bound(X_129,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity))),multiply(X_129,inverse(least_upper_bound(X_129,identity)))) )],[refute_0_750,refute_0_751]) ).

cnf(refute_0_753,plain,
    inverse(least_upper_bound(identity,inverse(X_129))) = multiply(X_129,inverse(least_upper_bound(X_129,identity))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_129))),multiply(inverse(inverse(X_129)),inverse(least_upper_bound(X_129,identity)))) )],[refute_0_745,refute_0_752]) ).

cnf(refute_0_754,plain,
    inverse(least_upper_bound(identity,inverse(X_561))) = multiply(X_561,inverse(least_upper_bound(X_561,identity))),
    inference(subst,[],[refute_0_753:[bind(X_129,$fot(X_561))]]) ).

cnf(refute_0_755,plain,
    ( inverse(least_upper_bound(identity,inverse(X_561))) != multiply(X_561,inverse(least_upper_bound(X_561,identity)))
    | multiply(X_561,inverse(least_upper_bound(X_561,identity))) = inverse(least_upper_bound(identity,inverse(X_561))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_561))))),bind(Y0,$fot(multiply(X_561,inverse(least_upper_bound(X_561,identity)))))]]) ).

cnf(refute_0_756,plain,
    multiply(X_561,inverse(least_upper_bound(X_561,identity))) = inverse(least_upper_bound(identity,inverse(X_561))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_561))),multiply(X_561,inverse(least_upper_bound(X_561,identity)))) )],[refute_0_754,refute_0_755]) ).

cnf(refute_0_757,plain,
    ( multiply(X_561,inverse(least_upper_bound(X_561,identity))) != inverse(least_upper_bound(identity,inverse(X_561)))
    | multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(X_561,inverse(least_upper_bound(X_561,identity)))))
    | multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(X_561,inverse(least_upper_bound(X_561,identity)))))) ),[1,1,1],$fot(inverse(least_upper_bound(identity,inverse(X_561))))]]) ).

cnf(refute_0_758,plain,
    ( multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(X_561,inverse(least_upper_bound(X_561,identity)))))
    | multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))) ),
    inference(resolve,[$cnf( $equal(multiply(X_561,inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))) )],[refute_0_756,refute_0_757]) ).

cnf(refute_0_759,plain,
    multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(X_561,inverse(least_upper_bound(X_561,identity)))))) )],[refute_0_740,refute_0_758]) ).

cnf(refute_0_760,plain,
    inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))) = multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity))),
    inference(subst,[],[refute_0_293:[bind(X,$fot(greatest_lower_bound(X_561,identity))),bind(X_29,$fot(least_upper_bound(X_561,identity)))]]) ).

cnf(refute_0_761,plain,
    multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))) = multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))))]]) ).

cnf(refute_0_762,plain,
    ( multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))) != multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))))
    | inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))) != multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))
    | multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))) = multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))),multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))))) ),[1,1],$fot(multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity))))]]) ).

cnf(refute_0_763,plain,
    ( inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))) != multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))
    | multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))) = multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))),multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))))) )],[refute_0_761,refute_0_762]) ).

cnf(refute_0_764,plain,
    multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))) = multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) )],[refute_0_760,refute_0_763]) ).

cnf(refute_0_765,plain,
    inverse(multiply(X_29,inverse(multiply(X_78,inverse(X_77))))) = multiply(multiply(X_78,inverse(X_77)),inverse(X_29)),
    inference(subst,[],[refute_0_293:[bind(X,$fot(multiply(X_78,inverse(X_77))))]]) ).

cnf(refute_0_766,plain,
    inverse(multiply(X_78,inverse(X_77))) = multiply(X_77,inverse(X_78)),
    inference(subst,[],[refute_0_293:[bind(X,$fot(X_77)),bind(X_29,$fot(X_78))]]) ).

cnf(refute_0_767,plain,
    ( inverse(multiply(X_29,inverse(multiply(X_78,inverse(X_77))))) != multiply(multiply(X_78,inverse(X_77)),inverse(X_29))
    | inverse(multiply(X_78,inverse(X_77))) != multiply(X_77,inverse(X_78))
    | inverse(multiply(X_29,multiply(X_77,inverse(X_78)))) = multiply(multiply(X_78,inverse(X_77)),inverse(X_29)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_29,inverse(multiply(X_78,inverse(X_77))))),multiply(multiply(X_78,inverse(X_77)),inverse(X_29))) ),[0,0,1],$fot(multiply(X_77,inverse(X_78)))]]) ).

cnf(refute_0_768,plain,
    ( inverse(multiply(X_29,inverse(multiply(X_78,inverse(X_77))))) != multiply(multiply(X_78,inverse(X_77)),inverse(X_29))
    | inverse(multiply(X_29,multiply(X_77,inverse(X_78)))) = multiply(multiply(X_78,inverse(X_77)),inverse(X_29)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_78,inverse(X_77))),multiply(X_77,inverse(X_78))) )],[refute_0_766,refute_0_767]) ).

cnf(refute_0_769,plain,
    inverse(multiply(X_29,multiply(X_77,inverse(X_78)))) = multiply(multiply(X_78,inverse(X_77)),inverse(X_29)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_29,inverse(multiply(X_78,inverse(X_77))))),multiply(multiply(X_78,inverse(X_77)),inverse(X_29))) )],[refute_0_765,refute_0_768]) ).

cnf(refute_0_770,plain,
    multiply(inverse(X_77),inverse(X_29)) = inverse(multiply(X_29,X_77)),
    inference(subst,[],[refute_0_221:[bind(X,$fot(X_29)),bind(Y,$fot(X_77))]]) ).

cnf(refute_0_771,plain,
    multiply(X_78,multiply(inverse(X_77),inverse(X_29))) = multiply(X_78,multiply(inverse(X_77),inverse(X_29))),
    introduced(tautology,[refl,[$fot(multiply(X_78,multiply(inverse(X_77),inverse(X_29))))]]) ).

cnf(refute_0_772,plain,
    ( multiply(X_78,multiply(inverse(X_77),inverse(X_29))) != multiply(X_78,multiply(inverse(X_77),inverse(X_29)))
    | multiply(inverse(X_77),inverse(X_29)) != inverse(multiply(X_29,X_77))
    | multiply(X_78,multiply(inverse(X_77),inverse(X_29))) = multiply(X_78,inverse(multiply(X_29,X_77))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_78,multiply(inverse(X_77),inverse(X_29))),multiply(X_78,multiply(inverse(X_77),inverse(X_29)))) ),[1,1],$fot(inverse(multiply(X_29,X_77)))]]) ).

cnf(refute_0_773,plain,
    ( multiply(inverse(X_77),inverse(X_29)) != inverse(multiply(X_29,X_77))
    | multiply(X_78,multiply(inverse(X_77),inverse(X_29))) = multiply(X_78,inverse(multiply(X_29,X_77))) ),
    inference(resolve,[$cnf( $equal(multiply(X_78,multiply(inverse(X_77),inverse(X_29))),multiply(X_78,multiply(inverse(X_77),inverse(X_29)))) )],[refute_0_771,refute_0_772]) ).

cnf(refute_0_774,plain,
    multiply(X_78,multiply(inverse(X_77),inverse(X_29))) = multiply(X_78,inverse(multiply(X_29,X_77))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_77),inverse(X_29)),inverse(multiply(X_29,X_77))) )],[refute_0_770,refute_0_773]) ).

cnf(refute_0_775,plain,
    multiply(multiply(X_78,inverse(X_77)),inverse(X_29)) = multiply(X_78,multiply(inverse(X_77),inverse(X_29))),
    inference(subst,[],[associativity:[bind(X,$fot(X_78)),bind(Y,$fot(inverse(X_77))),bind(Z,$fot(inverse(X_29)))]]) ).

cnf(refute_0_776,plain,
    ( multiply(X_78,multiply(inverse(X_77),inverse(X_29))) != multiply(X_78,inverse(multiply(X_29,X_77)))
    | multiply(multiply(X_78,inverse(X_77)),inverse(X_29)) != multiply(X_78,multiply(inverse(X_77),inverse(X_29)))
    | multiply(multiply(X_78,inverse(X_77)),inverse(X_29)) = multiply(X_78,inverse(multiply(X_29,X_77))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(multiply(X_78,inverse(X_77)),inverse(X_29)))),bind(Y0,$fot(multiply(X_78,multiply(inverse(X_77),inverse(X_29))))),bind(Z0,$fot(multiply(X_78,inverse(multiply(X_29,X_77)))))]]) ).

cnf(refute_0_777,plain,
    ( multiply(X_78,multiply(inverse(X_77),inverse(X_29))) != multiply(X_78,inverse(multiply(X_29,X_77)))
    | multiply(multiply(X_78,inverse(X_77)),inverse(X_29)) = multiply(X_78,inverse(multiply(X_29,X_77))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_78,inverse(X_77)),inverse(X_29)),multiply(X_78,multiply(inverse(X_77),inverse(X_29)))) )],[refute_0_775,refute_0_776]) ).

cnf(refute_0_778,plain,
    multiply(multiply(X_78,inverse(X_77)),inverse(X_29)) = multiply(X_78,inverse(multiply(X_29,X_77))),
    inference(resolve,[$cnf( $equal(multiply(X_78,multiply(inverse(X_77),inverse(X_29))),multiply(X_78,inverse(multiply(X_29,X_77)))) )],[refute_0_774,refute_0_777]) ).

cnf(refute_0_779,plain,
    ( multiply(multiply(X_78,inverse(X_77)),inverse(X_29)) != multiply(X_78,inverse(multiply(X_29,X_77)))
    | inverse(multiply(X_29,multiply(X_77,inverse(X_78)))) != multiply(multiply(X_78,inverse(X_77)),inverse(X_29))
    | inverse(multiply(X_29,multiply(X_77,inverse(X_78)))) = multiply(X_78,inverse(multiply(X_29,X_77))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_29,multiply(X_77,inverse(X_78)))),multiply(multiply(X_78,inverse(X_77)),inverse(X_29))) ),[1],$fot(multiply(X_78,inverse(multiply(X_29,X_77))))]]) ).

cnf(refute_0_780,plain,
    ( inverse(multiply(X_29,multiply(X_77,inverse(X_78)))) != multiply(multiply(X_78,inverse(X_77)),inverse(X_29))
    | inverse(multiply(X_29,multiply(X_77,inverse(X_78)))) = multiply(X_78,inverse(multiply(X_29,X_77))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_78,inverse(X_77)),inverse(X_29)),multiply(X_78,inverse(multiply(X_29,X_77)))) )],[refute_0_778,refute_0_779]) ).

cnf(refute_0_781,plain,
    inverse(multiply(X_29,multiply(X_77,inverse(X_78)))) = multiply(X_78,inverse(multiply(X_29,X_77))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_29,multiply(X_77,inverse(X_78)))),multiply(multiply(X_78,inverse(X_77)),inverse(X_29))) )],[refute_0_769,refute_0_780]) ).

cnf(refute_0_782,plain,
    inverse(multiply(least_upper_bound(X_561,identity),multiply(inverse(greatest_lower_bound(X_561,identity)),inverse(least_upper_bound(X_561,identity))))) = multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))),
    inference(subst,[],[refute_0_781:[bind(X_29,$fot(least_upper_bound(X_561,identity))),bind(X_77,$fot(inverse(greatest_lower_bound(X_561,identity)))),bind(X_78,$fot(least_upper_bound(X_561,identity)))]]) ).

cnf(refute_0_783,plain,
    inverse(multiply(X,multiply(inverse(X_36),X_37))) = multiply(inverse(multiply(inverse(X_36),X_37)),inverse(X)),
    inference(subst,[],[p11_3:[bind(Y,$fot(multiply(inverse(X_36),X_37)))]]) ).

cnf(refute_0_784,plain,
    inverse(multiply(inverse(X_36),X_37)) = multiply(inverse(X_37),X_36),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_36)),bind(X_30,$fot(X_37))]]) ).

cnf(refute_0_785,plain,
    ( inverse(multiply(X,multiply(inverse(X_36),X_37))) != multiply(inverse(multiply(inverse(X_36),X_37)),inverse(X))
    | inverse(multiply(inverse(X_36),X_37)) != multiply(inverse(X_37),X_36)
    | inverse(multiply(X,multiply(inverse(X_36),X_37))) = multiply(multiply(inverse(X_37),X_36),inverse(X)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,multiply(inverse(X_36),X_37))),multiply(inverse(multiply(inverse(X_36),X_37)),inverse(X))) ),[1,0],$fot(multiply(inverse(X_37),X_36))]]) ).

cnf(refute_0_786,plain,
    ( inverse(multiply(X,multiply(inverse(X_36),X_37))) != multiply(inverse(multiply(inverse(X_36),X_37)),inverse(X))
    | inverse(multiply(X,multiply(inverse(X_36),X_37))) = multiply(multiply(inverse(X_37),X_36),inverse(X)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_36),X_37)),multiply(inverse(X_37),X_36)) )],[refute_0_784,refute_0_785]) ).

cnf(refute_0_787,plain,
    inverse(multiply(X,multiply(inverse(X_36),X_37))) = multiply(multiply(inverse(X_37),X_36),inverse(X)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,multiply(inverse(X_36),X_37))),multiply(inverse(multiply(inverse(X_36),X_37)),inverse(X))) )],[refute_0_783,refute_0_786]) ).

cnf(refute_0_788,plain,
    multiply(multiply(inverse(X_37),X_36),inverse(X)) = multiply(inverse(X_37),multiply(X_36,inverse(X))),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_37))),bind(Y,$fot(X_36)),bind(Z,$fot(inverse(X)))]]) ).

cnf(refute_0_789,plain,
    ( multiply(multiply(inverse(X_37),X_36),inverse(X)) != multiply(inverse(X_37),multiply(X_36,inverse(X)))
    | inverse(multiply(X,multiply(inverse(X_36),X_37))) != multiply(multiply(inverse(X_37),X_36),inverse(X))
    | inverse(multiply(X,multiply(inverse(X_36),X_37))) = multiply(inverse(X_37),multiply(X_36,inverse(X))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,multiply(inverse(X_36),X_37))),multiply(multiply(inverse(X_37),X_36),inverse(X))) ),[1],$fot(multiply(inverse(X_37),multiply(X_36,inverse(X))))]]) ).

cnf(refute_0_790,plain,
    ( inverse(multiply(X,multiply(inverse(X_36),X_37))) != multiply(multiply(inverse(X_37),X_36),inverse(X))
    | inverse(multiply(X,multiply(inverse(X_36),X_37))) = multiply(inverse(X_37),multiply(X_36,inverse(X))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_37),X_36),inverse(X)),multiply(inverse(X_37),multiply(X_36,inverse(X)))) )],[refute_0_788,refute_0_789]) ).

cnf(refute_0_791,plain,
    inverse(multiply(X,multiply(inverse(X_36),X_37))) = multiply(inverse(X_37),multiply(X_36,inverse(X))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,multiply(inverse(X_36),X_37))),multiply(multiply(inverse(X_37),X_36),inverse(X))) )],[refute_0_787,refute_0_790]) ).

cnf(refute_0_792,plain,
    ( inverse(multiply(X,multiply(inverse(X_36),X_37))) != multiply(inverse(X_37),multiply(X_36,inverse(X)))
    | multiply(inverse(X_37),multiply(X_36,inverse(X))) = inverse(multiply(X,multiply(inverse(X_36),X_37))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(multiply(X,multiply(inverse(X_36),X_37))))),bind(Y0,$fot(multiply(inverse(X_37),multiply(X_36,inverse(X)))))]]) ).

cnf(refute_0_793,plain,
    multiply(inverse(X_37),multiply(X_36,inverse(X))) = inverse(multiply(X,multiply(inverse(X_36),X_37))),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,multiply(inverse(X_36),X_37))),multiply(inverse(X_37),multiply(X_36,inverse(X)))) )],[refute_0_791,refute_0_792]) ).

cnf(refute_0_794,plain,
    multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = inverse(multiply(least_upper_bound(X_561,identity),multiply(inverse(greatest_lower_bound(X_561,identity)),inverse(least_upper_bound(X_561,identity))))),
    inference(subst,[],[refute_0_793:[bind(X,$fot(least_upper_bound(X_561,identity))),bind(X_36,$fot(greatest_lower_bound(X_561,identity))),bind(X_37,$fot(inverse(least_upper_bound(X_561,identity))))]]) ).

cnf(refute_0_795,plain,
    ( multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != inverse(multiply(least_upper_bound(X_561,identity),multiply(inverse(greatest_lower_bound(X_561,identity)),inverse(least_upper_bound(X_561,identity)))))
    | inverse(multiply(least_upper_bound(X_561,identity),multiply(inverse(greatest_lower_bound(X_561,identity)),inverse(least_upper_bound(X_561,identity))))) != multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))))
    | multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(X_561,identity),multiply(inverse(greatest_lower_bound(X_561,identity)),inverse(least_upper_bound(X_561,identity))))))),bind(Z0,$fot(multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))))))]]) ).

cnf(refute_0_796,plain,
    ( inverse(multiply(least_upper_bound(X_561,identity),multiply(inverse(greatest_lower_bound(X_561,identity)),inverse(least_upper_bound(X_561,identity))))) != multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))))
    | multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),inverse(multiply(least_upper_bound(X_561,identity),multiply(inverse(greatest_lower_bound(X_561,identity)),inverse(least_upper_bound(X_561,identity)))))) )],[refute_0_794,refute_0_795]) ).

cnf(refute_0_797,plain,
    multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_561,identity),multiply(inverse(greatest_lower_bound(X_561,identity)),inverse(least_upper_bound(X_561,identity))))),multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))))) )],[refute_0_782,refute_0_796]) ).

cnf(refute_0_798,plain,
    ( multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))))
    | multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))) != multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity))))
    | multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))))),bind(Y0,$fot(multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))))),bind(Z0,$fot(multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity))))))]]) ).

cnf(refute_0_799,plain,
    ( multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))) != multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity))))
    | multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity)))))) )],[refute_0_797,refute_0_798]) ).

cnf(refute_0_800,plain,
    multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_561,identity),inverse(multiply(least_upper_bound(X_561,identity),inverse(greatest_lower_bound(X_561,identity))))),multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity))))) )],[refute_0_764,refute_0_799]) ).

cnf(refute_0_801,plain,
    ( multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity))))
    | multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))
    | multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))) ),[0],$fot(multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))))]]) ).

cnf(refute_0_802,plain,
    ( multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))
    | multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity))))) )],[refute_0_800,refute_0_801]) ).

cnf(refute_0_803,plain,
    ( X_144 != multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144))))
    | multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))) = X_144 ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X_144)),bind(Y0,$fot(multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144))))))]]) ).

cnf(refute_0_804,plain,
    multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))) = X_144,
    inference(resolve,[$cnf( $equal(X_144,multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144))))) )],[refute_0_463,refute_0_803]) ).

cnf(refute_0_805,plain,
    multiply(least_upper_bound(X_561,identity),inverse(least_upper_bound(identity,inverse(X_561)))) = X_561,
    inference(subst,[],[refute_0_804:[bind(X_144,$fot(X_561))]]) ).

cnf(refute_0_806,plain,
    inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))) = multiply(least_upper_bound(X_561,identity),inverse(least_upper_bound(identity,inverse(X_561)))),
    inference(subst,[],[refute_0_293:[bind(X,$fot(least_upper_bound(X_561,identity))),bind(X_29,$fot(least_upper_bound(identity,inverse(X_561))))]]) ).

cnf(refute_0_807,plain,
    ( multiply(least_upper_bound(X_561,identity),inverse(least_upper_bound(identity,inverse(X_561)))) != X_561
    | inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))) != multiply(least_upper_bound(X_561,identity),inverse(least_upper_bound(identity,inverse(X_561))))
    | inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))) = X_561 ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))))),bind(Y0,$fot(multiply(least_upper_bound(X_561,identity),inverse(least_upper_bound(identity,inverse(X_561)))))),bind(Z0,$fot(X_561))]]) ).

cnf(refute_0_808,plain,
    ( multiply(least_upper_bound(X_561,identity),inverse(least_upper_bound(identity,inverse(X_561)))) != X_561
    | inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))) = X_561 ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))),multiply(least_upper_bound(X_561,identity),inverse(least_upper_bound(identity,inverse(X_561))))) )],[refute_0_806,refute_0_807]) ).

cnf(refute_0_809,plain,
    inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))) = X_561,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_561,identity),inverse(least_upper_bound(identity,inverse(X_561)))),X_561) )],[refute_0_805,refute_0_808]) ).

cnf(refute_0_810,plain,
    multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))) = inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))),
    inference(subst,[],[refute_0_221:[bind(X,$fot(least_upper_bound(identity,inverse(X_561)))),bind(Y,$fot(inverse(least_upper_bound(X_561,identity))))]]) ).

cnf(refute_0_811,plain,
    ( multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))) != inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity))))
    | inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))) != X_561
    | multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))) = X_561 ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))))),bind(Z0,$fot(X_561))]]) ).

cnf(refute_0_812,plain,
    ( inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))) != X_561
    | multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))) = X_561 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))),inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity))))) )],[refute_0_810,refute_0_811]) ).

cnf(refute_0_813,plain,
    multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))) = X_561,
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(X_561)),inverse(least_upper_bound(X_561,identity)))),X_561) )],[refute_0_809,refute_0_812]) ).

cnf(refute_0_814,plain,
    greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))) = greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))))]]) ).

cnf(refute_0_815,plain,
    ( multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))) != X_561
    | greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))
    | greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))) = greatest_lower_bound(identity,X_561) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))) ),[1,1],$fot(X_561)]]) ).

cnf(refute_0_816,plain,
    ( multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))) != X_561
    | greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))) = greatest_lower_bound(identity,X_561) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))) )],[refute_0_814,refute_0_815]) ).

cnf(refute_0_817,plain,
    greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))) = greatest_lower_bound(identity,X_561),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))),X_561) )],[refute_0_813,refute_0_816]) ).

cnf(refute_0_818,plain,
    ( multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))
    | greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))) != greatest_lower_bound(identity,X_561)
    | multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = greatest_lower_bound(identity,X_561) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),greatest_lower_bound(identity,X_561)) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))))]]) ).

cnf(refute_0_819,plain,
    ( multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))
    | multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = greatest_lower_bound(identity,X_561) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561))))),greatest_lower_bound(identity,X_561)) )],[refute_0_817,refute_0_818]) ).

cnf(refute_0_820,plain,
    ( multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))
    | multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = greatest_lower_bound(identity,X_561) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))) )],[refute_0_802,refute_0_819]) ).

cnf(refute_0_821,plain,
    multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = greatest_lower_bound(identity,X_561),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_561,identity))),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))))) )],[refute_0_759,refute_0_820]) ).

cnf(refute_0_822,plain,
    multiply(multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),greatest_lower_bound(X_467,identity)),Z) = multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(greatest_lower_bound(identity,inverse(X_467))))),bind(Y,$fot(greatest_lower_bound(X_467,identity)))]]) ).

cnf(refute_0_823,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(X_81,identity)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81)),
    inference(subst,[],[refute_0_680:[bind(X_79,$fot(inverse(greatest_lower_bound(identity,inverse(X_81))))),bind(X_80,$fot(identity))]]) ).

cnf(refute_0_824,plain,
    inverse(inverse(X_92)) = multiply(inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))),greatest_lower_bound(identity,X_92)),
    inference(subst,[],[refute_0_622:[bind(X,$fot(greatest_lower_bound(identity,X_92))),bind(X_70,$fot(inverse(X_92)))]]) ).

cnf(refute_0_825,plain,
    ( multiply(greatest_lower_bound(identity,X_92),inverse(X_92)) != greatest_lower_bound(identity,inverse(X_92))
    | inverse(inverse(X_92)) != multiply(inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))),greatest_lower_bound(identity,X_92))
    | inverse(inverse(X_92)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_92))),greatest_lower_bound(identity,X_92)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_92)),multiply(inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))),greatest_lower_bound(identity,X_92))) ),[1,0,0],$fot(greatest_lower_bound(identity,inverse(X_92)))]]) ).

cnf(refute_0_826,plain,
    ( inverse(inverse(X_92)) != multiply(inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))),greatest_lower_bound(identity,X_92))
    | inverse(inverse(X_92)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_92))),greatest_lower_bound(identity,X_92)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_92),inverse(X_92)),greatest_lower_bound(identity,inverse(X_92))) )],[refute_0_286,refute_0_825]) ).

cnf(refute_0_827,plain,
    inverse(inverse(X_92)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_92))),greatest_lower_bound(identity,X_92)),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_92)),multiply(inverse(multiply(greatest_lower_bound(identity,X_92),inverse(X_92))),greatest_lower_bound(identity,X_92))) )],[refute_0_824,refute_0_826]) ).

cnf(refute_0_828,plain,
    inverse(inverse(X_92)) = X_92,
    inference(subst,[],[p11_2:[bind(X,$fot(X_92))]]) ).

cnf(refute_0_829,plain,
    ( inverse(inverse(X_92)) != X_92
    | inverse(inverse(X_92)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_92))),greatest_lower_bound(identity,X_92))
    | X_92 = multiply(inverse(greatest_lower_bound(identity,inverse(X_92))),greatest_lower_bound(identity,X_92)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_92)),multiply(inverse(greatest_lower_bound(identity,inverse(X_92))),greatest_lower_bound(identity,X_92))) ),[0],$fot(X_92)]]) ).

cnf(refute_0_830,plain,
    ( inverse(inverse(X_92)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_92))),greatest_lower_bound(identity,X_92))
    | X_92 = multiply(inverse(greatest_lower_bound(identity,inverse(X_92))),greatest_lower_bound(identity,X_92)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_92)),X_92) )],[refute_0_828,refute_0_829]) ).

cnf(refute_0_831,plain,
    X_92 = multiply(inverse(greatest_lower_bound(identity,inverse(X_92))),greatest_lower_bound(identity,X_92)),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_92)),multiply(inverse(greatest_lower_bound(identity,inverse(X_92))),greatest_lower_bound(identity,X_92))) )],[refute_0_827,refute_0_830]) ).

cnf(refute_0_832,plain,
    X_81 = multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81)),
    inference(subst,[],[refute_0_831:[bind(X_92,$fot(X_81))]]) ).

cnf(refute_0_833,plain,
    ( X_81 != multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81))
    | multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81)) = X_81 ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X_81)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81))))]]) ).

cnf(refute_0_834,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81)) = X_81,
    inference(resolve,[$cnf( $equal(X_81,multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81))) )],[refute_0_832,refute_0_833]) ).

cnf(refute_0_835,plain,
    ( multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(X_81,identity)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81))
    | multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81)) != X_81
    | multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(X_81,identity)) = X_81 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(X_81,identity)),X_81) ),[0],$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81)))]]) ).

cnf(refute_0_836,plain,
    ( multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(X_81,identity)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81))
    | multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(X_81,identity)) = X_81 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81)),X_81) )],[refute_0_834,refute_0_835]) ).

cnf(refute_0_837,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(X_81,identity)) = X_81,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(X_81,identity)),multiply(inverse(greatest_lower_bound(identity,inverse(X_81))),greatest_lower_bound(identity,X_81))) )],[refute_0_823,refute_0_836]) ).

cnf(refute_0_838,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),greatest_lower_bound(X_467,identity)) = X_467,
    inference(subst,[],[refute_0_837:[bind(X_81,$fot(X_467))]]) ).

cnf(refute_0_839,plain,
    ( multiply(multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),greatest_lower_bound(X_467,identity)),Z) != multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z))
    | multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),greatest_lower_bound(X_467,identity)) != X_467
    | multiply(X_467,Z) = multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),greatest_lower_bound(X_467,identity)),Z),multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z))) ),[0,0],$fot(X_467)]]) ).

cnf(refute_0_840,plain,
    ( multiply(multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),greatest_lower_bound(X_467,identity)),Z) != multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z))
    | multiply(X_467,Z) = multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),greatest_lower_bound(X_467,identity)),X_467) )],[refute_0_838,refute_0_839]) ).

cnf(refute_0_841,plain,
    multiply(X_467,Z) = multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),greatest_lower_bound(X_467,identity)),Z),multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z))) )],[refute_0_822,refute_0_840]) ).

cnf(refute_0_842,plain,
    X_68 = multiply(inverse(greatest_lower_bound(X_161,inverse(X_68))),multiply(greatest_lower_bound(X_161,inverse(X_68)),X_68)),
    inference(subst,[],[refute_0_9:[bind(X_67,$fot(greatest_lower_bound(X_161,inverse(X_68))))]]) ).

cnf(refute_0_843,plain,
    multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87) = greatest_lower_bound(multiply(X_88,X_87),multiply(inverse(X_87),X_87)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_87)),bind(Y,$fot(X_88)),bind(Z,$fot(inverse(X_87)))]]) ).

cnf(refute_0_844,plain,
    ( multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87) != greatest_lower_bound(multiply(X_88,X_87),multiply(inverse(X_87),X_87))
    | multiply(inverse(X_87),X_87) != identity
    | multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87) = greatest_lower_bound(multiply(X_88,X_87),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(inverse(X_87),X_87))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_845,plain,
    ( multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87) != greatest_lower_bound(multiply(X_88,X_87),multiply(inverse(X_87),X_87))
    | multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87) = greatest_lower_bound(multiply(X_88,X_87),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_87),X_87),identity) )],[refute_0_717,refute_0_844]) ).

cnf(refute_0_846,plain,
    multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87) = greatest_lower_bound(multiply(X_88,X_87),identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(inverse(X_87),X_87))) )],[refute_0_843,refute_0_845]) ).

cnf(refute_0_847,plain,
    greatest_lower_bound(multiply(X_88,X_87),identity) = greatest_lower_bound(identity,multiply(X_88,X_87)),
    inference(subst,[],[refute_0_35:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_88,X_87)))]]) ).

cnf(refute_0_848,plain,
    ( multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87) != greatest_lower_bound(multiply(X_88,X_87),identity)
    | greatest_lower_bound(multiply(X_88,X_87),identity) != greatest_lower_bound(identity,multiply(X_88,X_87))
    | multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87) = greatest_lower_bound(identity,multiply(X_88,X_87)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87),greatest_lower_bound(identity,multiply(X_88,X_87))) ),[0],$fot(greatest_lower_bound(multiply(X_88,X_87),identity))]]) ).

cnf(refute_0_849,plain,
    ( multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87) != greatest_lower_bound(multiply(X_88,X_87),identity)
    | multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87) = greatest_lower_bound(identity,multiply(X_88,X_87)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_87),identity),greatest_lower_bound(identity,multiply(X_88,X_87))) )],[refute_0_847,refute_0_848]) ).

cnf(refute_0_850,plain,
    multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87) = greatest_lower_bound(identity,multiply(X_88,X_87)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,inverse(X_87)),X_87),greatest_lower_bound(multiply(X_88,X_87),identity)) )],[refute_0_846,refute_0_849]) ).

cnf(refute_0_851,plain,
    multiply(greatest_lower_bound(X_161,inverse(X_68)),X_68) = greatest_lower_bound(identity,multiply(X_161,X_68)),
    inference(subst,[],[refute_0_850:[bind(X_87,$fot(X_68)),bind(X_88,$fot(X_161))]]) ).

cnf(refute_0_852,plain,
    ( X_68 != multiply(inverse(greatest_lower_bound(X_161,inverse(X_68))),multiply(greatest_lower_bound(X_161,inverse(X_68)),X_68))
    | multiply(greatest_lower_bound(X_161,inverse(X_68)),X_68) != greatest_lower_bound(identity,multiply(X_161,X_68))
    | X_68 = multiply(inverse(greatest_lower_bound(X_161,inverse(X_68))),greatest_lower_bound(identity,multiply(X_161,X_68))) ),
    introduced(tautology,[equality,[$cnf( $equal(X_68,multiply(inverse(greatest_lower_bound(X_161,inverse(X_68))),multiply(greatest_lower_bound(X_161,inverse(X_68)),X_68))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_161,X_68)))]]) ).

cnf(refute_0_853,plain,
    ( X_68 != multiply(inverse(greatest_lower_bound(X_161,inverse(X_68))),multiply(greatest_lower_bound(X_161,inverse(X_68)),X_68))
    | X_68 = multiply(inverse(greatest_lower_bound(X_161,inverse(X_68))),greatest_lower_bound(identity,multiply(X_161,X_68))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_161,inverse(X_68)),X_68),greatest_lower_bound(identity,multiply(X_161,X_68))) )],[refute_0_851,refute_0_852]) ).

cnf(refute_0_854,plain,
    X_68 = multiply(inverse(greatest_lower_bound(X_161,inverse(X_68))),greatest_lower_bound(identity,multiply(X_161,X_68))),
    inference(resolve,[$cnf( $equal(X_68,multiply(inverse(greatest_lower_bound(X_161,inverse(X_68))),multiply(greatest_lower_bound(X_161,inverse(X_68)),X_68))) )],[refute_0_842,refute_0_853]) ).

cnf(refute_0_855,plain,
    least_upper_bound(X_129,identity) = multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity)))),
    inference(subst,[],[refute_0_854:[bind(X_161,$fot(inverse(least_upper_bound(identity,inverse(X_129))))),bind(X_68,$fot(least_upper_bound(X_129,identity)))]]) ).

cnf(refute_0_856,plain,
    inverse(inverse(X_129)) = multiply(inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))),least_upper_bound(X_129,identity)),
    inference(subst,[],[refute_0_622:[bind(X,$fot(least_upper_bound(X_129,identity))),bind(X_70,$fot(inverse(X_129)))]]) ).

cnf(refute_0_857,plain,
    ( multiply(least_upper_bound(X_129,identity),inverse(X_129)) != least_upper_bound(identity,inverse(X_129))
    | inverse(inverse(X_129)) != multiply(inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))),least_upper_bound(X_129,identity))
    | inverse(inverse(X_129)) = multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_129)),multiply(inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))),least_upper_bound(X_129,identity))) ),[1,0,0],$fot(least_upper_bound(identity,inverse(X_129)))]]) ).

cnf(refute_0_858,plain,
    ( inverse(inverse(X_129)) != multiply(inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))),least_upper_bound(X_129,identity))
    | inverse(inverse(X_129)) = multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_129,identity),inverse(X_129)),least_upper_bound(identity,inverse(X_129))) )],[refute_0_742,refute_0_857]) ).

cnf(refute_0_859,plain,
    inverse(inverse(X_129)) = multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_129)),multiply(inverse(multiply(least_upper_bound(X_129,identity),inverse(X_129))),least_upper_bound(X_129,identity))) )],[refute_0_856,refute_0_858]) ).

cnf(refute_0_860,plain,
    inverse(inverse(X_129)) = X_129,
    inference(subst,[],[p11_2:[bind(X,$fot(X_129))]]) ).

cnf(refute_0_861,plain,
    ( inverse(inverse(X_129)) != X_129
    | inverse(inverse(X_129)) != multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity))
    | X_129 = multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_129)),multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity))) ),[0],$fot(X_129)]]) ).

cnf(refute_0_862,plain,
    ( inverse(inverse(X_129)) != multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity))
    | X_129 = multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_129)),X_129) )],[refute_0_860,refute_0_861]) ).

cnf(refute_0_863,plain,
    X_129 = multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_129)),multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity))) )],[refute_0_859,refute_0_862]) ).

cnf(refute_0_864,plain,
    ( X_129 != multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity))
    | multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity)) = X_129 ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X_129)),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity))))]]) ).

cnf(refute_0_865,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity)) = X_129,
    inference(resolve,[$cnf( $equal(X_129,multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity))) )],[refute_0_863,refute_0_864]) ).

cnf(refute_0_866,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity)) != X_129
    | least_upper_bound(X_129,identity) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity))))
    | least_upper_bound(X_129,identity) = multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,X_129)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_129,identity),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity))))) ),[1,1,1],$fot(X_129)]]) ).

cnf(refute_0_867,plain,
    ( least_upper_bound(X_129,identity) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity))))
    | least_upper_bound(X_129,identity) = multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,X_129)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity)),X_129) )],[refute_0_865,refute_0_866]) ).

cnf(refute_0_868,plain,
    least_upper_bound(X_129,identity) = multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,X_129)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_129,identity),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_129))),least_upper_bound(X_129,identity))))) )],[refute_0_855,refute_0_867]) ).

cnf(refute_0_869,plain,
    inverse(multiply(inverse(X),greatest_lower_bound(X_154,X_153))) = multiply(inverse(greatest_lower_bound(X_154,X_153)),X),
    inference(subst,[],[refute_0_22:[bind(X_30,$fot(greatest_lower_bound(X_154,X_153)))]]) ).

cnf(refute_0_870,plain,
    multiply(inverse(X),greatest_lower_bound(X_154,X_153)) = multiply(inverse(X),greatest_lower_bound(X_153,X_154)),
    inference(subst,[],[refute_0_680:[bind(X_79,$fot(inverse(X))),bind(X_80,$fot(X_153)),bind(X_81,$fot(X_154))]]) ).

cnf(refute_0_871,plain,
    ( multiply(inverse(X),greatest_lower_bound(X_154,X_153)) != multiply(inverse(X),greatest_lower_bound(X_153,X_154))
    | inverse(multiply(inverse(X),greatest_lower_bound(X_154,X_153))) != multiply(inverse(greatest_lower_bound(X_154,X_153)),X)
    | inverse(multiply(inverse(X),greatest_lower_bound(X_153,X_154))) = multiply(inverse(greatest_lower_bound(X_154,X_153)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_154,X_153))),multiply(inverse(greatest_lower_bound(X_154,X_153)),X)) ),[0,0],$fot(multiply(inverse(X),greatest_lower_bound(X_153,X_154)))]]) ).

cnf(refute_0_872,plain,
    ( inverse(multiply(inverse(X),greatest_lower_bound(X_154,X_153))) != multiply(inverse(greatest_lower_bound(X_154,X_153)),X)
    | inverse(multiply(inverse(X),greatest_lower_bound(X_153,X_154))) = multiply(inverse(greatest_lower_bound(X_154,X_153)),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X),greatest_lower_bound(X_154,X_153)),multiply(inverse(X),greatest_lower_bound(X_153,X_154))) )],[refute_0_870,refute_0_871]) ).

cnf(refute_0_873,plain,
    inverse(multiply(inverse(X),greatest_lower_bound(X_153,X_154))) = multiply(inverse(greatest_lower_bound(X_154,X_153)),X),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_154,X_153))),multiply(inverse(greatest_lower_bound(X_154,X_153)),X)) )],[refute_0_869,refute_0_872]) ).

cnf(refute_0_874,plain,
    inverse(multiply(inverse(X),greatest_lower_bound(X_153,X_154))) = multiply(inverse(greatest_lower_bound(X_153,X_154)),X),
    inference(subst,[],[refute_0_22:[bind(X_30,$fot(greatest_lower_bound(X_153,X_154)))]]) ).

cnf(refute_0_875,plain,
    ( inverse(multiply(inverse(X),greatest_lower_bound(X_153,X_154))) != multiply(inverse(greatest_lower_bound(X_153,X_154)),X)
    | inverse(multiply(inverse(X),greatest_lower_bound(X_153,X_154))) != multiply(inverse(greatest_lower_bound(X_154,X_153)),X)
    | multiply(inverse(greatest_lower_bound(X_153,X_154)),X) = multiply(inverse(greatest_lower_bound(X_154,X_153)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_153,X_154))),multiply(inverse(greatest_lower_bound(X_154,X_153)),X)) ),[0],$fot(multiply(inverse(greatest_lower_bound(X_153,X_154)),X))]]) ).

cnf(refute_0_876,plain,
    ( inverse(multiply(inverse(X),greatest_lower_bound(X_153,X_154))) != multiply(inverse(greatest_lower_bound(X_154,X_153)),X)
    | multiply(inverse(greatest_lower_bound(X_153,X_154)),X) = multiply(inverse(greatest_lower_bound(X_154,X_153)),X) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_153,X_154))),multiply(inverse(greatest_lower_bound(X_153,X_154)),X)) )],[refute_0_874,refute_0_875]) ).

cnf(refute_0_877,plain,
    multiply(inverse(greatest_lower_bound(X_153,X_154)),X) = multiply(inverse(greatest_lower_bound(X_154,X_153)),X),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(X_153,X_154))),multiply(inverse(greatest_lower_bound(X_154,X_153)),X)) )],[refute_0_873,refute_0_876]) ).

cnf(refute_0_878,plain,
    ( multiply(inverse(greatest_lower_bound(X_153,X_154)),X) != multiply(inverse(greatest_lower_bound(X_154,X_153)),X)
    | multiply(inverse(greatest_lower_bound(X_154,X_153)),X) = multiply(inverse(greatest_lower_bound(X_153,X_154)),X) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_153,X_154)),X))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_154,X_153)),X)))]]) ).

cnf(refute_0_879,plain,
    multiply(inverse(greatest_lower_bound(X_154,X_153)),X) = multiply(inverse(greatest_lower_bound(X_153,X_154)),X),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_153,X_154)),X),multiply(inverse(greatest_lower_bound(X_154,X_153)),X)) )],[refute_0_877,refute_0_878]) ).

cnf(refute_0_880,plain,
    multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,X_129)) = multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)),
    inference(subst,[],[refute_0_879:[bind(X,$fot(greatest_lower_bound(identity,X_129))),bind(X_153,$fot(inverse(least_upper_bound(X_129,identity)))),bind(X_154,$fot(inverse(least_upper_bound(identity,inverse(X_129)))))]]) ).

cnf(refute_0_881,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,X_129)) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129))
    | least_upper_bound(X_129,identity) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,X_129))
    | least_upper_bound(X_129,identity) = multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_129,identity),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,X_129))) ),[1],$fot(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)))]]) ).

cnf(refute_0_882,plain,
    ( least_upper_bound(X_129,identity) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,X_129))
    | least_upper_bound(X_129,identity) = multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,X_129)),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129))) )],[refute_0_880,refute_0_881]) ).

cnf(refute_0_883,plain,
    least_upper_bound(X_129,identity) = multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_129,identity),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,inverse(X_129))),inverse(least_upper_bound(X_129,identity)))),greatest_lower_bound(identity,X_129))) )],[refute_0_868,refute_0_882]) ).

cnf(refute_0_884,plain,
    multiply(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),greatest_lower_bound(identity,X_129)) = multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(greatest_lower_bound(X_129,identity)))),bind(Y,$fot(least_upper_bound(X_129,identity))),bind(Z,$fot(greatest_lower_bound(identity,X_129)))]]) ).

cnf(refute_0_885,plain,
    inverse(multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity))) = multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),
    inference(subst,[],[refute_0_22:[bind(X,$fot(least_upper_bound(X_129,identity))),bind(X_30,$fot(greatest_lower_bound(X_129,identity)))]]) ).

cnf(refute_0_886,plain,
    multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)) = greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),multiply(inverse(least_upper_bound(X_80,identity)),X_80)),
    inference(subst,[],[refute_0_106:[bind(X_79,$fot(inverse(least_upper_bound(X_80,identity))))]]) ).

cnf(refute_0_887,plain,
    inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))) = multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))),
    inference(subst,[],[p11_3:[bind(X,$fot(inverse(X_144))),bind(Y,$fot(least_upper_bound(X_144,identity)))]]) ).

cnf(refute_0_888,plain,
    ( multiply(inverse(X_144),least_upper_bound(X_144,identity)) != least_upper_bound(identity,inverse(X_144))
    | inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))) != multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144)))
    | inverse(least_upper_bound(identity,inverse(X_144))) = multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))),multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144)))) ),[0,0],$fot(least_upper_bound(identity,inverse(X_144)))]]) ).

cnf(refute_0_889,plain,
    ( inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))) != multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144)))
    | inverse(least_upper_bound(identity,inverse(X_144))) = multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_144),least_upper_bound(X_144,identity)),least_upper_bound(identity,inverse(X_144))) )],[refute_0_456,refute_0_888]) ).

cnf(refute_0_890,plain,
    inverse(least_upper_bound(identity,inverse(X_144))) = multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))),multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144)))) )],[refute_0_887,refute_0_889]) ).

cnf(refute_0_891,plain,
    inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))) = multiply(inverse(least_upper_bound(X_144,identity)),X_144),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_144)),bind(X_30,$fot(least_upper_bound(X_144,identity)))]]) ).

cnf(refute_0_892,plain,
    multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))) = inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))),
    inference(subst,[],[refute_0_221:[bind(X,$fot(inverse(X_144))),bind(Y,$fot(least_upper_bound(X_144,identity)))]]) ).

cnf(refute_0_893,plain,
    ( multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))) != inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity)))
    | inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))) != multiply(inverse(least_upper_bound(X_144,identity)),X_144)
    | multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))) = multiply(inverse(least_upper_bound(X_144,identity)),X_144) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))))),bind(Y0,$fot(inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(X_144,identity)),X_144)))]]) ).

cnf(refute_0_894,plain,
    ( inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))) != multiply(inverse(least_upper_bound(X_144,identity)),X_144)
    | multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))) = multiply(inverse(least_upper_bound(X_144,identity)),X_144) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))),inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity)))) )],[refute_0_892,refute_0_893]) ).

cnf(refute_0_895,plain,
    multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))) = multiply(inverse(least_upper_bound(X_144,identity)),X_144),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_144),least_upper_bound(X_144,identity))),multiply(inverse(least_upper_bound(X_144,identity)),X_144)) )],[refute_0_891,refute_0_894]) ).

cnf(refute_0_896,plain,
    ( multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))) != multiply(inverse(least_upper_bound(X_144,identity)),X_144)
    | inverse(least_upper_bound(identity,inverse(X_144))) != multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144)))
    | inverse(least_upper_bound(identity,inverse(X_144))) = multiply(inverse(least_upper_bound(X_144,identity)),X_144) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_144))),multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144)))) ),[1],$fot(multiply(inverse(least_upper_bound(X_144,identity)),X_144))]]) ).

cnf(refute_0_897,plain,
    ( inverse(least_upper_bound(identity,inverse(X_144))) != multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144)))
    | inverse(least_upper_bound(identity,inverse(X_144))) = multiply(inverse(least_upper_bound(X_144,identity)),X_144) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144))),multiply(inverse(least_upper_bound(X_144,identity)),X_144)) )],[refute_0_895,refute_0_896]) ).

cnf(refute_0_898,plain,
    inverse(least_upper_bound(identity,inverse(X_144))) = multiply(inverse(least_upper_bound(X_144,identity)),X_144),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_144))),multiply(inverse(least_upper_bound(X_144,identity)),inverse(inverse(X_144)))) )],[refute_0_890,refute_0_897]) ).

cnf(refute_0_899,plain,
    inverse(least_upper_bound(identity,inverse(X_80))) = multiply(inverse(least_upper_bound(X_80,identity)),X_80),
    inference(subst,[],[refute_0_898:[bind(X_144,$fot(X_80))]]) ).

cnf(refute_0_900,plain,
    ( inverse(least_upper_bound(identity,inverse(X_80))) != multiply(inverse(least_upper_bound(X_80,identity)),X_80)
    | multiply(inverse(least_upper_bound(X_80,identity)),X_80) = inverse(least_upper_bound(identity,inverse(X_80))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_80))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_80,identity)),X_80)))]]) ).

cnf(refute_0_901,plain,
    multiply(inverse(least_upper_bound(X_80,identity)),X_80) = inverse(least_upper_bound(identity,inverse(X_80))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_80))),multiply(inverse(least_upper_bound(X_80,identity)),X_80)) )],[refute_0_899,refute_0_900]) ).

cnf(refute_0_902,plain,
    ( multiply(inverse(least_upper_bound(X_80,identity)),X_80) != inverse(least_upper_bound(identity,inverse(X_80)))
    | multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)) != greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),multiply(inverse(least_upper_bound(X_80,identity)),X_80))
    | multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)) = greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),inverse(least_upper_bound(identity,inverse(X_80)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)),greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),multiply(inverse(least_upper_bound(X_80,identity)),X_80))) ),[1,1],$fot(inverse(least_upper_bound(identity,inverse(X_80))))]]) ).

cnf(refute_0_903,plain,
    ( multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)) != greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),multiply(inverse(least_upper_bound(X_80,identity)),X_80))
    | multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)) = greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),inverse(least_upper_bound(identity,inverse(X_80)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_80,identity)),X_80),inverse(least_upper_bound(identity,inverse(X_80)))) )],[refute_0_901,refute_0_902]) ).

cnf(refute_0_904,plain,
    multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)) = greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),inverse(least_upper_bound(identity,inverse(X_80)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)),greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),multiply(inverse(least_upper_bound(X_80,identity)),X_80))) )],[refute_0_886,refute_0_903]) ).

cnf(refute_0_905,plain,
    ( multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)) != greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),inverse(least_upper_bound(identity,inverse(X_80))))
    | greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),inverse(least_upper_bound(identity,inverse(X_80)))) = multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)))),bind(Y0,$fot(greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),inverse(least_upper_bound(identity,inverse(X_80))))))]]) ).

cnf(refute_0_906,plain,
    greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),inverse(least_upper_bound(identity,inverse(X_80)))) = multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_80,identity)),greatest_lower_bound(X_80,identity)),greatest_lower_bound(inverse(least_upper_bound(X_80,identity)),inverse(least_upper_bound(identity,inverse(X_80))))) )],[refute_0_904,refute_0_905]) ).

cnf(refute_0_907,plain,
    greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129)))) = multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity)),
    inference(subst,[],[refute_0_906:[bind(X_80,$fot(X_129))]]) ).

cnf(refute_0_908,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))) = inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))))]]) ).

cnf(refute_0_909,plain,
    ( greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129)))) != multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))) != inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129)))))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))) = inverse(multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129)))))) ),[1,0],$fot(multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity)))]]) ).

cnf(refute_0_910,plain,
    ( greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129)))) != multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))) = inverse(multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129)))))) )],[refute_0_908,refute_0_909]) ).

cnf(refute_0_911,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))) = inverse(multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129)))),multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity))) )],[refute_0_907,refute_0_910]) ).

cnf(refute_0_912,plain,
    ( inverse(multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity))) != multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))) != inverse(multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity)))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))) = multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))))),bind(Y0,$fot(inverse(multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity))))]]) ).

cnf(refute_0_913,plain,
    ( inverse(multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity))) != multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))) = multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),inverse(multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity)))) )],[refute_0_911,refute_0_912]) ).

cnf(refute_0_914,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))) = multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(X_129,identity)),greatest_lower_bound(X_129,identity))),multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity))) )],[refute_0_885,refute_0_913]) ).

cnf(refute_0_915,plain,
    multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) = multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)))]]) ).

cnf(refute_0_916,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))) != multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity))
    | multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) = multiply(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),greatest_lower_bound(identity,X_129)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129))) ),[1,0],$fot(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)))]]) ).

cnf(refute_0_917,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))) != multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity))
    | multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) = multiply(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),greatest_lower_bound(identity,X_129)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129))) )],[refute_0_915,refute_0_916]) ).

cnf(refute_0_918,plain,
    multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) = multiply(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),greatest_lower_bound(identity,X_129)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity))) )],[refute_0_914,refute_0_917]) ).

cnf(refute_0_919,plain,
    ( multiply(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),greatest_lower_bound(identity,X_129)) != multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129)))
    | multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) != multiply(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),greatest_lower_bound(identity,X_129))
    | multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) = multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)))),bind(Y0,$fot(multiply(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),greatest_lower_bound(identity,X_129)))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129)))))]]) ).

cnf(refute_0_920,plain,
    ( multiply(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),greatest_lower_bound(identity,X_129)) != multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129)))
    | multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) = multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)),multiply(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),greatest_lower_bound(identity,X_129))) )],[refute_0_918,refute_0_919]) ).

cnf(refute_0_921,plain,
    multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) = multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(greatest_lower_bound(X_129,identity)),least_upper_bound(X_129,identity)),greatest_lower_bound(identity,X_129)),multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129)))) )],[refute_0_884,refute_0_920]) ).

cnf(refute_0_922,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)) != multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129)))
    | least_upper_bound(X_129,identity) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129))
    | least_upper_bound(X_129,identity) = multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_129,identity),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129))) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))))]]) ).

cnf(refute_0_923,plain,
    ( least_upper_bound(X_129,identity) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129))
    | least_upper_bound(X_129,identity) = multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129)),multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129)))) )],[refute_0_921,refute_0_922]) ).

cnf(refute_0_924,plain,
    least_upper_bound(X_129,identity) = multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_129,identity),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(X_129,identity)),inverse(least_upper_bound(identity,inverse(X_129))))),greatest_lower_bound(identity,X_129))) )],[refute_0_883,refute_0_923]) ).

cnf(refute_0_925,plain,
    inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) = multiply(inverse(greatest_lower_bound(identity,multiply(X_88,identity))),multiply(X_88,identity)),
    inference(subst,[],[refute_0_254:[bind(X_86,$fot(multiply(X_88,identity)))]]) ).

cnf(refute_0_926,plain,
    multiply(greatest_lower_bound(X_88,identity),X_87) = greatest_lower_bound(multiply(X_88,X_87),multiply(identity,X_87)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_87)),bind(Y,$fot(X_88)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_927,plain,
    multiply(identity,X_87) = X_87,
    inference(subst,[],[left_identity:[bind(X,$fot(X_87))]]) ).

cnf(refute_0_928,plain,
    ( multiply(greatest_lower_bound(X_88,identity),X_87) != greatest_lower_bound(multiply(X_88,X_87),multiply(identity,X_87))
    | multiply(identity,X_87) != X_87
    | multiply(greatest_lower_bound(X_88,identity),X_87) = greatest_lower_bound(multiply(X_88,X_87),X_87) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_88,identity),X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(identity,X_87))) ),[1,1],$fot(X_87)]]) ).

cnf(refute_0_929,plain,
    ( multiply(greatest_lower_bound(X_88,identity),X_87) != greatest_lower_bound(multiply(X_88,X_87),multiply(identity,X_87))
    | multiply(greatest_lower_bound(X_88,identity),X_87) = greatest_lower_bound(multiply(X_88,X_87),X_87) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_87),X_87) )],[refute_0_927,refute_0_928]) ).

cnf(refute_0_930,plain,
    multiply(greatest_lower_bound(X_88,identity),X_87) = greatest_lower_bound(multiply(X_88,X_87),X_87),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,identity),X_87),greatest_lower_bound(multiply(X_88,X_87),multiply(identity,X_87))) )],[refute_0_926,refute_0_929]) ).

cnf(refute_0_931,plain,
    greatest_lower_bound(multiply(X_88,X_87),X_87) = greatest_lower_bound(X_87,multiply(X_88,X_87)),
    inference(subst,[],[refute_0_35:[bind(X,$fot(X_87)),bind(Y,$fot(multiply(X_88,X_87)))]]) ).

cnf(refute_0_932,plain,
    ( multiply(greatest_lower_bound(X_88,identity),X_87) != greatest_lower_bound(multiply(X_88,X_87),X_87)
    | greatest_lower_bound(multiply(X_88,X_87),X_87) != greatest_lower_bound(X_87,multiply(X_88,X_87))
    | multiply(greatest_lower_bound(X_88,identity),X_87) = greatest_lower_bound(X_87,multiply(X_88,X_87)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_88,identity),X_87),greatest_lower_bound(X_87,multiply(X_88,X_87))) ),[0],$fot(greatest_lower_bound(multiply(X_88,X_87),X_87))]]) ).

cnf(refute_0_933,plain,
    ( multiply(greatest_lower_bound(X_88,identity),X_87) != greatest_lower_bound(multiply(X_88,X_87),X_87)
    | multiply(greatest_lower_bound(X_88,identity),X_87) = greatest_lower_bound(X_87,multiply(X_88,X_87)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_88,X_87),X_87),greatest_lower_bound(X_87,multiply(X_88,X_87))) )],[refute_0_931,refute_0_932]) ).

cnf(refute_0_934,plain,
    multiply(greatest_lower_bound(X_88,identity),X_87) = greatest_lower_bound(X_87,multiply(X_88,X_87)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,identity),X_87),greatest_lower_bound(multiply(X_88,X_87),X_87)) )],[refute_0_930,refute_0_933]) ).

cnf(refute_0_935,plain,
    multiply(greatest_lower_bound(X_88,identity),identity) = greatest_lower_bound(identity,multiply(X_88,identity)),
    inference(subst,[],[refute_0_934:[bind(X_87,$fot(identity))]]) ).

cnf(refute_0_936,plain,
    ( multiply(greatest_lower_bound(X_88,identity),identity) != greatest_lower_bound(identity,multiply(X_88,identity))
    | greatest_lower_bound(identity,multiply(X_88,identity)) = multiply(greatest_lower_bound(X_88,identity),identity) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(X_88,identity),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_88,identity))))]]) ).

cnf(refute_0_937,plain,
    greatest_lower_bound(identity,multiply(X_88,identity)) = multiply(greatest_lower_bound(X_88,identity),identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,identity),identity),greatest_lower_bound(identity,multiply(X_88,identity))) )],[refute_0_935,refute_0_936]) ).

cnf(refute_0_938,plain,
    ( greatest_lower_bound(identity,multiply(X_88,identity)) != multiply(greatest_lower_bound(X_88,identity),identity)
    | inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) != multiply(inverse(greatest_lower_bound(identity,multiply(X_88,identity))),multiply(X_88,identity))
    | inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) = multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))),multiply(inverse(greatest_lower_bound(identity,multiply(X_88,identity))),multiply(X_88,identity))) ),[1,0,0],$fot(multiply(greatest_lower_bound(X_88,identity),identity))]]) ).

cnf(refute_0_939,plain,
    ( inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) != multiply(inverse(greatest_lower_bound(identity,multiply(X_88,identity))),multiply(X_88,identity))
    | inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) = multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_88,identity)),multiply(greatest_lower_bound(X_88,identity),identity)) )],[refute_0_937,refute_0_938]) ).

cnf(refute_0_940,plain,
    inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) = multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))),multiply(inverse(greatest_lower_bound(identity,multiply(X_88,identity))),multiply(X_88,identity))) )],[refute_0_925,refute_0_939]) ).

cnf(refute_0_941,plain,
    ( X != multiply(X,identity)
    | multiply(X,identity) = X ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,identity)))]]) ).

cnf(refute_0_942,plain,
    multiply(X,identity) = X,
    inference(resolve,[$cnf( $equal(X,multiply(X,identity)) )],[refute_0_96,refute_0_941]) ).

cnf(refute_0_943,plain,
    multiply(X_88,identity) = X_88,
    inference(subst,[],[refute_0_942:[bind(X,$fot(X_88))]]) ).

cnf(refute_0_944,plain,
    inverse(multiply(X_88,identity)) = inverse(multiply(X_88,identity)),
    introduced(tautology,[refl,[$fot(inverse(multiply(X_88,identity)))]]) ).

cnf(refute_0_945,plain,
    ( multiply(X_88,identity) != X_88
    | inverse(multiply(X_88,identity)) != inverse(multiply(X_88,identity))
    | inverse(multiply(X_88,identity)) = inverse(X_88) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_88,identity)),inverse(multiply(X_88,identity))) ),[1,0],$fot(X_88)]]) ).

cnf(refute_0_946,plain,
    ( multiply(X_88,identity) != X_88
    | inverse(multiply(X_88,identity)) = inverse(X_88) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_88,identity)),inverse(multiply(X_88,identity))) )],[refute_0_944,refute_0_945]) ).

cnf(refute_0_947,plain,
    inverse(multiply(X_88,identity)) = inverse(X_88),
    inference(resolve,[$cnf( $equal(multiply(X_88,identity),X_88) )],[refute_0_943,refute_0_946]) ).

cnf(refute_0_948,plain,
    greatest_lower_bound(identity,inverse(multiply(X_88,identity))) = greatest_lower_bound(identity,inverse(multiply(X_88,identity))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,inverse(multiply(X_88,identity))))]]) ).

cnf(refute_0_949,plain,
    ( greatest_lower_bound(identity,inverse(multiply(X_88,identity))) != greatest_lower_bound(identity,inverse(multiply(X_88,identity)))
    | inverse(multiply(X_88,identity)) != inverse(X_88)
    | greatest_lower_bound(identity,inverse(multiply(X_88,identity))) = greatest_lower_bound(identity,inverse(X_88)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_88,identity))),greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) ),[1,1],$fot(inverse(X_88))]]) ).

cnf(refute_0_950,plain,
    ( inverse(multiply(X_88,identity)) != inverse(X_88)
    | greatest_lower_bound(identity,inverse(multiply(X_88,identity))) = greatest_lower_bound(identity,inverse(X_88)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_88,identity))),greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) )],[refute_0_948,refute_0_949]) ).

cnf(refute_0_951,plain,
    greatest_lower_bound(identity,inverse(multiply(X_88,identity))) = greatest_lower_bound(identity,inverse(X_88)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_88,identity)),inverse(X_88)) )],[refute_0_947,refute_0_950]) ).

cnf(refute_0_952,plain,
    inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) = inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))))]]) ).

cnf(refute_0_953,plain,
    ( greatest_lower_bound(identity,inverse(multiply(X_88,identity))) != greatest_lower_bound(identity,inverse(X_88))
    | inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) != inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity))))
    | inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) = inverse(greatest_lower_bound(identity,inverse(X_88))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))),inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity))))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(X_88)))]]) ).

cnf(refute_0_954,plain,
    ( greatest_lower_bound(identity,inverse(multiply(X_88,identity))) != greatest_lower_bound(identity,inverse(X_88))
    | inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) = inverse(greatest_lower_bound(identity,inverse(X_88))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))),inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity))))) )],[refute_0_952,refute_0_953]) ).

cnf(refute_0_955,plain,
    inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) = inverse(greatest_lower_bound(identity,inverse(X_88))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_88,identity))),greatest_lower_bound(identity,inverse(X_88))) )],[refute_0_951,refute_0_954]) ).

cnf(refute_0_956,plain,
    ( inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) != multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))
    | inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) != inverse(greatest_lower_bound(identity,inverse(X_88)))
    | inverse(greatest_lower_bound(identity,inverse(X_88))) = multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))),multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))) ),[0],$fot(inverse(greatest_lower_bound(identity,inverse(X_88))))]]) ).

cnf(refute_0_957,plain,
    ( inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) != multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))
    | inverse(greatest_lower_bound(identity,inverse(X_88))) = multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))),inverse(greatest_lower_bound(identity,inverse(X_88)))) )],[refute_0_955,refute_0_956]) ).

cnf(refute_0_958,plain,
    multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)) = multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)))]]) ).

cnf(refute_0_959,plain,
    ( multiply(X_88,identity) != X_88
    | multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)) != multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity))
    | multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)) = multiply(inverse(greatest_lower_bound(X_88,identity)),X_88) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)),multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity))) ),[1,1],$fot(X_88)]]) ).

cnf(refute_0_960,plain,
    ( multiply(X_88,identity) != X_88
    | multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)) = multiply(inverse(greatest_lower_bound(X_88,identity)),X_88) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)),multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity))) )],[refute_0_958,refute_0_959]) ).

cnf(refute_0_961,plain,
    multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)) = multiply(inverse(greatest_lower_bound(X_88,identity)),X_88),
    inference(resolve,[$cnf( $equal(multiply(X_88,identity),X_88) )],[refute_0_943,refute_0_960]) ).

cnf(refute_0_962,plain,
    multiply(greatest_lower_bound(X_88,identity),identity) = greatest_lower_bound(X_88,identity),
    inference(subst,[],[refute_0_942:[bind(X,$fot(greatest_lower_bound(X_88,identity)))]]) ).

cnf(refute_0_963,plain,
    inverse(multiply(greatest_lower_bound(X_88,identity),identity)) = inverse(multiply(greatest_lower_bound(X_88,identity),identity)),
    introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(X_88,identity),identity)))]]) ).

cnf(refute_0_964,plain,
    ( multiply(greatest_lower_bound(X_88,identity),identity) != greatest_lower_bound(X_88,identity)
    | inverse(multiply(greatest_lower_bound(X_88,identity),identity)) != inverse(multiply(greatest_lower_bound(X_88,identity),identity))
    | inverse(multiply(greatest_lower_bound(X_88,identity),identity)) = inverse(greatest_lower_bound(X_88,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),inverse(multiply(greatest_lower_bound(X_88,identity),identity))) ),[1,0],$fot(greatest_lower_bound(X_88,identity))]]) ).

cnf(refute_0_965,plain,
    ( multiply(greatest_lower_bound(X_88,identity),identity) != greatest_lower_bound(X_88,identity)
    | inverse(multiply(greatest_lower_bound(X_88,identity),identity)) = inverse(greatest_lower_bound(X_88,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),inverse(multiply(greatest_lower_bound(X_88,identity),identity))) )],[refute_0_963,refute_0_964]) ).

cnf(refute_0_966,plain,
    inverse(multiply(greatest_lower_bound(X_88,identity),identity)) = inverse(greatest_lower_bound(X_88,identity)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,identity),identity),greatest_lower_bound(X_88,identity)) )],[refute_0_962,refute_0_965]) ).

cnf(refute_0_967,plain,
    multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) = multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)),
    introduced(tautology,[refl,[$fot(multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)))]]) ).

cnf(refute_0_968,plain,
    ( multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) != multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))
    | inverse(multiply(greatest_lower_bound(X_88,identity),identity)) != inverse(greatest_lower_bound(X_88,identity))
    | multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) = multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)),multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))) ),[1,0],$fot(inverse(greatest_lower_bound(X_88,identity)))]]) ).

cnf(refute_0_969,plain,
    ( inverse(multiply(greatest_lower_bound(X_88,identity),identity)) != inverse(greatest_lower_bound(X_88,identity))
    | multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) = multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)),multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))) )],[refute_0_967,refute_0_968]) ).

cnf(refute_0_970,plain,
    multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) = multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),inverse(greatest_lower_bound(X_88,identity))) )],[refute_0_966,refute_0_969]) ).

cnf(refute_0_971,plain,
    ( multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) != multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity))
    | multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)) != multiply(inverse(greatest_lower_bound(X_88,identity)),X_88)
    | multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) = multiply(inverse(greatest_lower_bound(X_88,identity)),X_88) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_88,identity)),X_88)))]]) ).

cnf(refute_0_972,plain,
    ( multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)) != multiply(inverse(greatest_lower_bound(X_88,identity)),X_88)
    | multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) = multiply(inverse(greatest_lower_bound(X_88,identity)),X_88) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)),multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity))) )],[refute_0_970,refute_0_971]) ).

cnf(refute_0_973,plain,
    multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) = multiply(inverse(greatest_lower_bound(X_88,identity)),X_88),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_88,identity)),multiply(X_88,identity)),multiply(inverse(greatest_lower_bound(X_88,identity)),X_88)) )],[refute_0_961,refute_0_972]) ).

cnf(refute_0_974,plain,
    ( multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)) != multiply(inverse(greatest_lower_bound(X_88,identity)),X_88)
    | inverse(greatest_lower_bound(identity,inverse(X_88))) != multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))
    | inverse(greatest_lower_bound(identity,inverse(X_88))) = multiply(inverse(greatest_lower_bound(X_88,identity)),X_88) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_88))),multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_88,identity)),X_88))]]) ).

cnf(refute_0_975,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_88))) != multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))
    | inverse(greatest_lower_bound(identity,inverse(X_88))) = multiply(inverse(greatest_lower_bound(X_88,identity)),X_88) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity)),multiply(inverse(greatest_lower_bound(X_88,identity)),X_88)) )],[refute_0_973,refute_0_974]) ).

cnf(refute_0_976,plain,
    ( inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))) != multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))
    | inverse(greatest_lower_bound(identity,inverse(X_88))) = multiply(inverse(greatest_lower_bound(X_88,identity)),X_88) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_88))),multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))) )],[refute_0_957,refute_0_975]) ).

cnf(refute_0_977,plain,
    inverse(greatest_lower_bound(identity,inverse(X_88))) = multiply(inverse(greatest_lower_bound(X_88,identity)),X_88),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(multiply(X_88,identity)))),multiply(inverse(multiply(greatest_lower_bound(X_88,identity),identity)),multiply(X_88,identity))) )],[refute_0_940,refute_0_976]) ).

cnf(refute_0_978,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_88))) != multiply(inverse(greatest_lower_bound(X_88,identity)),X_88)
    | multiply(inverse(greatest_lower_bound(X_88,identity)),X_88) = inverse(greatest_lower_bound(identity,inverse(X_88))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_88))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_88,identity)),X_88)))]]) ).

cnf(refute_0_979,plain,
    multiply(inverse(greatest_lower_bound(X_88,identity)),X_88) = inverse(greatest_lower_bound(identity,inverse(X_88))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_88))),multiply(inverse(greatest_lower_bound(X_88,identity)),X_88)) )],[refute_0_977,refute_0_978]) ).

cnf(refute_0_980,plain,
    multiply(inverse(greatest_lower_bound(X_129,identity)),X_129) = inverse(greatest_lower_bound(identity,inverse(X_129))),
    inference(subst,[],[refute_0_979:[bind(X_88,$fot(X_129))]]) ).

cnf(refute_0_981,plain,
    multiply(multiply(inverse(multiply(Y,X_72)),Y),Z) = multiply(inverse(multiply(Y,X_72)),multiply(Y,Z)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(multiply(Y,X_72))))]]) ).

cnf(refute_0_982,plain,
    inverse(X_72) = multiply(inverse(multiply(Y,X_72)),Y),
    inference(subst,[],[refute_0_622:[bind(X,$fot(Y)),bind(X_70,$fot(X_72))]]) ).

cnf(refute_0_983,plain,
    ( inverse(X_72) != multiply(inverse(multiply(Y,X_72)),Y)
    | multiply(inverse(multiply(Y,X_72)),Y) = inverse(X_72) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X_72))),bind(Y0,$fot(multiply(inverse(multiply(Y,X_72)),Y)))]]) ).

cnf(refute_0_984,plain,
    multiply(inverse(multiply(Y,X_72)),Y) = inverse(X_72),
    inference(resolve,[$cnf( $equal(inverse(X_72),multiply(inverse(multiply(Y,X_72)),Y)) )],[refute_0_982,refute_0_983]) ).

cnf(refute_0_985,plain,
    ( multiply(multiply(inverse(multiply(Y,X_72)),Y),Z) != multiply(inverse(multiply(Y,X_72)),multiply(Y,Z))
    | multiply(inverse(multiply(Y,X_72)),Y) != inverse(X_72)
    | multiply(inverse(X_72),Z) = multiply(inverse(multiply(Y,X_72)),multiply(Y,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(multiply(Y,X_72)),Y),Z),multiply(inverse(multiply(Y,X_72)),multiply(Y,Z))) ),[0,0],$fot(inverse(X_72))]]) ).

cnf(refute_0_986,plain,
    ( multiply(multiply(inverse(multiply(Y,X_72)),Y),Z) != multiply(inverse(multiply(Y,X_72)),multiply(Y,Z))
    | multiply(inverse(X_72),Z) = multiply(inverse(multiply(Y,X_72)),multiply(Y,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(Y,X_72)),Y),inverse(X_72)) )],[refute_0_984,refute_0_985]) ).

cnf(refute_0_987,plain,
    multiply(inverse(X_72),Z) = multiply(inverse(multiply(Y,X_72)),multiply(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(multiply(Y,X_72)),Y),Z),multiply(inverse(multiply(Y,X_72)),multiply(Y,Z))) )],[refute_0_981,refute_0_986]) ).

cnf(refute_0_988,plain,
    multiply(inverse(X_525),X_524) = multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),multiply(inverse(least_upper_bound(X_524,identity)),X_524)),
    inference(subst,[],[refute_0_987:[bind(Y,$fot(inverse(least_upper_bound(X_524,identity)))),bind(Z,$fot(X_524)),bind(X_72,$fot(X_525))]]) ).

cnf(refute_0_989,plain,
    inverse(least_upper_bound(identity,inverse(X_524))) = multiply(inverse(least_upper_bound(X_524,identity)),X_524),
    inference(subst,[],[refute_0_898:[bind(X_144,$fot(X_524))]]) ).

cnf(refute_0_990,plain,
    ( inverse(least_upper_bound(identity,inverse(X_524))) != multiply(inverse(least_upper_bound(X_524,identity)),X_524)
    | multiply(inverse(least_upper_bound(X_524,identity)),X_524) = inverse(least_upper_bound(identity,inverse(X_524))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_524))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_524,identity)),X_524)))]]) ).

cnf(refute_0_991,plain,
    multiply(inverse(least_upper_bound(X_524,identity)),X_524) = inverse(least_upper_bound(identity,inverse(X_524))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_524))),multiply(inverse(least_upper_bound(X_524,identity)),X_524)) )],[refute_0_989,refute_0_990]) ).

cnf(refute_0_992,plain,
    ( multiply(inverse(X_525),X_524) != multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),multiply(inverse(least_upper_bound(X_524,identity)),X_524))
    | multiply(inverse(least_upper_bound(X_524,identity)),X_524) != inverse(least_upper_bound(identity,inverse(X_524)))
    | multiply(inverse(X_525),X_524) = multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),inverse(least_upper_bound(identity,inverse(X_524)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_525),X_524),multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),multiply(inverse(least_upper_bound(X_524,identity)),X_524))) ),[1,1],$fot(inverse(least_upper_bound(identity,inverse(X_524))))]]) ).

cnf(refute_0_993,plain,
    ( multiply(inverse(X_525),X_524) != multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),multiply(inverse(least_upper_bound(X_524,identity)),X_524))
    | multiply(inverse(X_525),X_524) = multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),inverse(least_upper_bound(identity,inverse(X_524)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_524,identity)),X_524),inverse(least_upper_bound(identity,inverse(X_524)))) )],[refute_0_991,refute_0_992]) ).

cnf(refute_0_994,plain,
    multiply(inverse(X_525),X_524) = multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),inverse(least_upper_bound(identity,inverse(X_524)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_525),X_524),multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),multiply(inverse(least_upper_bound(X_524,identity)),X_524))) )],[refute_0_988,refute_0_993]) ).

cnf(refute_0_995,plain,
    multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),inverse(least_upper_bound(identity,inverse(X_524)))) = inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))),
    inference(subst,[],[refute_0_221:[bind(X,$fot(least_upper_bound(identity,inverse(X_524)))),bind(Y,$fot(multiply(inverse(least_upper_bound(X_524,identity)),X_525)))]]) ).

cnf(refute_0_996,plain,
    ( multiply(inverse(X_525),X_524) != multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),inverse(least_upper_bound(identity,inverse(X_524))))
    | multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),inverse(least_upper_bound(identity,inverse(X_524)))) != inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525)))
    | multiply(inverse(X_525),X_524) = inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_525),X_524),inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525)))) ),[0],$fot(multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),inverse(least_upper_bound(identity,inverse(X_524)))))]]) ).

cnf(refute_0_997,plain,
    ( multiply(inverse(X_525),X_524) != multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),inverse(least_upper_bound(identity,inverse(X_524))))
    | multiply(inverse(X_525),X_524) = inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),inverse(least_upper_bound(identity,inverse(X_524)))),inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525)))) )],[refute_0_995,refute_0_996]) ).

cnf(refute_0_998,plain,
    multiply(inverse(X_525),X_524) = inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_525),X_524),multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),inverse(least_upper_bound(identity,inverse(X_524))))) )],[refute_0_994,refute_0_997]) ).

cnf(refute_0_999,plain,
    multiply(multiply(inverse(X_525),least_upper_bound(X_524,identity)),greatest_lower_bound(identity,X_524)) = multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_525))),bind(Y,$fot(least_upper_bound(X_524,identity))),bind(Z,$fot(greatest_lower_bound(identity,X_524)))]]) ).

cnf(refute_0_1000,plain,
    inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)) = multiply(inverse(X_525),least_upper_bound(X_524,identity)),
    inference(subst,[],[refute_0_22:[bind(X,$fot(least_upper_bound(X_524,identity))),bind(X_30,$fot(X_525))]]) ).

cnf(refute_0_1001,plain,
    multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)) = multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)),
    introduced(tautology,[refl,[$fot(multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)))]]) ).

cnf(refute_0_1002,plain,
    ( multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)) != multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524))
    | inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)) != multiply(inverse(X_525),least_upper_bound(X_524,identity))
    | multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)) = multiply(multiply(inverse(X_525),least_upper_bound(X_524,identity)),greatest_lower_bound(identity,X_524)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)),multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524))) ),[1,0],$fot(multiply(inverse(X_525),least_upper_bound(X_524,identity)))]]) ).

cnf(refute_0_1003,plain,
    ( inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)) != multiply(inverse(X_525),least_upper_bound(X_524,identity))
    | multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)) = multiply(multiply(inverse(X_525),least_upper_bound(X_524,identity)),greatest_lower_bound(identity,X_524)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)),multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524))) )],[refute_0_1001,refute_0_1002]) ).

cnf(refute_0_1004,plain,
    multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)) = multiply(multiply(inverse(X_525),least_upper_bound(X_524,identity)),greatest_lower_bound(identity,X_524)),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),multiply(inverse(X_525),least_upper_bound(X_524,identity))) )],[refute_0_1000,refute_0_1003]) ).

cnf(refute_0_1005,plain,
    ( multiply(multiply(inverse(X_525),least_upper_bound(X_524,identity)),greatest_lower_bound(identity,X_524)) != multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))
    | multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)) != multiply(multiply(inverse(X_525),least_upper_bound(X_524,identity)),greatest_lower_bound(identity,X_524))
    | multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)) = multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)))),bind(Y0,$fot(multiply(multiply(inverse(X_525),least_upper_bound(X_524,identity)),greatest_lower_bound(identity,X_524)))),bind(Z0,$fot(multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))))]]) ).

cnf(refute_0_1006,plain,
    ( multiply(multiply(inverse(X_525),least_upper_bound(X_524,identity)),greatest_lower_bound(identity,X_524)) != multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))
    | multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)) = multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)),multiply(multiply(inverse(X_525),least_upper_bound(X_524,identity)),greatest_lower_bound(identity,X_524))) )],[refute_0_1004,refute_0_1005]) ).

cnf(refute_0_1007,plain,
    multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)) = multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_525),least_upper_bound(X_524,identity)),greatest_lower_bound(identity,X_524)),multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))) )],[refute_0_999,refute_0_1006]) ).

cnf(refute_0_1008,plain,
    multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),multiply(inverse(multiply(X_81,X_70)),X_81)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(multiply(X_81,X_70)))),bind(Y,$fot(X_80)),bind(Z,$fot(X_81))]]) ).

cnf(refute_0_1009,plain,
    inverse(X_70) = multiply(inverse(multiply(X_81,X_70)),X_81),
    inference(subst,[],[refute_0_622:[bind(X,$fot(X_81))]]) ).

cnf(refute_0_1010,plain,
    ( inverse(X_70) != multiply(inverse(multiply(X_81,X_70)),X_81)
    | multiply(inverse(multiply(X_81,X_70)),X_81) = inverse(X_70) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X_70))),bind(Y0,$fot(multiply(inverse(multiply(X_81,X_70)),X_81)))]]) ).

cnf(refute_0_1011,plain,
    multiply(inverse(multiply(X_81,X_70)),X_81) = inverse(X_70),
    inference(resolve,[$cnf( $equal(inverse(X_70),multiply(inverse(multiply(X_81,X_70)),X_81)) )],[refute_0_1009,refute_0_1010]) ).

cnf(refute_0_1012,plain,
    ( multiply(inverse(multiply(X_81,X_70)),X_81) != inverse(X_70)
    | multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)) != greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),multiply(inverse(multiply(X_81,X_70)),X_81))
    | multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),inverse(X_70)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)),greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),multiply(inverse(multiply(X_81,X_70)),X_81))) ),[1,1],$fot(inverse(X_70))]]) ).

cnf(refute_0_1013,plain,
    ( multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)) != greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),multiply(inverse(multiply(X_81,X_70)),X_81))
    | multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),inverse(X_70)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_81,X_70)),X_81),inverse(X_70)) )],[refute_0_1011,refute_0_1012]) ).

cnf(refute_0_1014,plain,
    multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),inverse(X_70)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)),greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),multiply(inverse(multiply(X_81,X_70)),X_81))) )],[refute_0_1008,refute_0_1013]) ).

cnf(refute_0_1015,plain,
    greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),inverse(X_70)) = greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(X_81,X_70)),X_80)),
    inference(subst,[],[refute_0_35:[bind(X,$fot(inverse(X_70))),bind(Y,$fot(multiply(inverse(multiply(X_81,X_70)),X_80)))]]) ).

cnf(refute_0_1016,plain,
    ( multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)) != greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),inverse(X_70))
    | greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),inverse(X_70)) != greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(X_81,X_70)),X_80))
    | multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(X_81,X_70)),X_80)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)),greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(X_81,X_70)),X_80))) ),[0],$fot(greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),inverse(X_70)))]]) ).

cnf(refute_0_1017,plain,
    ( multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)) != greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),inverse(X_70))
    | multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(X_81,X_70)),X_80)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),inverse(X_70)),greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(X_81,X_70)),X_80))) )],[refute_0_1015,refute_0_1016]) ).

cnf(refute_0_1018,plain,
    multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)) = greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(X_81,X_70)),X_80)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_81,X_70)),greatest_lower_bound(X_80,X_81)),greatest_lower_bound(multiply(inverse(multiply(X_81,X_70)),X_80),inverse(X_70))) )],[refute_0_1014,refute_0_1017]) ).

cnf(refute_0_1019,plain,
    multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612)))) = greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))),
    inference(subst,[],[refute_0_1018:[bind(X_80,$fot(least_upper_bound(X_612,identity))),bind(X_81,$fot(least_upper_bound(identity,inverse(X_612))))]]) ).

cnf(refute_0_1020,plain,
    multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)) = greatest_lower_bound(least_upper_bound(X_129,identity),multiply(least_upper_bound(X_129,identity),inverse(X_129))),
    inference(subst,[],[refute_0_106:[bind(X_79,$fot(least_upper_bound(X_129,identity))),bind(X_80,$fot(inverse(X_129)))]]) ).

cnf(refute_0_1021,plain,
    ( multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)) != greatest_lower_bound(least_upper_bound(X_129,identity),multiply(least_upper_bound(X_129,identity),inverse(X_129)))
    | multiply(least_upper_bound(X_129,identity),inverse(X_129)) != least_upper_bound(identity,inverse(X_129))
    | multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)) = greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)),greatest_lower_bound(least_upper_bound(X_129,identity),multiply(least_upper_bound(X_129,identity),inverse(X_129)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_129)))]]) ).

cnf(refute_0_1022,plain,
    ( multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)) != greatest_lower_bound(least_upper_bound(X_129,identity),multiply(least_upper_bound(X_129,identity),inverse(X_129)))
    | multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)) = greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_129,identity),inverse(X_129)),least_upper_bound(identity,inverse(X_129))) )],[refute_0_742,refute_0_1021]) ).

cnf(refute_0_1023,plain,
    multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)) = greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)),greatest_lower_bound(least_upper_bound(X_129,identity),multiply(least_upper_bound(X_129,identity),inverse(X_129)))) )],[refute_0_1020,refute_0_1022]) ).

cnf(refute_0_1024,plain,
    greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) = greatest_lower_bound(X_19,multiply(X_19,X_113)),
    inference(subst,[],[refute_0_354:[bind(X_18,$fot(multiply(X_19,X_113)))]]) ).

cnf(refute_0_1025,plain,
    multiply(X_19,greatest_lower_bound(X_113,identity)) = greatest_lower_bound(X_19,multiply(X_19,X_113)),
    inference(subst,[],[refute_0_106:[bind(X_79,$fot(X_19)),bind(X_80,$fot(X_113))]]) ).

cnf(refute_0_1026,plain,
    ( multiply(X_19,greatest_lower_bound(X_113,identity)) != greatest_lower_bound(X_19,multiply(X_19,X_113))
    | greatest_lower_bound(X_19,multiply(X_19,X_113)) = multiply(X_19,greatest_lower_bound(X_113,identity)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_19,greatest_lower_bound(X_113,identity)))),bind(Y0,$fot(greatest_lower_bound(X_19,multiply(X_19,X_113))))]]) ).

cnf(refute_0_1027,plain,
    greatest_lower_bound(X_19,multiply(X_19,X_113)) = multiply(X_19,greatest_lower_bound(X_113,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_19,greatest_lower_bound(X_113,identity)),greatest_lower_bound(X_19,multiply(X_19,X_113))) )],[refute_0_1025,refute_0_1026]) ).

cnf(refute_0_1028,plain,
    ( greatest_lower_bound(X_19,multiply(X_19,X_113)) != multiply(X_19,greatest_lower_bound(X_113,identity))
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) != greatest_lower_bound(X_19,multiply(X_19,X_113))
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) = multiply(X_19,greatest_lower_bound(X_113,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))),greatest_lower_bound(X_19,multiply(X_19,X_113))) ),[1],$fot(multiply(X_19,greatest_lower_bound(X_113,identity)))]]) ).

cnf(refute_0_1029,plain,
    ( greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) != greatest_lower_bound(X_19,multiply(X_19,X_113))
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) = multiply(X_19,greatest_lower_bound(X_113,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(X_19,X_113)),multiply(X_19,greatest_lower_bound(X_113,identity))) )],[refute_0_1027,refute_0_1028]) ).

cnf(refute_0_1030,plain,
    greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) = multiply(X_19,greatest_lower_bound(X_113,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))),greatest_lower_bound(X_19,multiply(X_19,X_113))) )],[refute_0_1024,refute_0_1029]) ).

cnf(refute_0_1031,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)) = greatest_lower_bound(identity,X_113),
    inference(subst,[],[refute_0_347:[bind(Y,$fot(X_113)),bind(X_17,$fot(identity))]]) ).

cnf(refute_0_1032,plain,
    multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))),
    introduced(tautology,[refl,[$fot(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))))]]) ).

cnf(refute_0_1033,plain,
    ( multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))) != multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))
    | greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)) != greatest_lower_bound(identity,X_113)
    | multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))) = multiply(X_19,greatest_lower_bound(identity,X_113)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))),multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,X_113))]]) ).

cnf(refute_0_1034,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)) != greatest_lower_bound(identity,X_113)
    | multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))) = multiply(X_19,greatest_lower_bound(identity,X_113)) ),
    inference(resolve,[$cnf( $equal(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))),multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))) )],[refute_0_1032,refute_0_1033]) ).

cnf(refute_0_1035,plain,
    multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))) = multiply(X_19,greatest_lower_bound(identity,X_113)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)),greatest_lower_bound(identity,X_113)) )],[refute_0_1031,refute_0_1034]) ).

cnf(refute_0_1036,plain,
    ( multiply(X_79,greatest_lower_bound(X_81,X_80)) != multiply(X_79,greatest_lower_bound(X_80,X_81))
    | multiply(X_79,greatest_lower_bound(X_80,X_81)) = multiply(X_79,greatest_lower_bound(X_81,X_80)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_79,greatest_lower_bound(X_81,X_80)))),bind(Y0,$fot(multiply(X_79,greatest_lower_bound(X_80,X_81))))]]) ).

cnf(refute_0_1037,plain,
    multiply(X_79,greatest_lower_bound(X_80,X_81)) = multiply(X_79,greatest_lower_bound(X_81,X_80)),
    inference(resolve,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_81,X_80)),multiply(X_79,greatest_lower_bound(X_80,X_81))) )],[refute_0_680,refute_0_1036]) ).

cnf(refute_0_1038,plain,
    multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_113,identity),identity)) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))),
    inference(subst,[],[refute_0_1037:[bind(X_79,$fot(X_19)),bind(X_80,$fot(greatest_lower_bound(X_113,identity))),bind(X_81,$fot(identity))]]) ).

cnf(refute_0_1039,plain,
    ( multiply(X_79,greatest_lower_bound(X_80,identity)) != greatest_lower_bound(X_79,multiply(X_79,X_80))
    | greatest_lower_bound(X_79,multiply(X_79,X_80)) = multiply(X_79,greatest_lower_bound(X_80,identity)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_79,greatest_lower_bound(X_80,identity)))),bind(Y0,$fot(greatest_lower_bound(X_79,multiply(X_79,X_80))))]]) ).

cnf(refute_0_1040,plain,
    greatest_lower_bound(X_79,multiply(X_79,X_80)) = multiply(X_79,greatest_lower_bound(X_80,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_79,greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_79,multiply(X_79,X_80))) )],[refute_0_106,refute_0_1039]) ).

cnf(refute_0_1041,plain,
    greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))) = multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_113,identity),identity)),
    inference(subst,[],[refute_0_1040:[bind(X_79,$fot(X_19)),bind(X_80,$fot(greatest_lower_bound(X_113,identity)))]]) ).

cnf(refute_0_1042,plain,
    ( multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_113,identity),identity)) != multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))
    | greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))) != multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_113,identity),identity))
    | greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))))),bind(Y0,$fot(multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_113,identity),identity)))),bind(Z0,$fot(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))))]]) ).

cnf(refute_0_1043,plain,
    ( multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_113,identity),identity)) != multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))
    | greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))),multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_113,identity),identity))) )],[refute_0_1041,refute_0_1042]) ).

cnf(refute_0_1044,plain,
    greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))),
    inference(resolve,[$cnf( $equal(multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_113,identity),identity)),multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))) )],[refute_0_1038,refute_0_1043]) ).

cnf(refute_0_1045,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) = greatest_lower_bound(greatest_lower_bound(X_33,greatest_lower_bound(Y,X_33)),X_35),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_33)),bind(Y,$fot(greatest_lower_bound(Y,X_33))),bind(Z,$fot(X_35))]]) ).

cnf(refute_0_1046,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(Y,X_33)) = greatest_lower_bound(X_33,Y),
    inference(subst,[],[refute_0_347:[bind(X_17,$fot(X_33))]]) ).

cnf(refute_0_1047,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(Y,X_33)) != greatest_lower_bound(X_33,Y)
    | greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) != greatest_lower_bound(greatest_lower_bound(X_33,greatest_lower_bound(Y,X_33)),X_35)
    | greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) = greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)),greatest_lower_bound(greatest_lower_bound(X_33,greatest_lower_bound(Y,X_33)),X_35)) ),[1,0],$fot(greatest_lower_bound(X_33,Y))]]) ).

cnf(refute_0_1048,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) != greatest_lower_bound(greatest_lower_bound(X_33,greatest_lower_bound(Y,X_33)),X_35)
    | greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) = greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(Y,X_33)),greatest_lower_bound(X_33,Y)) )],[refute_0_1046,refute_0_1047]) ).

cnf(refute_0_1049,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) = greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)),greatest_lower_bound(greatest_lower_bound(X_33,greatest_lower_bound(Y,X_33)),X_35)) )],[refute_0_1045,refute_0_1048]) ).

cnf(refute_0_1050,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_34,greatest_lower_bound(Y,X_34))) = greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_33)),bind(Y,$fot(X_34)),bind(Z,$fot(greatest_lower_bound(Y,X_34)))]]) ).

cnf(refute_0_1051,plain,
    greatest_lower_bound(X_34,greatest_lower_bound(Y,X_34)) = greatest_lower_bound(X_34,Y),
    inference(subst,[],[refute_0_347:[bind(X_17,$fot(X_34))]]) ).

cnf(refute_0_1052,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_34,greatest_lower_bound(Y,X_34))) != greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34))
    | greatest_lower_bound(X_34,greatest_lower_bound(Y,X_34)) != greatest_lower_bound(X_34,Y)
    | greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)) = greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_34,greatest_lower_bound(Y,X_34))),greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34))) ),[0,1],$fot(greatest_lower_bound(X_34,Y))]]) ).

cnf(refute_0_1053,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_34,greatest_lower_bound(Y,X_34))) != greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)) = greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_34,greatest_lower_bound(Y,X_34)),greatest_lower_bound(X_34,Y)) )],[refute_0_1051,refute_0_1052]) ).

cnf(refute_0_1054,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)) = greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_34,greatest_lower_bound(Y,X_34))),greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34))) )],[refute_0_1050,refute_0_1053]) ).

cnf(refute_0_1055,plain,
    greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)),
    inference(subst,[],[refute_0_343:[bind(X,$fot(X_33)),bind(Y,$fot(X_34)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_1056,plain,
    greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)) = greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)))]]) ).

cnf(refute_0_1057,plain,
    ( greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)) != greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y))
    | greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y) != greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))
    | greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)) = greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)),greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y))) ),[1,1],$fot(greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))]]) ).

cnf(refute_0_1058,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y) != greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))
    | greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)) = greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)),greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y))) )],[refute_0_1056,refute_0_1057]) ).

cnf(refute_0_1059,plain,
    greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)) = greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y),greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))) )],[refute_0_1055,refute_0_1058]) ).

cnf(refute_0_1060,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)) != greatest_lower_bound(X_33,greatest_lower_bound(X_34,X))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_34,X)) = greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)))),bind(Y0,$fot(greatest_lower_bound(X_33,greatest_lower_bound(X_34,X))))]]) ).

cnf(refute_0_1061,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_34,X)) = greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_33,X_34)),greatest_lower_bound(X_33,greatest_lower_bound(X_34,X))) )],[refute_0_380,refute_0_1060]) ).

cnf(refute_0_1062,plain,
    greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)) = greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)),
    inference(subst,[],[refute_0_1061:[bind(X,$fot(X_34)),bind(X_33,$fot(greatest_lower_bound(X_33,X_34))),bind(X_34,$fot(Y))]]) ).

cnf(refute_0_1063,plain,
    ( greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)) != greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))
    | greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)) != greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y))
    | greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)) = greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)))),bind(Y0,$fot(greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)))),bind(Z0,$fot(greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))))]]) ).

cnf(refute_0_1064,plain,
    ( greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)) != greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))
    | greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)) = greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)),greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y))) )],[refute_0_1062,refute_0_1063]) ).

cnf(refute_0_1065,plain,
    greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)) = greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_34,greatest_lower_bound(greatest_lower_bound(X_33,X_34),Y)),greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))) )],[refute_0_1059,refute_0_1064]) ).

cnf(refute_0_1066,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)) != greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34))
    | greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)) != greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)) = greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)),greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)))]]) ).

cnf(refute_0_1067,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)) != greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)) = greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34)),greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))) )],[refute_0_1065,refute_0_1066]) ).

cnf(refute_0_1068,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)) = greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)),greatest_lower_bound(greatest_lower_bound(X_33,X_34),greatest_lower_bound(Y,X_34))) )],[refute_0_1054,refute_0_1067]) ).

cnf(refute_0_1069,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)) != greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))
    | greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))),bind(Y0,$fot(greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))))]]) ).

cnf(refute_0_1070,plain,
    greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y))) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)),greatest_lower_bound(X_34,greatest_lower_bound(X_33,greatest_lower_bound(X_34,Y)))) )],[refute_0_1068,refute_0_1069]) ).

cnf(refute_0_1071,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))) = greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)),
    inference(subst,[],[refute_0_1070:[bind(Y,$fot(X_35)),bind(X_33,$fot(Y)),bind(X_34,$fot(X_33))]]) ).

cnf(refute_0_1072,plain,
    greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35) = greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)),
    inference(subst,[],[refute_0_343:[bind(X,$fot(Y)),bind(Y,$fot(X_33)),bind(Z,$fot(X_35))]]) ).

cnf(refute_0_1073,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) = greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)))]]) ).

cnf(refute_0_1074,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) != greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35))
    | greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35) != greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))
    | greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) = greatest_lower_bound(X_33,greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)),greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)))]]) ).

cnf(refute_0_1075,plain,
    ( greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35) != greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))
    | greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) = greatest_lower_bound(X_33,greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)),greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35))) )],[refute_0_1073,refute_0_1074]) ).

cnf(refute_0_1076,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) = greatest_lower_bound(X_33,greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35),greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))) )],[refute_0_1072,refute_0_1075]) ).

cnf(refute_0_1077,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))) != greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))
    | greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) != greatest_lower_bound(X_33,greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)))
    | greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)))),bind(Y0,$fot(greatest_lower_bound(X_33,greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))))]]) ).

cnf(refute_0_1078,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))) != greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))
    | greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)),greatest_lower_bound(X_33,greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)))) )],[refute_0_1076,refute_0_1077]) ).

cnf(refute_0_1079,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) = greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))),greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))) )],[refute_0_1071,refute_0_1078]) ).

cnf(refute_0_1080,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) != greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))
    | greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) != greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35)
    | greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)) = greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)),greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35)) ),[0],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)))]]) ).

cnf(refute_0_1081,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) != greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35)
    | greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)) = greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)),greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35))) )],[refute_0_1079,refute_0_1080]) ).

cnf(refute_0_1082,plain,
    greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35) = greatest_lower_bound(X_33,greatest_lower_bound(Y,X_35)),
    inference(subst,[],[refute_0_343:[bind(X,$fot(X_33)),bind(Z,$fot(X_35))]]) ).

cnf(refute_0_1083,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)) != greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35)
    | greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35) != greatest_lower_bound(X_33,greatest_lower_bound(Y,X_35))
    | greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)) = greatest_lower_bound(X_33,greatest_lower_bound(Y,X_35)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)),greatest_lower_bound(X_33,greatest_lower_bound(Y,X_35))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35))]]) ).

cnf(refute_0_1084,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)) != greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35)
    | greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)) = greatest_lower_bound(X_33,greatest_lower_bound(Y,X_35)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35),greatest_lower_bound(X_33,greatest_lower_bound(Y,X_35))) )],[refute_0_1082,refute_0_1083]) ).

cnf(refute_0_1085,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)) != greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35)
    | greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)) = greatest_lower_bound(X_33,greatest_lower_bound(Y,X_35)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)),greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35)) )],[refute_0_1081,refute_0_1084]) ).

cnf(refute_0_1086,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_33,X_35)) = greatest_lower_bound(X_33,greatest_lower_bound(Y,X_35)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(greatest_lower_bound(Y,X_33),X_35)),greatest_lower_bound(greatest_lower_bound(X_33,Y),X_35)) )],[refute_0_1049,refute_0_1085]) ).

cnf(refute_0_1087,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_33,multiply(Y,X_113))) = greatest_lower_bound(X_33,greatest_lower_bound(Y,multiply(Y,X_113))),
    inference(subst,[],[refute_0_1086:[bind(X_35,$fot(multiply(Y,X_113)))]]) ).

cnf(refute_0_1088,plain,
    multiply(Y,greatest_lower_bound(X_113,identity)) = greatest_lower_bound(Y,multiply(Y,X_113)),
    inference(subst,[],[refute_0_106:[bind(X_79,$fot(Y)),bind(X_80,$fot(X_113))]]) ).

cnf(refute_0_1089,plain,
    ( multiply(Y,greatest_lower_bound(X_113,identity)) != greatest_lower_bound(Y,multiply(Y,X_113))
    | greatest_lower_bound(Y,multiply(Y,X_113)) = multiply(Y,greatest_lower_bound(X_113,identity)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(Y,greatest_lower_bound(X_113,identity)))),bind(Y0,$fot(greatest_lower_bound(Y,multiply(Y,X_113))))]]) ).

cnf(refute_0_1090,plain,
    greatest_lower_bound(Y,multiply(Y,X_113)) = multiply(Y,greatest_lower_bound(X_113,identity)),
    inference(resolve,[$cnf( $equal(multiply(Y,greatest_lower_bound(X_113,identity)),greatest_lower_bound(Y,multiply(Y,X_113))) )],[refute_0_1088,refute_0_1089]) ).

cnf(refute_0_1091,plain,
    ( greatest_lower_bound(Y,multiply(Y,X_113)) != multiply(Y,greatest_lower_bound(X_113,identity))
    | greatest_lower_bound(Y,greatest_lower_bound(X_33,multiply(Y,X_113))) != greatest_lower_bound(X_33,greatest_lower_bound(Y,multiply(Y,X_113)))
    | greatest_lower_bound(Y,greatest_lower_bound(X_33,multiply(Y,X_113))) = greatest_lower_bound(X_33,multiply(Y,greatest_lower_bound(X_113,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_33,multiply(Y,X_113))),greatest_lower_bound(X_33,greatest_lower_bound(Y,multiply(Y,X_113)))) ),[1,1],$fot(multiply(Y,greatest_lower_bound(X_113,identity)))]]) ).

cnf(refute_0_1092,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_33,multiply(Y,X_113))) != greatest_lower_bound(X_33,greatest_lower_bound(Y,multiply(Y,X_113)))
    | greatest_lower_bound(Y,greatest_lower_bound(X_33,multiply(Y,X_113))) = greatest_lower_bound(X_33,multiply(Y,greatest_lower_bound(X_113,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,multiply(Y,X_113)),multiply(Y,greatest_lower_bound(X_113,identity))) )],[refute_0_1090,refute_0_1091]) ).

cnf(refute_0_1093,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_33,multiply(Y,X_113))) = greatest_lower_bound(X_33,multiply(Y,greatest_lower_bound(X_113,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_33,multiply(Y,X_113))),greatest_lower_bound(X_33,greatest_lower_bound(Y,multiply(Y,X_113)))) )],[refute_0_1087,refute_0_1092]) ).

cnf(refute_0_1094,plain,
    greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) = greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))),
    inference(subst,[],[refute_0_1093:[bind(Y,$fot(X_19)),bind(X_33,$fot(X_19))]]) ).

cnf(refute_0_1095,plain,
    ( greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))) != multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) != greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity)))
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))))),bind(Y0,$fot(greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))))),bind(Z0,$fot(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))))]]) ).

cnf(refute_0_1096,plain,
    ( greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))) != multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))),greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity)))) )],[refute_0_1094,refute_0_1095]) ).

cnf(refute_0_1097,plain,
    greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_113,identity))),multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))) )],[refute_0_1044,refute_0_1096]) ).

cnf(refute_0_1098,plain,
    ( multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))) != multiply(X_19,greatest_lower_bound(identity,X_113))
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) != multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) = multiply(X_19,greatest_lower_bound(identity,X_113)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))))),bind(Y0,$fot(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))))),bind(Z0,$fot(multiply(X_19,greatest_lower_bound(identity,X_113))))]]) ).

cnf(refute_0_1099,plain,
    ( multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))) != multiply(X_19,greatest_lower_bound(identity,X_113))
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) = multiply(X_19,greatest_lower_bound(identity,X_113)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))),multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity)))) )],[refute_0_1097,refute_0_1098]) ).

cnf(refute_0_1100,plain,
    greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) = multiply(X_19,greatest_lower_bound(identity,X_113)),
    inference(resolve,[$cnf( $equal(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_113,identity))),multiply(X_19,greatest_lower_bound(identity,X_113))) )],[refute_0_1035,refute_0_1099]) ).

cnf(refute_0_1101,plain,
    ( greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) != multiply(X_19,greatest_lower_bound(X_113,identity))
    | greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) != multiply(X_19,greatest_lower_bound(identity,X_113))
    | multiply(X_19,greatest_lower_bound(identity,X_113)) = multiply(X_19,greatest_lower_bound(X_113,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))),multiply(X_19,greatest_lower_bound(X_113,identity))) ),[0],$fot(multiply(X_19,greatest_lower_bound(identity,X_113)))]]) ).

cnf(refute_0_1102,plain,
    ( greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))) != multiply(X_19,greatest_lower_bound(X_113,identity))
    | multiply(X_19,greatest_lower_bound(identity,X_113)) = multiply(X_19,greatest_lower_bound(X_113,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))),multiply(X_19,greatest_lower_bound(identity,X_113))) )],[refute_0_1100,refute_0_1101]) ).

cnf(refute_0_1103,plain,
    multiply(X_19,greatest_lower_bound(identity,X_113)) = multiply(X_19,greatest_lower_bound(X_113,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_113))),multiply(X_19,greatest_lower_bound(X_113,identity))) )],[refute_0_1030,refute_0_1102]) ).

cnf(refute_0_1104,plain,
    ( multiply(X_19,greatest_lower_bound(identity,X_113)) != multiply(X_19,greatest_lower_bound(X_113,identity))
    | multiply(X_19,greatest_lower_bound(X_113,identity)) = multiply(X_19,greatest_lower_bound(identity,X_113)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_19,greatest_lower_bound(identity,X_113)))),bind(Y0,$fot(multiply(X_19,greatest_lower_bound(X_113,identity))))]]) ).

cnf(refute_0_1105,plain,
    multiply(X_19,greatest_lower_bound(X_113,identity)) = multiply(X_19,greatest_lower_bound(identity,X_113)),
    inference(resolve,[$cnf( $equal(multiply(X_19,greatest_lower_bound(identity,X_113)),multiply(X_19,greatest_lower_bound(X_113,identity))) )],[refute_0_1103,refute_0_1104]) ).

cnf(refute_0_1106,plain,
    multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)) = multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))),
    inference(subst,[],[refute_0_1105:[bind(X_113,$fot(inverse(X_129))),bind(X_19,$fot(least_upper_bound(X_129,identity)))]]) ).

cnf(refute_0_1107,plain,
    ( multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)) != multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129)))
    | multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)) != greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129)))
    | multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))) = greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)),greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129)))) ),[0],$fot(multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))))]]) ).

cnf(refute_0_1108,plain,
    ( multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)) != greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129)))
    | multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))) = greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129)))) )],[refute_0_1106,refute_0_1107]) ).

cnf(refute_0_1109,plain,
    multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))) = greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_129,identity),greatest_lower_bound(inverse(X_129),identity)),greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129)))) )],[refute_0_1023,refute_0_1108]) ).

cnf(refute_0_1110,plain,
    multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))) = least_upper_bound(inverse(multiply(X,X_148)),multiply(X_148,inverse(multiply(X,X_148)))),
    inference(subst,[],[refute_0_269:[bind(X_120,$fot(inverse(multiply(X,X_148)))),bind(X_121,$fot(X_148))]]) ).

cnf(refute_0_1111,plain,
    inverse(X) = multiply(X_148,inverse(multiply(X,X_148))),
    inference(subst,[],[refute_0_172:[bind(X_69,$fot(X_148))]]) ).

cnf(refute_0_1112,plain,
    ( inverse(X) != multiply(X_148,inverse(multiply(X,X_148)))
    | multiply(X_148,inverse(multiply(X,X_148))) = inverse(X) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X))),bind(Y0,$fot(multiply(X_148,inverse(multiply(X,X_148)))))]]) ).

cnf(refute_0_1113,plain,
    multiply(X_148,inverse(multiply(X,X_148))) = inverse(X),
    inference(resolve,[$cnf( $equal(inverse(X),multiply(X_148,inverse(multiply(X,X_148)))) )],[refute_0_1111,refute_0_1112]) ).

cnf(refute_0_1114,plain,
    ( multiply(X_148,inverse(multiply(X,X_148))) != inverse(X)
    | multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))) != least_upper_bound(inverse(multiply(X,X_148)),multiply(X_148,inverse(multiply(X,X_148))))
    | multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))) = least_upper_bound(inverse(multiply(X,X_148)),inverse(X)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))),least_upper_bound(inverse(multiply(X,X_148)),multiply(X_148,inverse(multiply(X,X_148))))) ),[1,1],$fot(inverse(X))]]) ).

cnf(refute_0_1115,plain,
    ( multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))) != least_upper_bound(inverse(multiply(X,X_148)),multiply(X_148,inverse(multiply(X,X_148))))
    | multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))) = least_upper_bound(inverse(multiply(X,X_148)),inverse(X)) ),
    inference(resolve,[$cnf( $equal(multiply(X_148,inverse(multiply(X,X_148))),inverse(X)) )],[refute_0_1113,refute_0_1114]) ).

cnf(refute_0_1116,plain,
    multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))) = least_upper_bound(inverse(multiply(X,X_148)),inverse(X)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))),least_upper_bound(inverse(multiply(X,X_148)),multiply(X_148,inverse(multiply(X,X_148))))) )],[refute_0_1110,refute_0_1115]) ).

cnf(refute_0_1117,plain,
    multiply(least_upper_bound(inverse(Y),identity),inverse(X)) = least_upper_bound(inverse(X),multiply(inverse(Y),inverse(X))),
    inference(subst,[],[refute_0_269:[bind(X_120,$fot(inverse(X))),bind(X_121,$fot(inverse(Y)))]]) ).

cnf(refute_0_1118,plain,
    ( multiply(inverse(Y),inverse(X)) != inverse(multiply(X,Y))
    | multiply(least_upper_bound(inverse(Y),identity),inverse(X)) != least_upper_bound(inverse(X),multiply(inverse(Y),inverse(X)))
    | multiply(least_upper_bound(inverse(Y),identity),inverse(X)) = least_upper_bound(inverse(X),inverse(multiply(X,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(Y),identity),inverse(X)),least_upper_bound(inverse(X),multiply(inverse(Y),inverse(X)))) ),[1,1],$fot(inverse(multiply(X,Y)))]]) ).

cnf(refute_0_1119,plain,
    ( multiply(least_upper_bound(inverse(Y),identity),inverse(X)) != least_upper_bound(inverse(X),multiply(inverse(Y),inverse(X)))
    | multiply(least_upper_bound(inverse(Y),identity),inverse(X)) = least_upper_bound(inverse(X),inverse(multiply(X,Y))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(Y),inverse(X)),inverse(multiply(X,Y))) )],[refute_0_221,refute_0_1118]) ).

cnf(refute_0_1120,plain,
    multiply(least_upper_bound(inverse(Y),identity),inverse(X)) = least_upper_bound(inverse(X),inverse(multiply(X,Y))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(Y),identity),inverse(X)),least_upper_bound(inverse(X),multiply(inverse(Y),inverse(X)))) )],[refute_0_1117,refute_0_1119]) ).

cnf(refute_0_1121,plain,
    multiply(least_upper_bound(inverse(Y),identity),inverse(X)) = multiply(least_upper_bound(identity,inverse(Y)),inverse(X)),
    inference(subst,[],[refute_0_596:[bind(X_148,$fot(inverse(Y))),bind(X_22,$fot(inverse(X)))]]) ).

cnf(refute_0_1122,plain,
    ( multiply(least_upper_bound(inverse(Y),identity),inverse(X)) != multiply(least_upper_bound(identity,inverse(Y)),inverse(X))
    | multiply(least_upper_bound(inverse(Y),identity),inverse(X)) != least_upper_bound(inverse(X),inverse(multiply(X,Y)))
    | multiply(least_upper_bound(identity,inverse(Y)),inverse(X)) = least_upper_bound(inverse(X),inverse(multiply(X,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(Y),identity),inverse(X)),least_upper_bound(inverse(X),inverse(multiply(X,Y)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(Y)),inverse(X)))]]) ).

cnf(refute_0_1123,plain,
    ( multiply(least_upper_bound(inverse(Y),identity),inverse(X)) != least_upper_bound(inverse(X),inverse(multiply(X,Y)))
    | multiply(least_upper_bound(identity,inverse(Y)),inverse(X)) = least_upper_bound(inverse(X),inverse(multiply(X,Y))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(Y),identity),inverse(X)),multiply(least_upper_bound(identity,inverse(Y)),inverse(X))) )],[refute_0_1121,refute_0_1122]) ).

cnf(refute_0_1124,plain,
    multiply(least_upper_bound(identity,inverse(Y)),inverse(X)) = least_upper_bound(inverse(X),inverse(multiply(X,Y))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(Y),identity),inverse(X)),least_upper_bound(inverse(X),inverse(multiply(X,Y)))) )],[refute_0_1120,refute_0_1123]) ).

cnf(refute_0_1125,plain,
    ( multiply(least_upper_bound(identity,inverse(Y)),inverse(X)) != least_upper_bound(inverse(X),inverse(multiply(X,Y)))
    | least_upper_bound(inverse(X),inverse(multiply(X,Y))) = multiply(least_upper_bound(identity,inverse(Y)),inverse(X)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(Y)),inverse(X)))),bind(Y0,$fot(least_upper_bound(inverse(X),inverse(multiply(X,Y)))))]]) ).

cnf(refute_0_1126,plain,
    least_upper_bound(inverse(X),inverse(multiply(X,Y))) = multiply(least_upper_bound(identity,inverse(Y)),inverse(X)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(Y)),inverse(X)),least_upper_bound(inverse(X),inverse(multiply(X,Y)))) )],[refute_0_1124,refute_0_1125]) ).

cnf(refute_0_1127,plain,
    least_upper_bound(inverse(X),inverse(multiply(X,X_148))) = multiply(least_upper_bound(identity,inverse(X_148)),inverse(X)),
    inference(subst,[],[refute_0_1126:[bind(Y,$fot(X_148))]]) ).

cnf(refute_0_1128,plain,
    least_upper_bound(inverse(multiply(X,X_148)),inverse(X)) = least_upper_bound(inverse(X),inverse(multiply(X,X_148))),
    inference(subst,[],[refute_0_180:[bind(X,$fot(inverse(X))),bind(Y,$fot(inverse(multiply(X,X_148))))]]) ).

cnf(refute_0_1129,plain,
    ( least_upper_bound(inverse(X),inverse(multiply(X,X_148))) != multiply(least_upper_bound(identity,inverse(X_148)),inverse(X))
    | least_upper_bound(inverse(multiply(X,X_148)),inverse(X)) != least_upper_bound(inverse(X),inverse(multiply(X,X_148)))
    | least_upper_bound(inverse(multiply(X,X_148)),inverse(X)) = multiply(least_upper_bound(identity,inverse(X_148)),inverse(X)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(inverse(multiply(X,X_148)),inverse(X)))),bind(Y0,$fot(least_upper_bound(inverse(X),inverse(multiply(X,X_148))))),bind(Z0,$fot(multiply(least_upper_bound(identity,inverse(X_148)),inverse(X))))]]) ).

cnf(refute_0_1130,plain,
    ( least_upper_bound(inverse(X),inverse(multiply(X,X_148))) != multiply(least_upper_bound(identity,inverse(X_148)),inverse(X))
    | least_upper_bound(inverse(multiply(X,X_148)),inverse(X)) = multiply(least_upper_bound(identity,inverse(X_148)),inverse(X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(multiply(X,X_148)),inverse(X)),least_upper_bound(inverse(X),inverse(multiply(X,X_148)))) )],[refute_0_1128,refute_0_1129]) ).

cnf(refute_0_1131,plain,
    least_upper_bound(inverse(multiply(X,X_148)),inverse(X)) = multiply(least_upper_bound(identity,inverse(X_148)),inverse(X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(multiply(X,X_148))),multiply(least_upper_bound(identity,inverse(X_148)),inverse(X))) )],[refute_0_1127,refute_0_1130]) ).

cnf(refute_0_1132,plain,
    ( multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))) != least_upper_bound(inverse(multiply(X,X_148)),inverse(X))
    | least_upper_bound(inverse(multiply(X,X_148)),inverse(X)) != multiply(least_upper_bound(identity,inverse(X_148)),inverse(X))
    | multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))) = multiply(least_upper_bound(identity,inverse(X_148)),inverse(X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))),multiply(least_upper_bound(identity,inverse(X_148)),inverse(X))) ),[0],$fot(least_upper_bound(inverse(multiply(X,X_148)),inverse(X)))]]) ).

cnf(refute_0_1133,plain,
    ( multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))) != least_upper_bound(inverse(multiply(X,X_148)),inverse(X))
    | multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))) = multiply(least_upper_bound(identity,inverse(X_148)),inverse(X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(multiply(X,X_148)),inverse(X)),multiply(least_upper_bound(identity,inverse(X_148)),inverse(X))) )],[refute_0_1131,refute_0_1132]) ).

cnf(refute_0_1134,plain,
    multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))) = multiply(least_upper_bound(identity,inverse(X_148)),inverse(X)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_148,identity),inverse(multiply(X,X_148))),least_upper_bound(inverse(multiply(X,X_148)),inverse(X))) )],[refute_0_1116,refute_0_1133]) ).

cnf(refute_0_1135,plain,
    multiply(least_upper_bound(X_503,identity),inverse(multiply(inverse(greatest_lower_bound(identity,X_503)),X_503))) = multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))),
    inference(subst,[],[refute_0_1134:[bind(X,$fot(inverse(greatest_lower_bound(identity,X_503)))),bind(X_148,$fot(X_503))]]) ).

cnf(refute_0_1136,plain,
    inverse(greatest_lower_bound(identity,inverse(X_503))) = multiply(inverse(greatest_lower_bound(identity,X_503)),X_503),
    inference(subst,[],[refute_0_254:[bind(X_86,$fot(X_503))]]) ).

cnf(refute_0_1137,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_503))) != multiply(inverse(greatest_lower_bound(identity,X_503)),X_503)
    | multiply(inverse(greatest_lower_bound(identity,X_503)),X_503) = inverse(greatest_lower_bound(identity,inverse(X_503))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_503))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_503)),X_503)))]]) ).

cnf(refute_0_1138,plain,
    multiply(inverse(greatest_lower_bound(identity,X_503)),X_503) = inverse(greatest_lower_bound(identity,inverse(X_503))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_503))),multiply(inverse(greatest_lower_bound(identity,X_503)),X_503)) )],[refute_0_1136,refute_0_1137]) ).

cnf(refute_0_1139,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_503)),X_503) != inverse(greatest_lower_bound(identity,inverse(X_503)))
    | multiply(least_upper_bound(X_503,identity),inverse(multiply(inverse(greatest_lower_bound(identity,X_503)),X_503))) != multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))
    | multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) = multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_503,identity),inverse(multiply(inverse(greatest_lower_bound(identity,X_503)),X_503))),multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))) ),[0,1,0],$fot(inverse(greatest_lower_bound(identity,inverse(X_503))))]]) ).

cnf(refute_0_1140,plain,
    ( multiply(least_upper_bound(X_503,identity),inverse(multiply(inverse(greatest_lower_bound(identity,X_503)),X_503))) != multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))
    | multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) = multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_503)),X_503),inverse(greatest_lower_bound(identity,inverse(X_503)))) )],[refute_0_1138,refute_0_1139]) ).

cnf(refute_0_1141,plain,
    multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) = multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_503,identity),inverse(multiply(inverse(greatest_lower_bound(identity,X_503)),X_503))),multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))) )],[refute_0_1135,refute_0_1140]) ).

cnf(refute_0_1142,plain,
    inverse(inverse(greatest_lower_bound(identity,inverse(X_503)))) = greatest_lower_bound(identity,inverse(X_503)),
    inference(subst,[],[p11_2:[bind(X,$fot(greatest_lower_bound(identity,inverse(X_503))))]]) ).

cnf(refute_0_1143,plain,
    multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) = multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))))]]) ).

cnf(refute_0_1144,plain,
    ( multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) != multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503)))))
    | inverse(inverse(greatest_lower_bound(identity,inverse(X_503)))) != greatest_lower_bound(identity,inverse(X_503))
    | multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) = multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))),multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503)))))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_503)))]]) ).

cnf(refute_0_1145,plain,
    ( inverse(inverse(greatest_lower_bound(identity,inverse(X_503)))) != greatest_lower_bound(identity,inverse(X_503))
    | multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) = multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))),multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503)))))) )],[refute_0_1143,refute_0_1144]) ).

cnf(refute_0_1146,plain,
    multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) = multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,inverse(X_503)))),greatest_lower_bound(identity,inverse(X_503))) )],[refute_0_1142,refute_0_1145]) ).

cnf(refute_0_1147,plain,
    ( multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) != multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503)))
    | multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) != multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))
    | multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))) = multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))),multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))) ),[0],$fot(multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))))]]) ).

cnf(refute_0_1148,plain,
    ( multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) != multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))
    | multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))) = multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))),multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503)))) )],[refute_0_1146,refute_0_1147]) ).

cnf(refute_0_1149,plain,
    multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)) = least_upper_bound(greatest_lower_bound(identity,X_85),multiply(inverse(X_85),greatest_lower_bound(identity,X_85))),
    inference(subst,[],[refute_0_269:[bind(X_120,$fot(greatest_lower_bound(identity,X_85))),bind(X_121,$fot(inverse(X_85)))]]) ).

cnf(refute_0_1150,plain,
    ( multiply(inverse(X_85),greatest_lower_bound(identity,X_85)) != greatest_lower_bound(identity,inverse(X_85))
    | multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)) != least_upper_bound(greatest_lower_bound(identity,X_85),multiply(inverse(X_85),greatest_lower_bound(identity,X_85)))
    | multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)) = least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)),least_upper_bound(greatest_lower_bound(identity,X_85),multiply(inverse(X_85),greatest_lower_bound(identity,X_85)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_85)))]]) ).

cnf(refute_0_1151,plain,
    ( multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)) != least_upper_bound(greatest_lower_bound(identity,X_85),multiply(inverse(X_85),greatest_lower_bound(identity,X_85)))
    | multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)) = least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_85),greatest_lower_bound(identity,X_85)),greatest_lower_bound(identity,inverse(X_85))) )],[refute_0_206,refute_0_1150]) ).

cnf(refute_0_1152,plain,
    multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)) = least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)),least_upper_bound(greatest_lower_bound(identity,X_85),multiply(inverse(X_85),greatest_lower_bound(identity,X_85)))) )],[refute_0_1149,refute_0_1151]) ).

cnf(refute_0_1153,plain,
    multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)) = multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)),
    inference(subst,[],[refute_0_596:[bind(X_148,$fot(inverse(X_85))),bind(X_22,$fot(greatest_lower_bound(identity,X_85)))]]) ).

cnf(refute_0_1154,plain,
    ( multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)) != multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85))
    | multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)) != least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85)))
    | multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)) = least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)),least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)))]]) ).

cnf(refute_0_1155,plain,
    ( multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)) != least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85)))
    | multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)) = least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)),multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85))) )],[refute_0_1153,refute_0_1154]) ).

cnf(refute_0_1156,plain,
    multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)) = least_upper_bound(greatest_lower_bound(identity,X_91),multiply(greatest_lower_bound(identity,X_91),inverse(X_91))),
    inference(subst,[],[refute_0_241:[bind(X_115,$fot(greatest_lower_bound(identity,X_91))),bind(X_116,$fot(inverse(X_91)))]]) ).

cnf(refute_0_1157,plain,
    ( multiply(greatest_lower_bound(identity,X_91),inverse(X_91)) != greatest_lower_bound(identity,inverse(X_91))
    | multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)) != least_upper_bound(greatest_lower_bound(identity,X_91),multiply(greatest_lower_bound(identity,X_91),inverse(X_91)))
    | multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)) = least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)),least_upper_bound(greatest_lower_bound(identity,X_91),multiply(greatest_lower_bound(identity,X_91),inverse(X_91)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_91)))]]) ).

cnf(refute_0_1158,plain,
    ( multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)) != least_upper_bound(greatest_lower_bound(identity,X_91),multiply(greatest_lower_bound(identity,X_91),inverse(X_91)))
    | multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)) = least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_91),inverse(X_91)),greatest_lower_bound(identity,inverse(X_91))) )],[refute_0_285,refute_0_1157]) ).

cnf(refute_0_1159,plain,
    multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)) = least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)),least_upper_bound(greatest_lower_bound(identity,X_91),multiply(greatest_lower_bound(identity,X_91),inverse(X_91)))) )],[refute_0_1156,refute_0_1158]) ).

cnf(refute_0_1160,plain,
    least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) = least_upper_bound(X_22,multiply(X_22,X_143)),
    inference(subst,[],[refute_0_481:[bind(X_23,$fot(multiply(X_22,X_143)))]]) ).

cnf(refute_0_1161,plain,
    multiply(X_22,least_upper_bound(X_143,identity)) = least_upper_bound(X_22,multiply(X_22,X_143)),
    inference(subst,[],[refute_0_241:[bind(X_115,$fot(X_22)),bind(X_116,$fot(X_143))]]) ).

cnf(refute_0_1162,plain,
    ( multiply(X_22,least_upper_bound(X_143,identity)) != least_upper_bound(X_22,multiply(X_22,X_143))
    | least_upper_bound(X_22,multiply(X_22,X_143)) = multiply(X_22,least_upper_bound(X_143,identity)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_22,least_upper_bound(X_143,identity)))),bind(Y0,$fot(least_upper_bound(X_22,multiply(X_22,X_143))))]]) ).

cnf(refute_0_1163,plain,
    least_upper_bound(X_22,multiply(X_22,X_143)) = multiply(X_22,least_upper_bound(X_143,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_22,least_upper_bound(X_143,identity)),least_upper_bound(X_22,multiply(X_22,X_143))) )],[refute_0_1161,refute_0_1162]) ).

cnf(refute_0_1164,plain,
    ( least_upper_bound(X_22,multiply(X_22,X_143)) != multiply(X_22,least_upper_bound(X_143,identity))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) != least_upper_bound(X_22,multiply(X_22,X_143))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) = multiply(X_22,least_upper_bound(X_143,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))),least_upper_bound(X_22,multiply(X_22,X_143))) ),[1],$fot(multiply(X_22,least_upper_bound(X_143,identity)))]]) ).

cnf(refute_0_1165,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) != least_upper_bound(X_22,multiply(X_22,X_143))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) = multiply(X_22,least_upper_bound(X_143,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,multiply(X_22,X_143)),multiply(X_22,least_upper_bound(X_143,identity))) )],[refute_0_1163,refute_0_1164]) ).

cnf(refute_0_1166,plain,
    least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) = multiply(X_22,least_upper_bound(X_143,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))),least_upper_bound(X_22,multiply(X_22,X_143))) )],[refute_0_1160,refute_0_1165]) ).

cnf(refute_0_1167,plain,
    least_upper_bound(identity,least_upper_bound(X_143,identity)) = least_upper_bound(identity,X_143),
    inference(subst,[],[refute_0_409:[bind(X_11,$fot(identity)),bind(X_15,$fot(X_143))]]) ).

cnf(refute_0_1168,plain,
    multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))) = multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))),
    introduced(tautology,[refl,[$fot(multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))))]]) ).

cnf(refute_0_1169,plain,
    ( multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))) != multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))
    | least_upper_bound(identity,least_upper_bound(X_143,identity)) != least_upper_bound(identity,X_143)
    | multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))) = multiply(X_22,least_upper_bound(identity,X_143)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))),multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_143))]]) ).

cnf(refute_0_1170,plain,
    ( least_upper_bound(identity,least_upper_bound(X_143,identity)) != least_upper_bound(identity,X_143)
    | multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))) = multiply(X_22,least_upper_bound(identity,X_143)) ),
    inference(resolve,[$cnf( $equal(multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))),multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))) )],[refute_0_1168,refute_0_1169]) ).

cnf(refute_0_1171,plain,
    multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))) = multiply(X_22,least_upper_bound(identity,X_143)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_143,identity)),least_upper_bound(identity,X_143)) )],[refute_0_1167,refute_0_1170]) ).

cnf(refute_0_1172,plain,
    greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
    inference(subst,[],[refute_0_413:[bind(X_15,$fot(multiply(X,Y))),bind(X_23,$fot(multiply(X,Z)))]]) ).

cnf(refute_0_1173,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_12:[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_1174,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_1173]) ).

cnf(refute_0_1175,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | least_upper_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).

cnf(refute_0_1176,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,Z)),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_1174,refute_0_1175]) ).

cnf(refute_0_1177,plain,
    greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_1172,refute_0_1176]) ).

cnf(refute_0_1178,plain,
    multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
    introduced(tautology,[refl,[$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))]]) ).

cnf(refute_0_1179,plain,
    ( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
    | greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
    | multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) ),[1,1],$fot(least_upper_bound(Y,Z))]]) ).

cnf(refute_0_1180,plain,
    ( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
    | multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_1178,refute_0_1179]) ).

cnf(refute_0_1181,plain,
    multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_500,refute_0_1180]) ).

cnf(refute_0_1182,plain,
    greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
    inference(subst,[],[refute_0_663:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).

cnf(refute_0_1183,plain,
    ( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Y0,$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).

cnf(refute_0_1184,plain,
    ( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_1182,refute_0_1183]) ).

cnf(refute_0_1185,plain,
    greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_1181,refute_0_1184]) ).

cnf(refute_0_1186,plain,
    least_upper_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,least_upper_bound(Z,Y)),
    inference(subst,[],[refute_0_1174:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_1187,plain,
    greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).

cnf(refute_0_1188,plain,
    ( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
    | least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,least_upper_bound(Z,Y)))]]) ).

cnf(refute_0_1189,plain,
    ( least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_1187,refute_0_1188]) ).

cnf(refute_0_1190,plain,
    greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_1186,refute_0_1189]) ).

cnf(refute_0_1191,plain,
    ( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).

cnf(refute_0_1192,plain,
    ( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))) )],[refute_0_1190,refute_0_1191]) ).

cnf(refute_0_1193,plain,
    greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_1185,refute_0_1192]) ).

cnf(refute_0_1194,plain,
    greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
    inference(subst,[],[refute_0_35:[bind(X,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y,$fot(least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).

cnf(refute_0_1195,plain,
    ( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).

cnf(refute_0_1196,plain,
    ( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_1194,refute_0_1195]) ).

cnf(refute_0_1197,plain,
    greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_1193,refute_0_1196]) ).

cnf(refute_0_1198,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).

cnf(refute_0_1199,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_1197,refute_0_1198]) ).

cnf(refute_0_1200,plain,
    ( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
    | multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),[0],$fot(least_upper_bound(multiply(X,Z),multiply(X,Y)))]]) ).

cnf(refute_0_1201,plain,
    ( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_1186,refute_0_1200]) ).

cnf(refute_0_1202,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_1199,refute_0_1201]) ).

cnf(refute_0_1203,plain,
    multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_1177,refute_0_1202]) ).

cnf(refute_0_1204,plain,
    ( multiply(X,least_upper_bound(Y,Z)) != multiply(X,least_upper_bound(Z,Y))
    | multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(multiply(X,least_upper_bound(Z,Y))))]]) ).

cnf(refute_0_1205,plain,
    multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_1203,refute_0_1204]) ).

cnf(refute_0_1206,plain,
    multiply(X_22,least_upper_bound(least_upper_bound(X_143,identity),identity)) = multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))),
    inference(subst,[],[refute_0_1205:[bind(X,$fot(X_22)),bind(Y,$fot(identity)),bind(Z,$fot(least_upper_bound(X_143,identity)))]]) ).

cnf(refute_0_1207,plain,
    ( multiply(X_115,least_upper_bound(X_116,identity)) != least_upper_bound(X_115,multiply(X_115,X_116))
    | least_upper_bound(X_115,multiply(X_115,X_116)) = multiply(X_115,least_upper_bound(X_116,identity)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_115,least_upper_bound(X_116,identity)))),bind(Y0,$fot(least_upper_bound(X_115,multiply(X_115,X_116))))]]) ).

cnf(refute_0_1208,plain,
    least_upper_bound(X_115,multiply(X_115,X_116)) = multiply(X_115,least_upper_bound(X_116,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(X_116,identity)),least_upper_bound(X_115,multiply(X_115,X_116))) )],[refute_0_241,refute_0_1207]) ).

cnf(refute_0_1209,plain,
    least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))) = multiply(X_22,least_upper_bound(least_upper_bound(X_143,identity),identity)),
    inference(subst,[],[refute_0_1208:[bind(X_115,$fot(X_22)),bind(X_116,$fot(least_upper_bound(X_143,identity)))]]) ).

cnf(refute_0_1210,plain,
    ( multiply(X_22,least_upper_bound(least_upper_bound(X_143,identity),identity)) != multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))
    | least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))) != multiply(X_22,least_upper_bound(least_upper_bound(X_143,identity),identity))
    | least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))) = multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))))),bind(Y0,$fot(multiply(X_22,least_upper_bound(least_upper_bound(X_143,identity),identity)))),bind(Z0,$fot(multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))))]]) ).

cnf(refute_0_1211,plain,
    ( multiply(X_22,least_upper_bound(least_upper_bound(X_143,identity),identity)) != multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))
    | least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))) = multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))),multiply(X_22,least_upper_bound(least_upper_bound(X_143,identity),identity))) )],[refute_0_1209,refute_0_1210]) ).

cnf(refute_0_1212,plain,
    least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))) = multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))),
    inference(resolve,[$cnf( $equal(multiply(X_22,least_upper_bound(least_upper_bound(X_143,identity),identity)),multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))) )],[refute_0_1206,refute_0_1211]) ).

cnf(refute_0_1213,plain,
    least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_15,X_143))) = least_upper_bound(X_26,least_upper_bound(X_15,multiply(X_15,X_143))),
    inference(subst,[],[refute_0_577:[bind(X_28,$fot(multiply(X_15,X_143)))]]) ).

cnf(refute_0_1214,plain,
    multiply(X_15,least_upper_bound(X_143,identity)) = least_upper_bound(X_15,multiply(X_15,X_143)),
    inference(subst,[],[refute_0_241:[bind(X_115,$fot(X_15)),bind(X_116,$fot(X_143))]]) ).

cnf(refute_0_1215,plain,
    ( multiply(X_15,least_upper_bound(X_143,identity)) != least_upper_bound(X_15,multiply(X_15,X_143))
    | least_upper_bound(X_15,multiply(X_15,X_143)) = multiply(X_15,least_upper_bound(X_143,identity)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_15,least_upper_bound(X_143,identity)))),bind(Y0,$fot(least_upper_bound(X_15,multiply(X_15,X_143))))]]) ).

cnf(refute_0_1216,plain,
    least_upper_bound(X_15,multiply(X_15,X_143)) = multiply(X_15,least_upper_bound(X_143,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_15,least_upper_bound(X_143,identity)),least_upper_bound(X_15,multiply(X_15,X_143))) )],[refute_0_1214,refute_0_1215]) ).

cnf(refute_0_1217,plain,
    ( least_upper_bound(X_15,multiply(X_15,X_143)) != multiply(X_15,least_upper_bound(X_143,identity))
    | least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_15,X_143))) != least_upper_bound(X_26,least_upper_bound(X_15,multiply(X_15,X_143)))
    | least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_15,X_143))) = least_upper_bound(X_26,multiply(X_15,least_upper_bound(X_143,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_15,X_143))),least_upper_bound(X_26,least_upper_bound(X_15,multiply(X_15,X_143)))) ),[1,1],$fot(multiply(X_15,least_upper_bound(X_143,identity)))]]) ).

cnf(refute_0_1218,plain,
    ( least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_15,X_143))) != least_upper_bound(X_26,least_upper_bound(X_15,multiply(X_15,X_143)))
    | least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_15,X_143))) = least_upper_bound(X_26,multiply(X_15,least_upper_bound(X_143,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_15,X_143)),multiply(X_15,least_upper_bound(X_143,identity))) )],[refute_0_1216,refute_0_1217]) ).

cnf(refute_0_1219,plain,
    least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_15,X_143))) = least_upper_bound(X_26,multiply(X_15,least_upper_bound(X_143,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_26,multiply(X_15,X_143))),least_upper_bound(X_26,least_upper_bound(X_15,multiply(X_15,X_143)))) )],[refute_0_1213,refute_0_1218]) ).

cnf(refute_0_1220,plain,
    least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) = least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))),
    inference(subst,[],[refute_0_1219:[bind(X_15,$fot(X_22)),bind(X_26,$fot(X_22))]]) ).

cnf(refute_0_1221,plain,
    ( least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))) != multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) != least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity)))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) = multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))))),bind(Y0,$fot(least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))))),bind(Z0,$fot(multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))))]]) ).

cnf(refute_0_1222,plain,
    ( least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))) != multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) = multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))),least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity)))) )],[refute_0_1220,refute_0_1221]) ).

cnf(refute_0_1223,plain,
    least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) = multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,multiply(X_22,least_upper_bound(X_143,identity))),multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))) )],[refute_0_1212,refute_0_1222]) ).

cnf(refute_0_1224,plain,
    ( multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))) != multiply(X_22,least_upper_bound(identity,X_143))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) != multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) = multiply(X_22,least_upper_bound(identity,X_143)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))))),bind(Y0,$fot(multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))))),bind(Z0,$fot(multiply(X_22,least_upper_bound(identity,X_143))))]]) ).

cnf(refute_0_1225,plain,
    ( multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))) != multiply(X_22,least_upper_bound(identity,X_143))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) = multiply(X_22,least_upper_bound(identity,X_143)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))),multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity)))) )],[refute_0_1223,refute_0_1224]) ).

cnf(refute_0_1226,plain,
    least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) = multiply(X_22,least_upper_bound(identity,X_143)),
    inference(resolve,[$cnf( $equal(multiply(X_22,least_upper_bound(identity,least_upper_bound(X_143,identity))),multiply(X_22,least_upper_bound(identity,X_143))) )],[refute_0_1171,refute_0_1225]) ).

cnf(refute_0_1227,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) != multiply(X_22,least_upper_bound(X_143,identity))
    | least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) != multiply(X_22,least_upper_bound(identity,X_143))
    | multiply(X_22,least_upper_bound(identity,X_143)) = multiply(X_22,least_upper_bound(X_143,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))),multiply(X_22,least_upper_bound(X_143,identity))) ),[0],$fot(multiply(X_22,least_upper_bound(identity,X_143)))]]) ).

cnf(refute_0_1228,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))) != multiply(X_22,least_upper_bound(X_143,identity))
    | multiply(X_22,least_upper_bound(identity,X_143)) = multiply(X_22,least_upper_bound(X_143,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))),multiply(X_22,least_upper_bound(identity,X_143))) )],[refute_0_1226,refute_0_1227]) ).

cnf(refute_0_1229,plain,
    multiply(X_22,least_upper_bound(identity,X_143)) = multiply(X_22,least_upper_bound(X_143,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_22,multiply(X_22,X_143))),multiply(X_22,least_upper_bound(X_143,identity))) )],[refute_0_1166,refute_0_1228]) ).

cnf(refute_0_1230,plain,
    ( multiply(X_22,least_upper_bound(identity,X_143)) != multiply(X_22,least_upper_bound(X_143,identity))
    | multiply(X_22,least_upper_bound(X_143,identity)) = multiply(X_22,least_upper_bound(identity,X_143)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_22,least_upper_bound(identity,X_143)))),bind(Y0,$fot(multiply(X_22,least_upper_bound(X_143,identity))))]]) ).

cnf(refute_0_1231,plain,
    multiply(X_22,least_upper_bound(X_143,identity)) = multiply(X_22,least_upper_bound(identity,X_143)),
    inference(resolve,[$cnf( $equal(multiply(X_22,least_upper_bound(identity,X_143)),multiply(X_22,least_upper_bound(X_143,identity))) )],[refute_0_1229,refute_0_1230]) ).

cnf(refute_0_1232,plain,
    multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)) = multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91))),
    inference(subst,[],[refute_0_1231:[bind(X_143,$fot(inverse(X_91))),bind(X_22,$fot(greatest_lower_bound(identity,X_91)))]]) ).

cnf(refute_0_1233,plain,
    ( multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)) != multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91)))
    | multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)) != least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91)))
    | multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91))) = least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)),least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91))))]]) ).

cnf(refute_0_1234,plain,
    ( multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)) != least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91)))
    | multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91))) = least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)),multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91)))) )],[refute_0_1232,refute_0_1233]) ).

cnf(refute_0_1235,plain,
    multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91))) = least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_91),least_upper_bound(inverse(X_91),identity)),least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91)))) )],[refute_0_1159,refute_0_1234]) ).

cnf(refute_0_1236,plain,
    ( multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91))) != least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91)))
    | least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91))) = multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91)))))]]) ).

cnf(refute_0_1237,plain,
    least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91))) = multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_91),least_upper_bound(identity,inverse(X_91))),least_upper_bound(greatest_lower_bound(identity,X_91),greatest_lower_bound(identity,inverse(X_91)))) )],[refute_0_1235,refute_0_1236]) ).

cnf(refute_0_1238,plain,
    least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85))) = multiply(greatest_lower_bound(identity,X_85),least_upper_bound(identity,inverse(X_85))),
    inference(subst,[],[refute_0_1237:[bind(X_91,$fot(X_85))]]) ).

cnf(refute_0_1239,plain,
    ( multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)) != least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85)))
    | least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85))) != multiply(greatest_lower_bound(identity,X_85),least_upper_bound(identity,inverse(X_85)))
    | multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)) = multiply(greatest_lower_bound(identity,X_85),least_upper_bound(identity,inverse(X_85))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)),multiply(greatest_lower_bound(identity,X_85),least_upper_bound(identity,inverse(X_85)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85))))]]) ).

cnf(refute_0_1240,plain,
    ( multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)) != least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85)))
    | multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)) = multiply(greatest_lower_bound(identity,X_85),least_upper_bound(identity,inverse(X_85))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85))),multiply(greatest_lower_bound(identity,X_85),least_upper_bound(identity,inverse(X_85)))) )],[refute_0_1238,refute_0_1239]) ).

cnf(refute_0_1241,plain,
    ( multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)) != least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85)))
    | multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)) = multiply(greatest_lower_bound(identity,X_85),least_upper_bound(identity,inverse(X_85))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)),least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85)))) )],[refute_0_1155,refute_0_1240]) ).

cnf(refute_0_1242,plain,
    multiply(least_upper_bound(identity,inverse(X_85)),greatest_lower_bound(identity,X_85)) = multiply(greatest_lower_bound(identity,X_85),least_upper_bound(identity,inverse(X_85))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_85),identity),greatest_lower_bound(identity,X_85)),least_upper_bound(greatest_lower_bound(identity,X_85),greatest_lower_bound(identity,inverse(X_85)))) )],[refute_0_1152,refute_0_1241]) ).

cnf(refute_0_1243,plain,
    multiply(least_upper_bound(identity,inverse(X_503)),greatest_lower_bound(identity,X_503)) = multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503))),
    inference(subst,[],[refute_0_1242:[bind(X_85,$fot(X_503))]]) ).

cnf(refute_0_1244,plain,
    inverse(inverse(greatest_lower_bound(identity,X_503))) = greatest_lower_bound(identity,X_503),
    inference(subst,[],[p11_2:[bind(X,$fot(greatest_lower_bound(identity,X_503)))]]) ).

cnf(refute_0_1245,plain,
    multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) = multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))))]]) ).

cnf(refute_0_1246,plain,
    ( multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) != multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))
    | inverse(inverse(greatest_lower_bound(identity,X_503))) != greatest_lower_bound(identity,X_503)
    | multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) = multiply(least_upper_bound(identity,inverse(X_503)),greatest_lower_bound(identity,X_503)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))),multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))) ),[1,1],$fot(greatest_lower_bound(identity,X_503))]]) ).

cnf(refute_0_1247,plain,
    ( inverse(inverse(greatest_lower_bound(identity,X_503))) != greatest_lower_bound(identity,X_503)
    | multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) = multiply(least_upper_bound(identity,inverse(X_503)),greatest_lower_bound(identity,X_503)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))),multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))) )],[refute_0_1245,refute_0_1246]) ).

cnf(refute_0_1248,plain,
    multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) = multiply(least_upper_bound(identity,inverse(X_503)),greatest_lower_bound(identity,X_503)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,X_503))),greatest_lower_bound(identity,X_503)) )],[refute_0_1244,refute_0_1247]) ).

cnf(refute_0_1249,plain,
    ( multiply(least_upper_bound(identity,inverse(X_503)),greatest_lower_bound(identity,X_503)) != multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503)))
    | multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) != multiply(least_upper_bound(identity,inverse(X_503)),greatest_lower_bound(identity,X_503))
    | multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) = multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_503)),greatest_lower_bound(identity,X_503)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503)))))]]) ).

cnf(refute_0_1250,plain,
    ( multiply(least_upper_bound(identity,inverse(X_503)),greatest_lower_bound(identity,X_503)) != multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503)))
    | multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) = multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))),multiply(least_upper_bound(identity,inverse(X_503)),greatest_lower_bound(identity,X_503))) )],[refute_0_1248,refute_0_1249]) ).

cnf(refute_0_1251,plain,
    multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) = multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_503)),greatest_lower_bound(identity,X_503)),multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503)))) )],[refute_0_1243,refute_0_1250]) ).

cnf(refute_0_1252,plain,
    ( multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))) != multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))
    | multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))) != multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503)))
    | multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))) = multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))),multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))))]]) ).

cnf(refute_0_1253,plain,
    ( multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))) != multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))
    | multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))) = multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503)))),multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503)))) )],[refute_0_1251,refute_0_1252]) ).

cnf(refute_0_1254,plain,
    ( multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))) != multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))
    | multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))) = multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))),multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))) )],[refute_0_1148,refute_0_1253]) ).

cnf(refute_0_1255,plain,
    multiply(least_upper_bound(X_503,identity),greatest_lower_bound(identity,inverse(X_503))) = multiply(greatest_lower_bound(identity,X_503),least_upper_bound(identity,inverse(X_503))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_503,identity),inverse(inverse(greatest_lower_bound(identity,inverse(X_503))))),multiply(least_upper_bound(identity,inverse(X_503)),inverse(inverse(greatest_lower_bound(identity,X_503))))) )],[refute_0_1141,refute_0_1254]) ).

cnf(refute_0_1256,plain,
    multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))) = multiply(greatest_lower_bound(identity,X_129),least_upper_bound(identity,inverse(X_129))),
    inference(subst,[],[refute_0_1255:[bind(X_503,$fot(X_129))]]) ).

cnf(refute_0_1257,plain,
    ( multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))) != multiply(greatest_lower_bound(identity,X_129),least_upper_bound(identity,inverse(X_129)))
    | multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))) != greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129)))
    | multiply(greatest_lower_bound(identity,X_129),least_upper_bound(identity,inverse(X_129))) = greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))),greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_129),least_upper_bound(identity,inverse(X_129))))]]) ).

cnf(refute_0_1258,plain,
    ( multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))) != greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129)))
    | multiply(greatest_lower_bound(identity,X_129),least_upper_bound(identity,inverse(X_129))) = greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))),multiply(greatest_lower_bound(identity,X_129),least_upper_bound(identity,inverse(X_129)))) )],[refute_0_1256,refute_0_1257]) ).

cnf(refute_0_1259,plain,
    multiply(greatest_lower_bound(identity,X_129),least_upper_bound(identity,inverse(X_129))) = greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,inverse(X_129))),greatest_lower_bound(least_upper_bound(X_129,identity),least_upper_bound(identity,inverse(X_129)))) )],[refute_0_1109,refute_0_1258]) ).

cnf(refute_0_1260,plain,
    multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))) = greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612))),
    inference(subst,[],[refute_0_1259:[bind(X_129,$fot(X_612))]]) ).

cnf(refute_0_1261,plain,
    ( multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))) != greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612)))
    | greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612))) = multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612)))))]]) ).

cnf(refute_0_1262,plain,
    greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612))) = multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))),greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612)))) )],[refute_0_1260,refute_0_1261]) ).

cnf(refute_0_1263,plain,
    ( multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612)))) != greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity)))
    | greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612))) != multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))
    | multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612)))),greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity)))) ),[0,1],$fot(multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))))]]) ).

cnf(refute_0_1264,plain,
    ( multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612)))) != greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity)))
    | multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612))),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) )],[refute_0_1262,refute_0_1263]) ).

cnf(refute_0_1265,plain,
    multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),greatest_lower_bound(least_upper_bound(X_612,identity),least_upper_bound(identity,inverse(X_612)))),greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity)))) )],[refute_0_1019,refute_0_1264]) ).

cnf(refute_0_1266,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)) = X_612,
    inference(subst,[],[refute_0_865:[bind(X_129,$fot(X_612))]]) ).

cnf(refute_0_1267,plain,
    greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))))]]) ).

cnf(refute_0_1268,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)) != X_612
    | greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))
    | greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))) = greatest_lower_bound(identity,X_612) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))) ),[1,1],$fot(X_612)]]) ).

cnf(refute_0_1269,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)) != X_612
    | greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))) = greatest_lower_bound(identity,X_612) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))) )],[refute_0_1267,refute_0_1268]) ).

cnf(refute_0_1270,plain,
    greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))) = greatest_lower_bound(identity,X_612),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)),X_612) )],[refute_0_1266,refute_0_1269]) ).

cnf(refute_0_1271,plain,
    multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))) = multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))),
    introduced(tautology,[refl,[$fot(multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))))]]) ).

cnf(refute_0_1272,plain,
    ( multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))) != multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))))
    | greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))) != greatest_lower_bound(identity,X_612)
    | multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))),multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))))) ),[1,1],$fot(greatest_lower_bound(identity,X_612))]]) ).

cnf(refute_0_1273,plain,
    ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))) != greatest_lower_bound(identity,X_612)
    | multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))),multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))))) )],[refute_0_1271,refute_0_1272]) ).

cnf(refute_0_1274,plain,
    multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))),greatest_lower_bound(identity,X_612)) )],[refute_0_1270,refute_0_1273]) ).

cnf(refute_0_1275,plain,
    multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396)),
    inference(subst,[],[refute_0_1018:[bind(X_70,$fot(X_395)),bind(X_80,$fot(X_396)),bind(X_81,$fot(least_upper_bound(X_121,X_122)))]]) ).

cnf(refute_0_1276,plain,
    least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120)),
    inference(subst,[],[refute_0_481:[bind(X_22,$fot(multiply(X_121,X_120))),bind(X_23,$fot(multiply(X_122,X_120)))]]) ).

cnf(refute_0_1277,plain,
    multiply(least_upper_bound(X_121,X_122),X_120) = least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_120)),bind(Y,$fot(X_121)),bind(Z,$fot(X_122))]]) ).

cnf(refute_0_1278,plain,
    ( multiply(least_upper_bound(X_121,X_122),X_120) != least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))
    | least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120)) = multiply(least_upper_bound(X_121,X_122),X_120) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_121,X_122),X_120))),bind(Y0,$fot(least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))))]]) ).

cnf(refute_0_1279,plain,
    least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120)) = multiply(least_upper_bound(X_121,X_122),X_120),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,X_122),X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) )],[refute_0_1277,refute_0_1278]) ).

cnf(refute_0_1280,plain,
    ( least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120)) != multiply(least_upper_bound(X_121,X_122),X_120)
    | least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) != least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))
    | least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = multiply(least_upper_bound(X_121,X_122),X_120) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) ),[1],$fot(multiply(least_upper_bound(X_121,X_122),X_120))]]) ).

cnf(refute_0_1281,plain,
    ( least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) != least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))
    | least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = multiply(least_upper_bound(X_121,X_122),X_120) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120)),multiply(least_upper_bound(X_121,X_122),X_120)) )],[refute_0_1279,refute_0_1280]) ).

cnf(refute_0_1282,plain,
    least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = multiply(least_upper_bound(X_121,X_122),X_120),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) )],[refute_0_1276,refute_0_1281]) ).

cnf(refute_0_1283,plain,
    least_upper_bound(X_121,X_121) = X_121,
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_121))]]) ).

cnf(refute_0_1284,plain,
    least_upper_bound(X_122,least_upper_bound(X_121,X_121)) = least_upper_bound(X_122,least_upper_bound(X_121,X_121)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_122,least_upper_bound(X_121,X_121)))]]) ).

cnf(refute_0_1285,plain,
    ( least_upper_bound(X_121,X_121) != X_121
    | least_upper_bound(X_122,least_upper_bound(X_121,X_121)) != least_upper_bound(X_122,least_upper_bound(X_121,X_121))
    | least_upper_bound(X_122,least_upper_bound(X_121,X_121)) = least_upper_bound(X_122,X_121) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),least_upper_bound(X_122,least_upper_bound(X_121,X_121))) ),[1,1],$fot(X_121)]]) ).

cnf(refute_0_1286,plain,
    ( least_upper_bound(X_121,X_121) != X_121
    | least_upper_bound(X_122,least_upper_bound(X_121,X_121)) = least_upper_bound(X_122,X_121) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),least_upper_bound(X_122,least_upper_bound(X_121,X_121))) )],[refute_0_1284,refute_0_1285]) ).

cnf(refute_0_1287,plain,
    least_upper_bound(X_122,least_upper_bound(X_121,X_121)) = least_upper_bound(X_122,X_121),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_121,X_121),X_121) )],[refute_0_1283,refute_0_1286]) ).

cnf(refute_0_1288,plain,
    multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120) = multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120))]]) ).

cnf(refute_0_1289,plain,
    ( multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120) != multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120)
    | least_upper_bound(X_122,least_upper_bound(X_121,X_121)) != least_upper_bound(X_122,X_121)
    | multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120) = multiply(least_upper_bound(X_122,X_121),X_120) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120),multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120)) ),[1,0],$fot(least_upper_bound(X_122,X_121))]]) ).

cnf(refute_0_1290,plain,
    ( least_upper_bound(X_122,least_upper_bound(X_121,X_121)) != least_upper_bound(X_122,X_121)
    | multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120) = multiply(least_upper_bound(X_122,X_121),X_120) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120),multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120)) )],[refute_0_1288,refute_0_1289]) ).

cnf(refute_0_1291,plain,
    multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120) = multiply(least_upper_bound(X_122,X_121),X_120),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),least_upper_bound(X_122,X_121)) )],[refute_0_1287,refute_0_1290]) ).

cnf(refute_0_1292,plain,
    least_upper_bound(multiply(X_122,X_120),multiply(least_upper_bound(X_121,X_121),X_120)) = multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120),
    inference(subst,[],[refute_0_496:[bind(X,$fot(X_120)),bind(Y,$fot(X_122)),bind(Z,$fot(least_upper_bound(X_121,X_121)))]]) ).

cnf(refute_0_1293,plain,
    least_upper_bound(X,least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X)),
    inference(subst,[],[refute_0_128:[bind(X_26,$fot(multiply(X_121,X_120))),bind(X_27,$fot(multiply(X_122,X_120)))]]) ).

cnf(refute_0_1294,plain,
    ( least_upper_bound(X,least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) != least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X))
    | least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120)) != multiply(least_upper_bound(X_121,X_122),X_120)
    | least_upper_bound(X,multiply(least_upper_bound(X_121,X_122),X_120)) = least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))),least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X))) ),[0,1],$fot(multiply(least_upper_bound(X_121,X_122),X_120))]]) ).

cnf(refute_0_1295,plain,
    ( least_upper_bound(X,least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) != least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X))
    | least_upper_bound(X,multiply(least_upper_bound(X_121,X_122),X_120)) = least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120)),multiply(least_upper_bound(X_121,X_122),X_120)) )],[refute_0_1279,refute_0_1294]) ).

cnf(refute_0_1296,plain,
    least_upper_bound(X,multiply(least_upper_bound(X_121,X_122),X_120)) = least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))),least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X))) )],[refute_0_1293,refute_0_1295]) ).

cnf(refute_0_1297,plain,
    ( least_upper_bound(X,multiply(least_upper_bound(X_121,X_122),X_120)) != least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X))
    | least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X)) = least_upper_bound(X,multiply(least_upper_bound(X_121,X_122),X_120)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,multiply(least_upper_bound(X_121,X_122),X_120)))),bind(Y0,$fot(least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X))))]]) ).

cnf(refute_0_1298,plain,
    least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X)) = least_upper_bound(X,multiply(least_upper_bound(X_121,X_122),X_120)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(least_upper_bound(X_121,X_122),X_120)),least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_122,X_120),X))) )],[refute_0_1296,refute_0_1297]) ).

cnf(refute_0_1299,plain,
    least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = least_upper_bound(multiply(X_122,X_120),multiply(least_upper_bound(X_121,X_121),X_120)),
    inference(subst,[],[refute_0_1298:[bind(X,$fot(multiply(X_122,X_120))),bind(X_122,$fot(X_121))]]) ).

cnf(refute_0_1300,plain,
    ( least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) != least_upper_bound(multiply(X_122,X_120),multiply(least_upper_bound(X_121,X_121),X_120))
    | least_upper_bound(multiply(X_122,X_120),multiply(least_upper_bound(X_121,X_121),X_120)) != multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120)
    | least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))))),bind(Y0,$fot(least_upper_bound(multiply(X_122,X_120),multiply(least_upper_bound(X_121,X_121),X_120)))),bind(Z0,$fot(multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120)))]]) ).

cnf(refute_0_1301,plain,
    ( least_upper_bound(multiply(X_122,X_120),multiply(least_upper_bound(X_121,X_121),X_120)) != multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120)
    | least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))),least_upper_bound(multiply(X_122,X_120),multiply(least_upper_bound(X_121,X_121),X_120))) )],[refute_0_1299,refute_0_1300]) ).

cnf(refute_0_1302,plain,
    least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_122,X_120),multiply(least_upper_bound(X_121,X_121),X_120)),multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120)) )],[refute_0_1292,refute_0_1301]) ).

cnf(refute_0_1303,plain,
    ( multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120) != multiply(least_upper_bound(X_122,X_121),X_120)
    | least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) != multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120)
    | least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = multiply(least_upper_bound(X_122,X_121),X_120) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))))),bind(Y0,$fot(multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120))),bind(Z0,$fot(multiply(least_upper_bound(X_122,X_121),X_120)))]]) ).

cnf(refute_0_1304,plain,
    ( multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120) != multiply(least_upper_bound(X_122,X_121),X_120)
    | least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = multiply(least_upper_bound(X_122,X_121),X_120) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))),multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120)) )],[refute_0_1302,refute_0_1303]) ).

cnf(refute_0_1305,plain,
    least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) = multiply(least_upper_bound(X_122,X_121),X_120),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_122,least_upper_bound(X_121,X_121)),X_120),multiply(least_upper_bound(X_122,X_121),X_120)) )],[refute_0_1291,refute_0_1304]) ).

cnf(refute_0_1306,plain,
    ( least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) != multiply(least_upper_bound(X_121,X_122),X_120)
    | least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) != multiply(least_upper_bound(X_122,X_121),X_120)
    | multiply(least_upper_bound(X_122,X_121),X_120) = multiply(least_upper_bound(X_121,X_122),X_120) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))),multiply(least_upper_bound(X_121,X_122),X_120)) ),[0],$fot(multiply(least_upper_bound(X_122,X_121),X_120))]]) ).

cnf(refute_0_1307,plain,
    ( least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))) != multiply(least_upper_bound(X_121,X_122),X_120)
    | multiply(least_upper_bound(X_122,X_121),X_120) = multiply(least_upper_bound(X_121,X_122),X_120) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))),multiply(least_upper_bound(X_122,X_121),X_120)) )],[refute_0_1305,refute_0_1306]) ).

cnf(refute_0_1308,plain,
    multiply(least_upper_bound(X_122,X_121),X_120) = multiply(least_upper_bound(X_121,X_122),X_120),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_121,X_120),least_upper_bound(multiply(X_121,X_120),multiply(X_122,X_120))),multiply(least_upper_bound(X_121,X_122),X_120)) )],[refute_0_1282,refute_0_1307]) ).

cnf(refute_0_1309,plain,
    multiply(least_upper_bound(X_122,X_121),X_395) = multiply(least_upper_bound(X_121,X_122),X_395),
    inference(subst,[],[refute_0_1308:[bind(X_120,$fot(X_395))]]) ).

cnf(refute_0_1310,plain,
    ( multiply(least_upper_bound(X_122,X_121),X_395) != multiply(least_upper_bound(X_121,X_122),X_395)
    | multiply(least_upper_bound(X_121,X_122),X_395) = multiply(least_upper_bound(X_122,X_121),X_395) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_122,X_121),X_395))),bind(Y0,$fot(multiply(least_upper_bound(X_121,X_122),X_395)))]]) ).

cnf(refute_0_1311,plain,
    multiply(least_upper_bound(X_121,X_122),X_395) = multiply(least_upper_bound(X_122,X_121),X_395),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_122,X_121),X_395),multiply(least_upper_bound(X_121,X_122),X_395)) )],[refute_0_1309,refute_0_1310]) ).

cnf(refute_0_1312,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))
    | multiply(least_upper_bound(X_121,X_122),X_395) != multiply(least_upper_bound(X_122,X_121),X_395)
    | multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))) ),[0,0,0],$fot(multiply(least_upper_bound(X_122,X_121),X_395))]]) ).

cnf(refute_0_1313,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))
    | multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,X_122),X_395),multiply(least_upper_bound(X_122,X_121),X_395)) )],[refute_0_1311,refute_0_1312]) ).

cnf(refute_0_1314,plain,
    multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))) )],[refute_0_1275,refute_0_1313]) ).

cnf(refute_0_1315,plain,
    multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_15,X_23))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396)),
    inference(subst,[],[refute_0_1018:[bind(X_70,$fot(X_395)),bind(X_80,$fot(X_396)),bind(X_81,$fot(least_upper_bound(X_15,X_23)))]]) ).

cnf(refute_0_1316,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35)) = greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_33)),bind(Y,$fot(X_34)),bind(Z,$fot(X_35))]]) ).

cnf(refute_0_1317,plain,
    greatest_lower_bound(X_35,X_34) = greatest_lower_bound(X_34,X_35),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_35)),bind(Y,$fot(X_34))]]) ).

cnf(refute_0_1318,plain,
    ( greatest_lower_bound(X_35,X_34) != greatest_lower_bound(X_34,X_35)
    | greatest_lower_bound(X_34,X_35) = greatest_lower_bound(X_35,X_34) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_35,X_34))),bind(Y0,$fot(greatest_lower_bound(X_34,X_35)))]]) ).

cnf(refute_0_1319,plain,
    greatest_lower_bound(X_34,X_35) = greatest_lower_bound(X_35,X_34),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_35,X_34),greatest_lower_bound(X_34,X_35)) )],[refute_0_1317,refute_0_1318]) ).

cnf(refute_0_1320,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35)) != greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35)
    | greatest_lower_bound(X_34,X_35) != greatest_lower_bound(X_35,X_34)
    | greatest_lower_bound(X_33,greatest_lower_bound(X_35,X_34)) = greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35)),greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35)) ),[0,1],$fot(greatest_lower_bound(X_35,X_34))]]) ).

cnf(refute_0_1321,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35)) != greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35)
    | greatest_lower_bound(X_33,greatest_lower_bound(X_35,X_34)) = greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_34,X_35),greatest_lower_bound(X_35,X_34)) )],[refute_0_1319,refute_0_1320]) ).

cnf(refute_0_1322,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_35,X_34)) = greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35)),greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35)) )],[refute_0_1316,refute_0_1321]) ).

cnf(refute_0_1323,plain,
    greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35)),
    inference(subst,[],[refute_0_343:[bind(X,$fot(X_33)),bind(Y,$fot(X_34)),bind(Z,$fot(X_35))]]) ).

cnf(refute_0_1324,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_35,X_34)) != greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35)
    | greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35) != greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_35,X_34)) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_35,X_34)),greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35))]]) ).

cnf(refute_0_1325,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_35,X_34)) != greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35)
    | greatest_lower_bound(X_33,greatest_lower_bound(X_35,X_34)) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35),greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35))) )],[refute_0_1323,refute_0_1324]) ).

cnf(refute_0_1326,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_35,X_34)) = greatest_lower_bound(X_33,greatest_lower_bound(X_34,X_35)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_35,X_34)),greatest_lower_bound(greatest_lower_bound(X_33,X_34),X_35)) )],[refute_0_1322,refute_0_1325]) ).

cnf(refute_0_1327,plain,
    greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23))) = greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),
    inference(subst,[],[refute_0_1326:[bind(X_33,$fot(X_215)),bind(X_34,$fot(least_upper_bound(X_15,X_23))),bind(X_35,$fot(least_upper_bound(X_23,X_15)))]]) ).

cnf(refute_0_1328,plain,
    ( greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23))) != greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))
    | greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)) != least_upper_bound(X_23,X_15)
    | greatest_lower_bound(X_215,least_upper_bound(X_23,X_15)) = greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23))),greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) ),[0,1],$fot(least_upper_bound(X_23,X_15))]]) ).

cnf(refute_0_1329,plain,
    ( greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23))) != greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))
    | greatest_lower_bound(X_215,least_upper_bound(X_23,X_15)) = greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23)),least_upper_bound(X_23,X_15)) )],[refute_0_413,refute_0_1328]) ).

cnf(refute_0_1330,plain,
    greatest_lower_bound(X_215,least_upper_bound(X_23,X_15)) = greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_23,X_15),least_upper_bound(X_15,X_23))),greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) )],[refute_0_1327,refute_0_1329]) ).

cnf(refute_0_1331,plain,
    greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) = greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))))]]) ).

cnf(refute_0_1332,plain,
    ( greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) != greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))
    | greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)) != least_upper_bound(X_15,X_23)
    | greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) = greatest_lower_bound(X_215,least_upper_bound(X_15,X_23)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) ),[1,1],$fot(least_upper_bound(X_15,X_23))]]) ).

cnf(refute_0_1333,plain,
    ( greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)) != least_upper_bound(X_15,X_23)
    | greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) = greatest_lower_bound(X_215,least_upper_bound(X_15,X_23)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) )],[refute_0_1331,refute_0_1332]) ).

cnf(refute_0_1334,plain,
    greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) = greatest_lower_bound(X_215,least_upper_bound(X_15,X_23)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)),least_upper_bound(X_15,X_23)) )],[refute_0_417,refute_0_1333]) ).

cnf(refute_0_1335,plain,
    ( greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))) != greatest_lower_bound(X_215,least_upper_bound(X_15,X_23))
    | greatest_lower_bound(X_215,least_upper_bound(X_23,X_15)) != greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))
    | greatest_lower_bound(X_215,least_upper_bound(X_23,X_15)) = greatest_lower_bound(X_215,least_upper_bound(X_15,X_23)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_215,least_upper_bound(X_23,X_15)),greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) ),[1],$fot(greatest_lower_bound(X_215,least_upper_bound(X_15,X_23)))]]) ).

cnf(refute_0_1336,plain,
    ( greatest_lower_bound(X_215,least_upper_bound(X_23,X_15)) != greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))
    | greatest_lower_bound(X_215,least_upper_bound(X_23,X_15)) = greatest_lower_bound(X_215,least_upper_bound(X_15,X_23)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15))),greatest_lower_bound(X_215,least_upper_bound(X_15,X_23))) )],[refute_0_1334,refute_0_1335]) ).

cnf(refute_0_1337,plain,
    greatest_lower_bound(X_215,least_upper_bound(X_23,X_15)) = greatest_lower_bound(X_215,least_upper_bound(X_15,X_23)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_215,least_upper_bound(X_23,X_15)),greatest_lower_bound(X_215,greatest_lower_bound(least_upper_bound(X_15,X_23),least_upper_bound(X_23,X_15)))) )],[refute_0_1330,refute_0_1336]) ).

cnf(refute_0_1338,plain,
    greatest_lower_bound(X_396,least_upper_bound(X_23,X_15)) = greatest_lower_bound(X_396,least_upper_bound(X_15,X_23)),
    inference(subst,[],[refute_0_1337:[bind(X_215,$fot(X_396))]]) ).

cnf(refute_0_1339,plain,
    ( greatest_lower_bound(X_396,least_upper_bound(X_23,X_15)) != greatest_lower_bound(X_396,least_upper_bound(X_15,X_23))
    | greatest_lower_bound(X_396,least_upper_bound(X_15,X_23)) = greatest_lower_bound(X_396,least_upper_bound(X_23,X_15)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(X_396,least_upper_bound(X_23,X_15)))),bind(Y0,$fot(greatest_lower_bound(X_396,least_upper_bound(X_15,X_23))))]]) ).

cnf(refute_0_1340,plain,
    greatest_lower_bound(X_396,least_upper_bound(X_15,X_23)) = greatest_lower_bound(X_396,least_upper_bound(X_23,X_15)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_396,least_upper_bound(X_23,X_15)),greatest_lower_bound(X_396,least_upper_bound(X_15,X_23))) )],[refute_0_1338,refute_0_1339]) ).

cnf(refute_0_1341,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_15,X_23))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396))
    | greatest_lower_bound(X_396,least_upper_bound(X_15,X_23)) != greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))
    | multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_15,X_23))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396))) ),[0,1],$fot(greatest_lower_bound(X_396,least_upper_bound(X_23,X_15)))]]) ).

cnf(refute_0_1342,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_15,X_23))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396))
    | multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_396,least_upper_bound(X_15,X_23)),greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))) )],[refute_0_1340,refute_0_1341]) ).

cnf(refute_0_1343,plain,
    multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_15,X_23))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396))) )],[refute_0_1315,refute_0_1342]) ).

cnf(refute_0_1344,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))
    | multiply(least_upper_bound(X_121,X_122),X_395) != multiply(least_upper_bound(X_122,X_121),X_395)
    | multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))) ),[1,1,0,0],$fot(multiply(least_upper_bound(X_122,X_121),X_395))]]) ).

cnf(refute_0_1345,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))
    | multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,X_122),X_395),multiply(least_upper_bound(X_122,X_121),X_395)) )],[refute_0_1311,refute_0_1344]) ).

cnf(refute_0_1346,plain,
    multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))) )],[refute_0_1275,refute_0_1345]) ).

cnf(refute_0_1347,plain,
    multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))) = multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144))))),
    inference(subst,[],[refute_0_987:[bind(Y,$fot(least_upper_bound(X_144,identity))),bind(Z,$fot(inverse(least_upper_bound(identity,inverse(X_144))))),bind(X_72,$fot(X_525))]]) ).

cnf(refute_0_1348,plain,
    ( multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))) != multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))))
    | multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))) != X_144
    | multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))) = multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))),multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))))) ),[1,1],$fot(X_144)]]) ).

cnf(refute_0_1349,plain,
    ( multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))) != multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))))
    | multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))) = multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))),X_144) )],[refute_0_804,refute_0_1348]) ).

cnf(refute_0_1350,plain,
    multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))) = multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))),multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),multiply(least_upper_bound(X_144,identity),inverse(least_upper_bound(identity,inverse(X_144)))))) )],[refute_0_1347,refute_0_1349]) ).

cnf(refute_0_1351,plain,
    multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))) = inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525)),
    inference(subst,[],[refute_0_221:[bind(X,$fot(least_upper_bound(identity,inverse(X_144)))),bind(Y,$fot(X_525))]]) ).

cnf(refute_0_1352,plain,
    ( multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))) != multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144)
    | multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))) != inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525))
    | inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525)) = multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))),multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144)) ),[0],$fot(inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525)))]]) ).

cnf(refute_0_1353,plain,
    ( multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))) != multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144)
    | inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525)) = multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))),inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525))) )],[refute_0_1351,refute_0_1352]) ).

cnf(refute_0_1354,plain,
    inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525)) = multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_525),inverse(least_upper_bound(identity,inverse(X_144)))),multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144)) )],[refute_0_1350,refute_0_1353]) ).

cnf(refute_0_1355,plain,
    inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) = multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),
    inference(subst,[],[refute_0_1354:[bind(X_144,$fot(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))))]]) ).

cnf(refute_0_1356,plain,
    inverse(multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_150))) = multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X),
    inference(subst,[],[refute_0_22:[bind(X_30,$fot(greatest_lower_bound(inverse(inverse(X)),X_150)))]]) ).

cnf(refute_0_1357,plain,
    multiply(X_79,greatest_lower_bound(inverse(X_79),X_81)) = greatest_lower_bound(multiply(X_79,inverse(X_79)),multiply(X_79,X_81)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_79)),bind(Y,$fot(inverse(X_79))),bind(Z,$fot(X_81))]]) ).

cnf(refute_0_1358,plain,
    ( multiply(X_79,greatest_lower_bound(inverse(X_79),X_81)) != greatest_lower_bound(multiply(X_79,inverse(X_79)),multiply(X_79,X_81))
    | multiply(X_79,inverse(X_79)) != identity
    | multiply(X_79,greatest_lower_bound(inverse(X_79),X_81)) = greatest_lower_bound(identity,multiply(X_79,X_81)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_79,greatest_lower_bound(inverse(X_79),X_81)),greatest_lower_bound(multiply(X_79,inverse(X_79)),multiply(X_79,X_81))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1359,plain,
    ( multiply(X_79,greatest_lower_bound(inverse(X_79),X_81)) != greatest_lower_bound(multiply(X_79,inverse(X_79)),multiply(X_79,X_81))
    | multiply(X_79,greatest_lower_bound(inverse(X_79),X_81)) = greatest_lower_bound(identity,multiply(X_79,X_81)) ),
    inference(resolve,[$cnf( $equal(multiply(X_79,inverse(X_79)),identity) )],[refute_0_30,refute_0_1358]) ).

cnf(refute_0_1360,plain,
    multiply(X_79,greatest_lower_bound(inverse(X_79),X_81)) = greatest_lower_bound(identity,multiply(X_79,X_81)),
    inference(resolve,[$cnf( $equal(multiply(X_79,greatest_lower_bound(inverse(X_79),X_81)),greatest_lower_bound(multiply(X_79,inverse(X_79)),multiply(X_79,X_81))) )],[refute_0_1357,refute_0_1359]) ).

cnf(refute_0_1361,plain,
    multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_150)) = greatest_lower_bound(identity,multiply(inverse(X),X_150)),
    inference(subst,[],[refute_0_1360:[bind(X_79,$fot(inverse(X))),bind(X_81,$fot(X_150))]]) ).

cnf(refute_0_1362,plain,
    ( multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_150)) != greatest_lower_bound(identity,multiply(inverse(X),X_150))
    | inverse(multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_150))) != multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_150))) = multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_150))),multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X)) ),[0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X),X_150)))]]) ).

cnf(refute_0_1363,plain,
    ( inverse(multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_150))) != multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_150))) = multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_150)),greatest_lower_bound(identity,multiply(inverse(X),X_150))) )],[refute_0_1361,refute_0_1362]) ).

cnf(refute_0_1364,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X),X_150))) = multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),greatest_lower_bound(inverse(inverse(X)),X_150))),multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X)) )],[refute_0_1356,refute_0_1363]) ).

cnf(refute_0_1365,plain,
    greatest_lower_bound(inverse(inverse(X)),X_150) = greatest_lower_bound(inverse(inverse(X)),X_150),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(inverse(X)),X_150))]]) ).

cnf(refute_0_1366,plain,
    ( greatest_lower_bound(inverse(inverse(X)),X_150) != greatest_lower_bound(inverse(inverse(X)),X_150)
    | inverse(inverse(X)) != X
    | greatest_lower_bound(inverse(inverse(X)),X_150) = greatest_lower_bound(X,X_150) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X)),X_150),greatest_lower_bound(inverse(inverse(X)),X_150)) ),[1,0],$fot(X)]]) ).

cnf(refute_0_1367,plain,
    ( inverse(inverse(X)) != X
    | greatest_lower_bound(inverse(inverse(X)),X_150) = greatest_lower_bound(X,X_150) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X)),X_150),greatest_lower_bound(inverse(inverse(X)),X_150)) )],[refute_0_1365,refute_0_1366]) ).

cnf(refute_0_1368,plain,
    greatest_lower_bound(inverse(inverse(X)),X_150) = greatest_lower_bound(X,X_150),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p11_2,refute_0_1367]) ).

cnf(refute_0_1369,plain,
    inverse(greatest_lower_bound(inverse(inverse(X)),X_150)) = inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)))]]) ).

cnf(refute_0_1370,plain,
    ( greatest_lower_bound(inverse(inverse(X)),X_150) != greatest_lower_bound(X,X_150)
    | inverse(greatest_lower_bound(inverse(inverse(X)),X_150)) != inverse(greatest_lower_bound(inverse(inverse(X)),X_150))
    | inverse(greatest_lower_bound(inverse(inverse(X)),X_150)) = inverse(greatest_lower_bound(X,X_150)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),inverse(greatest_lower_bound(inverse(inverse(X)),X_150))) ),[1,0],$fot(greatest_lower_bound(X,X_150))]]) ).

cnf(refute_0_1371,plain,
    ( greatest_lower_bound(inverse(inverse(X)),X_150) != greatest_lower_bound(X,X_150)
    | inverse(greatest_lower_bound(inverse(inverse(X)),X_150)) = inverse(greatest_lower_bound(X,X_150)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),inverse(greatest_lower_bound(inverse(inverse(X)),X_150))) )],[refute_0_1369,refute_0_1370]) ).

cnf(refute_0_1372,plain,
    inverse(greatest_lower_bound(inverse(inverse(X)),X_150)) = inverse(greatest_lower_bound(X,X_150)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(X)),X_150),greatest_lower_bound(X,X_150)) )],[refute_0_1368,refute_0_1371]) ).

cnf(refute_0_1373,plain,
    multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X) = multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X))]]) ).

cnf(refute_0_1374,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X) != multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X)
    | inverse(greatest_lower_bound(inverse(inverse(X)),X_150)) != inverse(greatest_lower_bound(X,X_150))
    | multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X) = multiply(inverse(greatest_lower_bound(X,X_150)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X),multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X)) ),[1,0],$fot(inverse(greatest_lower_bound(X,X_150)))]]) ).

cnf(refute_0_1375,plain,
    ( inverse(greatest_lower_bound(inverse(inverse(X)),X_150)) != inverse(greatest_lower_bound(X,X_150))
    | multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X) = multiply(inverse(greatest_lower_bound(X,X_150)),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X),multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X)) )],[refute_0_1373,refute_0_1374]) ).

cnf(refute_0_1376,plain,
    multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X) = multiply(inverse(greatest_lower_bound(X,X_150)),X),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),inverse(greatest_lower_bound(X,X_150))) )],[refute_0_1372,refute_0_1375]) ).

cnf(refute_0_1377,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X) != multiply(inverse(greatest_lower_bound(X,X_150)),X)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_150))) != multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_150))) = multiply(inverse(greatest_lower_bound(X,X_150)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_150))),multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X)) ),[1],$fot(multiply(inverse(greatest_lower_bound(X,X_150)),X))]]) ).

cnf(refute_0_1378,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(X),X_150))) != multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_150))) = multiply(inverse(greatest_lower_bound(X,X_150)),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X),multiply(inverse(greatest_lower_bound(X,X_150)),X)) )],[refute_0_1376,refute_0_1377]) ).

cnf(refute_0_1379,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X),X_150))) = multiply(inverse(greatest_lower_bound(X,X_150)),X),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_150))),multiply(inverse(greatest_lower_bound(inverse(inverse(X)),X_150)),X)) )],[refute_0_1364,refute_0_1378]) ).

cnf(refute_0_1380,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) = multiply(inverse(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396))),inverse(X_395)),
    inference(subst,[],[refute_0_1379:[bind(X,$fot(inverse(X_395))),bind(X_150,$fot(multiply(inverse(multiply(X_397,X_395)),X_396)))]]) ).

cnf(refute_0_1381,plain,
    multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396)),
    inference(subst,[],[refute_0_1018:[bind(X_70,$fot(X_395)),bind(X_80,$fot(X_396)),bind(X_81,$fot(X_397))]]) ).

cnf(refute_0_1382,plain,
    ( multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396))
    | greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396)) = multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396))))]]) ).

cnf(refute_0_1383,plain,
    greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396)) = multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396))) )],[refute_0_1381,refute_0_1382]) ).

cnf(refute_0_1384,plain,
    ( greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396)) != multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))
    | inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) != multiply(inverse(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396))),inverse(X_395))
    | inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) = multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))),multiply(inverse(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396))),inverse(X_395))) ),[1,0,0],$fot(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))]]) ).

cnf(refute_0_1385,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) != multiply(inverse(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396))),inverse(X_395))
    | inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) = multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396)),multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))) )],[refute_0_1383,refute_0_1384]) ).

cnf(refute_0_1386,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) = multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))),multiply(inverse(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(X_397,X_395)),X_396))),inverse(X_395))) )],[refute_0_1380,refute_0_1385]) ).

cnf(refute_0_1387,plain,
    ( inverse(X) != multiply(X_69,inverse(multiply(X,X_69)))
    | multiply(X_69,inverse(multiply(X,X_69))) = inverse(X) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X))),bind(Y0,$fot(multiply(X_69,inverse(multiply(X,X_69)))))]]) ).

cnf(refute_0_1388,plain,
    multiply(X_69,inverse(multiply(X,X_69))) = inverse(X),
    inference(resolve,[$cnf( $equal(inverse(X),multiply(X_69,inverse(multiply(X,X_69)))) )],[refute_0_172,refute_0_1387]) ).

cnf(refute_0_1389,plain,
    multiply(X_395,inverse(multiply(X_397,X_395))) = inverse(X_397),
    inference(subst,[],[refute_0_1388:[bind(X,$fot(X_397)),bind(X_69,$fot(X_395))]]) ).

cnf(refute_0_1390,plain,
    inverse(multiply(multiply(X_397,X_395),inverse(X_395))) = multiply(X_395,inverse(multiply(X_397,X_395))),
    inference(subst,[],[refute_0_293:[bind(X,$fot(X_395)),bind(X_29,$fot(multiply(X_397,X_395)))]]) ).

cnf(refute_0_1391,plain,
    ( multiply(X_395,inverse(multiply(X_397,X_395))) != inverse(X_397)
    | inverse(multiply(multiply(X_397,X_395),inverse(X_395))) != multiply(X_395,inverse(multiply(X_397,X_395)))
    | inverse(multiply(multiply(X_397,X_395),inverse(X_395))) = inverse(X_397) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(inverse(multiply(multiply(X_397,X_395),inverse(X_395))))),bind(Y0,$fot(multiply(X_395,inverse(multiply(X_397,X_395))))),bind(Z0,$fot(inverse(X_397)))]]) ).

cnf(refute_0_1392,plain,
    ( multiply(X_395,inverse(multiply(X_397,X_395))) != inverse(X_397)
    | inverse(multiply(multiply(X_397,X_395),inverse(X_395))) = inverse(X_397) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),multiply(X_395,inverse(multiply(X_397,X_395)))) )],[refute_0_1390,refute_0_1391]) ).

cnf(refute_0_1393,plain,
    inverse(multiply(multiply(X_397,X_395),inverse(X_395))) = inverse(X_397),
    inference(resolve,[$cnf( $equal(multiply(X_395,inverse(multiply(X_397,X_395))),inverse(X_397)) )],[refute_0_1389,refute_0_1392]) ).

cnf(refute_0_1394,plain,
    multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396) = multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396),
    introduced(tautology,[refl,[$fot(multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396))]]) ).

cnf(refute_0_1395,plain,
    ( multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396) != multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396)
    | inverse(multiply(multiply(X_397,X_395),inverse(X_395))) != inverse(X_397)
    | multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396) = multiply(inverse(X_397),X_396) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396),multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396)) ),[1,0],$fot(inverse(X_397))]]) ).

cnf(refute_0_1396,plain,
    ( inverse(multiply(multiply(X_397,X_395),inverse(X_395))) != inverse(X_397)
    | multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396) = multiply(inverse(X_397),X_396) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396),multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396)) )],[refute_0_1394,refute_0_1395]) ).

cnf(refute_0_1397,plain,
    multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396) = multiply(inverse(X_397),X_396),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),inverse(X_397)) )],[refute_0_1393,refute_0_1396]) ).

cnf(refute_0_1398,plain,
    inverse(multiply(inverse(multiply(inverse(X_36),X_37)),X_30)) = multiply(inverse(X_30),multiply(inverse(X_36),X_37)),
    inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(inverse(X_36),X_37)))]]) ).

cnf(refute_0_1399,plain,
    ( inverse(multiply(inverse(X_36),X_37)) != multiply(inverse(X_37),X_36)
    | inverse(multiply(inverse(multiply(inverse(X_36),X_37)),X_30)) != multiply(inverse(X_30),multiply(inverse(X_36),X_37))
    | inverse(multiply(multiply(inverse(X_37),X_36),X_30)) = multiply(inverse(X_30),multiply(inverse(X_36),X_37)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(multiply(inverse(X_36),X_37)),X_30)),multiply(inverse(X_30),multiply(inverse(X_36),X_37))) ),[0,0,0],$fot(multiply(inverse(X_37),X_36))]]) ).

cnf(refute_0_1400,plain,
    ( inverse(multiply(inverse(multiply(inverse(X_36),X_37)),X_30)) != multiply(inverse(X_30),multiply(inverse(X_36),X_37))
    | inverse(multiply(multiply(inverse(X_37),X_36),X_30)) = multiply(inverse(X_30),multiply(inverse(X_36),X_37)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_36),X_37)),multiply(inverse(X_37),X_36)) )],[refute_0_784,refute_0_1399]) ).

cnf(refute_0_1401,plain,
    inverse(multiply(multiply(inverse(X_37),X_36),X_30)) = multiply(inverse(X_30),multiply(inverse(X_36),X_37)),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(inverse(X_36),X_37)),X_30)),multiply(inverse(X_30),multiply(inverse(X_36),X_37))) )],[refute_0_1398,refute_0_1400]) ).

cnf(refute_0_1402,plain,
    inverse(multiply(inverse(X_37),multiply(X_36,X_30))) = multiply(inverse(multiply(X_36,X_30)),X_37),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_37)),bind(X_30,$fot(multiply(X_36,X_30)))]]) ).

cnf(refute_0_1403,plain,
    multiply(multiply(inverse(X_37),X_36),X_30) = multiply(inverse(X_37),multiply(X_36,X_30)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_37))),bind(Y,$fot(X_36)),bind(Z,$fot(X_30))]]) ).

cnf(refute_0_1404,plain,
    inverse(multiply(multiply(inverse(X_37),X_36),X_30)) = inverse(multiply(multiply(inverse(X_37),X_36),X_30)),
    introduced(tautology,[refl,[$fot(inverse(multiply(multiply(inverse(X_37),X_36),X_30)))]]) ).

cnf(refute_0_1405,plain,
    ( multiply(multiply(inverse(X_37),X_36),X_30) != multiply(inverse(X_37),multiply(X_36,X_30))
    | inverse(multiply(multiply(inverse(X_37),X_36),X_30)) != inverse(multiply(multiply(inverse(X_37),X_36),X_30))
    | inverse(multiply(multiply(inverse(X_37),X_36),X_30)) = inverse(multiply(inverse(X_37),multiply(X_36,X_30))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(inverse(X_37),X_36),X_30)),inverse(multiply(multiply(inverse(X_37),X_36),X_30))) ),[1,0],$fot(multiply(inverse(X_37),multiply(X_36,X_30)))]]) ).

cnf(refute_0_1406,plain,
    ( multiply(multiply(inverse(X_37),X_36),X_30) != multiply(inverse(X_37),multiply(X_36,X_30))
    | inverse(multiply(multiply(inverse(X_37),X_36),X_30)) = inverse(multiply(inverse(X_37),multiply(X_36,X_30))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(X_37),X_36),X_30)),inverse(multiply(multiply(inverse(X_37),X_36),X_30))) )],[refute_0_1404,refute_0_1405]) ).

cnf(refute_0_1407,plain,
    inverse(multiply(multiply(inverse(X_37),X_36),X_30)) = inverse(multiply(inverse(X_37),multiply(X_36,X_30))),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_37),X_36),X_30),multiply(inverse(X_37),multiply(X_36,X_30))) )],[refute_0_1403,refute_0_1406]) ).

cnf(refute_0_1408,plain,
    ( inverse(multiply(multiply(inverse(X_37),X_36),X_30)) != inverse(multiply(inverse(X_37),multiply(X_36,X_30)))
    | inverse(multiply(inverse(X_37),multiply(X_36,X_30))) != multiply(inverse(multiply(X_36,X_30)),X_37)
    | inverse(multiply(multiply(inverse(X_37),X_36),X_30)) = multiply(inverse(multiply(X_36,X_30)),X_37) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(inverse(multiply(multiply(inverse(X_37),X_36),X_30)))),bind(Y0,$fot(inverse(multiply(inverse(X_37),multiply(X_36,X_30))))),bind(Z0,$fot(multiply(inverse(multiply(X_36,X_30)),X_37)))]]) ).

cnf(refute_0_1409,plain,
    ( inverse(multiply(inverse(X_37),multiply(X_36,X_30))) != multiply(inverse(multiply(X_36,X_30)),X_37)
    | inverse(multiply(multiply(inverse(X_37),X_36),X_30)) = multiply(inverse(multiply(X_36,X_30)),X_37) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(X_37),X_36),X_30)),inverse(multiply(inverse(X_37),multiply(X_36,X_30)))) )],[refute_0_1407,refute_0_1408]) ).

cnf(refute_0_1410,plain,
    inverse(multiply(multiply(inverse(X_37),X_36),X_30)) = multiply(inverse(multiply(X_36,X_30)),X_37),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_37),multiply(X_36,X_30))),multiply(inverse(multiply(X_36,X_30)),X_37)) )],[refute_0_1402,refute_0_1409]) ).

cnf(refute_0_1411,plain,
    ( inverse(multiply(multiply(inverse(X_37),X_36),X_30)) != multiply(inverse(X_30),multiply(inverse(X_36),X_37))
    | inverse(multiply(multiply(inverse(X_37),X_36),X_30)) != multiply(inverse(multiply(X_36,X_30)),X_37)
    | multiply(inverse(multiply(X_36,X_30)),X_37) = multiply(inverse(X_30),multiply(inverse(X_36),X_37)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(inverse(X_37),X_36),X_30)),multiply(inverse(X_30),multiply(inverse(X_36),X_37))) ),[0],$fot(multiply(inverse(multiply(X_36,X_30)),X_37))]]) ).

cnf(refute_0_1412,plain,
    ( inverse(multiply(multiply(inverse(X_37),X_36),X_30)) != multiply(inverse(X_30),multiply(inverse(X_36),X_37))
    | multiply(inverse(multiply(X_36,X_30)),X_37) = multiply(inverse(X_30),multiply(inverse(X_36),X_37)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(X_37),X_36),X_30)),multiply(inverse(multiply(X_36,X_30)),X_37)) )],[refute_0_1410,refute_0_1411]) ).

cnf(refute_0_1413,plain,
    multiply(inverse(multiply(X_36,X_30)),X_37) = multiply(inverse(X_30),multiply(inverse(X_36),X_37)),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(inverse(X_37),X_36),X_30)),multiply(inverse(X_30),multiply(inverse(X_36),X_37))) )],[refute_0_1401,refute_0_1412]) ).

cnf(refute_0_1414,plain,
    ( multiply(inverse(multiply(X_36,X_30)),X_37) != multiply(inverse(X_30),multiply(inverse(X_36),X_37))
    | multiply(inverse(X_30),multiply(inverse(X_36),X_37)) = multiply(inverse(multiply(X_36,X_30)),X_37) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(multiply(X_36,X_30)),X_37))),bind(Y0,$fot(multiply(inverse(X_30),multiply(inverse(X_36),X_37))))]]) ).

cnf(refute_0_1415,plain,
    multiply(inverse(X_30),multiply(inverse(X_36),X_37)) = multiply(inverse(multiply(X_36,X_30)),X_37),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_36,X_30)),X_37),multiply(inverse(X_30),multiply(inverse(X_36),X_37))) )],[refute_0_1413,refute_0_1414]) ).

cnf(refute_0_1416,plain,
    multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)) = multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396),
    inference(subst,[],[refute_0_1415:[bind(X_30,$fot(inverse(X_395))),bind(X_36,$fot(multiply(X_397,X_395))),bind(X_37,$fot(X_396))]]) ).

cnf(refute_0_1417,plain,
    ( multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396) != multiply(inverse(X_397),X_396)
    | multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)) != multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396)
    | multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)) = multiply(inverse(X_397),X_396) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))),bind(Y0,$fot(multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396))),bind(Z0,$fot(multiply(inverse(X_397),X_396)))]]) ).

cnf(refute_0_1418,plain,
    ( multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396) != multiply(inverse(X_397),X_396)
    | multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)) = multiply(inverse(X_397),X_396) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)),multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396)) )],[refute_0_1416,refute_0_1417]) ).

cnf(refute_0_1419,plain,
    multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)) = multiply(inverse(X_397),X_396),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(multiply(X_397,X_395),inverse(X_395))),X_396),multiply(inverse(X_397),X_396)) )],[refute_0_1397,refute_0_1418]) ).

cnf(refute_0_1420,plain,
    greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))) = greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))))]]) ).

cnf(refute_0_1421,plain,
    ( multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)) != multiply(inverse(X_397),X_396)
    | greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))) != greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))
    | greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))) = greatest_lower_bound(identity,multiply(inverse(X_397),X_396)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))),greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) ),[1,1],$fot(multiply(inverse(X_397),X_396))]]) ).

cnf(refute_0_1422,plain,
    ( multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)) != multiply(inverse(X_397),X_396)
    | greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))) = greatest_lower_bound(identity,multiply(inverse(X_397),X_396)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))),greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) )],[refute_0_1420,refute_0_1421]) ).

cnf(refute_0_1423,plain,
    greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))) = greatest_lower_bound(identity,multiply(inverse(X_397),X_396)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)),multiply(inverse(X_397),X_396)) )],[refute_0_1419,refute_0_1422]) ).

cnf(refute_0_1424,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) = inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))))]]) ).

cnf(refute_0_1425,plain,
    ( greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))) != greatest_lower_bound(identity,multiply(inverse(X_397),X_396))
    | inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) != inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))))
    | inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_397),X_396)))]]) ).

cnf(refute_0_1426,plain,
    ( greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))) != greatest_lower_bound(identity,multiply(inverse(X_397),X_396))
    | inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))),inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))))) )],[refute_0_1424,refute_0_1425]) ).

cnf(refute_0_1427,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396))),greatest_lower_bound(identity,multiply(inverse(X_397),X_396))) )],[refute_0_1423,refute_0_1426]) ).

cnf(refute_0_1428,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) != multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395))
    | inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396)))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))) = multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))),multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))))]]) ).

cnf(refute_0_1429,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) != multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))) = multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))),inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396)))) )],[refute_0_1427,refute_0_1428]) ).

cnf(refute_0_1430,plain,
    inverse(multiply(inverse(X_397),greatest_lower_bound(X_396,X_397))) = multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_397)),bind(X_30,$fot(greatest_lower_bound(X_396,X_397)))]]) ).

cnf(refute_0_1431,plain,
    multiply(multiply(X,inverse(multiply(X_75,X))),Z) = multiply(X,multiply(inverse(multiply(X_75,X)),Z)),
    inference(subst,[],[associativity:[bind(Y,$fot(inverse(multiply(X_75,X))))]]) ).

cnf(refute_0_1432,plain,
    inverse(X_75) = multiply(X,inverse(multiply(X_75,X))),
    inference(subst,[],[refute_0_172:[bind(X,$fot(X_75)),bind(X_69,$fot(X))]]) ).

cnf(refute_0_1433,plain,
    ( inverse(X_75) != multiply(X,inverse(multiply(X_75,X)))
    | multiply(X,inverse(multiply(X_75,X))) = inverse(X_75) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X_75))),bind(Y0,$fot(multiply(X,inverse(multiply(X_75,X)))))]]) ).

cnf(refute_0_1434,plain,
    multiply(X,inverse(multiply(X_75,X))) = inverse(X_75),
    inference(resolve,[$cnf( $equal(inverse(X_75),multiply(X,inverse(multiply(X_75,X)))) )],[refute_0_1432,refute_0_1433]) ).

cnf(refute_0_1435,plain,
    ( multiply(X,inverse(multiply(X_75,X))) != inverse(X_75)
    | multiply(multiply(X,inverse(multiply(X_75,X))),Z) != multiply(X,multiply(inverse(multiply(X_75,X)),Z))
    | multiply(inverse(X_75),Z) = multiply(X,multiply(inverse(multiply(X_75,X)),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X,inverse(multiply(X_75,X))),Z),multiply(X,multiply(inverse(multiply(X_75,X)),Z))) ),[0,0],$fot(inverse(X_75))]]) ).

cnf(refute_0_1436,plain,
    ( multiply(multiply(X,inverse(multiply(X_75,X))),Z) != multiply(X,multiply(inverse(multiply(X_75,X)),Z))
    | multiply(inverse(X_75),Z) = multiply(X,multiply(inverse(multiply(X_75,X)),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(X,inverse(multiply(X_75,X))),inverse(X_75)) )],[refute_0_1434,refute_0_1435]) ).

cnf(refute_0_1437,plain,
    multiply(inverse(X_75),Z) = multiply(X,multiply(inverse(multiply(X_75,X)),Z)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,inverse(multiply(X_75,X))),Z),multiply(X,multiply(inverse(multiply(X_75,X)),Z))) )],[refute_0_1431,refute_0_1436]) ).

cnf(refute_0_1438,plain,
    ( multiply(inverse(X_75),Z) != multiply(X,multiply(inverse(multiply(X_75,X)),Z))
    | multiply(X,multiply(inverse(multiply(X_75,X)),Z)) = multiply(inverse(X_75),Z) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_75),Z))),bind(Y0,$fot(multiply(X,multiply(inverse(multiply(X_75,X)),Z))))]]) ).

cnf(refute_0_1439,plain,
    multiply(X,multiply(inverse(multiply(X_75,X)),Z)) = multiply(inverse(X_75),Z),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_75),Z),multiply(X,multiply(inverse(multiply(X_75,X)),Z))) )],[refute_0_1437,refute_0_1438]) ).

cnf(refute_0_1440,plain,
    multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))) = multiply(inverse(X_397),greatest_lower_bound(X_396,X_397)),
    inference(subst,[],[refute_0_1439:[bind(X,$fot(X_395)),bind(Z,$fot(greatest_lower_bound(X_396,X_397))),bind(X_75,$fot(X_397))]]) ).

cnf(refute_0_1441,plain,
    inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))) = inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))),
    introduced(tautology,[refl,[$fot(inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))))]]) ).

cnf(refute_0_1442,plain,
    ( multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))) != multiply(inverse(X_397),greatest_lower_bound(X_396,X_397))
    | inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))) != inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))))
    | inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))) = inverse(multiply(inverse(X_397),greatest_lower_bound(X_396,X_397))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))),inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))))) ),[1,0],$fot(multiply(inverse(X_397),greatest_lower_bound(X_396,X_397)))]]) ).

cnf(refute_0_1443,plain,
    ( multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))) != multiply(inverse(X_397),greatest_lower_bound(X_396,X_397))
    | inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))) = inverse(multiply(inverse(X_397),greatest_lower_bound(X_396,X_397))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))),inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))))) )],[refute_0_1441,refute_0_1442]) ).

cnf(refute_0_1444,plain,
    inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))) = inverse(multiply(inverse(X_397),greatest_lower_bound(X_396,X_397))),
    inference(resolve,[$cnf( $equal(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),multiply(inverse(X_397),greatest_lower_bound(X_396,X_397))) )],[refute_0_1440,refute_0_1443]) ).

cnf(refute_0_1445,plain,
    ( inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))) != inverse(multiply(inverse(X_397),greatest_lower_bound(X_396,X_397)))
    | inverse(multiply(inverse(X_397),greatest_lower_bound(X_396,X_397))) != multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397)
    | inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))) = multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))))),bind(Y0,$fot(inverse(multiply(inverse(X_397),greatest_lower_bound(X_396,X_397))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397)))]]) ).

cnf(refute_0_1446,plain,
    ( inverse(multiply(inverse(X_397),greatest_lower_bound(X_396,X_397))) != multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397)
    | inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))) = multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))),inverse(multiply(inverse(X_397),greatest_lower_bound(X_396,X_397)))) )],[refute_0_1444,refute_0_1445]) ).

cnf(refute_0_1447,plain,
    inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))) = multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_397),greatest_lower_bound(X_396,X_397))),multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397)) )],[refute_0_1430,refute_0_1446]) ).

cnf(refute_0_1448,plain,
    multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)) = inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))),
    inference(subst,[],[refute_0_221:[bind(X,$fot(X_395)),bind(Y,$fot(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))))]]) ).

cnf(refute_0_1449,plain,
    ( multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)) != inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))))
    | inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))) != multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397)
    | multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)) = multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)))),bind(Y0,$fot(inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397)))]]) ).

cnf(refute_0_1450,plain,
    ( inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))) != multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397)
    | multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)) = multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)),inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))))) )],[refute_0_1448,refute_0_1449]) ).

cnf(refute_0_1451,plain,
    multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)) = multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_395,multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397)))),multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397)) )],[refute_0_1447,refute_0_1450]) ).

cnf(refute_0_1452,plain,
    ( multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)) != multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))) != multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))) = multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))),multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395))) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397))]]) ).

cnf(refute_0_1453,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))) != multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))) = multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395)),multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397)) )],[refute_0_1451,refute_0_1452]) ).

cnf(refute_0_1454,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))) != multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))) = multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))),multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395))) )],[refute_0_1429,refute_0_1453]) ).

cnf(refute_0_1455,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X_397),X_396))) = multiply(inverse(greatest_lower_bound(X_396,X_397)),X_397),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(inverse(X_395)),multiply(inverse(multiply(X_397,X_395)),X_396)))),multiply(inverse(multiply(inverse(multiply(X_397,X_395)),greatest_lower_bound(X_396,X_397))),inverse(X_395))) )],[refute_0_1386,refute_0_1454]) ).

cnf(refute_0_1456,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) = multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),
    inference(subst,[],[refute_0_1455:[bind(X_396,$fot(X_579)),bind(X_397,$fot(X_580))]]) ).

cnf(refute_0_1457,plain,
    ( inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) != multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) != multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)
    | inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) = multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)),multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) ),[0,0,0,1],$fot(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580))]]) ).

cnf(refute_0_1458,plain,
    ( inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) != multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) = multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)) )],[refute_0_1456,refute_0_1457]) ).

cnf(refute_0_1459,plain,
    inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) = multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)),multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) )],[refute_0_1355,refute_0_1458]) ).

cnf(refute_0_1460,plain,
    inverse(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))) = multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)),
    inference(subst,[],[refute_0_22:[bind(X,$fot(greatest_lower_bound(X_579,X_580))),bind(X_30,$fot(multiply(X_580,X_525)))]]) ).

cnf(refute_0_1461,plain,
    multiply(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),X_525) = multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(greatest_lower_bound(X_579,X_580)))),bind(Y,$fot(X_580)),bind(Z,$fot(X_525))]]) ).

cnf(refute_0_1462,plain,
    multiply(inverse(X),least_upper_bound(X_119,inverse(inverse(X)))) = least_upper_bound(identity,multiply(inverse(X),X_119)),
    inference(subst,[],[refute_0_184:[bind(X_115,$fot(inverse(X))),bind(X_116,$fot(X_119))]]) ).

cnf(refute_0_1463,plain,
    ( multiply(inverse(X),least_upper_bound(X_119,inverse(inverse(X)))) != least_upper_bound(identity,multiply(inverse(X),X_119))
    | inverse(inverse(X)) != X
    | multiply(inverse(X),least_upper_bound(X_119,X)) = least_upper_bound(identity,multiply(inverse(X),X_119)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X),least_upper_bound(X_119,inverse(inverse(X)))),least_upper_bound(identity,multiply(inverse(X),X_119))) ),[0,1,1],$fot(X)]]) ).

cnf(refute_0_1464,plain,
    ( multiply(inverse(X),least_upper_bound(X_119,inverse(inverse(X)))) != least_upper_bound(identity,multiply(inverse(X),X_119))
    | multiply(inverse(X),least_upper_bound(X_119,X)) = least_upper_bound(identity,multiply(inverse(X),X_119)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p11_2,refute_0_1463]) ).

cnf(refute_0_1465,plain,
    multiply(inverse(X),least_upper_bound(X_119,X)) = least_upper_bound(identity,multiply(inverse(X),X_119)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X),least_upper_bound(X_119,inverse(inverse(X)))),least_upper_bound(identity,multiply(inverse(X),X_119))) )],[refute_0_1462,refute_0_1464]) ).

cnf(refute_0_1466,plain,
    multiply(inverse(greatest_lower_bound(X_11,X_201)),least_upper_bound(X_201,greatest_lower_bound(X_11,X_201))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201)),
    inference(subst,[],[refute_0_1465:[bind(X,$fot(greatest_lower_bound(X_11,X_201))),bind(X_119,$fot(X_201))]]) ).

cnf(refute_0_1467,plain,
    least_upper_bound(X_201,greatest_lower_bound(X_11,X_201)) = X_201,
    inference(subst,[],[refute_0_71:[bind(X_10,$fot(X_201))]]) ).

cnf(refute_0_1468,plain,
    ( multiply(inverse(greatest_lower_bound(X_11,X_201)),least_upper_bound(X_201,greatest_lower_bound(X_11,X_201))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201))
    | least_upper_bound(X_201,greatest_lower_bound(X_11,X_201)) != X_201
    | multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_11,X_201)),least_upper_bound(X_201,greatest_lower_bound(X_11,X_201))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201))) ),[0,1],$fot(X_201)]]) ).

cnf(refute_0_1469,plain,
    ( multiply(inverse(greatest_lower_bound(X_11,X_201)),least_upper_bound(X_201,greatest_lower_bound(X_11,X_201))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201))
    | multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_201,greatest_lower_bound(X_11,X_201)),X_201) )],[refute_0_1467,refute_0_1468]) ).

cnf(refute_0_1470,plain,
    multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_11,X_201)),least_upper_bound(X_201,greatest_lower_bound(X_11,X_201))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201))) )],[refute_0_1466,refute_0_1469]) ).

cnf(refute_0_1471,plain,
    ( multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201))
    | least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201)) = multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201))))]]) ).

cnf(refute_0_1472,plain,
    least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201)) = multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_11,X_201)),X_201))) )],[refute_0_1470,refute_0_1471]) ).

cnf(refute_0_1473,plain,
    least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)) = multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),
    inference(subst,[],[refute_0_1472:[bind(X_11,$fot(X_579)),bind(X_201,$fot(X_580))]]) ).

cnf(refute_0_1474,plain,
    multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525) = multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525))]]) ).

cnf(refute_0_1475,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525) != multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)
    | least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)) != multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)
    | multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525) = multiply(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),X_525) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525),multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) ),[1,0],$fot(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580))]]) ).

cnf(refute_0_1476,plain,
    ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)) != multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)
    | multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525) = multiply(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),X_525) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525),multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) )],[refute_0_1474,refute_0_1475]) ).

cnf(refute_0_1477,plain,
    multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525) = multiply(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),X_525),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)) )],[refute_0_1473,refute_0_1476]) ).

cnf(refute_0_1478,plain,
    ( multiply(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),X_525) != multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))
    | multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525) != multiply(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),X_525)
    | multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525) = multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525))),bind(Y0,$fot(multiply(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),X_525))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))))]]) ).

cnf(refute_0_1479,plain,
    ( multiply(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),X_525) != multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))
    | multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525) = multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525),multiply(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),X_525)) )],[refute_0_1477,refute_0_1478]) ).

cnf(refute_0_1480,plain,
    multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525) = multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580),X_525),multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))) )],[refute_0_1461,refute_0_1479]) ).

cnf(refute_0_1481,plain,
    inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) = inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)),
    introduced(tautology,[refl,[$fot(inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)))]]) ).

cnf(refute_0_1482,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525) != multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))
    | inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) != inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525))
    | inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) = inverse(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)),inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525))) ),[1,0],$fot(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525)))]]) ).

cnf(refute_0_1483,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525) != multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))
    | inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) = inverse(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)),inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525))) )],[refute_0_1481,refute_0_1482]) ).

cnf(refute_0_1484,plain,
    inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) = inverse(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525),multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))) )],[refute_0_1480,refute_0_1483]) ).

cnf(refute_0_1485,plain,
    ( inverse(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))) != multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580))
    | inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) != inverse(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525)))
    | inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) = multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)))),bind(Y0,$fot(inverse(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))))),bind(Z0,$fot(multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580))))]]) ).

cnf(refute_0_1486,plain,
    ( inverse(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))) != multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580))
    | inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) = multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)),inverse(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525)))) )],[refute_0_1484,refute_0_1485]) ).

cnf(refute_0_1487,plain,
    inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) = multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(X_579,X_580)),multiply(X_580,X_525))),multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580))) )],[refute_0_1460,refute_0_1486]) ).

cnf(refute_0_1488,plain,
    ( inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) != multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580))
    | inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) != multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)) = multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)),multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) ),[0],$fot(multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)))]]) ).

cnf(refute_0_1489,plain,
    ( inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) != multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)) = multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)),multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580))) )],[refute_0_1487,refute_0_1488]) ).

cnf(refute_0_1490,plain,
    inverse(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525)) = multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),
    inference(subst,[],[refute_0_22:[bind(X,$fot(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),bind(X_30,$fot(X_525))]]) ).

cnf(refute_0_1491,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104)))) = inverse(greatest_lower_bound(identity,X_104)),
    inference(subst,[],[refute_0_71:[bind(X_10,$fot(inverse(greatest_lower_bound(identity,X_104)))),bind(X_11,$fot(identity))]]) ).

cnf(refute_0_1492,plain,
    multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_18))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18))),
    inference(subst,[],[refute_0_206:[bind(X_85,$fot(greatest_lower_bound(identity,X_18)))]]) ).

cnf(refute_0_1493,plain,
    greatest_lower_bound(identity,greatest_lower_bound(identity,X_18)) = greatest_lower_bound(identity,X_18),
    inference(subst,[],[refute_0_354:[bind(X_19,$fot(identity))]]) ).

cnf(refute_0_1494,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_18))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18)))
    | greatest_lower_bound(identity,greatest_lower_bound(identity,X_18)) != greatest_lower_bound(identity,X_18)
    | multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,X_18)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_18))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18)))) ),[0,1],$fot(greatest_lower_bound(identity,X_18))]]) ).

cnf(refute_0_1495,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_18))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18)))
    | multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,X_18)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,X_18)) )],[refute_0_1493,refute_0_1494]) ).

cnf(refute_0_1496,plain,
    multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,X_18)) = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,greatest_lower_bound(identity,X_18))),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18)))) )],[refute_0_1492,refute_0_1495]) ).

cnf(refute_0_1497,plain,
    multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,X_18)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(greatest_lower_bound(identity,X_18)))]]) ).

cnf(refute_0_1498,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,X_18)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18)))
    | multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,X_18)) != identity
    | identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18)))) ),[0],$fot(identity)]]) ).

cnf(refute_0_1499,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,X_18)) != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18)))
    | identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,X_18)),identity) )],[refute_0_1497,refute_0_1498]) ).

cnf(refute_0_1500,plain,
    identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,X_18)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_18)))) )],[refute_0_1496,refute_0_1499]) ).

cnf(refute_0_1501,plain,
    identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104))),
    inference(subst,[],[refute_0_1500:[bind(X_18,$fot(X_104))]]) ).

cnf(refute_0_1502,plain,
    ( identity != greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104)))
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104))) = identity ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104)))))]]) ).

cnf(refute_0_1503,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104))) = identity,
    inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104)))) )],[refute_0_1501,refute_0_1502]) ).

cnf(refute_0_1504,plain,
    ( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104))) != identity
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104)))) != inverse(greatest_lower_bound(identity,X_104))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),identity) = inverse(greatest_lower_bound(identity,X_104)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104)))),inverse(greatest_lower_bound(identity,X_104))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_1505,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104)))) != inverse(greatest_lower_bound(identity,X_104))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),identity) = inverse(greatest_lower_bound(identity,X_104)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104))),identity) )],[refute_0_1503,refute_0_1504]) ).

cnf(refute_0_1506,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),identity) = inverse(greatest_lower_bound(identity,X_104)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X_104)))),inverse(greatest_lower_bound(identity,X_104))) )],[refute_0_1491,refute_0_1505]) ).

cnf(refute_0_1507,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_104))),
    inference(subst,[],[refute_0_180:[bind(X,$fot(identity)),bind(Y,$fot(inverse(greatest_lower_bound(identity,X_104))))]]) ).

cnf(refute_0_1508,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),identity) != inverse(greatest_lower_bound(identity,X_104))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_104)))
    | least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_104))) = inverse(greatest_lower_bound(identity,X_104)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),identity),inverse(greatest_lower_bound(identity,X_104))) ),[0],$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_104))))]]) ).

cnf(refute_0_1509,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),identity) != inverse(greatest_lower_bound(identity,X_104))
    | least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_104))) = inverse(greatest_lower_bound(identity,X_104)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_104)))) )],[refute_0_1507,refute_0_1508]) ).

cnf(refute_0_1510,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_104))) = inverse(greatest_lower_bound(identity,X_104)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_104)),identity),inverse(greatest_lower_bound(identity,X_104))) )],[refute_0_1506,refute_0_1509]) ).

cnf(refute_0_1511,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) = inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),
    inference(subst,[],[refute_0_1510:[bind(X_104,$fot(multiply(inverse(X_580),X_579)))]]) ).

cnf(refute_0_1512,plain,
    multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525) = multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525))]]) ).

cnf(refute_0_1513,plain,
    ( multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525) != multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)
    | least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525),multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) ),[1,0],$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))))]]) ).

cnf(refute_0_1514,plain,
    ( least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) != inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525),multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) )],[refute_0_1512,refute_0_1513]) ).

cnf(refute_0_1515,plain,
    multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525) = multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) )],[refute_0_1511,refute_0_1514]) ).

cnf(refute_0_1516,plain,
    inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) = inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)),
    introduced(tautology,[refl,[$fot(inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)))]]) ).

cnf(refute_0_1517,plain,
    ( multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525)
    | inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) != inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525))
    | inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) = inverse(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)),inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525))) ),[1,0],$fot(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525))]]) ).

cnf(refute_0_1518,plain,
    ( multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525) != multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525)
    | inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) = inverse(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)),inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525))) )],[refute_0_1516,refute_0_1517]) ).

cnf(refute_0_1519,plain,
    inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) = inverse(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525),multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525)) )],[refute_0_1515,refute_0_1518]) ).

cnf(refute_0_1520,plain,
    ( inverse(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525)) != multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) != inverse(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525))
    | inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) = multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)))),bind(Y0,$fot(inverse(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525)))),bind(Z0,$fot(multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))))]]) ).

cnf(refute_0_1521,plain,
    ( inverse(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525)) != multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) = multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)),inverse(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525))) )],[refute_0_1519,refute_0_1520]) ).

cnf(refute_0_1522,plain,
    inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) = multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),X_525)),multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) )],[refute_0_1490,refute_0_1521]) ).

cnf(refute_0_1523,plain,
    ( inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525)) != multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144)
    | multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144) = inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525)))),bind(Y0,$fot(multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144)))]]) ).

cnf(refute_0_1524,plain,
    multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144) = inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525)),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(X_144)),X_525)),multiply(inverse(multiply(least_upper_bound(X_144,identity),X_525)),X_144)) )],[refute_0_1354,refute_0_1523]) ).

cnf(refute_0_1525,plain,
    multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) = inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)),
    inference(subst,[],[refute_0_1524:[bind(X_144,$fot(greatest_lower_bound(identity,multiply(inverse(X_580),X_579))))]]) ).

cnf(refute_0_1526,plain,
    ( multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) != inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525))
    | inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) != multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) = multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)))),bind(Z0,$fot(multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))))]]) ).

cnf(refute_0_1527,plain,
    ( inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)) != multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) = multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525))) )],[refute_0_1525,refute_0_1526]) ).

cnf(refute_0_1528,plain,
    multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) = multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))),X_525)),multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) )],[refute_0_1522,refute_0_1527]) ).

cnf(refute_0_1529,plain,
    ( multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)) != multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) != multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)) = multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)),multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) ),[0],$fot(multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))))]]) ).

cnf(refute_0_1530,plain,
    ( multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)) != multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)) = multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) )],[refute_0_1528,refute_0_1529]) ).

cnf(refute_0_1531,plain,
    ( inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)) != multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))
    | multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)) = multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)),multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) )],[refute_0_1489,refute_0_1530]) ).

cnf(refute_0_1532,plain,
    multiply(inverse(multiply(X_580,X_525)),greatest_lower_bound(X_579,X_580)) = multiply(inverse(X_525),greatest_lower_bound(identity,multiply(inverse(X_580),X_579))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_579,X_580)),X_580)),X_525)),multiply(inverse(multiply(least_upper_bound(greatest_lower_bound(identity,multiply(inverse(X_580),X_579)),identity),X_525)),greatest_lower_bound(identity,multiply(inverse(X_580),X_579)))) )],[refute_0_1459,refute_0_1531]) ).

cnf(refute_0_1533,plain,
    multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))),
    inference(subst,[],[refute_0_1532:[bind(X_525,$fot(X_395)),bind(X_579,$fot(X_396)),bind(X_580,$fot(least_upper_bound(X_121,X_122)))]]) ).

cnf(refute_0_1534,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) != multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396)))
    | multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396))
    | multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396))) ),[0],$fot(multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))))]]) ).

cnf(refute_0_1535,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396))
    | multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))),multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396)))) )],[refute_0_1533,refute_0_1534]) ).

cnf(refute_0_1536,plain,
    multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396))) )],[refute_0_1346,refute_0_1535]) ).

cnf(refute_0_1537,plain,
    ( multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396))
    | greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396)) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))))),bind(Y0,$fot(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396))))]]) ).

cnf(refute_0_1538,plain,
    greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396)) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),X_396))) )],[refute_0_1536,refute_0_1537]) ).

cnf(refute_0_1539,plain,
    greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396)) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_23,X_15)),X_396))),
    inference(subst,[],[refute_0_1538:[bind(X_121,$fot(X_23)),bind(X_122,$fot(X_15))]]) ).

cnf(refute_0_1540,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396))
    | greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396)) != multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_23,X_15)),X_396)))
    | multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_23,X_15)),X_396))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))),multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_23,X_15)),X_396)))) ),[0],$fot(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396)))]]) ).

cnf(refute_0_1541,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396))
    | multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_23,X_15)),X_396))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396)),multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_23,X_15)),X_396)))) )],[refute_0_1539,refute_0_1540]) ).

cnf(refute_0_1542,plain,
    multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_23,X_15)),X_396))),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_23,X_15))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_15,X_23),X_395)),X_396))) )],[refute_0_1343,refute_0_1541]) ).

cnf(refute_0_1543,plain,
    multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))),
    inference(subst,[],[refute_0_1542:[bind(X_15,$fot(X_122)),bind(X_23,$fot(X_121))]]) ).

cnf(refute_0_1544,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) != multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396)))
    | multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))
    | multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))) ),[0],$fot(multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))))]]) ).

cnf(refute_0_1545,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))
    | multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) = greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))),multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396)))) )],[refute_0_1543,refute_0_1544]) ).

cnf(refute_0_1546,plain,
    greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396)) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396))),
    inference(subst,[],[refute_0_1538:[bind(X_121,$fot(X_122)),bind(X_122,$fot(X_121))]]) ).

cnf(refute_0_1547,plain,
    ( multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))
    | greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396)) != multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396)))
    | multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))),multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396)))) ),[0],$fot(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396)))]]) ).

cnf(refute_0_1548,plain,
    ( multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))
    | multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396)),multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396)))) )],[refute_0_1546,refute_0_1547]) ).

cnf(refute_0_1549,plain,
    ( multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))) != greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))
    | multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))) )],[refute_0_1545,refute_0_1548]) ).

cnf(refute_0_1550,plain,
    multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396))),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(X_122,X_121),X_395)),greatest_lower_bound(X_396,least_upper_bound(X_121,X_122))),greatest_lower_bound(inverse(X_395),multiply(inverse(multiply(least_upper_bound(X_121,X_122),X_395)),X_396))) )],[refute_0_1314,refute_0_1549]) ).

cnf(refute_0_1551,plain,
    ( multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) != multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396)))
    | multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396))) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))))),bind(Y0,$fot(multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396)))))]]) ).

cnf(refute_0_1552,plain,
    multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396))) = multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_121,X_122)),X_396))),multiply(inverse(X_395),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_122,X_121)),X_396)))) )],[refute_0_1550,refute_0_1551]) ).

cnf(refute_0_1553,plain,
    multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_612),identity)),least_upper_bound(X_612,identity)))) = multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))),
    inference(subst,[],[refute_0_1552:[bind(X_121,$fot(identity)),bind(X_122,$fot(inverse(X_612))),bind(X_395,$fot(X_70)),bind(X_396,$fot(least_upper_bound(X_612,identity)))]]) ).

cnf(refute_0_1554,plain,
    greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) = multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_612),identity)),least_upper_bound(X_612,identity)))),
    inference(subst,[],[refute_0_1538:[bind(X_121,$fot(inverse(X_612))),bind(X_122,$fot(identity)),bind(X_395,$fot(X_70)),bind(X_396,$fot(least_upper_bound(X_612,identity)))]]) ).

cnf(refute_0_1555,plain,
    ( multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_612),identity)),least_upper_bound(X_612,identity)))) != multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))))
    | greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) != multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_612),identity)),least_upper_bound(X_612,identity))))
    | greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) = multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))))),bind(Y0,$fot(multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_612),identity)),least_upper_bound(X_612,identity)))))),bind(Z0,$fot(multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))))))]]) ).

cnf(refute_0_1556,plain,
    ( multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_612),identity)),least_upper_bound(X_612,identity)))) != multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))))
    | greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) = multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))),multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_612),identity)),least_upper_bound(X_612,identity))))) )],[refute_0_1554,refute_0_1555]) ).

cnf(refute_0_1557,plain,
    greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) = multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(inverse(X_612),identity)),least_upper_bound(X_612,identity)))),multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))))) )],[refute_0_1553,refute_0_1556]) ).

cnf(refute_0_1558,plain,
    ( multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))) != multiply(inverse(X_70),greatest_lower_bound(identity,X_612))
    | greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) != multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))))
    | greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))))),bind(Y0,$fot(multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))))),bind(Z0,$fot(multiply(inverse(X_70),greatest_lower_bound(identity,X_612))))]]) ).

cnf(refute_0_1559,plain,
    ( multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))) != multiply(inverse(X_70),greatest_lower_bound(identity,X_612))
    | greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))),multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity))))) )],[refute_0_1557,refute_0_1558]) ).

cnf(refute_0_1560,plain,
    greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_70),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_612))),least_upper_bound(X_612,identity)))),multiply(inverse(X_70),greatest_lower_bound(identity,X_612))) )],[refute_0_1274,refute_0_1559]) ).

cnf(refute_0_1561,plain,
    ( multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) != greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity)))
    | greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))) != multiply(inverse(X_70),greatest_lower_bound(identity,X_612))
    | multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))),multiply(inverse(X_70),greatest_lower_bound(identity,X_612))) ),[0],$fot(greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))))]]) ).

cnf(refute_0_1562,plain,
    ( multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) != greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity)))
    | multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity))),multiply(inverse(X_70),greatest_lower_bound(identity,X_612))) )],[refute_0_1560,refute_0_1561]) ).

cnf(refute_0_1563,plain,
    multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))),greatest_lower_bound(inverse(X_70),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),least_upper_bound(X_612,identity)))) )],[refute_0_1265,refute_0_1562]) ).

cnf(refute_0_1564,plain,
    multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),identity) = inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),
    inference(subst,[],[refute_0_942:[bind(X,$fot(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70))))]]) ).

cnf(refute_0_1565,plain,
    least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,greatest_lower_bound(least_upper_bound(X_60,X_11),X_62))) = greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),
    inference(subst,[],[refute_0_71:[bind(X_10,$fot(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)))]]) ).

cnf(refute_0_1566,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(least_upper_bound(X_15,X_33),X_35)) = greatest_lower_bound(greatest_lower_bound(X_33,least_upper_bound(X_15,X_33)),X_35),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_33)),bind(Y,$fot(least_upper_bound(X_15,X_33))),bind(Z,$fot(X_35))]]) ).

cnf(refute_0_1567,plain,
    greatest_lower_bound(X_33,least_upper_bound(X_15,X_33)) = X_33,
    inference(subst,[],[refute_0_336:[bind(X_14,$fot(X_33))]]) ).

cnf(refute_0_1568,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(least_upper_bound(X_15,X_33),X_35)) != greatest_lower_bound(greatest_lower_bound(X_33,least_upper_bound(X_15,X_33)),X_35)
    | greatest_lower_bound(X_33,least_upper_bound(X_15,X_33)) != X_33
    | greatest_lower_bound(X_33,greatest_lower_bound(least_upper_bound(X_15,X_33),X_35)) = greatest_lower_bound(X_33,X_35) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(least_upper_bound(X_15,X_33),X_35)),greatest_lower_bound(greatest_lower_bound(X_33,least_upper_bound(X_15,X_33)),X_35)) ),[1,0],$fot(X_33)]]) ).

cnf(refute_0_1569,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(least_upper_bound(X_15,X_33),X_35)) != greatest_lower_bound(greatest_lower_bound(X_33,least_upper_bound(X_15,X_33)),X_35)
    | greatest_lower_bound(X_33,greatest_lower_bound(least_upper_bound(X_15,X_33),X_35)) = greatest_lower_bound(X_33,X_35) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,least_upper_bound(X_15,X_33)),X_33) )],[refute_0_1567,refute_0_1568]) ).

cnf(refute_0_1570,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(least_upper_bound(X_15,X_33),X_35)) = greatest_lower_bound(X_33,X_35),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(least_upper_bound(X_15,X_33),X_35)),greatest_lower_bound(greatest_lower_bound(X_33,least_upper_bound(X_15,X_33)),X_35)) )],[refute_0_1566,refute_0_1569]) ).

cnf(refute_0_1571,plain,
    greatest_lower_bound(X_11,greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)) = greatest_lower_bound(X_11,X_62),
    inference(subst,[],[refute_0_1570:[bind(X_15,$fot(X_60)),bind(X_33,$fot(X_11)),bind(X_35,$fot(X_62))]]) ).

cnf(refute_0_1572,plain,
    ( greatest_lower_bound(X_11,greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)) != greatest_lower_bound(X_11,X_62)
    | least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,greatest_lower_bound(least_upper_bound(X_60,X_11),X_62))) != greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)
    | least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,X_62)) = greatest_lower_bound(least_upper_bound(X_60,X_11),X_62) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,greatest_lower_bound(least_upper_bound(X_60,X_11),X_62))),greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)) ),[0,1],$fot(greatest_lower_bound(X_11,X_62))]]) ).

cnf(refute_0_1573,plain,
    ( least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,greatest_lower_bound(least_upper_bound(X_60,X_11),X_62))) != greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)
    | least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,X_62)) = greatest_lower_bound(least_upper_bound(X_60,X_11),X_62) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)),greatest_lower_bound(X_11,X_62)) )],[refute_0_1571,refute_0_1572]) ).

cnf(refute_0_1574,plain,
    least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,X_62)) = greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,greatest_lower_bound(least_upper_bound(X_60,X_11),X_62))),greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)) )],[refute_0_1565,refute_0_1573]) ).

cnf(refute_0_1575,plain,
    least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,X_62)) = least_upper_bound(greatest_lower_bound(X_11,X_62),greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)),
    inference(subst,[],[refute_0_180:[bind(X,$fot(greatest_lower_bound(X_11,X_62))),bind(Y,$fot(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)))]]) ).

cnf(refute_0_1576,plain,
    ( least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,X_62)) != greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)
    | least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,X_62)) != least_upper_bound(greatest_lower_bound(X_11,X_62),greatest_lower_bound(least_upper_bound(X_60,X_11),X_62))
    | least_upper_bound(greatest_lower_bound(X_11,X_62),greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)) = greatest_lower_bound(least_upper_bound(X_60,X_11),X_62) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,X_62)),greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_11,X_62),greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)))]]) ).

cnf(refute_0_1577,plain,
    ( least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,X_62)) != greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)
    | least_upper_bound(greatest_lower_bound(X_11,X_62),greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)) = greatest_lower_bound(least_upper_bound(X_60,X_11),X_62) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,X_62)),least_upper_bound(greatest_lower_bound(X_11,X_62),greatest_lower_bound(least_upper_bound(X_60,X_11),X_62))) )],[refute_0_1575,refute_0_1576]) ).

cnf(refute_0_1578,plain,
    least_upper_bound(greatest_lower_bound(X_11,X_62),greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)) = greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(least_upper_bound(X_60,X_11),X_62),greatest_lower_bound(X_11,X_62)),greatest_lower_bound(least_upper_bound(X_60,X_11),X_62)) )],[refute_0_1574,refute_0_1577]) ).

cnf(refute_0_1579,plain,
    least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))) = greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))),
    inference(subst,[],[refute_0_1578:[bind(X_11,$fot(identity)),bind(X_62,$fot(least_upper_bound(identity,inverse(X_60))))]]) ).

cnf(refute_0_1580,plain,
    multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))) = greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))),
    inference(subst,[],[refute_0_1259:[bind(X_129,$fot(X_60))]]) ).

cnf(refute_0_1581,plain,
    ( multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))) != greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))
    | greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))) = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))))]]) ).

cnf(refute_0_1582,plain,
    greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))) = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))),greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))) )],[refute_0_1580,refute_0_1581]) ).

cnf(refute_0_1583,plain,
    ( greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))) != multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))
    | least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))) != greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))
    | least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))),greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))) ),[0,1],$fot(multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))))]]) ).

cnf(refute_0_1584,plain,
    ( least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))) != greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))
    | least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) )],[refute_0_1582,refute_0_1583]) ).

cnf(refute_0_1585,plain,
    least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))),greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))) )],[refute_0_1579,refute_0_1584]) ).

cnf(refute_0_1586,plain,
    least_upper_bound(identity,greatest_lower_bound(identity,X_60)) = identity,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_60))]]) ).

cnf(refute_0_1587,plain,
    multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) = least_upper_bound(X_115,multiply(X_115,least_upper_bound(inverse(X_115),X_176))),
    inference(subst,[],[refute_0_241:[bind(X_116,$fot(least_upper_bound(inverse(X_115),X_176)))]]) ).

cnf(refute_0_1588,plain,
    multiply(X_115,least_upper_bound(inverse(X_115),X_117)) = least_upper_bound(multiply(X_115,inverse(X_115)),multiply(X_115,X_117)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_115)),bind(Y,$fot(inverse(X_115))),bind(Z,$fot(X_117))]]) ).

cnf(refute_0_1589,plain,
    ( multiply(X_115,inverse(X_115)) != identity
    | multiply(X_115,least_upper_bound(inverse(X_115),X_117)) != least_upper_bound(multiply(X_115,inverse(X_115)),multiply(X_115,X_117))
    | multiply(X_115,least_upper_bound(inverse(X_115),X_117)) = least_upper_bound(identity,multiply(X_115,X_117)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_115,least_upper_bound(inverse(X_115),X_117)),least_upper_bound(multiply(X_115,inverse(X_115)),multiply(X_115,X_117))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1590,plain,
    ( multiply(X_115,least_upper_bound(inverse(X_115),X_117)) != least_upper_bound(multiply(X_115,inverse(X_115)),multiply(X_115,X_117))
    | multiply(X_115,least_upper_bound(inverse(X_115),X_117)) = least_upper_bound(identity,multiply(X_115,X_117)) ),
    inference(resolve,[$cnf( $equal(multiply(X_115,inverse(X_115)),identity) )],[refute_0_175,refute_0_1589]) ).

cnf(refute_0_1591,plain,
    multiply(X_115,least_upper_bound(inverse(X_115),X_117)) = least_upper_bound(identity,multiply(X_115,X_117)),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(inverse(X_115),X_117)),least_upper_bound(multiply(X_115,inverse(X_115)),multiply(X_115,X_117))) )],[refute_0_1588,refute_0_1590]) ).

cnf(refute_0_1592,plain,
    multiply(X_115,least_upper_bound(inverse(X_115),X_176)) = least_upper_bound(identity,multiply(X_115,X_176)),
    inference(subst,[],[refute_0_1591:[bind(X_117,$fot(X_176))]]) ).

cnf(refute_0_1593,plain,
    ( multiply(X_115,least_upper_bound(inverse(X_115),X_176)) != least_upper_bound(identity,multiply(X_115,X_176))
    | multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) != least_upper_bound(X_115,multiply(X_115,least_upper_bound(inverse(X_115),X_176)))
    | multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) = least_upper_bound(X_115,least_upper_bound(identity,multiply(X_115,X_176))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)),least_upper_bound(X_115,multiply(X_115,least_upper_bound(inverse(X_115),X_176)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_115,X_176)))]]) ).

cnf(refute_0_1594,plain,
    ( multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) != least_upper_bound(X_115,multiply(X_115,least_upper_bound(inverse(X_115),X_176)))
    | multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) = least_upper_bound(X_115,least_upper_bound(identity,multiply(X_115,X_176))) ),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(inverse(X_115),X_176)),least_upper_bound(identity,multiply(X_115,X_176))) )],[refute_0_1592,refute_0_1593]) ).

cnf(refute_0_1595,plain,
    multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) = least_upper_bound(X_115,least_upper_bound(identity,multiply(X_115,X_176))),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)),least_upper_bound(X_115,multiply(X_115,least_upper_bound(inverse(X_115),X_176)))) )],[refute_0_1587,refute_0_1594]) ).

cnf(refute_0_1596,plain,
    multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) = least_upper_bound(multiply(X,least_upper_bound(X_119,inverse(X))),multiply(X,Z)),
    inference(subst,[],[monotony_lub1:[bind(Y,$fot(least_upper_bound(X_119,inverse(X))))]]) ).

cnf(refute_0_1597,plain,
    ( multiply(X,least_upper_bound(X_119,inverse(X))) != least_upper_bound(identity,multiply(X,X_119))
    | multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) != least_upper_bound(multiply(X,least_upper_bound(X_119,inverse(X))),multiply(X,Z))
    | multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)),least_upper_bound(multiply(X,least_upper_bound(X_119,inverse(X))),multiply(X,Z))) ),[1,0],$fot(least_upper_bound(identity,multiply(X,X_119)))]]) ).

cnf(refute_0_1598,plain,
    ( multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) != least_upper_bound(multiply(X,least_upper_bound(X_119,inverse(X))),multiply(X,Z))
    | multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_119,inverse(X))),least_upper_bound(identity,multiply(X,X_119))) )],[refute_0_185,refute_0_1597]) ).

cnf(refute_0_1599,plain,
    multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)),least_upper_bound(multiply(X,least_upper_bound(X_119,inverse(X))),multiply(X,Z))) )],[refute_0_1596,refute_0_1598]) ).

cnf(refute_0_1600,plain,
    least_upper_bound(least_upper_bound(X_119,inverse(X)),Z) = least_upper_bound(X_119,least_upper_bound(inverse(X),Z)),
    inference(subst,[],[refute_0_405:[bind(X,$fot(X_119)),bind(Y,$fot(inverse(X)))]]) ).

cnf(refute_0_1601,plain,
    multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) = multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)),
    introduced(tautology,[refl,[$fot(multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)))]]) ).

cnf(refute_0_1602,plain,
    ( multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) != multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z))
    | least_upper_bound(least_upper_bound(X_119,inverse(X)),Z) != least_upper_bound(X_119,least_upper_bound(inverse(X),Z))
    | multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) = multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)),multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z))) ),[1,1],$fot(least_upper_bound(X_119,least_upper_bound(inverse(X),Z)))]]) ).

cnf(refute_0_1603,plain,
    ( least_upper_bound(least_upper_bound(X_119,inverse(X)),Z) != least_upper_bound(X_119,least_upper_bound(inverse(X),Z))
    | multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) = multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))) ),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)),multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z))) )],[refute_0_1601,refute_0_1602]) ).

cnf(refute_0_1604,plain,
    multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) = multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_119,inverse(X)),Z),least_upper_bound(X_119,least_upper_bound(inverse(X),Z))) )],[refute_0_1600,refute_0_1603]) ).

cnf(refute_0_1605,plain,
    ( multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) != multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z)))
    | multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z))
    | multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))) = least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z))) ),[0],$fot(multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))))]]) ).

cnf(refute_0_1606,plain,
    ( multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z))
    | multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))) = least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)),multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z)))) )],[refute_0_1604,refute_0_1605]) ).

cnf(refute_0_1607,plain,
    least_upper_bound(multiply(X,X_119),multiply(X,Z)) = multiply(X,least_upper_bound(X_119,Z)),
    inference(subst,[],[refute_0_1174:[bind(Y,$fot(X_119))]]) ).

cnf(refute_0_1608,plain,
    least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))) = least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))))]]) ).

cnf(refute_0_1609,plain,
    ( least_upper_bound(multiply(X,X_119),multiply(X,Z)) != multiply(X,least_upper_bound(X_119,Z))
    | least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))) != least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z)))
    | least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))),least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z)))) ),[1,1],$fot(multiply(X,least_upper_bound(X_119,Z)))]]) ).

cnf(refute_0_1610,plain,
    ( least_upper_bound(multiply(X,X_119),multiply(X,Z)) != multiply(X,least_upper_bound(X_119,Z))
    | least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))),least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z)))) )],[refute_0_1608,refute_0_1609]) ).

cnf(refute_0_1611,plain,
    least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,X_119),multiply(X,Z)),multiply(X,least_upper_bound(X_119,Z))) )],[refute_0_1607,refute_0_1610]) ).

cnf(refute_0_1612,plain,
    least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)) = least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))),
    inference(subst,[],[refute_0_405:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X,X_119))),bind(Z,$fot(multiply(X,Z)))]]) ).

cnf(refute_0_1613,plain,
    ( least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))) != least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z)))
    | least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)) != least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z)))
    | least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z)))))]]) ).

cnf(refute_0_1614,plain,
    ( least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))) != least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z)))
    | least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)),least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z)))) )],[refute_0_1612,refute_0_1613]) ).

cnf(refute_0_1615,plain,
    least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)) = least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X,X_119),multiply(X,Z))),least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z)))) )],[refute_0_1611,refute_0_1614]) ).

cnf(refute_0_1616,plain,
    ( multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))) != least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z))
    | least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)) != least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z)))
    | multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))),least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z)))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)))]]) ).

cnf(refute_0_1617,plain,
    ( multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))) != least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z))
    | multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z)),least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z)))) )],[refute_0_1615,refute_0_1616]) ).

cnf(refute_0_1618,plain,
    ( multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z))
    | multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z))) ),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))),least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z))) )],[refute_0_1606,refute_0_1617]) ).

cnf(refute_0_1619,plain,
    multiply(X,least_upper_bound(X_119,least_upper_bound(inverse(X),Z))) = least_upper_bound(identity,multiply(X,least_upper_bound(X_119,Z))),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(least_upper_bound(X_119,inverse(X)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X,X_119)),multiply(X,Z))) )],[refute_0_1599,refute_0_1618]) ).

cnf(refute_0_1620,plain,
    multiply(X_115,least_upper_bound(identity,least_upper_bound(inverse(X_115),X_176))) = least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176))),
    inference(subst,[],[refute_0_1619:[bind(X,$fot(X_115)),bind(Z,$fot(X_176)),bind(X_119,$fot(identity))]]) ).

cnf(refute_0_1621,plain,
    multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) = multiply(X_115,least_upper_bound(identity,least_upper_bound(inverse(X_115),X_176))),
    inference(subst,[],[refute_0_693:[bind(X_15,$fot(least_upper_bound(inverse(X_115),X_176))),bind(X_152,$fot(X_115)),bind(X_23,$fot(identity))]]) ).

cnf(refute_0_1622,plain,
    ( multiply(X_115,least_upper_bound(identity,least_upper_bound(inverse(X_115),X_176))) != least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176)))
    | multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) != multiply(X_115,least_upper_bound(identity,least_upper_bound(inverse(X_115),X_176)))
    | multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) = least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)))),bind(Y0,$fot(multiply(X_115,least_upper_bound(identity,least_upper_bound(inverse(X_115),X_176))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176)))))]]) ).

cnf(refute_0_1623,plain,
    ( multiply(X_115,least_upper_bound(identity,least_upper_bound(inverse(X_115),X_176))) != least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176)))
    | multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) = least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176))) ),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)),multiply(X_115,least_upper_bound(identity,least_upper_bound(inverse(X_115),X_176)))) )],[refute_0_1621,refute_0_1622]) ).

cnf(refute_0_1624,plain,
    multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) = least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176))),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(identity,least_upper_bound(inverse(X_115),X_176))),least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176)))) )],[refute_0_1620,refute_0_1623]) ).

cnf(refute_0_1625,plain,
    ( multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) != least_upper_bound(X_115,least_upper_bound(identity,multiply(X_115,X_176)))
    | multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) != least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176)))
    | least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176))) = least_upper_bound(X_115,least_upper_bound(identity,multiply(X_115,X_176))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)),least_upper_bound(X_115,least_upper_bound(identity,multiply(X_115,X_176)))) ),[0],$fot(least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176))))]]) ).

cnf(refute_0_1626,plain,
    ( multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)) != least_upper_bound(X_115,least_upper_bound(identity,multiply(X_115,X_176)))
    | least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176))) = least_upper_bound(X_115,least_upper_bound(identity,multiply(X_115,X_176))) ),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)),least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176)))) )],[refute_0_1624,refute_0_1625]) ).

cnf(refute_0_1627,plain,
    least_upper_bound(identity,multiply(X_115,least_upper_bound(identity,X_176))) = least_upper_bound(X_115,least_upper_bound(identity,multiply(X_115,X_176))),
    inference(resolve,[$cnf( $equal(multiply(X_115,least_upper_bound(least_upper_bound(inverse(X_115),X_176),identity)),least_upper_bound(X_115,least_upper_bound(identity,multiply(X_115,X_176)))) )],[refute_0_1595,refute_0_1626]) ).

cnf(refute_0_1628,plain,
    least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))) = least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)))),
    inference(subst,[],[refute_0_1627:[bind(X_115,$fot(greatest_lower_bound(X_88,X_89))),bind(X_176,$fot(inverse(X_89)))]]) ).

cnf(refute_0_1629,plain,
    ( multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)) != greatest_lower_bound(identity,multiply(X_88,inverse(X_89)))
    | least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))) != least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),inverse(X_89))))
    | least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))) = least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))),least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),inverse(X_89))))) ),[1,1,1],$fot(greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))]]) ).

cnf(refute_0_1630,plain,
    ( least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))) != least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),inverse(X_89))))
    | least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))) = least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_88,X_89),inverse(X_89)),greatest_lower_bound(identity,multiply(X_88,inverse(X_89)))) )],[refute_0_280,refute_0_1629]) ).

cnf(refute_0_1631,plain,
    least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))) = least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))),least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),inverse(X_89))))) )],[refute_0_1628,refute_0_1630]) ).

cnf(refute_0_1632,plain,
    X_68 = multiply(inverse(least_upper_bound(inverse(X_68),X_188)),multiply(least_upper_bound(inverse(X_68),X_188),X_68)),
    inference(subst,[],[refute_0_9:[bind(X_67,$fot(least_upper_bound(inverse(X_68),X_188)))]]) ).

cnf(refute_0_1633,plain,
    multiply(least_upper_bound(inverse(X_120),X_122),X_120) = least_upper_bound(multiply(inverse(X_120),X_120),multiply(X_122,X_120)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_120)),bind(Y,$fot(inverse(X_120))),bind(Z,$fot(X_122))]]) ).

cnf(refute_0_1634,plain,
    multiply(inverse(X_120),X_120) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_120))]]) ).

cnf(refute_0_1635,plain,
    ( multiply(inverse(X_120),X_120) != identity
    | multiply(least_upper_bound(inverse(X_120),X_122),X_120) != least_upper_bound(multiply(inverse(X_120),X_120),multiply(X_122,X_120))
    | multiply(least_upper_bound(inverse(X_120),X_122),X_120) = least_upper_bound(identity,multiply(X_122,X_120)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_120),X_122),X_120),least_upper_bound(multiply(inverse(X_120),X_120),multiply(X_122,X_120))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1636,plain,
    ( multiply(least_upper_bound(inverse(X_120),X_122),X_120) != least_upper_bound(multiply(inverse(X_120),X_120),multiply(X_122,X_120))
    | multiply(least_upper_bound(inverse(X_120),X_122),X_120) = least_upper_bound(identity,multiply(X_122,X_120)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_120),X_120),identity) )],[refute_0_1634,refute_0_1635]) ).

cnf(refute_0_1637,plain,
    multiply(least_upper_bound(inverse(X_120),X_122),X_120) = least_upper_bound(identity,multiply(X_122,X_120)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_120),X_122),X_120),least_upper_bound(multiply(inverse(X_120),X_120),multiply(X_122,X_120))) )],[refute_0_1633,refute_0_1636]) ).

cnf(refute_0_1638,plain,
    multiply(least_upper_bound(inverse(X_68),X_188),X_68) = least_upper_bound(identity,multiply(X_188,X_68)),
    inference(subst,[],[refute_0_1637:[bind(X_120,$fot(X_68)),bind(X_122,$fot(X_188))]]) ).

cnf(refute_0_1639,plain,
    ( X_68 != multiply(inverse(least_upper_bound(inverse(X_68),X_188)),multiply(least_upper_bound(inverse(X_68),X_188),X_68))
    | multiply(least_upper_bound(inverse(X_68),X_188),X_68) != least_upper_bound(identity,multiply(X_188,X_68))
    | X_68 = multiply(inverse(least_upper_bound(inverse(X_68),X_188)),least_upper_bound(identity,multiply(X_188,X_68))) ),
    introduced(tautology,[equality,[$cnf( $equal(X_68,multiply(inverse(least_upper_bound(inverse(X_68),X_188)),multiply(least_upper_bound(inverse(X_68),X_188),X_68))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_188,X_68)))]]) ).

cnf(refute_0_1640,plain,
    ( X_68 != multiply(inverse(least_upper_bound(inverse(X_68),X_188)),multiply(least_upper_bound(inverse(X_68),X_188),X_68))
    | X_68 = multiply(inverse(least_upper_bound(inverse(X_68),X_188)),least_upper_bound(identity,multiply(X_188,X_68))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_68),X_188),X_68),least_upper_bound(identity,multiply(X_188,X_68))) )],[refute_0_1638,refute_0_1639]) ).

cnf(refute_0_1641,plain,
    X_68 = multiply(inverse(least_upper_bound(inverse(X_68),X_188)),least_upper_bound(identity,multiply(X_188,X_68))),
    inference(resolve,[$cnf( $equal(X_68,multiply(inverse(least_upper_bound(inverse(X_68),X_188)),multiply(least_upper_bound(inverse(X_68),X_188),X_68))) )],[refute_0_1632,refute_0_1640]) ).

cnf(refute_0_1642,plain,
    least_upper_bound(X_143,identity) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(X_143,identity)))),
    inference(subst,[],[refute_0_1641:[bind(X_188,$fot(X_243)),bind(X_68,$fot(least_upper_bound(X_143,identity)))]]) ).

cnf(refute_0_1643,plain,
    multiply(X_243,least_upper_bound(identity,X_143)) = multiply(X_243,least_upper_bound(X_143,identity)),
    inference(subst,[],[refute_0_1229:[bind(X_22,$fot(X_243))]]) ).

cnf(refute_0_1644,plain,
    ( multiply(X_243,least_upper_bound(identity,X_143)) != multiply(X_243,least_upper_bound(X_143,identity))
    | multiply(X_243,least_upper_bound(X_143,identity)) = multiply(X_243,least_upper_bound(identity,X_143)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_243,least_upper_bound(identity,X_143)))),bind(Y0,$fot(multiply(X_243,least_upper_bound(X_143,identity))))]]) ).

cnf(refute_0_1645,plain,
    multiply(X_243,least_upper_bound(X_143,identity)) = multiply(X_243,least_upper_bound(identity,X_143)),
    inference(resolve,[$cnf( $equal(multiply(X_243,least_upper_bound(identity,X_143)),multiply(X_243,least_upper_bound(X_143,identity))) )],[refute_0_1643,refute_0_1644]) ).

cnf(refute_0_1646,plain,
    ( multiply(X_243,least_upper_bound(X_143,identity)) != multiply(X_243,least_upper_bound(identity,X_143))
    | least_upper_bound(X_143,identity) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(X_143,identity))))
    | least_upper_bound(X_143,identity) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(identity,X_143)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_143,identity),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(X_143,identity))))) ),[1,1,1],$fot(multiply(X_243,least_upper_bound(identity,X_143)))]]) ).

cnf(refute_0_1647,plain,
    ( least_upper_bound(X_143,identity) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(X_143,identity))))
    | least_upper_bound(X_143,identity) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(identity,X_143)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_243,least_upper_bound(X_143,identity)),multiply(X_243,least_upper_bound(identity,X_143))) )],[refute_0_1645,refute_0_1646]) ).

cnf(refute_0_1648,plain,
    least_upper_bound(X_143,identity) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(identity,X_143)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_143,identity),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(X_143,identity))))) )],[refute_0_1642,refute_0_1647]) ).

cnf(refute_0_1649,plain,
    least_upper_bound(X_270,X_269) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_270,X_269)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269)))),
    inference(subst,[],[refute_0_1641:[bind(X_68,$fot(least_upper_bound(X_270,X_269)))]]) ).

cnf(refute_0_1650,plain,
    inverse(least_upper_bound(X_139,X_138)) = multiply(inverse(least_upper_bound(X_138,X_139)),inverse(multiply(least_upper_bound(X_139,X_138),inverse(least_upper_bound(X_138,X_139))))),
    inference(subst,[],[refute_0_172:[bind(X,$fot(least_upper_bound(X_139,X_138))),bind(X_69,$fot(inverse(least_upper_bound(X_138,X_139))))]]) ).

cnf(refute_0_1651,plain,
    multiply(greatest_lower_bound(least_upper_bound(X_137,X_136),least_upper_bound(X_136,X_137)),inverse(least_upper_bound(X_136,X_137))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137)))),
    inference(subst,[],[refute_0_280:[bind(X_88,$fot(least_upper_bound(X_137,X_136))),bind(X_89,$fot(least_upper_bound(X_136,X_137)))]]) ).

cnf(refute_0_1652,plain,
    greatest_lower_bound(least_upper_bound(X_137,X_136),least_upper_bound(X_136,X_137)) = least_upper_bound(X_137,X_136),
    inference(subst,[],[refute_0_413:[bind(X_15,$fot(X_136)),bind(X_23,$fot(X_137))]]) ).

cnf(refute_0_1653,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(X_137,X_136),least_upper_bound(X_136,X_137)),inverse(least_upper_bound(X_136,X_137))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))))
    | greatest_lower_bound(least_upper_bound(X_137,X_136),least_upper_bound(X_136,X_137)) != least_upper_bound(X_137,X_136)
    | multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_137,X_136),least_upper_bound(X_136,X_137)),inverse(least_upper_bound(X_136,X_137))),greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))))) ),[0,0],$fot(least_upper_bound(X_137,X_136))]]) ).

cnf(refute_0_1654,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(X_137,X_136),least_upper_bound(X_136,X_137)),inverse(least_upper_bound(X_136,X_137))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))))
    | multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_137,X_136),least_upper_bound(X_136,X_137)),least_upper_bound(X_137,X_136)) )],[refute_0_1652,refute_0_1653]) ).

cnf(refute_0_1655,plain,
    multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_137,X_136),least_upper_bound(X_136,X_137)),inverse(least_upper_bound(X_136,X_137))),greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))))) )],[refute_0_1651,refute_0_1654]) ).

cnf(refute_0_1656,plain,
    multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))) = greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))),
    inference(subst,[],[refute_0_39:[bind(X_79,$fot(least_upper_bound(X_125,X_126))),bind(X_80,$fot(inverse(X_126)))]]) ).

cnf(refute_0_1657,plain,
    multiply(least_upper_bound(X_125,X_126),inverse(X_126)) = least_upper_bound(identity,multiply(X_125,inverse(X_126))),
    inference(subst,[],[refute_0_152:[bind(X_121,$fot(X_125)),bind(X_122,$fot(X_126))]]) ).

cnf(refute_0_1658,plain,
    ( multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126)))
    | multiply(least_upper_bound(X_125,X_126),inverse(X_126)) != least_upper_bound(identity,multiply(X_125,inverse(X_126)))
    | multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))) = greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))),greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_125,inverse(X_126))))]]) ).

cnf(refute_0_1659,plain,
    ( multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126)))
    | multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))) = greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_125,X_126),inverse(X_126)),least_upper_bound(identity,multiply(X_125,inverse(X_126)))) )],[refute_0_1657,refute_0_1658]) ).

cnf(refute_0_1660,plain,
    multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))) = greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))),greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126)))) )],[refute_0_1656,refute_0_1659]) ).

cnf(refute_0_1661,plain,
    ( multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126)))
    | multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))) != greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126))))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))) = greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126))))) ),[0],$fot(greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))))]]) ).

cnf(refute_0_1662,plain,
    ( multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))) != greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126))))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))) = greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))),greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126)))) )],[refute_0_1656,refute_0_1661]) ).

cnf(refute_0_1663,plain,
    greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126)))) = identity,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_125,inverse(X_126))))]]) ).

cnf(refute_0_1664,plain,
    ( greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))) != greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126))))
    | greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126)))) != identity
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))) = identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))),identity) ),[0],$fot(greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126)))))]]) ).

cnf(refute_0_1665,plain,
    ( greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))) != greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126))))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126)))),identity) )],[refute_0_1663,refute_0_1664]) ).

cnf(refute_0_1666,plain,
    ( multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))) != greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126))))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126))))) )],[refute_0_1662,refute_0_1665]) ).

cnf(refute_0_1667,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(X_125,X_126),inverse(X_126))) = identity,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_125,X_126),greatest_lower_bound(inverse(X_126),inverse(least_upper_bound(X_125,X_126)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(X_125,inverse(X_126))))) )],[refute_0_1660,refute_0_1666]) ).

cnf(refute_0_1668,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(X_132,least_upper_bound(X_15,X_132)),inverse(least_upper_bound(X_15,X_132)))) = identity,
    inference(subst,[],[refute_0_1667:[bind(X_125,$fot(X_132)),bind(X_126,$fot(least_upper_bound(X_15,X_132)))]]) ).

cnf(refute_0_1669,plain,
    least_upper_bound(X_132,least_upper_bound(X_15,X_132)) = least_upper_bound(X_132,X_15),
    inference(subst,[],[refute_0_409:[bind(X_11,$fot(X_132))]]) ).

cnf(refute_0_1670,plain,
    ( greatest_lower_bound(identity,multiply(least_upper_bound(X_132,least_upper_bound(X_15,X_132)),inverse(least_upper_bound(X_15,X_132)))) != identity
    | least_upper_bound(X_132,least_upper_bound(X_15,X_132)) != least_upper_bound(X_132,X_15)
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_132,X_15),inverse(least_upper_bound(X_15,X_132)))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_132,least_upper_bound(X_15,X_132)),inverse(least_upper_bound(X_15,X_132)))),identity) ),[0,1,0],$fot(least_upper_bound(X_132,X_15))]]) ).

cnf(refute_0_1671,plain,
    ( greatest_lower_bound(identity,multiply(least_upper_bound(X_132,least_upper_bound(X_15,X_132)),inverse(least_upper_bound(X_15,X_132)))) != identity
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_132,X_15),inverse(least_upper_bound(X_15,X_132)))) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_132,least_upper_bound(X_15,X_132)),least_upper_bound(X_132,X_15)) )],[refute_0_1669,refute_0_1670]) ).

cnf(refute_0_1672,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(X_132,X_15),inverse(least_upper_bound(X_15,X_132)))) = identity,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_132,least_upper_bound(X_15,X_132)),inverse(least_upper_bound(X_15,X_132)))),identity) )],[refute_0_1668,refute_0_1671]) ).

cnf(refute_0_1673,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137)))) = identity,
    inference(subst,[],[refute_0_1672:[bind(X_132,$fot(X_137)),bind(X_15,$fot(X_136))]]) ).

cnf(refute_0_1674,plain,
    ( multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137)))) != identity
    | multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))) = identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137)))))]]) ).

cnf(refute_0_1675,plain,
    ( multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))) != greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))))
    | multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137)))),identity) )],[refute_0_1673,refute_0_1674]) ).

cnf(refute_0_1676,plain,
    multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))) = identity,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))),greatest_lower_bound(identity,multiply(least_upper_bound(X_137,X_136),inverse(least_upper_bound(X_136,X_137))))) )],[refute_0_1655,refute_0_1675]) ).

cnf(refute_0_1677,plain,
    multiply(least_upper_bound(X_139,X_138),inverse(least_upper_bound(X_138,X_139))) = identity,
    inference(subst,[],[refute_0_1676:[bind(X_136,$fot(X_138)),bind(X_137,$fot(X_139))]]) ).

cnf(refute_0_1678,plain,
    ( multiply(least_upper_bound(X_139,X_138),inverse(least_upper_bound(X_138,X_139))) != identity
    | inverse(least_upper_bound(X_139,X_138)) != multiply(inverse(least_upper_bound(X_138,X_139)),inverse(multiply(least_upper_bound(X_139,X_138),inverse(least_upper_bound(X_138,X_139)))))
    | inverse(least_upper_bound(X_139,X_138)) = multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_139,X_138)),multiply(inverse(least_upper_bound(X_138,X_139)),inverse(multiply(least_upper_bound(X_139,X_138),inverse(least_upper_bound(X_138,X_139)))))) ),[1,1,0],$fot(identity)]]) ).

cnf(refute_0_1679,plain,
    ( inverse(least_upper_bound(X_139,X_138)) != multiply(inverse(least_upper_bound(X_138,X_139)),inverse(multiply(least_upper_bound(X_139,X_138),inverse(least_upper_bound(X_138,X_139)))))
    | inverse(least_upper_bound(X_139,X_138)) = multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_139,X_138),inverse(least_upper_bound(X_138,X_139))),identity) )],[refute_0_1677,refute_0_1678]) ).

cnf(refute_0_1680,plain,
    inverse(least_upper_bound(X_139,X_138)) = multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_139,X_138)),multiply(inverse(least_upper_bound(X_138,X_139)),inverse(multiply(least_upper_bound(X_139,X_138),inverse(least_upper_bound(X_138,X_139)))))) )],[refute_0_1650,refute_0_1679]) ).

cnf(refute_0_1681,plain,
    multiply(identity,least_upper_bound(X_138,X_139)) = least_upper_bound(X_138,X_139),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_138,X_139)))]]) ).

cnf(refute_0_1682,plain,
    inverse(multiply(identity,least_upper_bound(X_138,X_139))) = inverse(multiply(identity,least_upper_bound(X_138,X_139))),
    introduced(tautology,[refl,[$fot(inverse(multiply(identity,least_upper_bound(X_138,X_139))))]]) ).

cnf(refute_0_1683,plain,
    ( multiply(identity,least_upper_bound(X_138,X_139)) != least_upper_bound(X_138,X_139)
    | inverse(multiply(identity,least_upper_bound(X_138,X_139))) != inverse(multiply(identity,least_upper_bound(X_138,X_139)))
    | inverse(multiply(identity,least_upper_bound(X_138,X_139))) = inverse(least_upper_bound(X_138,X_139)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,least_upper_bound(X_138,X_139))),inverse(multiply(identity,least_upper_bound(X_138,X_139)))) ),[1,0],$fot(least_upper_bound(X_138,X_139))]]) ).

cnf(refute_0_1684,plain,
    ( multiply(identity,least_upper_bound(X_138,X_139)) != least_upper_bound(X_138,X_139)
    | inverse(multiply(identity,least_upper_bound(X_138,X_139))) = inverse(least_upper_bound(X_138,X_139)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,least_upper_bound(X_138,X_139))),inverse(multiply(identity,least_upper_bound(X_138,X_139)))) )],[refute_0_1682,refute_0_1683]) ).

cnf(refute_0_1685,plain,
    inverse(multiply(identity,least_upper_bound(X_138,X_139))) = inverse(least_upper_bound(X_138,X_139)),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_138,X_139)),least_upper_bound(X_138,X_139)) )],[refute_0_1681,refute_0_1684]) ).

cnf(refute_0_1686,plain,
    multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)) = inverse(multiply(identity,least_upper_bound(X_138,X_139))),
    inference(subst,[],[refute_0_221:[bind(X,$fot(identity)),bind(Y,$fot(least_upper_bound(X_138,X_139)))]]) ).

cnf(refute_0_1687,plain,
    ( multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)) != inverse(multiply(identity,least_upper_bound(X_138,X_139)))
    | inverse(multiply(identity,least_upper_bound(X_138,X_139))) != inverse(least_upper_bound(X_138,X_139))
    | multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)) = inverse(least_upper_bound(X_138,X_139)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)))),bind(Y0,$fot(inverse(multiply(identity,least_upper_bound(X_138,X_139))))),bind(Z0,$fot(inverse(least_upper_bound(X_138,X_139))))]]) ).

cnf(refute_0_1688,plain,
    ( inverse(multiply(identity,least_upper_bound(X_138,X_139))) != inverse(least_upper_bound(X_138,X_139))
    | multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)) = inverse(least_upper_bound(X_138,X_139)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)),inverse(multiply(identity,least_upper_bound(X_138,X_139)))) )],[refute_0_1686,refute_0_1687]) ).

cnf(refute_0_1689,plain,
    multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)) = inverse(least_upper_bound(X_138,X_139)),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,least_upper_bound(X_138,X_139))),inverse(least_upper_bound(X_138,X_139))) )],[refute_0_1685,refute_0_1688]) ).

cnf(refute_0_1690,plain,
    ( multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)) != inverse(least_upper_bound(X_138,X_139))
    | inverse(least_upper_bound(X_139,X_138)) != multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity))
    | inverse(least_upper_bound(X_139,X_138)) = inverse(least_upper_bound(X_138,X_139)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_139,X_138)),multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity))) ),[1],$fot(inverse(least_upper_bound(X_138,X_139)))]]) ).

cnf(refute_0_1691,plain,
    ( inverse(least_upper_bound(X_139,X_138)) != multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity))
    | inverse(least_upper_bound(X_139,X_138)) = inverse(least_upper_bound(X_138,X_139)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity)),inverse(least_upper_bound(X_138,X_139))) )],[refute_0_1689,refute_0_1690]) ).

cnf(refute_0_1692,plain,
    inverse(least_upper_bound(X_139,X_138)) = inverse(least_upper_bound(X_138,X_139)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_139,X_138)),multiply(inverse(least_upper_bound(X_138,X_139)),inverse(identity))) )],[refute_0_1680,refute_0_1691]) ).

cnf(refute_0_1693,plain,
    inverse(least_upper_bound(X_270,X_269)) = inverse(least_upper_bound(X_269,X_270)),
    inference(subst,[],[refute_0_1692:[bind(X_138,$fot(X_269)),bind(X_139,$fot(X_270))]]) ).

cnf(refute_0_1694,plain,
    ( inverse(least_upper_bound(X_270,X_269)) != inverse(least_upper_bound(X_269,X_270))
    | least_upper_bound(X_270,X_269) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_270,X_269)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269))))
    | least_upper_bound(X_270,X_269) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_269,X_270)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_270,X_269),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_270,X_269)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269))))) ),[1,0,0,0],$fot(inverse(least_upper_bound(X_269,X_270)))]]) ).

cnf(refute_0_1695,plain,
    ( least_upper_bound(X_270,X_269) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_270,X_269)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269))))
    | least_upper_bound(X_270,X_269) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_269,X_270)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269)))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_270,X_269)),inverse(least_upper_bound(X_269,X_270))) )],[refute_0_1693,refute_0_1694]) ).

cnf(refute_0_1696,plain,
    least_upper_bound(X_270,X_269) = multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_269,X_270)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_270,X_269),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_270,X_269)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269))))) )],[refute_0_1649,refute_0_1695]) ).

cnf(refute_0_1697,plain,
    ( least_upper_bound(X_270,X_269) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_269,X_270)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269))))
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_269,X_270)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269)))) = least_upper_bound(X_270,X_269) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_270,X_269))),bind(Y0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_269,X_270)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269))))))]]) ).

cnf(refute_0_1698,plain,
    multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_269,X_270)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269)))) = least_upper_bound(X_270,X_269),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_270,X_269),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_269,X_270)),X_188)),least_upper_bound(identity,multiply(X_188,least_upper_bound(X_270,X_269))))) )],[refute_0_1696,refute_0_1697]) ).

cnf(refute_0_1699,plain,
    multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(identity,X_143)))) = least_upper_bound(identity,X_143),
    inference(subst,[],[refute_0_1698:[bind(X_188,$fot(X_243)),bind(X_269,$fot(X_143)),bind(X_270,$fot(identity))]]) ).

cnf(refute_0_1700,plain,
    ( multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(identity,X_143)))) != least_upper_bound(identity,X_143)
    | least_upper_bound(X_143,identity) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(identity,X_143))))
    | least_upper_bound(X_143,identity) = least_upper_bound(identity,X_143) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_143,identity),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(identity,X_143))))) ),[1],$fot(least_upper_bound(identity,X_143))]]) ).

cnf(refute_0_1701,plain,
    ( least_upper_bound(X_143,identity) != multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(identity,X_143))))
    | least_upper_bound(X_143,identity) = least_upper_bound(identity,X_143) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(identity,X_143)))),least_upper_bound(identity,X_143)) )],[refute_0_1699,refute_0_1700]) ).

cnf(refute_0_1702,plain,
    least_upper_bound(X_143,identity) = least_upper_bound(identity,X_143),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_143,identity),multiply(inverse(least_upper_bound(inverse(least_upper_bound(X_143,identity)),X_243)),least_upper_bound(identity,multiply(X_243,least_upper_bound(identity,X_143))))) )],[refute_0_1648,refute_0_1701]) ).

cnf(refute_0_1703,plain,
    least_upper_bound(greatest_lower_bound(X_88,X_89),identity) = least_upper_bound(identity,greatest_lower_bound(X_88,X_89)),
    inference(subst,[],[refute_0_1702:[bind(X_143,$fot(greatest_lower_bound(X_88,X_89)))]]) ).

cnf(refute_0_1704,plain,
    least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)) = least_upper_bound(X_46,least_upper_bound(X_47,greatest_lower_bound(X_47,Y))),
    inference(subst,[],[refute_0_128:[bind(X,$fot(greatest_lower_bound(X_47,Y))),bind(X_26,$fot(X_46)),bind(X_27,$fot(X_47))]]) ).

cnf(refute_0_1705,plain,
    least_upper_bound(X_47,greatest_lower_bound(X_47,Y)) = X_47,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_47))]]) ).

cnf(refute_0_1706,plain,
    ( least_upper_bound(X_47,greatest_lower_bound(X_47,Y)) != X_47
    | least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)) != least_upper_bound(X_46,least_upper_bound(X_47,greatest_lower_bound(X_47,Y)))
    | least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)) = least_upper_bound(X_46,X_47) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)),least_upper_bound(X_46,least_upper_bound(X_47,greatest_lower_bound(X_47,Y)))) ),[1,1],$fot(X_47)]]) ).

cnf(refute_0_1707,plain,
    ( least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)) != least_upper_bound(X_46,least_upper_bound(X_47,greatest_lower_bound(X_47,Y)))
    | least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)) = least_upper_bound(X_46,X_47) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_47,greatest_lower_bound(X_47,Y)),X_47) )],[refute_0_1705,refute_0_1706]) ).

cnf(refute_0_1708,plain,
    least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)) = least_upper_bound(X_46,X_47),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)),least_upper_bound(X_46,least_upper_bound(X_47,greatest_lower_bound(X_47,Y)))) )],[refute_0_1704,refute_0_1707]) ).

cnf(refute_0_1709,plain,
    least_upper_bound(X_45,least_upper_bound(X_46,least_upper_bound(X_15,X_46))) = least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)),
    inference(subst,[],[refute_0_128:[bind(X,$fot(X_45)),bind(X_26,$fot(X_46)),bind(X_27,$fot(least_upper_bound(X_15,X_46)))]]) ).

cnf(refute_0_1710,plain,
    least_upper_bound(X_46,least_upper_bound(X_15,X_46)) = least_upper_bound(X_46,X_15),
    inference(subst,[],[refute_0_409:[bind(X_11,$fot(X_46))]]) ).

cnf(refute_0_1711,plain,
    ( least_upper_bound(X_45,least_upper_bound(X_46,least_upper_bound(X_15,X_46))) != least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45))
    | least_upper_bound(X_46,least_upper_bound(X_15,X_46)) != least_upper_bound(X_46,X_15)
    | least_upper_bound(X_45,least_upper_bound(X_46,X_15)) = least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(X_46,least_upper_bound(X_15,X_46))),least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45))) ),[0,1],$fot(least_upper_bound(X_46,X_15))]]) ).

cnf(refute_0_1712,plain,
    ( least_upper_bound(X_45,least_upper_bound(X_46,least_upper_bound(X_15,X_46))) != least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45))
    | least_upper_bound(X_45,least_upper_bound(X_46,X_15)) = least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_46,least_upper_bound(X_15,X_46)),least_upper_bound(X_46,X_15)) )],[refute_0_1710,refute_0_1711]) ).

cnf(refute_0_1713,plain,
    least_upper_bound(X_45,least_upper_bound(X_46,X_15)) = least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(X_46,least_upper_bound(X_15,X_46))),least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45))) )],[refute_0_1709,refute_0_1712]) ).

cnf(refute_0_1714,plain,
    least_upper_bound(X_46,least_upper_bound(X_15,least_upper_bound(X_46,X_45))) = least_upper_bound(X_15,least_upper_bound(X_46,X_45)),
    inference(subst,[],[refute_0_561:[bind(X_15,$fot(X_45)),bind(X_26,$fot(X_15)),bind(X_27,$fot(X_46))]]) ).

cnf(refute_0_1715,plain,
    least_upper_bound(least_upper_bound(X_15,X_46),X_45) = least_upper_bound(X_15,least_upper_bound(X_46,X_45)),
    inference(subst,[],[refute_0_405:[bind(X,$fot(X_15)),bind(Y,$fot(X_46)),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_1716,plain,
    least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) = least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)))]]) ).

cnf(refute_0_1717,plain,
    ( least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) != least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45))
    | least_upper_bound(least_upper_bound(X_15,X_46),X_45) != least_upper_bound(X_15,least_upper_bound(X_46,X_45))
    | least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) = least_upper_bound(X_46,least_upper_bound(X_15,least_upper_bound(X_46,X_45))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)),least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45))) ),[1,1],$fot(least_upper_bound(X_15,least_upper_bound(X_46,X_45)))]]) ).

cnf(refute_0_1718,plain,
    ( least_upper_bound(least_upper_bound(X_15,X_46),X_45) != least_upper_bound(X_15,least_upper_bound(X_46,X_45))
    | least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) = least_upper_bound(X_46,least_upper_bound(X_15,least_upper_bound(X_46,X_45))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)),least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45))) )],[refute_0_1716,refute_0_1717]) ).

cnf(refute_0_1719,plain,
    least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) = least_upper_bound(X_46,least_upper_bound(X_15,least_upper_bound(X_46,X_45))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_15,X_46),X_45),least_upper_bound(X_15,least_upper_bound(X_46,X_45))) )],[refute_0_1715,refute_0_1718]) ).

cnf(refute_0_1720,plain,
    ( least_upper_bound(X_46,least_upper_bound(X_15,least_upper_bound(X_46,X_45))) != least_upper_bound(X_15,least_upper_bound(X_46,X_45))
    | least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) != least_upper_bound(X_46,least_upper_bound(X_15,least_upper_bound(X_46,X_45)))
    | least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) = least_upper_bound(X_15,least_upper_bound(X_46,X_45)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)))),bind(Y0,$fot(least_upper_bound(X_46,least_upper_bound(X_15,least_upper_bound(X_46,X_45))))),bind(Z0,$fot(least_upper_bound(X_15,least_upper_bound(X_46,X_45))))]]) ).

cnf(refute_0_1721,plain,
    ( least_upper_bound(X_46,least_upper_bound(X_15,least_upper_bound(X_46,X_45))) != least_upper_bound(X_15,least_upper_bound(X_46,X_45))
    | least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) = least_upper_bound(X_15,least_upper_bound(X_46,X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)),least_upper_bound(X_46,least_upper_bound(X_15,least_upper_bound(X_46,X_45)))) )],[refute_0_1719,refute_0_1720]) ).

cnf(refute_0_1722,plain,
    least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) = least_upper_bound(X_15,least_upper_bound(X_46,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_46,least_upper_bound(X_15,least_upper_bound(X_46,X_45))),least_upper_bound(X_15,least_upper_bound(X_46,X_45))) )],[refute_0_1714,refute_0_1721]) ).

cnf(refute_0_1723,plain,
    ( least_upper_bound(X_45,least_upper_bound(X_46,X_15)) != least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45))
    | least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)) != least_upper_bound(X_15,least_upper_bound(X_46,X_45))
    | least_upper_bound(X_45,least_upper_bound(X_46,X_15)) = least_upper_bound(X_15,least_upper_bound(X_46,X_45)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_45,least_upper_bound(X_46,X_15)),least_upper_bound(X_15,least_upper_bound(X_46,X_45))) ),[0],$fot(least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)))]]) ).

cnf(refute_0_1724,plain,
    ( least_upper_bound(X_45,least_upper_bound(X_46,X_15)) != least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45))
    | least_upper_bound(X_45,least_upper_bound(X_46,X_15)) = least_upper_bound(X_15,least_upper_bound(X_46,X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45)),least_upper_bound(X_15,least_upper_bound(X_46,X_45))) )],[refute_0_1722,refute_0_1723]) ).

cnf(refute_0_1725,plain,
    least_upper_bound(X_45,least_upper_bound(X_46,X_15)) = least_upper_bound(X_15,least_upper_bound(X_46,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(X_46,X_15)),least_upper_bound(X_46,least_upper_bound(least_upper_bound(X_15,X_46),X_45))) )],[refute_0_1713,refute_0_1724]) ).

cnf(refute_0_1726,plain,
    ( least_upper_bound(X_45,least_upper_bound(X_46,X_15)) != least_upper_bound(X_15,least_upper_bound(X_46,X_45))
    | least_upper_bound(X_15,least_upper_bound(X_46,X_45)) = least_upper_bound(X_45,least_upper_bound(X_46,X_15)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_45,least_upper_bound(X_46,X_15)))),bind(Y0,$fot(least_upper_bound(X_15,least_upper_bound(X_46,X_45))))]]) ).

cnf(refute_0_1727,plain,
    least_upper_bound(X_15,least_upper_bound(X_46,X_45)) = least_upper_bound(X_45,least_upper_bound(X_46,X_15)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(X_46,X_15)),least_upper_bound(X_15,least_upper_bound(X_46,X_45))) )],[refute_0_1725,refute_0_1726]) ).

cnf(refute_0_1728,plain,
    least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)) = least_upper_bound(X_47,least_upper_bound(X_46,greatest_lower_bound(X_47,Y))),
    inference(subst,[],[refute_0_1727:[bind(X_15,$fot(greatest_lower_bound(X_47,Y))),bind(X_45,$fot(X_47))]]) ).

cnf(refute_0_1729,plain,
    ( least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)) != least_upper_bound(X_46,X_47)
    | least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)) != least_upper_bound(X_47,least_upper_bound(X_46,greatest_lower_bound(X_47,Y)))
    | least_upper_bound(X_47,least_upper_bound(X_46,greatest_lower_bound(X_47,Y))) = least_upper_bound(X_46,X_47) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)),least_upper_bound(X_46,X_47)) ),[0],$fot(least_upper_bound(X_47,least_upper_bound(X_46,greatest_lower_bound(X_47,Y))))]]) ).

cnf(refute_0_1730,plain,
    ( least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)) != least_upper_bound(X_46,X_47)
    | least_upper_bound(X_47,least_upper_bound(X_46,greatest_lower_bound(X_47,Y))) = least_upper_bound(X_46,X_47) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)),least_upper_bound(X_47,least_upper_bound(X_46,greatest_lower_bound(X_47,Y)))) )],[refute_0_1728,refute_0_1729]) ).

cnf(refute_0_1731,plain,
    least_upper_bound(X_47,least_upper_bound(X_46,greatest_lower_bound(X_47,Y))) = least_upper_bound(X_46,X_47),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_47,Y),least_upper_bound(X_46,X_47)),least_upper_bound(X_46,X_47)) )],[refute_0_1708,refute_0_1730]) ).

cnf(refute_0_1732,plain,
    least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) = least_upper_bound(greatest_lower_bound(X_88,X_89),identity),
    inference(subst,[],[refute_0_1731:[bind(Y,$fot(multiply(X_88,inverse(X_89)))),bind(X_46,$fot(greatest_lower_bound(X_88,X_89))),bind(X_47,$fot(identity))]]) ).

cnf(refute_0_1733,plain,
    ( least_upper_bound(greatest_lower_bound(X_88,X_89),identity) != least_upper_bound(identity,greatest_lower_bound(X_88,X_89))
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) != least_upper_bound(greatest_lower_bound(X_88,X_89),identity)
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) = least_upper_bound(identity,greatest_lower_bound(X_88,X_89)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_88,X_89),identity))),bind(Z0,$fot(least_upper_bound(identity,greatest_lower_bound(X_88,X_89))))]]) ).

cnf(refute_0_1734,plain,
    ( least_upper_bound(greatest_lower_bound(X_88,X_89),identity) != least_upper_bound(identity,greatest_lower_bound(X_88,X_89))
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) = least_upper_bound(identity,greatest_lower_bound(X_88,X_89)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))),least_upper_bound(greatest_lower_bound(X_88,X_89),identity)) )],[refute_0_1732,refute_0_1733]) ).

cnf(refute_0_1735,plain,
    least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) = least_upper_bound(identity,greatest_lower_bound(X_88,X_89)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_88,X_89),identity),least_upper_bound(identity,greatest_lower_bound(X_88,X_89))) )],[refute_0_1703,refute_0_1734]) ).

cnf(refute_0_1736,plain,
    least_upper_bound(X_11,least_upper_bound(least_upper_bound(X_26,X_27),X_11)) = least_upper_bound(X_11,least_upper_bound(X_26,X_27)),
    inference(subst,[],[refute_0_409:[bind(X_15,$fot(least_upper_bound(X_26,X_27)))]]) ).

cnf(refute_0_1737,plain,
    least_upper_bound(X_26,least_upper_bound(X_27,X_11)) = least_upper_bound(least_upper_bound(X_26,X_27),X_11),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(X_11))]]) ).

cnf(refute_0_1738,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_27,X_11)) != least_upper_bound(least_upper_bound(X_26,X_27),X_11)
    | least_upper_bound(least_upper_bound(X_26,X_27),X_11) = least_upper_bound(X_26,least_upper_bound(X_27,X_11)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_26,least_upper_bound(X_27,X_11)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_26,X_27),X_11)))]]) ).

cnf(refute_0_1739,plain,
    least_upper_bound(least_upper_bound(X_26,X_27),X_11) = least_upper_bound(X_26,least_upper_bound(X_27,X_11)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_27,X_11)),least_upper_bound(least_upper_bound(X_26,X_27),X_11)) )],[refute_0_1737,refute_0_1738]) ).

cnf(refute_0_1740,plain,
    ( least_upper_bound(X_11,least_upper_bound(least_upper_bound(X_26,X_27),X_11)) != least_upper_bound(X_11,least_upper_bound(X_26,X_27))
    | least_upper_bound(least_upper_bound(X_26,X_27),X_11) != least_upper_bound(X_26,least_upper_bound(X_27,X_11))
    | least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_27,X_11))) = least_upper_bound(X_11,least_upper_bound(X_26,X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(least_upper_bound(X_26,X_27),X_11)),least_upper_bound(X_11,least_upper_bound(X_26,X_27))) ),[0,1],$fot(least_upper_bound(X_26,least_upper_bound(X_27,X_11)))]]) ).

cnf(refute_0_1741,plain,
    ( least_upper_bound(X_11,least_upper_bound(least_upper_bound(X_26,X_27),X_11)) != least_upper_bound(X_11,least_upper_bound(X_26,X_27))
    | least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_27,X_11))) = least_upper_bound(X_11,least_upper_bound(X_26,X_27)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_26,X_27),X_11),least_upper_bound(X_26,least_upper_bound(X_27,X_11))) )],[refute_0_1739,refute_0_1740]) ).

cnf(refute_0_1742,plain,
    least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_27,X_11))) = least_upper_bound(X_11,least_upper_bound(X_26,X_27)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(least_upper_bound(X_26,X_27),X_11)),least_upper_bound(X_11,least_upper_bound(X_26,X_27))) )],[refute_0_1736,refute_0_1741]) ).

cnf(refute_0_1743,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27)),
    inference(subst,[],[refute_0_1742:[bind(X_11,$fot(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))]]) ).

cnf(refute_0_1744,plain,
    least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_26,Y),X_28)) = least_upper_bound(least_upper_bound(X_26,greatest_lower_bound(X_26,Y)),X_28),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_26)),bind(Y,$fot(greatest_lower_bound(X_26,Y))),bind(Z,$fot(X_28))]]) ).

cnf(refute_0_1745,plain,
    least_upper_bound(X_26,greatest_lower_bound(X_26,Y)) = X_26,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_26))]]) ).

cnf(refute_0_1746,plain,
    ( least_upper_bound(X_26,greatest_lower_bound(X_26,Y)) != X_26
    | least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_26,Y),X_28)) != least_upper_bound(least_upper_bound(X_26,greatest_lower_bound(X_26,Y)),X_28)
    | least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_26,Y),X_28)) = least_upper_bound(X_26,X_28) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_26,Y),X_28)),least_upper_bound(least_upper_bound(X_26,greatest_lower_bound(X_26,Y)),X_28)) ),[1,0],$fot(X_26)]]) ).

cnf(refute_0_1747,plain,
    ( least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_26,Y),X_28)) != least_upper_bound(least_upper_bound(X_26,greatest_lower_bound(X_26,Y)),X_28)
    | least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_26,Y),X_28)) = least_upper_bound(X_26,X_28) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,greatest_lower_bound(X_26,Y)),X_26) )],[refute_0_1745,refute_0_1746]) ).

cnf(refute_0_1748,plain,
    least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_26,Y),X_28)) = least_upper_bound(X_26,X_28),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_26,Y),X_28)),least_upper_bound(least_upper_bound(X_26,greatest_lower_bound(X_26,Y)),X_28)) )],[refute_0_1744,refute_0_1747]) ).

cnf(refute_0_1749,plain,
    least_upper_bound(X_27,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)) = least_upper_bound(X_27,X_210),
    inference(subst,[],[refute_0_1748:[bind(Y,$fot(X_208)),bind(X_26,$fot(X_27)),bind(X_28,$fot(X_210))]]) ).

cnf(refute_0_1750,plain,
    ( least_upper_bound(X_27,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)) != least_upper_bound(X_27,X_210)
    | least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))) ),[0,1,1],$fot(least_upper_bound(X_27,X_210))]]) ).

cnf(refute_0_1751,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)),least_upper_bound(X_27,X_210)) )],[refute_0_1749,refute_0_1750]) ).

cnf(refute_0_1752,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))) )],[refute_0_1743,refute_0_1751]) ).

cnf(refute_0_1753,plain,
    least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_207,X_206))) = least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)),
    inference(subst,[],[refute_0_128:[bind(X_27,$fot(least_upper_bound(X_207,X_206)))]]) ).

cnf(refute_0_1754,plain,
    least_upper_bound(X_26,least_upper_bound(X_27,X_28)) = least_upper_bound(least_upper_bound(X_26,X_27),X_28),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(X_28))]]) ).

cnf(refute_0_1755,plain,
    least_upper_bound(X_28,X_27) = least_upper_bound(X_27,X_28),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_28)),bind(Y,$fot(X_27))]]) ).

cnf(refute_0_1756,plain,
    ( least_upper_bound(X_28,X_27) != least_upper_bound(X_27,X_28)
    | least_upper_bound(X_27,X_28) = least_upper_bound(X_28,X_27) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_28,X_27))),bind(Y0,$fot(least_upper_bound(X_27,X_28)))]]) ).

cnf(refute_0_1757,plain,
    least_upper_bound(X_27,X_28) = least_upper_bound(X_28,X_27),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_28,X_27),least_upper_bound(X_27,X_28)) )],[refute_0_1755,refute_0_1756]) ).

cnf(refute_0_1758,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_27,X_28)) != least_upper_bound(least_upper_bound(X_26,X_27),X_28)
    | least_upper_bound(X_27,X_28) != least_upper_bound(X_28,X_27)
    | least_upper_bound(X_26,least_upper_bound(X_28,X_27)) = least_upper_bound(least_upper_bound(X_26,X_27),X_28) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_27,X_28)),least_upper_bound(least_upper_bound(X_26,X_27),X_28)) ),[0,1],$fot(least_upper_bound(X_28,X_27))]]) ).

cnf(refute_0_1759,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_27,X_28)) != least_upper_bound(least_upper_bound(X_26,X_27),X_28)
    | least_upper_bound(X_26,least_upper_bound(X_28,X_27)) = least_upper_bound(least_upper_bound(X_26,X_27),X_28) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,X_28),least_upper_bound(X_28,X_27)) )],[refute_0_1757,refute_0_1758]) ).

cnf(refute_0_1760,plain,
    least_upper_bound(X_26,least_upper_bound(X_28,X_27)) = least_upper_bound(least_upper_bound(X_26,X_27),X_28),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_27,X_28)),least_upper_bound(least_upper_bound(X_26,X_27),X_28)) )],[refute_0_1754,refute_0_1759]) ).

cnf(refute_0_1761,plain,
    least_upper_bound(least_upper_bound(X_26,X_27),X_28) = least_upper_bound(X_26,least_upper_bound(X_27,X_28)),
    inference(subst,[],[refute_0_405:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(Z,$fot(X_28))]]) ).

cnf(refute_0_1762,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_28,X_27)) != least_upper_bound(least_upper_bound(X_26,X_27),X_28)
    | least_upper_bound(least_upper_bound(X_26,X_27),X_28) != least_upper_bound(X_26,least_upper_bound(X_27,X_28))
    | least_upper_bound(X_26,least_upper_bound(X_28,X_27)) = least_upper_bound(X_26,least_upper_bound(X_27,X_28)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_26,least_upper_bound(X_28,X_27)),least_upper_bound(X_26,least_upper_bound(X_27,X_28))) ),[0],$fot(least_upper_bound(least_upper_bound(X_26,X_27),X_28))]]) ).

cnf(refute_0_1763,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_28,X_27)) != least_upper_bound(least_upper_bound(X_26,X_27),X_28)
    | least_upper_bound(X_26,least_upper_bound(X_28,X_27)) = least_upper_bound(X_26,least_upper_bound(X_27,X_28)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_26,X_27),X_28),least_upper_bound(X_26,least_upper_bound(X_27,X_28))) )],[refute_0_1761,refute_0_1762]) ).

cnf(refute_0_1764,plain,
    least_upper_bound(X_26,least_upper_bound(X_28,X_27)) = least_upper_bound(X_26,least_upper_bound(X_27,X_28)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_28,X_27)),least_upper_bound(least_upper_bound(X_26,X_27),X_28)) )],[refute_0_1760,refute_0_1763]) ).

cnf(refute_0_1765,plain,
    least_upper_bound(X_26,least_upper_bound(X_207,X_206)) = least_upper_bound(X_26,least_upper_bound(X_206,X_207)),
    inference(subst,[],[refute_0_1764:[bind(X_27,$fot(X_206)),bind(X_28,$fot(X_207))]]) ).

cnf(refute_0_1766,plain,
    ( least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_207,X_206))) != least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X))
    | least_upper_bound(X_26,least_upper_bound(X_207,X_206)) != least_upper_bound(X_26,least_upper_bound(X_206,X_207))
    | least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))) = least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_207,X_206))),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X))) ),[0,1],$fot(least_upper_bound(X_26,least_upper_bound(X_206,X_207)))]]) ).

cnf(refute_0_1767,plain,
    ( least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_207,X_206))) != least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X))
    | least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))) = least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_207,X_206)),least_upper_bound(X_26,least_upper_bound(X_206,X_207))) )],[refute_0_1765,refute_0_1766]) ).

cnf(refute_0_1768,plain,
    least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))) = least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_207,X_206))),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X))) )],[refute_0_1753,refute_0_1767]) ).

cnf(refute_0_1769,plain,
    least_upper_bound(least_upper_bound(X_207,X_206),X) = least_upper_bound(X_207,least_upper_bound(X_206,X)),
    inference(subst,[],[refute_0_405:[bind(X,$fot(X_207)),bind(Y,$fot(X_206)),bind(Z,$fot(X))]]) ).

cnf(refute_0_1770,plain,
    least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)) = least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)))]]) ).

cnf(refute_0_1771,plain,
    ( least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)) != least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X))
    | least_upper_bound(least_upper_bound(X_207,X_206),X) != least_upper_bound(X_207,least_upper_bound(X_206,X))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)) = least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X))) ),[1,1],$fot(least_upper_bound(X_207,least_upper_bound(X_206,X)))]]) ).

cnf(refute_0_1772,plain,
    ( least_upper_bound(least_upper_bound(X_207,X_206),X) != least_upper_bound(X_207,least_upper_bound(X_206,X))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)) = least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X))) )],[refute_0_1770,refute_0_1771]) ).

cnf(refute_0_1773,plain,
    least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)) = least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_207,X_206),X),least_upper_bound(X_207,least_upper_bound(X_206,X))) )],[refute_0_1769,refute_0_1772]) ).

cnf(refute_0_1774,plain,
    ( least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))) != least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)) != least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X)))
    | least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))) = least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))),least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X)))) ),[0],$fot(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)))]]) ).

cnf(refute_0_1775,plain,
    ( least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))) != least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X))
    | least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))) = least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X)),least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X)))) )],[refute_0_1773,refute_0_1774]) ).

cnf(refute_0_1776,plain,
    least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))) = least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_207,X_206),X))) )],[refute_0_1768,refute_0_1775]) ).

cnf(refute_0_1777,plain,
    least_upper_bound(greatest_lower_bound(X_27,X_208),least_upper_bound(X_27,least_upper_bound(X_210,X_26))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))),
    inference(subst,[],[refute_0_1776:[bind(X,$fot(greatest_lower_bound(X_27,X_208))),bind(X_206,$fot(X_210)),bind(X_207,$fot(X_26)),bind(X_26,$fot(X_27))]]) ).

cnf(refute_0_1778,plain,
    least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101)))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101))),
    inference(subst,[],[associativity_of_lub:[bind(Z,$fot(least_upper_bound(X_102,least_upper_bound(Y,X_101))))]]) ).

cnf(refute_0_1779,plain,
    least_upper_bound(X_102,least_upper_bound(Y,X_101)) = least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101))),
    inference(subst,[],[refute_0_559:[bind(X_15,$fot(X_101)),bind(X_26,$fot(X_102)),bind(X_27,$fot(Y))]]) ).

cnf(refute_0_1780,plain,
    ( least_upper_bound(X_102,least_upper_bound(Y,X_101)) != least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101)))
    | least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101))) = least_upper_bound(X_102,least_upper_bound(Y,X_101)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_102,least_upper_bound(Y,X_101)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101)))))]]) ).

cnf(refute_0_1781,plain,
    least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101))) = least_upper_bound(X_102,least_upper_bound(Y,X_101)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_102,least_upper_bound(Y,X_101)),least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101)))) )],[refute_0_1779,refute_0_1780]) ).

cnf(refute_0_1782,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101)))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101)))
    | least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101))) != least_upper_bound(X_102,least_upper_bound(Y,X_101))
    | least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101)))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101)))) ),[0,1],$fot(least_upper_bound(X_102,least_upper_bound(Y,X_101)))]]) ).

cnf(refute_0_1783,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101)))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101)))
    | least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101))),least_upper_bound(X_102,least_upper_bound(Y,X_101))) )],[refute_0_1781,refute_0_1782]) ).

cnf(refute_0_1784,plain,
    least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(Y,X_101)))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101)))) )],[refute_0_1778,refute_0_1783]) ).

cnf(refute_0_1785,plain,
    least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_52,X_53))) = least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)),
    inference(subst,[],[refute_0_128:[bind(X_27,$fot(least_upper_bound(X_52,X_53)))]]) ).

cnf(refute_0_1786,plain,
    least_upper_bound(X_26,least_upper_bound(X_52,X_53)) = least_upper_bound(X_52,least_upper_bound(X_26,X_53)),
    inference(subst,[],[refute_0_577:[bind(X_15,$fot(X_26)),bind(X_26,$fot(X_52)),bind(X_28,$fot(X_53))]]) ).

cnf(refute_0_1787,plain,
    ( least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_52,X_53))) != least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X))
    | least_upper_bound(X_26,least_upper_bound(X_52,X_53)) != least_upper_bound(X_52,least_upper_bound(X_26,X_53))
    | least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))) = least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_52,X_53))),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X))) ),[0,1],$fot(least_upper_bound(X_52,least_upper_bound(X_26,X_53)))]]) ).

cnf(refute_0_1788,plain,
    ( least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_52,X_53))) != least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X))
    | least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))) = least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_52,X_53)),least_upper_bound(X_52,least_upper_bound(X_26,X_53))) )],[refute_0_1786,refute_0_1787]) ).

cnf(refute_0_1789,plain,
    least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))) = least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_52,X_53))),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X))) )],[refute_0_1785,refute_0_1788]) ).

cnf(refute_0_1790,plain,
    least_upper_bound(least_upper_bound(X_52,X_53),X) = least_upper_bound(X_52,least_upper_bound(X_53,X)),
    inference(subst,[],[refute_0_405:[bind(X,$fot(X_52)),bind(Y,$fot(X_53)),bind(Z,$fot(X))]]) ).

cnf(refute_0_1791,plain,
    least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)) = least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)))]]) ).

cnf(refute_0_1792,plain,
    ( least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)) != least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X))
    | least_upper_bound(least_upper_bound(X_52,X_53),X) != least_upper_bound(X_52,least_upper_bound(X_53,X))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)) = least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X))) ),[1,1],$fot(least_upper_bound(X_52,least_upper_bound(X_53,X)))]]) ).

cnf(refute_0_1793,plain,
    ( least_upper_bound(least_upper_bound(X_52,X_53),X) != least_upper_bound(X_52,least_upper_bound(X_53,X))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)) = least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X))) )],[refute_0_1791,refute_0_1792]) ).

cnf(refute_0_1794,plain,
    least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)) = least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_52,X_53),X),least_upper_bound(X_52,least_upper_bound(X_53,X))) )],[refute_0_1790,refute_0_1793]) ).

cnf(refute_0_1795,plain,
    ( least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))) != least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X))
    | least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)) != least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X)))
    | least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))) = least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))),least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X)))) ),[0],$fot(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)))]]) ).

cnf(refute_0_1796,plain,
    ( least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))) != least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X))
    | least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))) = least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X)),least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X)))) )],[refute_0_1794,refute_0_1795]) ).

cnf(refute_0_1797,plain,
    least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))) = least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))),least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_52,X_53),X))) )],[refute_0_1789,refute_0_1796]) ).

cnf(refute_0_1798,plain,
    least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101))) = least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y)))),
    inference(subst,[],[refute_0_1797:[bind(X,$fot(least_upper_bound(X,Y))),bind(X_26,$fot(Y)),bind(X_52,$fot(X_102)),bind(X_53,$fot(X_101))]]) ).

cnf(refute_0_1799,plain,
    ( least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101)))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101))) != least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y))))
    | least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))) = least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))),least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y))))) ),[0],$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101))))]]) ).

cnf(refute_0_1800,plain,
    ( least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101)))
    | least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))) = least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101))),least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y))))) )],[refute_0_1798,refute_0_1799]) ).

cnf(refute_0_1801,plain,
    least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))) = least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_102,least_upper_bound(Y,X_101)))) )],[refute_0_1784,refute_0_1800]) ).

cnf(refute_0_1802,plain,
    ( least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))) != least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y))))
    | least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y)))) = least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y))))))]]) ).

cnf(refute_0_1803,plain,
    least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y)))) = least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_102,least_upper_bound(Y,X_101))),least_upper_bound(Y,least_upper_bound(X_102,least_upper_bound(X_101,least_upper_bound(X,Y))))) )],[refute_0_1801,refute_0_1802]) ).

cnf(refute_0_1804,plain,
    least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) = least_upper_bound(greatest_lower_bound(X_27,X_208),least_upper_bound(X_27,least_upper_bound(X_210,X_26))),
    inference(subst,[],[refute_0_1803:[bind(X,$fot(greatest_lower_bound(X_27,X_208))),bind(Y,$fot(X_210)),bind(X_101,$fot(X_26)),bind(X_102,$fot(X_27))]]) ).

cnf(refute_0_1805,plain,
    ( least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) != least_upper_bound(greatest_lower_bound(X_27,X_208),least_upper_bound(X_27,least_upper_bound(X_210,X_26)))
    | least_upper_bound(greatest_lower_bound(X_27,X_208),least_upper_bound(X_27,least_upper_bound(X_210,X_26))) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))
    | least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_27,X_208),least_upper_bound(X_27,least_upper_bound(X_210,X_26))))),bind(Z0,$fot(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))))]]) ).

cnf(refute_0_1806,plain,
    ( least_upper_bound(greatest_lower_bound(X_27,X_208),least_upper_bound(X_27,least_upper_bound(X_210,X_26))) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))
    | least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))),least_upper_bound(greatest_lower_bound(X_27,X_208),least_upper_bound(X_27,least_upper_bound(X_210,X_26)))) )],[refute_0_1804,refute_0_1805]) ).

cnf(refute_0_1807,plain,
    least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_27,X_208),least_upper_bound(X_27,least_upper_bound(X_210,X_26))),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))) )],[refute_0_1777,refute_0_1806]) ).

cnf(refute_0_1808,plain,
    least_upper_bound(X_205,least_upper_bound(least_upper_bound(X,Y),X_206)) = least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y))),
    inference(subst,[],[refute_0_1764:[bind(X_26,$fot(X_205)),bind(X_27,$fot(X_206)),bind(X_28,$fot(least_upper_bound(X,Y)))]]) ).

cnf(refute_0_1809,plain,
    least_upper_bound(X,least_upper_bound(Y,X_206)) = least_upper_bound(least_upper_bound(X,Y),X_206),
    inference(subst,[],[associativity_of_lub:[bind(Z,$fot(X_206))]]) ).

cnf(refute_0_1810,plain,
    ( least_upper_bound(X,least_upper_bound(Y,X_206)) != least_upper_bound(least_upper_bound(X,Y),X_206)
    | least_upper_bound(least_upper_bound(X,Y),X_206) = least_upper_bound(X,least_upper_bound(Y,X_206)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,X_206)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),X_206)))]]) ).

cnf(refute_0_1811,plain,
    least_upper_bound(least_upper_bound(X,Y),X_206) = least_upper_bound(X,least_upper_bound(Y,X_206)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_206)),least_upper_bound(least_upper_bound(X,Y),X_206)) )],[refute_0_1809,refute_0_1810]) ).

cnf(refute_0_1812,plain,
    ( least_upper_bound(X_205,least_upper_bound(least_upper_bound(X,Y),X_206)) != least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y)))
    | least_upper_bound(least_upper_bound(X,Y),X_206) != least_upper_bound(X,least_upper_bound(Y,X_206))
    | least_upper_bound(X_205,least_upper_bound(X,least_upper_bound(Y,X_206))) = least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_205,least_upper_bound(least_upper_bound(X,Y),X_206)),least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y)))) ),[0,1],$fot(least_upper_bound(X,least_upper_bound(Y,X_206)))]]) ).

cnf(refute_0_1813,plain,
    ( least_upper_bound(X_205,least_upper_bound(least_upper_bound(X,Y),X_206)) != least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y)))
    | least_upper_bound(X_205,least_upper_bound(X,least_upper_bound(Y,X_206))) = least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),X_206),least_upper_bound(X,least_upper_bound(Y,X_206))) )],[refute_0_1811,refute_0_1812]) ).

cnf(refute_0_1814,plain,
    least_upper_bound(X_205,least_upper_bound(X,least_upper_bound(Y,X_206))) = least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_205,least_upper_bound(least_upper_bound(X,Y),X_206)),least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y)))) )],[refute_0_1808,refute_0_1813]) ).

cnf(refute_0_1815,plain,
    ( least_upper_bound(X_205,least_upper_bound(X,least_upper_bound(Y,X_206))) != least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y)))
    | least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y))) = least_upper_bound(X_205,least_upper_bound(X,least_upper_bound(Y,X_206))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_205,least_upper_bound(X,least_upper_bound(Y,X_206))))),bind(Y0,$fot(least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y)))))]]) ).

cnf(refute_0_1816,plain,
    least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y))) = least_upper_bound(X_205,least_upper_bound(X,least_upper_bound(Y,X_206))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_205,least_upper_bound(X,least_upper_bound(Y,X_206))),least_upper_bound(X_205,least_upper_bound(X_206,least_upper_bound(X,Y)))) )],[refute_0_1814,refute_0_1815]) ).

cnf(refute_0_1817,plain,
    least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))) = least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))),
    inference(subst,[],[refute_0_1816:[bind(X,$fot(X_27)),bind(Y,$fot(X_26)),bind(X_205,$fot(X_210)),bind(X_206,$fot(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))]]) ).

cnf(refute_0_1818,plain,
    ( least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))
    | least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))) != least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))))
    | least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))))),bind(Y0,$fot(least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))))),bind(Z0,$fot(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))))]]) ).

cnf(refute_0_1819,plain,
    ( least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))
    | least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))),least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))))) )],[refute_0_1817,refute_0_1818]) ).

cnf(refute_0_1820,plain,
    least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_210,least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))) )],[refute_0_1807,refute_0_1819]) ).

cnf(refute_0_1821,plain,
    ( least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))) != least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X)))
    | least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X))) = least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))))),bind(Y0,$fot(least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X)))))]]) ).

cnf(refute_0_1822,plain,
    least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X))) = least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_26,least_upper_bound(X_206,X_207))),least_upper_bound(X_26,least_upper_bound(X_207,least_upper_bound(X_206,X)))) )],[refute_0_1776,refute_0_1821]) ).

cnf(refute_0_1823,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) = least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))),
    inference(subst,[],[refute_0_1822:[bind(X,$fot(X_210)),bind(X_206,$fot(X_27)),bind(X_207,$fot(X_26)),bind(X_26,$fot(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))]]) ).

cnf(refute_0_1824,plain,
    ( least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) != least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26)))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))))),bind(Y0,$fot(least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))))),bind(Z0,$fot(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))))]]) ).

cnf(refute_0_1825,plain,
    ( least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))),least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26)))) )],[refute_0_1823,refute_0_1824]) ).

cnf(refute_0_1826,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_210,least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_27,X_26))),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))) )],[refute_0_1820,refute_0_1825]) ).

cnf(refute_0_1827,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))
    | least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))) ),[0],$fot(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))))]]) ).

cnf(refute_0_1828,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))
    | least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208))))) )],[refute_0_1826,refute_0_1827]) ).

cnf(refute_0_1829,plain,
    least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) = least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_191,X_11))),
    inference(subst,[],[refute_0_1742:[bind(X_27,$fot(least_upper_bound(X_191,X_11)))]]) ).

cnf(refute_0_1830,plain,
    least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_191,X_11))) = least_upper_bound(X_11,least_upper_bound(X_26,X_191)),
    inference(subst,[],[refute_0_1742:[bind(X_27,$fot(X_191))]]) ).

cnf(refute_0_1831,plain,
    ( least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_191,X_11))) != least_upper_bound(X_11,least_upper_bound(X_26,X_191))
    | least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) != least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_191,X_11)))
    | least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) = least_upper_bound(X_11,least_upper_bound(X_26,X_191)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))),least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_191,X_11)))) ),[1],$fot(least_upper_bound(X_11,least_upper_bound(X_26,X_191)))]]) ).

cnf(refute_0_1832,plain,
    ( least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) != least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_191,X_11)))
    | least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) = least_upper_bound(X_11,least_upper_bound(X_26,X_191)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_191,X_11))),least_upper_bound(X_11,least_upper_bound(X_26,X_191))) )],[refute_0_1830,refute_0_1831]) ).

cnf(refute_0_1833,plain,
    least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) = least_upper_bound(X_11,least_upper_bound(X_26,X_191)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))),least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_191,X_11)))) )],[refute_0_1829,refute_0_1832]) ).

cnf(refute_0_1834,plain,
    least_upper_bound(X_11,X_11) = X_11,
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_11))]]) ).

cnf(refute_0_1835,plain,
    least_upper_bound(X_26,least_upper_bound(X_11,X_11)) = least_upper_bound(X_26,least_upper_bound(X_11,X_11)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_26,least_upper_bound(X_11,X_11)))]]) ).

cnf(refute_0_1836,plain,
    ( least_upper_bound(X_11,X_11) != X_11
    | least_upper_bound(X_26,least_upper_bound(X_11,X_11)) != least_upper_bound(X_26,least_upper_bound(X_11,X_11))
    | least_upper_bound(X_26,least_upper_bound(X_11,X_11)) = least_upper_bound(X_26,X_11) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_11,X_11)),least_upper_bound(X_26,least_upper_bound(X_11,X_11))) ),[1,1],$fot(X_11)]]) ).

cnf(refute_0_1837,plain,
    ( least_upper_bound(X_11,X_11) != X_11
    | least_upper_bound(X_26,least_upper_bound(X_11,X_11)) = least_upper_bound(X_26,X_11) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_11,X_11)),least_upper_bound(X_26,least_upper_bound(X_11,X_11))) )],[refute_0_1835,refute_0_1836]) ).

cnf(refute_0_1838,plain,
    least_upper_bound(X_26,least_upper_bound(X_11,X_11)) = least_upper_bound(X_26,X_11),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,X_11),X_11) )],[refute_0_1834,refute_0_1837]) ).

cnf(refute_0_1839,plain,
    least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))) = least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))))]]) ).

cnf(refute_0_1840,plain,
    ( least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))) != least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11)))
    | least_upper_bound(X_26,least_upper_bound(X_11,X_11)) != least_upper_bound(X_26,X_11)
    | least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))) = least_upper_bound(X_191,least_upper_bound(X_26,X_11)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))),least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11)))) ),[1,1],$fot(least_upper_bound(X_26,X_11))]]) ).

cnf(refute_0_1841,plain,
    ( least_upper_bound(X_26,least_upper_bound(X_11,X_11)) != least_upper_bound(X_26,X_11)
    | least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))) = least_upper_bound(X_191,least_upper_bound(X_26,X_11)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))),least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11)))) )],[refute_0_1839,refute_0_1840]) ).

cnf(refute_0_1842,plain,
    least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))) = least_upper_bound(X_191,least_upper_bound(X_26,X_11)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_26,least_upper_bound(X_11,X_11)),least_upper_bound(X_26,X_11)) )],[refute_0_1838,refute_0_1841]) ).

cnf(refute_0_1843,plain,
    least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_11,least_upper_bound(X_191,X_11)))) = least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))),
    inference(subst,[],[refute_0_1803:[bind(X,$fot(X_191)),bind(Y,$fot(X_11)),bind(X_101,$fot(X_11)),bind(X_102,$fot(X_26))]]) ).

cnf(refute_0_1844,plain,
    ( least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))) != least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X)))
    | least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X))) = least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))))),bind(Y0,$fot(least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X)))))]]) ).

cnf(refute_0_1845,plain,
    least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X))) = least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_52,least_upper_bound(X_26,X_53))),least_upper_bound(X_26,least_upper_bound(X_52,least_upper_bound(X_53,X)))) )],[refute_0_1797,refute_0_1844]) ).

cnf(refute_0_1846,plain,
    least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) = least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_11,least_upper_bound(X_191,X_11)))),
    inference(subst,[],[refute_0_1845:[bind(X,$fot(X_11)),bind(X_26,$fot(X_11)),bind(X_52,$fot(X_26)),bind(X_53,$fot(least_upper_bound(X_191,X_11)))]]) ).

cnf(refute_0_1847,plain,
    ( least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_11,least_upper_bound(X_191,X_11)))) != least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11)))
    | least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) != least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_11,least_upper_bound(X_191,X_11))))
    | least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) = least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))))),bind(Y0,$fot(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_11,least_upper_bound(X_191,X_11)))))),bind(Z0,$fot(least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11)))))]]) ).

cnf(refute_0_1848,plain,
    ( least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_11,least_upper_bound(X_191,X_11)))) != least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11)))
    | least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) = least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))),least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_11,least_upper_bound(X_191,X_11))))) )],[refute_0_1846,refute_0_1847]) ).

cnf(refute_0_1849,plain,
    least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) = least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(X_11,least_upper_bound(X_191,X_11)))),least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11)))) )],[refute_0_1843,refute_0_1848]) ).

cnf(refute_0_1850,plain,
    ( least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) != least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11)))
    | least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))) != least_upper_bound(X_191,least_upper_bound(X_26,X_11))
    | least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) = least_upper_bound(X_191,least_upper_bound(X_26,X_11)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))))),bind(Y0,$fot(least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))))),bind(Z0,$fot(least_upper_bound(X_191,least_upper_bound(X_26,X_11))))]]) ).

cnf(refute_0_1851,plain,
    ( least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))) != least_upper_bound(X_191,least_upper_bound(X_26,X_11))
    | least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) = least_upper_bound(X_191,least_upper_bound(X_26,X_11)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))),least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11)))) )],[refute_0_1849,refute_0_1850]) ).

cnf(refute_0_1852,plain,
    least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) = least_upper_bound(X_191,least_upper_bound(X_26,X_11)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_191,least_upper_bound(X_26,least_upper_bound(X_11,X_11))),least_upper_bound(X_191,least_upper_bound(X_26,X_11))) )],[refute_0_1842,refute_0_1851]) ).

cnf(refute_0_1853,plain,
    ( least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) != least_upper_bound(X_11,least_upper_bound(X_26,X_191))
    | least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) != least_upper_bound(X_191,least_upper_bound(X_26,X_11))
    | least_upper_bound(X_191,least_upper_bound(X_26,X_11)) = least_upper_bound(X_11,least_upper_bound(X_26,X_191)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))),least_upper_bound(X_11,least_upper_bound(X_26,X_191))) ),[0],$fot(least_upper_bound(X_191,least_upper_bound(X_26,X_11)))]]) ).

cnf(refute_0_1854,plain,
    ( least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))) != least_upper_bound(X_11,least_upper_bound(X_26,X_191))
    | least_upper_bound(X_191,least_upper_bound(X_26,X_11)) = least_upper_bound(X_11,least_upper_bound(X_26,X_191)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))),least_upper_bound(X_191,least_upper_bound(X_26,X_11))) )],[refute_0_1852,refute_0_1853]) ).

cnf(refute_0_1855,plain,
    least_upper_bound(X_191,least_upper_bound(X_26,X_11)) = least_upper_bound(X_11,least_upper_bound(X_26,X_191)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_26,least_upper_bound(least_upper_bound(X_191,X_11),X_11))),least_upper_bound(X_11,least_upper_bound(X_26,X_191))) )],[refute_0_1833,refute_0_1854]) ).

cnf(refute_0_1856,plain,
    ( least_upper_bound(X_191,least_upper_bound(X_26,X_11)) != least_upper_bound(X_11,least_upper_bound(X_26,X_191))
    | least_upper_bound(X_11,least_upper_bound(X_26,X_191)) = least_upper_bound(X_191,least_upper_bound(X_26,X_11)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_191,least_upper_bound(X_26,X_11)))),bind(Y0,$fot(least_upper_bound(X_11,least_upper_bound(X_26,X_191))))]]) ).

cnf(refute_0_1857,plain,
    least_upper_bound(X_11,least_upper_bound(X_26,X_191)) = least_upper_bound(X_191,least_upper_bound(X_26,X_11)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_191,least_upper_bound(X_26,X_11)),least_upper_bound(X_11,least_upper_bound(X_26,X_191))) )],[refute_0_1855,refute_0_1856]) ).

cnf(refute_0_1858,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))),
    inference(subst,[],[refute_0_1857:[bind(X_11,$fot(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))),bind(X_191,$fot(X_27))]]) ).

cnf(refute_0_1859,plain,
    ( least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27)) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))
    | least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) ),[0],$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27)))]]) ).

cnf(refute_0_1860,plain,
    ( least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))
    | least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27)),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) )],[refute_0_1858,refute_0_1859]) ).

cnf(refute_0_1861,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) != least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))
    | least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))) )],[refute_0_1828,refute_0_1860]) ).

cnf(refute_0_1862,plain,
    least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,least_upper_bound(X_27,X_210))),least_upper_bound(least_upper_bound(greatest_lower_bound(X_27,X_208),X_210),least_upper_bound(X_26,X_27))) )],[refute_0_1752,refute_0_1861]) ).

cnf(refute_0_1863,plain,
    least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))) = least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))),
    inference(subst,[],[refute_0_1748:[bind(Y,$fot(X_208)),bind(X_26,$fot(X_209)),bind(X_28,$fot(least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))))]]) ).

cnf(refute_0_1864,plain,
    least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))) = least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27)),
    inference(subst,[],[refute_0_1742:[bind(X_11,$fot(greatest_lower_bound(X_209,X_208)))]]) ).

cnf(refute_0_1865,plain,
    ( least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))) != least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))
    | least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))) != least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))
    | least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))) = least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))),least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))) ),[0,1],$fot(least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27)))]]) ).

cnf(refute_0_1866,plain,
    ( least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))) != least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))
    | least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))) = least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))),least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))) )],[refute_0_1864,refute_0_1865]) ).

cnf(refute_0_1867,plain,
    least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))) = least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))),least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))) )],[refute_0_1863,refute_0_1866]) ).

cnf(refute_0_1868,plain,
    least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))) = least_upper_bound(X_209,least_upper_bound(X_26,X_27)),
    inference(subst,[],[refute_0_1748:[bind(Y,$fot(X_208)),bind(X_26,$fot(X_209)),bind(X_28,$fot(least_upper_bound(X_26,X_27)))]]) ).

cnf(refute_0_1869,plain,
    ( least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))) != least_upper_bound(X_209,least_upper_bound(X_26,X_27))
    | least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))) != least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))
    | least_upper_bound(X_209,least_upper_bound(X_26,X_27)) = least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))),least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))) ),[0],$fot(least_upper_bound(X_209,least_upper_bound(X_26,X_27)))]]) ).

cnf(refute_0_1870,plain,
    ( least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))) != least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))
    | least_upper_bound(X_209,least_upper_bound(X_26,X_27)) = least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))),least_upper_bound(X_209,least_upper_bound(X_26,X_27))) )],[refute_0_1868,refute_0_1869]) ).

cnf(refute_0_1871,plain,
    least_upper_bound(X_209,least_upper_bound(X_26,X_27)) = least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_209,least_upper_bound(greatest_lower_bound(X_209,X_208),least_upper_bound(X_26,X_27))),least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))) )],[refute_0_1867,refute_0_1870]) ).

cnf(refute_0_1872,plain,
    ( least_upper_bound(X_209,least_upper_bound(X_26,X_27)) != least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))
    | least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))) = least_upper_bound(X_209,least_upper_bound(X_26,X_27)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_209,least_upper_bound(X_26,X_27)))),bind(Y0,$fot(least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))))]]) ).

cnf(refute_0_1873,plain,
    least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208)))) = least_upper_bound(X_209,least_upper_bound(X_26,X_27)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_209,least_upper_bound(X_26,X_27)),least_upper_bound(X_209,least_upper_bound(X_26,least_upper_bound(X_27,greatest_lower_bound(X_209,X_208))))) )],[refute_0_1871,refute_0_1872]) ).

cnf(refute_0_1874,plain,
    least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) = least_upper_bound(X_27,least_upper_bound(X_26,X_210)),
    inference(subst,[],[refute_0_1873:[bind(X_209,$fot(X_27)),bind(X_27,$fot(X_210))]]) ).

cnf(refute_0_1875,plain,
    ( least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) != least_upper_bound(X_27,least_upper_bound(X_26,X_210))
    | least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))
    | least_upper_bound(X_27,least_upper_bound(X_26,X_210)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) ),[0],$fot(least_upper_bound(X_27,least_upper_bound(X_26,X_210)))]]) ).

cnf(refute_0_1876,plain,
    ( least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))
    | least_upper_bound(X_27,least_upper_bound(X_26,X_210)) = least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))),least_upper_bound(X_27,least_upper_bound(X_26,X_210))) )],[refute_0_1874,refute_0_1875]) ).

cnf(refute_0_1877,plain,
    least_upper_bound(X_15,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210))) = least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210))),
    inference(subst,[],[refute_0_577:[bind(X_28,$fot(least_upper_bound(greatest_lower_bound(X_15,X_208),X_210)))]]) ).

cnf(refute_0_1878,plain,
    least_upper_bound(X_15,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210)) = least_upper_bound(X_15,X_210),
    inference(subst,[],[refute_0_1748:[bind(Y,$fot(X_208)),bind(X_26,$fot(X_15)),bind(X_28,$fot(X_210))]]) ).

cnf(refute_0_1879,plain,
    ( least_upper_bound(X_15,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210))) != least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210)))
    | least_upper_bound(X_15,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210)) != least_upper_bound(X_15,X_210)
    | least_upper_bound(X_15,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210))) = least_upper_bound(X_26,least_upper_bound(X_15,X_210)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210))),least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210)))) ),[1,1],$fot(least_upper_bound(X_15,X_210))]]) ).

cnf(refute_0_1880,plain,
    ( least_upper_bound(X_15,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210))) != least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210)))
    | least_upper_bound(X_15,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210))) = least_upper_bound(X_26,least_upper_bound(X_15,X_210)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210)),least_upper_bound(X_15,X_210)) )],[refute_0_1878,refute_0_1879]) ).

cnf(refute_0_1881,plain,
    least_upper_bound(X_15,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210))) = least_upper_bound(X_26,least_upper_bound(X_15,X_210)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210))),least_upper_bound(X_26,least_upper_bound(X_15,least_upper_bound(greatest_lower_bound(X_15,X_208),X_210)))) )],[refute_0_1877,refute_0_1880]) ).

cnf(refute_0_1882,plain,
    least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))) = least_upper_bound(X_26,least_upper_bound(X_27,X_210)),
    inference(subst,[],[refute_0_1881:[bind(X_15,$fot(X_27))]]) ).

cnf(refute_0_1883,plain,
    ( least_upper_bound(X_27,least_upper_bound(X_26,X_210)) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))
    | least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))) != least_upper_bound(X_26,least_upper_bound(X_27,X_210))
    | least_upper_bound(X_27,least_upper_bound(X_26,X_210)) = least_upper_bound(X_26,least_upper_bound(X_27,X_210)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_27,least_upper_bound(X_26,X_210)),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) ),[0],$fot(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))))]]) ).

cnf(refute_0_1884,plain,
    ( least_upper_bound(X_27,least_upper_bound(X_26,X_210)) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))
    | least_upper_bound(X_27,least_upper_bound(X_26,X_210)) = least_upper_bound(X_26,least_upper_bound(X_27,X_210)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210))),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) )],[refute_0_1882,refute_0_1883]) ).

cnf(refute_0_1885,plain,
    ( least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))) != least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))
    | least_upper_bound(X_27,least_upper_bound(X_26,X_210)) = least_upper_bound(X_26,least_upper_bound(X_27,X_210)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(X_26,X_210)),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) )],[refute_0_1876,refute_0_1884]) ).

cnf(refute_0_1886,plain,
    least_upper_bound(X_27,least_upper_bound(X_26,X_210)) = least_upper_bound(X_26,least_upper_bound(X_27,X_210)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(X_210,greatest_lower_bound(X_27,X_208)))),least_upper_bound(X_27,least_upper_bound(X_26,least_upper_bound(greatest_lower_bound(X_27,X_208),X_210)))) )],[refute_0_1862,refute_0_1885]) ).

cnf(refute_0_1887,plain,
    ( least_upper_bound(X_27,least_upper_bound(X_26,X_210)) != least_upper_bound(X_26,least_upper_bound(X_27,X_210))
    | least_upper_bound(X_26,least_upper_bound(X_27,X_210)) = least_upper_bound(X_27,least_upper_bound(X_26,X_210)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_27,least_upper_bound(X_26,X_210)))),bind(Y0,$fot(least_upper_bound(X_26,least_upper_bound(X_27,X_210))))]]) ).

cnf(refute_0_1888,plain,
    least_upper_bound(X_26,least_upper_bound(X_27,X_210)) = least_upper_bound(X_27,least_upper_bound(X_26,X_210)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(X_26,X_210)),least_upper_bound(X_26,least_upper_bound(X_27,X_210))) )],[refute_0_1886,refute_0_1887]) ).

cnf(refute_0_1889,plain,
    least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))),
    inference(subst,[],[refute_0_1888:[bind(X_210,$fot(greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))),bind(X_26,$fot(greatest_lower_bound(X_88,X_89))),bind(X_27,$fot(identity))]]) ).

cnf(refute_0_1890,plain,
    ( least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89)))))
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) != least_upper_bound(identity,greatest_lower_bound(X_88,X_89))
    | least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) = least_upper_bound(identity,greatest_lower_bound(X_88,X_89)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))))),bind(Z0,$fot(least_upper_bound(identity,greatest_lower_bound(X_88,X_89))))]]) ).

cnf(refute_0_1891,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) != least_upper_bound(identity,greatest_lower_bound(X_88,X_89))
    | least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) = least_upper_bound(identity,greatest_lower_bound(X_88,X_89)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89)))))) )],[refute_0_1889,refute_0_1890]) ).

cnf(refute_0_1892,plain,
    least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) = least_upper_bound(identity,greatest_lower_bound(X_88,X_89)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(X_88,X_89),greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_88,X_89))) )],[refute_0_1735,refute_0_1891]) ).

cnf(refute_0_1893,plain,
    ( least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))) != least_upper_bound(identity,greatest_lower_bound(X_88,X_89))
    | least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))) != least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89)))))
    | least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))) = least_upper_bound(identity,greatest_lower_bound(X_88,X_89)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))),least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89)))))) ),[1],$fot(least_upper_bound(identity,greatest_lower_bound(X_88,X_89)))]]) ).

cnf(refute_0_1894,plain,
    ( least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))) != least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89)))))
    | least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))) = least_upper_bound(identity,greatest_lower_bound(X_88,X_89)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89))))),least_upper_bound(identity,greatest_lower_bound(X_88,X_89))) )],[refute_0_1892,refute_0_1893]) ).

cnf(refute_0_1895,plain,
    least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))) = least_upper_bound(identity,greatest_lower_bound(X_88,X_89)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,inverse(X_89)))),least_upper_bound(greatest_lower_bound(X_88,X_89),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X_88,inverse(X_89)))))) )],[refute_0_1631,refute_0_1894]) ).

cnf(refute_0_1896,plain,
    least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = least_upper_bound(identity,greatest_lower_bound(identity,X_60)),
    inference(subst,[],[refute_0_1895:[bind(X_88,$fot(identity)),bind(X_89,$fot(X_60))]]) ).

cnf(refute_0_1897,plain,
    ( least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) != least_upper_bound(identity,greatest_lower_bound(identity,X_60))
    | least_upper_bound(identity,greatest_lower_bound(identity,X_60)) != identity
    | least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = identity ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))))),bind(Y0,$fot(least_upper_bound(identity,greatest_lower_bound(identity,X_60)))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_1898,plain,
    ( least_upper_bound(identity,greatest_lower_bound(identity,X_60)) != identity
    | least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))),least_upper_bound(identity,greatest_lower_bound(identity,X_60))) )],[refute_0_1896,refute_0_1897]) ).

cnf(refute_0_1899,plain,
    least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = identity,
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_60)),identity) )],[refute_0_1586,refute_0_1898]) ).

cnf(refute_0_1900,plain,
    greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))) = identity,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_60)))]]) ).

cnf(refute_0_1901,plain,
    least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))))]]) ).

cnf(refute_0_1902,plain,
    ( greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))) != identity
    | least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) != least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))))
    | least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))),least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1903,plain,
    ( greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))) != identity
    | least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))),least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))))) )],[refute_0_1901,refute_0_1902]) ).

cnf(refute_0_1904,plain,
    least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),identity) )],[refute_0_1900,refute_0_1903]) ).

cnf(refute_0_1905,plain,
    ( least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))))
    | least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) != identity
    | least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = identity ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_1906,plain,
    ( least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) != identity
    | least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))))) )],[refute_0_1904,refute_0_1905]) ).

cnf(refute_0_1907,plain,
    least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) = identity,
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))),identity) )],[refute_0_1899,refute_0_1906]) ).

cnf(refute_0_1908,plain,
    ( least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) != greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))
    | least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) != identity
    | identity = greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))),greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))) ),[0],$fot(identity)]]) ).

cnf(refute_0_1909,plain,
    ( least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) != greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))
    | identity = greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))),identity) )],[refute_0_1907,refute_0_1908]) ).

cnf(refute_0_1910,plain,
    ( greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))) != multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))
    | identity != greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))
    | identity = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))) ),
    introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))) ),[1],$fot(multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))))]]) ).

cnf(refute_0_1911,plain,
    ( identity != greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))
    | identity = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) )],[refute_0_1582,refute_0_1910]) ).

cnf(refute_0_1912,plain,
    ( least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) != greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))
    | identity = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))) ),
    inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))) )],[refute_0_1909,refute_0_1911]) ).

cnf(refute_0_1913,plain,
    identity = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X_60))),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))),greatest_lower_bound(least_upper_bound(X_60,identity),least_upper_bound(identity,inverse(X_60)))) )],[refute_0_1585,refute_0_1912]) ).

cnf(refute_0_1914,plain,
    ( identity != multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))
    | multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))) = identity ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))))]]) ).

cnf(refute_0_1915,plain,
    multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60))) = identity,
    inference(resolve,[$cnf( $equal(identity,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(identity,inverse(X_60)))) )],[refute_0_1913,refute_0_1914]) ).

cnf(refute_0_1916,plain,
    multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))) = identity,
    inference(subst,[],[refute_0_1915:[bind(X_60,$fot(X_612))]]) ).

cnf(refute_0_1917,plain,
    multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))),
    introduced(tautology,[refl,[$fot(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))))]]) ).

cnf(refute_0_1918,plain,
    ( multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))) != identity
    | multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) != multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))))
    | multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1919,plain,
    ( multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))) != identity
    | multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))))) )],[refute_0_1917,refute_0_1918]) ).

cnf(refute_0_1920,plain,
    multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612))),identity) )],[refute_0_1916,refute_0_1919]) ).

cnf(refute_0_1921,plain,
    ( multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) != multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),identity)
    | multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),identity) != inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70))
    | multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))))),bind(Y0,$fot(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),identity))),bind(Z0,$fot(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70))))]]) ).

cnf(refute_0_1922,plain,
    ( multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),identity) != inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70))
    | multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))),multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),identity)) )],[refute_0_1920,refute_0_1921]) ).

cnf(refute_0_1923,plain,
    multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) = inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),identity),inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70))) )],[refute_0_1564,refute_0_1922]) ).

cnf(refute_0_1924,plain,
    ( multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) != multiply(inverse(X_70),greatest_lower_bound(identity,X_612))
    | multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) != inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70))
    | inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))),multiply(inverse(X_70),greatest_lower_bound(identity,X_612))) ),[0],$fot(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)))]]) ).

cnf(refute_0_1925,plain,
    ( multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))) != multiply(inverse(X_70),greatest_lower_bound(identity,X_612))
    | inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))),inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70))) )],[refute_0_1923,refute_0_1924]) ).

cnf(refute_0_1926,plain,
    inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)) = multiply(inverse(X_70),greatest_lower_bound(identity,X_612)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(least_upper_bound(identity,inverse(X_612)),X_70)),multiply(greatest_lower_bound(identity,X_612),least_upper_bound(identity,inverse(X_612)))),multiply(inverse(X_70),greatest_lower_bound(identity,X_612))) )],[refute_0_1563,refute_0_1925]) ).

cnf(refute_0_1927,plain,
    inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))) = multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)),
    inference(subst,[],[refute_0_1926:[bind(X_612,$fot(X_524)),bind(X_70,$fot(multiply(inverse(least_upper_bound(X_524,identity)),X_525)))]]) ).

cnf(refute_0_1928,plain,
    ( multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)) != multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))
    | inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))) != multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524))
    | inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))) = multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))))),bind(Y0,$fot(multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)))),bind(Z0,$fot(multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))))]]) ).

cnf(refute_0_1929,plain,
    ( multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)) != multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))
    | inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))) = multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))),multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524))) )],[refute_0_1927,refute_0_1928]) ).

cnf(refute_0_1930,plain,
    inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))) = multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(inverse(least_upper_bound(X_524,identity)),X_525)),greatest_lower_bound(identity,X_524)),multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))) )],[refute_0_1007,refute_0_1929]) ).

cnf(refute_0_1931,plain,
    ( multiply(inverse(X_525),X_524) != inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525)))
    | inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))) != multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))
    | multiply(inverse(X_525),X_524) = multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_525),X_524),multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))) ),[0],$fot(inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))))]]) ).

cnf(refute_0_1932,plain,
    ( multiply(inverse(X_525),X_524) != inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525)))
    | multiply(inverse(X_525),X_524) = multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525))),multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))) )],[refute_0_1930,refute_0_1931]) ).

cnf(refute_0_1933,plain,
    multiply(inverse(X_525),X_524) = multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_525),X_524),inverse(multiply(least_upper_bound(identity,inverse(X_524)),multiply(inverse(least_upper_bound(X_524,identity)),X_525)))) )],[refute_0_998,refute_0_1932]) ).

cnf(refute_0_1934,plain,
    ( multiply(inverse(X_525),X_524) != multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))
    | multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))) = multiply(inverse(X_525),X_524) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_525),X_524))),bind(Y0,$fot(multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))))]]) ).

cnf(refute_0_1935,plain,
    multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524))) = multiply(inverse(X_525),X_524),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_525),X_524),multiply(inverse(X_525),multiply(least_upper_bound(X_524,identity),greatest_lower_bound(identity,X_524)))) )],[refute_0_1933,refute_0_1934]) ).

cnf(refute_0_1936,plain,
    multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))) = multiply(inverse(greatest_lower_bound(X_129,identity)),X_129),
    inference(subst,[],[refute_0_1935:[bind(X_524,$fot(X_129)),bind(X_525,$fot(greatest_lower_bound(X_129,identity)))]]) ).

cnf(refute_0_1937,plain,
    ( multiply(inverse(greatest_lower_bound(X_129,identity)),X_129) != inverse(greatest_lower_bound(identity,inverse(X_129)))
    | multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))) != multiply(inverse(greatest_lower_bound(X_129,identity)),X_129)
    | multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))) = inverse(greatest_lower_bound(identity,inverse(X_129))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_129,identity)),X_129))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,inverse(X_129)))))]]) ).

cnf(refute_0_1938,plain,
    ( multiply(inverse(greatest_lower_bound(X_129,identity)),X_129) != inverse(greatest_lower_bound(identity,inverse(X_129)))
    | multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))) = inverse(greatest_lower_bound(identity,inverse(X_129))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))),multiply(inverse(greatest_lower_bound(X_129,identity)),X_129)) )],[refute_0_1936,refute_0_1937]) ).

cnf(refute_0_1939,plain,
    multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))) = inverse(greatest_lower_bound(identity,inverse(X_129))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_129,identity)),X_129),inverse(greatest_lower_bound(identity,inverse(X_129)))) )],[refute_0_980,refute_0_1938]) ).

cnf(refute_0_1940,plain,
    ( multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))) != inverse(greatest_lower_bound(identity,inverse(X_129)))
    | least_upper_bound(X_129,identity) != multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129)))
    | least_upper_bound(X_129,identity) = inverse(greatest_lower_bound(identity,inverse(X_129))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_129,identity),multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129)))) ),[1],$fot(inverse(greatest_lower_bound(identity,inverse(X_129))))]]) ).

cnf(refute_0_1941,plain,
    ( least_upper_bound(X_129,identity) != multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129)))
    | least_upper_bound(X_129,identity) = inverse(greatest_lower_bound(identity,inverse(X_129))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129))),inverse(greatest_lower_bound(identity,inverse(X_129)))) )],[refute_0_1939,refute_0_1940]) ).

cnf(refute_0_1942,plain,
    least_upper_bound(X_129,identity) = inverse(greatest_lower_bound(identity,inverse(X_129))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_129,identity),multiply(inverse(greatest_lower_bound(X_129,identity)),multiply(least_upper_bound(X_129,identity),greatest_lower_bound(identity,X_129)))) )],[refute_0_924,refute_0_1941]) ).

cnf(refute_0_1943,plain,
    ( least_upper_bound(X_129,identity) != inverse(greatest_lower_bound(identity,inverse(X_129)))
    | inverse(greatest_lower_bound(identity,inverse(X_129))) = least_upper_bound(X_129,identity) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(X_129,identity))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,inverse(X_129)))))]]) ).

cnf(refute_0_1944,plain,
    inverse(greatest_lower_bound(identity,inverse(X_129))) = least_upper_bound(X_129,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_129,identity),inverse(greatest_lower_bound(identity,inverse(X_129)))) )],[refute_0_1942,refute_0_1943]) ).

cnf(refute_0_1945,plain,
    inverse(greatest_lower_bound(identity,inverse(X_467))) = least_upper_bound(X_467,identity),
    inference(subst,[],[refute_0_1944:[bind(X_129,$fot(X_467))]]) ).

cnf(refute_0_1946,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)))]]) ).

cnf(refute_0_1947,plain,
    ( multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z))
    | inverse(greatest_lower_bound(identity,inverse(X_467))) != least_upper_bound(X_467,identity)
    | multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)) = multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)),multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z))) ),[1,0],$fot(least_upper_bound(X_467,identity))]]) ).

cnf(refute_0_1948,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_467))) != least_upper_bound(X_467,identity)
    | multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)) = multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)),multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z))) )],[refute_0_1946,refute_0_1947]) ).

cnf(refute_0_1949,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)) = multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_467))),least_upper_bound(X_467,identity)) )],[refute_0_1945,refute_0_1948]) ).

cnf(refute_0_1950,plain,
    ( multiply(X_467,Z) != multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z))
    | multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)) != multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z))
    | multiply(X_467,Z) = multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_467,Z),multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z))) ),[0],$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)))]]) ).

cnf(refute_0_1951,plain,
    ( multiply(X_467,Z) != multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z))
    | multiply(X_467,Z) = multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z)),multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z))) )],[refute_0_1949,refute_0_1950]) ).

cnf(refute_0_1952,plain,
    multiply(X_467,Z) = multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z)),
    inference(resolve,[$cnf( $equal(multiply(X_467,Z),multiply(inverse(greatest_lower_bound(identity,inverse(X_467))),multiply(greatest_lower_bound(X_467,identity),Z))) )],[refute_0_841,refute_0_1951]) ).

cnf(refute_0_1953,plain,
    ( multiply(X_467,Z) != multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z))
    | multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z)) = multiply(X_467,Z) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(X_467,Z))),bind(Y0,$fot(multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z))))]]) ).

cnf(refute_0_1954,plain,
    multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z)) = multiply(X_467,Z),
    inference(resolve,[$cnf( $equal(multiply(X_467,Z),multiply(least_upper_bound(X_467,identity),multiply(greatest_lower_bound(X_467,identity),Z))) )],[refute_0_1952,refute_0_1953]) ).

cnf(refute_0_1955,plain,
    multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = multiply(X_561,inverse(least_upper_bound(X_561,identity))),
    inference(subst,[],[refute_0_1954:[bind(Z,$fot(inverse(least_upper_bound(X_561,identity)))),bind(X_467,$fot(X_561))]]) ).

cnf(refute_0_1956,plain,
    ( multiply(X_561,inverse(least_upper_bound(X_561,identity))) != inverse(least_upper_bound(identity,inverse(X_561)))
    | multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != multiply(X_561,inverse(least_upper_bound(X_561,identity)))
    | multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = inverse(least_upper_bound(identity,inverse(X_561))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))))),bind(Y0,$fot(multiply(X_561,inverse(least_upper_bound(X_561,identity))))),bind(Z0,$fot(inverse(least_upper_bound(identity,inverse(X_561)))))]]) ).

cnf(refute_0_1957,plain,
    ( multiply(X_561,inverse(least_upper_bound(X_561,identity))) != inverse(least_upper_bound(identity,inverse(X_561)))
    | multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = inverse(least_upper_bound(identity,inverse(X_561))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),multiply(X_561,inverse(least_upper_bound(X_561,identity)))) )],[refute_0_1955,refute_0_1956]) ).

cnf(refute_0_1958,plain,
    multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) = inverse(least_upper_bound(identity,inverse(X_561))),
    inference(resolve,[$cnf( $equal(multiply(X_561,inverse(least_upper_bound(X_561,identity))),inverse(least_upper_bound(identity,inverse(X_561)))) )],[refute_0_756,refute_0_1957]) ).

cnf(refute_0_1959,plain,
    ( multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != greatest_lower_bound(identity,X_561)
    | multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != inverse(least_upper_bound(identity,inverse(X_561)))
    | inverse(least_upper_bound(identity,inverse(X_561))) = greatest_lower_bound(identity,X_561) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),greatest_lower_bound(identity,X_561)) ),[0],$fot(inverse(least_upper_bound(identity,inverse(X_561))))]]) ).

cnf(refute_0_1960,plain,
    ( multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))) != greatest_lower_bound(identity,X_561)
    | inverse(least_upper_bound(identity,inverse(X_561))) = greatest_lower_bound(identity,X_561) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),inverse(least_upper_bound(identity,inverse(X_561)))) )],[refute_0_1958,refute_0_1959]) ).

cnf(refute_0_1961,plain,
    inverse(least_upper_bound(identity,inverse(X_561))) = greatest_lower_bound(identity,X_561),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_561,identity),multiply(greatest_lower_bound(X_561,identity),inverse(least_upper_bound(X_561,identity)))),greatest_lower_bound(identity,X_561)) )],[refute_0_821,refute_0_1960]) ).

cnf(refute_0_1962,plain,
    inverse(least_upper_bound(identity,inverse(X_169))) = greatest_lower_bound(identity,X_169),
    inference(subst,[],[refute_0_1961:[bind(X_561,$fot(X_169))]]) ).

cnf(refute_0_1963,plain,
    multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))))]]) ).

cnf(refute_0_1964,plain,
    ( multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) != multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169))))
    | inverse(least_upper_bound(identity,inverse(X_169))) != greatest_lower_bound(identity,X_169)
    | multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,X_169),greatest_lower_bound(identity,X_169)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))),multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169))))) ),[1,1],$fot(greatest_lower_bound(identity,X_169))]]) ).

cnf(refute_0_1965,plain,
    ( inverse(least_upper_bound(identity,inverse(X_169))) != greatest_lower_bound(identity,X_169)
    | multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,X_169),greatest_lower_bound(identity,X_169)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))),multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169))))) )],[refute_0_1963,refute_0_1964]) ).

cnf(refute_0_1966,plain,
    multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) = multiply(least_upper_bound(identity,X_169),greatest_lower_bound(identity,X_169)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_169))),greatest_lower_bound(identity,X_169)) )],[refute_0_1962,refute_0_1965]) ).

cnf(refute_0_1967,plain,
    ( multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) != X_169
    | multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) != multiply(least_upper_bound(identity,X_169),greatest_lower_bound(identity,X_169))
    | multiply(least_upper_bound(identity,X_169),greatest_lower_bound(identity,X_169)) = X_169 ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))),X_169) ),[0],$fot(multiply(least_upper_bound(identity,X_169),greatest_lower_bound(identity,X_169)))]]) ).

cnf(refute_0_1968,plain,
    ( multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))) != X_169
    | multiply(least_upper_bound(identity,X_169),greatest_lower_bound(identity,X_169)) = X_169 ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))),multiply(least_upper_bound(identity,X_169),greatest_lower_bound(identity,X_169))) )],[refute_0_1966,refute_0_1967]) ).

cnf(refute_0_1969,plain,
    multiply(least_upper_bound(identity,X_169),greatest_lower_bound(identity,X_169)) = X_169,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_169),inverse(least_upper_bound(identity,inverse(X_169)))),X_169) )],[refute_0_715,refute_0_1968]) ).

cnf(refute_0_1970,plain,
    multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)) = X_86,
    inference(subst,[],[refute_0_1969:[bind(X_169,$fot(X_86))]]) ).

cnf(refute_0_1971,plain,
    inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))) = inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))),
    introduced(tautology,[refl,[$fot(inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))]]) ).

cnf(refute_0_1972,plain,
    ( multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)) != X_86
    | inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))) != inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))
    | inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))) = inverse(X_86) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) ),[1,0],$fot(X_86)]]) ).

cnf(refute_0_1973,plain,
    ( multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)) != X_86
    | inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))) = inverse(X_86) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) )],[refute_0_1971,refute_0_1972]) ).

cnf(refute_0_1974,plain,
    inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))) = inverse(X_86),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)),X_86) )],[refute_0_1970,refute_0_1973]) ).

cnf(refute_0_1975,plain,
    multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) = multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))))]]) ).

cnf(refute_0_1976,plain,
    ( multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) != multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))
    | inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))) != inverse(X_86)
    | multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) = multiply(least_upper_bound(X_86,identity),inverse(X_86)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))),multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))) ),[1,1],$fot(inverse(X_86))]]) ).

cnf(refute_0_1977,plain,
    ( inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))) != inverse(X_86)
    | multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) = multiply(least_upper_bound(X_86,identity),inverse(X_86)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))),multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))) )],[refute_0_1975,refute_0_1976]) ).

cnf(refute_0_1978,plain,
    multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) = multiply(least_upper_bound(X_86,identity),inverse(X_86)),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))),inverse(X_86)) )],[refute_0_1974,refute_0_1977]) ).

cnf(refute_0_1979,plain,
    ( multiply(least_upper_bound(X_86,identity),inverse(X_86)) != least_upper_bound(identity,inverse(X_86))
    | multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) != multiply(least_upper_bound(X_86,identity),inverse(X_86))
    | multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) = least_upper_bound(identity,inverse(X_86)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))))),bind(Y0,$fot(multiply(least_upper_bound(X_86,identity),inverse(X_86)))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_86))))]]) ).

cnf(refute_0_1980,plain,
    ( multiply(least_upper_bound(X_86,identity),inverse(X_86)) != least_upper_bound(identity,inverse(X_86))
    | multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) = least_upper_bound(identity,inverse(X_86)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))),multiply(least_upper_bound(X_86,identity),inverse(X_86))) )],[refute_0_1978,refute_0_1979]) ).

cnf(refute_0_1981,plain,
    multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) = least_upper_bound(identity,inverse(X_86)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),inverse(X_86)),least_upper_bound(identity,inverse(X_86))) )],[refute_0_444,refute_0_1980]) ).

cnf(refute_0_1982,plain,
    ( multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))) != least_upper_bound(identity,inverse(X_86))
    | inverse(greatest_lower_bound(identity,X_86)) != multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))
    | inverse(greatest_lower_bound(identity,X_86)) = least_upper_bound(identity,inverse(X_86)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_86)),multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))) ),[1],$fot(least_upper_bound(identity,inverse(X_86)))]]) ).

cnf(refute_0_1983,plain,
    ( inverse(greatest_lower_bound(identity,X_86)) != multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))
    | inverse(greatest_lower_bound(identity,X_86)) = least_upper_bound(identity,inverse(X_86)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86)))),least_upper_bound(identity,inverse(X_86))) )],[refute_0_1981,refute_0_1982]) ).

cnf(refute_0_1984,plain,
    inverse(greatest_lower_bound(identity,X_86)) = least_upper_bound(identity,inverse(X_86)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_86)),multiply(least_upper_bound(X_86,identity),inverse(multiply(least_upper_bound(identity,X_86),greatest_lower_bound(identity,X_86))))) )],[refute_0_433,refute_0_1983]) ).

cnf(refute_0_1985,plain,
    ( inverse(greatest_lower_bound(identity,X_86)) != least_upper_bound(identity,inverse(X_86))
    | least_upper_bound(identity,inverse(X_86)) = inverse(greatest_lower_bound(identity,X_86)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_86)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_86))))]]) ).

cnf(refute_0_1986,plain,
    least_upper_bound(identity,inverse(X_86)) = inverse(greatest_lower_bound(identity,X_86)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_86)),least_upper_bound(identity,inverse(X_86))) )],[refute_0_1984,refute_0_1985]) ).

cnf(refute_0_1987,plain,
    least_upper_bound(identity,inverse(X_126)) = inverse(greatest_lower_bound(identity,X_126)),
    inference(subst,[],[refute_0_1986:[bind(X_86,$fot(X_126))]]) ).

cnf(refute_0_1988,plain,
    ( multiply(least_upper_bound(identity,X_126),inverse(X_126)) != least_upper_bound(identity,inverse(X_126))
    | least_upper_bound(identity,inverse(X_126)) != inverse(greatest_lower_bound(identity,X_126))
    | multiply(least_upper_bound(identity,X_126),inverse(X_126)) = inverse(greatest_lower_bound(identity,X_126)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_126),inverse(X_126)),inverse(greatest_lower_bound(identity,X_126))) ),[0],$fot(least_upper_bound(identity,inverse(X_126)))]]) ).

cnf(refute_0_1989,plain,
    ( multiply(least_upper_bound(identity,X_126),inverse(X_126)) != least_upper_bound(identity,inverse(X_126))
    | multiply(least_upper_bound(identity,X_126),inverse(X_126)) = inverse(greatest_lower_bound(identity,X_126)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_126)),inverse(greatest_lower_bound(identity,X_126))) )],[refute_0_1987,refute_0_1988]) ).

cnf(refute_0_1990,plain,
    multiply(least_upper_bound(identity,X_126),inverse(X_126)) = inverse(greatest_lower_bound(identity,X_126)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_126),inverse(X_126)),least_upper_bound(identity,inverse(X_126))) )],[refute_0_157,refute_0_1989]) ).

cnf(refute_0_1991,plain,
    multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),inverse(multiply(inverse(X),X_30))) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30))),
    inference(subst,[],[refute_0_1990:[bind(X_126,$fot(multiply(inverse(X),X_30)))]]) ).

cnf(refute_0_1992,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),inverse(multiply(inverse(X),X_30))) != inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30)))
    | inverse(multiply(inverse(X),X_30)) != multiply(inverse(X_30),X)
    | multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),inverse(multiply(inverse(X),X_30))),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30)))) ),[0,1],$fot(multiply(inverse(X_30),X))]]) ).

cnf(refute_0_1993,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),inverse(multiply(inverse(X),X_30))) != inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30)))
    | multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) )],[refute_0_22,refute_0_1992]) ).

cnf(refute_0_1994,plain,
    multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),inverse(multiply(inverse(X),X_30))),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30)))) )],[refute_0_1991,refute_0_1993]) ).

cnf(refute_0_1995,plain,
    multiply(identity,multiply(inverse(X_30),X)) = multiply(inverse(X_30),X),
    inference(subst,[],[left_identity:[bind(X,$fot(multiply(inverse(X_30),X)))]]) ).

cnf(refute_0_1996,plain,
    multiply(multiply(identity,inverse(X_30)),X) = multiply(identity,multiply(inverse(X_30),X)),
    inference(subst,[],[associativity:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_30))),bind(Z,$fot(X))]]) ).

cnf(refute_0_1997,plain,
    ( multiply(multiply(identity,inverse(X_30)),X) != multiply(identity,multiply(inverse(X_30),X))
    | multiply(identity,multiply(inverse(X_30),X)) != multiply(inverse(X_30),X)
    | multiply(multiply(identity,inverse(X_30)),X) = multiply(inverse(X_30),X) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(multiply(identity,inverse(X_30)),X))),bind(Y0,$fot(multiply(identity,multiply(inverse(X_30),X)))),bind(Z0,$fot(multiply(inverse(X_30),X)))]]) ).

cnf(refute_0_1998,plain,
    ( multiply(identity,multiply(inverse(X_30),X)) != multiply(inverse(X_30),X)
    | multiply(multiply(identity,inverse(X_30)),X) = multiply(inverse(X_30),X) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(identity,inverse(X_30)),X),multiply(identity,multiply(inverse(X_30),X))) )],[refute_0_1996,refute_0_1997]) ).

cnf(refute_0_1999,plain,
    multiply(multiply(identity,inverse(X_30)),X) = multiply(inverse(X_30),X),
    inference(resolve,[$cnf( $equal(multiply(identity,multiply(inverse(X_30),X)),multiply(inverse(X_30),X)) )],[refute_0_1995,refute_0_1998]) ).

cnf(refute_0_2000,plain,
    least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)) = least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)))]]) ).

cnf(refute_0_2001,plain,
    ( multiply(multiply(identity,inverse(X_30)),X) != multiply(inverse(X_30),X)
    | least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)) != least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X))
    | least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)) = least_upper_bound(identity,multiply(inverse(X_30),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)),least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X))) ),[1,1],$fot(multiply(inverse(X_30),X))]]) ).

cnf(refute_0_2002,plain,
    ( multiply(multiply(identity,inverse(X_30)),X) != multiply(inverse(X_30),X)
    | least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)) = least_upper_bound(identity,multiply(inverse(X_30),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)),least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X))) )],[refute_0_2000,refute_0_2001]) ).

cnf(refute_0_2003,plain,
    least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)) = least_upper_bound(identity,multiply(inverse(X_30),X)),
    inference(resolve,[$cnf( $equal(multiply(multiply(identity,inverse(X_30)),X),multiply(inverse(X_30),X)) )],[refute_0_1999,refute_0_2002]) ).

cnf(refute_0_2004,plain,
    multiply(least_upper_bound(inverse(X),multiply(identity,inverse(X_30))),X) = least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)),
    inference(subst,[],[refute_0_1637:[bind(X_120,$fot(X)),bind(X_122,$fot(multiply(identity,inverse(X_30))))]]) ).

cnf(refute_0_2005,plain,
    multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))) = least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),multiply(X_122,inverse(multiply(X,X_122)))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(multiply(X,X_122)))),bind(Y,$fot(X_121)),bind(Z,$fot(X_122))]]) ).

cnf(refute_0_2006,plain,
    inverse(X) = multiply(X_122,inverse(multiply(X,X_122))),
    inference(subst,[],[refute_0_172:[bind(X_69,$fot(X_122))]]) ).

cnf(refute_0_2007,plain,
    ( inverse(X) != multiply(X_122,inverse(multiply(X,X_122)))
    | multiply(X_122,inverse(multiply(X,X_122))) = inverse(X) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(inverse(X))),bind(Y0,$fot(multiply(X_122,inverse(multiply(X,X_122)))))]]) ).

cnf(refute_0_2008,plain,
    multiply(X_122,inverse(multiply(X,X_122))) = inverse(X),
    inference(resolve,[$cnf( $equal(inverse(X),multiply(X_122,inverse(multiply(X,X_122)))) )],[refute_0_2006,refute_0_2007]) ).

cnf(refute_0_2009,plain,
    ( multiply(X_122,inverse(multiply(X,X_122))) != inverse(X)
    | multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))) != least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),multiply(X_122,inverse(multiply(X,X_122))))
    | multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))) = least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),inverse(X)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))),least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),multiply(X_122,inverse(multiply(X,X_122))))) ),[1,1],$fot(inverse(X))]]) ).

cnf(refute_0_2010,plain,
    ( multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))) != least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),multiply(X_122,inverse(multiply(X,X_122))))
    | multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))) = least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),inverse(X)) ),
    inference(resolve,[$cnf( $equal(multiply(X_122,inverse(multiply(X,X_122))),inverse(X)) )],[refute_0_2008,refute_0_2009]) ).

cnf(refute_0_2011,plain,
    multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))) = least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),inverse(X)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))),least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),multiply(X_122,inverse(multiply(X,X_122))))) )],[refute_0_2005,refute_0_2010]) ).

cnf(refute_0_2012,plain,
    least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),inverse(X)) = least_upper_bound(inverse(X),multiply(X_121,inverse(multiply(X,X_122)))),
    inference(subst,[],[refute_0_148:[bind(X_11,$fot(X_121)),bind(X_113,$fot(inverse(multiply(X,X_122)))),bind(X_28,$fot(inverse(X)))]]) ).

cnf(refute_0_2013,plain,
    ( multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))) != least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),inverse(X))
    | least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),inverse(X)) != least_upper_bound(inverse(X),multiply(X_121,inverse(multiply(X,X_122))))
    | multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))) = least_upper_bound(inverse(X),multiply(X_121,inverse(multiply(X,X_122)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))),least_upper_bound(inverse(X),multiply(X_121,inverse(multiply(X,X_122))))) ),[0],$fot(least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),inverse(X)))]]) ).

cnf(refute_0_2014,plain,
    ( multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))) != least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),inverse(X))
    | multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))) = least_upper_bound(inverse(X),multiply(X_121,inverse(multiply(X,X_122)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),inverse(X)),least_upper_bound(inverse(X),multiply(X_121,inverse(multiply(X,X_122))))) )],[refute_0_2012,refute_0_2013]) ).

cnf(refute_0_2015,plain,
    multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))) = least_upper_bound(inverse(X),multiply(X_121,inverse(multiply(X,X_122)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,X_122),inverse(multiply(X,X_122))),least_upper_bound(multiply(X_121,inverse(multiply(X,X_122))),inverse(X))) )],[refute_0_2011,refute_0_2014]) ).

cnf(refute_0_2016,plain,
    multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))) = least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),
    inference(subst,[],[refute_0_2015:[bind(X,$fot(inverse(multiply(X_523,X_525)))),bind(X_122,$fot(multiply(X_523,X_524)))]]) ).

cnf(refute_0_2017,plain,
    multiply(inverse(X_525),X_524) = multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)),
    inference(subst,[],[refute_0_987:[bind(Y,$fot(X_523)),bind(Z,$fot(X_524)),bind(X_72,$fot(X_525))]]) ).

cnf(refute_0_2018,plain,
    ( multiply(inverse(X_525),X_524) != multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))
    | multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)) = multiply(inverse(X_525),X_524) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_525),X_524))),bind(Y0,$fot(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))]]) ).

cnf(refute_0_2019,plain,
    multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)) = multiply(inverse(X_525),X_524),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_525),X_524),multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))) )],[refute_0_2017,refute_0_2018]) ).

cnf(refute_0_2020,plain,
    ( multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)) != multiply(inverse(X_525),X_524)
    | multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))) != least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))
    | multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) = least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))),least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))) ),[0,1,0],$fot(multiply(inverse(X_525),X_524))]]) ).

cnf(refute_0_2021,plain,
    ( multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))) != least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))
    | multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) = least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)),multiply(inverse(X_525),X_524)) )],[refute_0_2019,refute_0_2020]) ).

cnf(refute_0_2022,plain,
    multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) = least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))),least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))) )],[refute_0_2016,refute_0_2021]) ).

cnf(refute_0_2023,plain,
    inverse(multiply(inverse(X_525),X_524)) = multiply(inverse(X_524),X_525),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_525)),bind(X_30,$fot(X_524))]]) ).

cnf(refute_0_2024,plain,
    multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) = multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))))]]) ).

cnf(refute_0_2025,plain,
    ( multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) != multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524)))
    | inverse(multiply(inverse(X_525),X_524)) != multiply(inverse(X_524),X_525)
    | multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) = multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))),multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524)))) ),[1,1],$fot(multiply(inverse(X_524),X_525))]]) ).

cnf(refute_0_2026,plain,
    ( inverse(multiply(inverse(X_525),X_524)) != multiply(inverse(X_524),X_525)
    | multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) = multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))),multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524)))) )],[refute_0_2024,refute_0_2025]) ).

cnf(refute_0_2027,plain,
    multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) = multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_525),X_524)),multiply(inverse(X_524),X_525)) )],[refute_0_2023,refute_0_2026]) ).

cnf(refute_0_2028,plain,
    ( multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) != multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525))
    | multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) != least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))
    | multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)) = least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))),least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))) ),[0],$fot(multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)))]]) ).

cnf(refute_0_2029,plain,
    ( multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) != least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))
    | multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)) = least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))),multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525))) )],[refute_0_2027,refute_0_2028]) ).

cnf(refute_0_2030,plain,
    multiply(least_upper_bound(X_121,multiply(X,Y)),X_120) = least_upper_bound(multiply(X_121,X_120),multiply(multiply(X,Y),X_120)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_120)),bind(Y,$fot(X_121)),bind(Z,$fot(multiply(X,Y)))]]) ).

cnf(refute_0_2031,plain,
    multiply(multiply(X,Y),X_120) = multiply(X,multiply(Y,X_120)),
    inference(subst,[],[associativity:[bind(Z,$fot(X_120))]]) ).

cnf(refute_0_2032,plain,
    ( multiply(multiply(X,Y),X_120) != multiply(X,multiply(Y,X_120))
    | multiply(least_upper_bound(X_121,multiply(X,Y)),X_120) != least_upper_bound(multiply(X_121,X_120),multiply(multiply(X,Y),X_120))
    | multiply(least_upper_bound(X_121,multiply(X,Y)),X_120) = least_upper_bound(multiply(X_121,X_120),multiply(X,multiply(Y,X_120))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_121,multiply(X,Y)),X_120),least_upper_bound(multiply(X_121,X_120),multiply(multiply(X,Y),X_120))) ),[1,1],$fot(multiply(X,multiply(Y,X_120)))]]) ).

cnf(refute_0_2033,plain,
    ( multiply(least_upper_bound(X_121,multiply(X,Y)),X_120) != least_upper_bound(multiply(X_121,X_120),multiply(multiply(X,Y),X_120))
    | multiply(least_upper_bound(X_121,multiply(X,Y)),X_120) = least_upper_bound(multiply(X_121,X_120),multiply(X,multiply(Y,X_120))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_120),multiply(X,multiply(Y,X_120))) )],[refute_0_2031,refute_0_2032]) ).

cnf(refute_0_2034,plain,
    multiply(least_upper_bound(X_121,multiply(X,Y)),X_120) = least_upper_bound(multiply(X_121,X_120),multiply(X,multiply(Y,X_120))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,multiply(X,Y)),X_120),least_upper_bound(multiply(X_121,X_120),multiply(multiply(X,Y),X_120))) )],[refute_0_2030,refute_0_2033]) ).

cnf(refute_0_2035,plain,
    ( multiply(least_upper_bound(X_121,multiply(X,Y)),X_120) != least_upper_bound(multiply(X_121,X_120),multiply(X,multiply(Y,X_120)))
    | least_upper_bound(multiply(X_121,X_120),multiply(X,multiply(Y,X_120))) = multiply(least_upper_bound(X_121,multiply(X,Y)),X_120) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(least_upper_bound(X_121,multiply(X,Y)),X_120))),bind(Y0,$fot(least_upper_bound(multiply(X_121,X_120),multiply(X,multiply(Y,X_120)))))]]) ).

cnf(refute_0_2036,plain,
    least_upper_bound(multiply(X_121,X_120),multiply(X,multiply(Y,X_120))) = multiply(least_upper_bound(X_121,multiply(X,Y)),X_120),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,multiply(X,Y)),X_120),least_upper_bound(multiply(X_121,X_120),multiply(X,multiply(Y,X_120)))) )],[refute_0_2034,refute_0_2035]) ).

cnf(refute_0_2037,plain,
    least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525))) = multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525),
    inference(subst,[],[refute_0_2036:[bind(X,$fot(X_121)),bind(Y,$fot(inverse(X_524))),bind(X_120,$fot(X_525)),bind(X_121,$fot(X_523))]]) ).

cnf(refute_0_2038,plain,
    ( multiply(inverse(X_72),Z) != multiply(inverse(multiply(Y,X_72)),multiply(Y,Z))
    | multiply(inverse(multiply(Y,X_72)),multiply(Y,Z)) = multiply(inverse(X_72),Z) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(multiply(inverse(X_72),Z))),bind(Y0,$fot(multiply(inverse(multiply(Y,X_72)),multiply(Y,Z))))]]) ).

cnf(refute_0_2039,plain,
    multiply(inverse(multiply(Y,X_72)),multiply(Y,Z)) = multiply(inverse(X_72),Z),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_72),Z),multiply(inverse(multiply(Y,X_72)),multiply(Y,Z))) )],[refute_0_987,refute_0_2038]) ).

cnf(refute_0_2040,plain,
    multiply(inverse(multiply(X_523,X_524)),multiply(X_523,X_525)) = multiply(inverse(X_524),X_525),
    inference(subst,[],[refute_0_2039:[bind(Y,$fot(X_523)),bind(Z,$fot(X_525)),bind(X_72,$fot(X_524))]]) ).

cnf(refute_0_2041,plain,
    inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))) = multiply(inverse(multiply(X_523,X_524)),multiply(X_523,X_525)),
    inference(subst,[],[refute_0_22:[bind(X,$fot(multiply(X_523,X_525))),bind(X_30,$fot(multiply(X_523,X_524)))]]) ).

cnf(refute_0_2042,plain,
    ( multiply(inverse(multiply(X_523,X_524)),multiply(X_523,X_525)) != multiply(inverse(X_524),X_525)
    | inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))) != multiply(inverse(multiply(X_523,X_524)),multiply(X_523,X_525))
    | inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))) = multiply(inverse(X_524),X_525) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),bind(Y0,$fot(multiply(inverse(multiply(X_523,X_524)),multiply(X_523,X_525)))),bind(Z0,$fot(multiply(inverse(X_524),X_525)))]]) ).

cnf(refute_0_2043,plain,
    ( multiply(inverse(multiply(X_523,X_524)),multiply(X_523,X_525)) != multiply(inverse(X_524),X_525)
    | inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))) = multiply(inverse(X_524),X_525) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))),multiply(inverse(multiply(X_523,X_524)),multiply(X_523,X_525))) )],[refute_0_2041,refute_0_2042]) ).

cnf(refute_0_2044,plain,
    inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))) = multiply(inverse(X_524),X_525),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_523,X_524)),multiply(X_523,X_525)),multiply(inverse(X_524),X_525)) )],[refute_0_2040,refute_0_2043]) ).

cnf(refute_0_2045,plain,
    multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))) = multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))),
    introduced(tautology,[refl,[$fot(multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))]]) ).

cnf(refute_0_2046,plain,
    ( multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))) != multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))
    | inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))) != multiply(inverse(X_524),X_525)
    | multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))) = multiply(X_121,multiply(inverse(X_524),X_525)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) ),[1,1],$fot(multiply(inverse(X_524),X_525))]]) ).

cnf(refute_0_2047,plain,
    ( inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))) != multiply(inverse(X_524),X_525)
    | multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))) = multiply(X_121,multiply(inverse(X_524),X_525)) ),
    inference(resolve,[$cnf( $equal(multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) )],[refute_0_2045,refute_0_2046]) ).

cnf(refute_0_2048,plain,
    multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))) = multiply(X_121,multiply(inverse(X_524),X_525)),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))),multiply(inverse(X_524),X_525)) )],[refute_0_2044,refute_0_2047]) ).

cnf(refute_0_2049,plain,
    least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))))]]) ).

cnf(refute_0_2050,plain,
    ( multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))) != multiply(X_121,multiply(inverse(X_524),X_525))
    | least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) != least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))
    | least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))) ),[1,1],$fot(multiply(X_121,multiply(inverse(X_524),X_525)))]]) ).

cnf(refute_0_2051,plain,
    ( multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))) != multiply(X_121,multiply(inverse(X_524),X_525))
    | least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))) )],[refute_0_2049,refute_0_2050]) ).

cnf(refute_0_2052,plain,
    least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525))),
    inference(resolve,[$cnf( $equal(multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))),multiply(X_121,multiply(inverse(X_524),X_525))) )],[refute_0_2048,refute_0_2051]) ).

cnf(refute_0_2053,plain,
    inverse(inverse(multiply(X_523,X_525))) = multiply(X_523,X_525),
    inference(subst,[],[p11_2:[bind(X,$fot(multiply(X_523,X_525)))]]) ).

cnf(refute_0_2054,plain,
    least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))))]]) ).

cnf(refute_0_2055,plain,
    ( inverse(inverse(multiply(X_523,X_525))) != multiply(X_523,X_525)
    | least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) != least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))
    | least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))) ),[1,0],$fot(multiply(X_523,X_525))]]) ).

cnf(refute_0_2056,plain,
    ( inverse(inverse(multiply(X_523,X_525))) != multiply(X_523,X_525)
    | least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))) )],[refute_0_2054,refute_0_2055]) ).

cnf(refute_0_2057,plain,
    least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),
    inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_523,X_525))),multiply(X_523,X_525)) )],[refute_0_2053,refute_0_2056]) ).

cnf(refute_0_2058,plain,
    ( least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) != least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525)))
    | least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) != least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))
    | least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525))) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))))),bind(Y0,$fot(least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))))),bind(Z0,$fot(least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525)))))]]) ).

cnf(refute_0_2059,plain,
    ( least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) != least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525)))
    | least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))) )],[refute_0_2057,refute_0_2058]) ).

cnf(refute_0_2060,plain,
    least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_523,X_525),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525)))) )],[refute_0_2052,refute_0_2059]) ).

cnf(refute_0_2061,plain,
    ( least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525))) != multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525)
    | least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) != least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525)))
    | least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))))),bind(Y0,$fot(least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525))))),bind(Z0,$fot(multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525)))]]) ).

cnf(refute_0_2062,plain,
    ( least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525))) != multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525)
    | least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525)))) )],[refute_0_2060,refute_0_2061]) ).

cnf(refute_0_2063,plain,
    least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) = multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_523,X_525),multiply(X_121,multiply(inverse(X_524),X_525))),multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525)) )],[refute_0_2037,refute_0_2062]) ).

cnf(refute_0_2064,plain,
    ( multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)) != least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))
    | least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))) != multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525)
    | multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)) = multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)),multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525)) ),[0],$fot(least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))))]]) ).

cnf(refute_0_2065,plain,
    ( multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)) != least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))
    | multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)) = multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524))))),multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525)) )],[refute_0_2063,refute_0_2064]) ).

cnf(refute_0_2066,plain,
    ( multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))) != least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))
    | multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)) = multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)),least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))) )],[refute_0_2029,refute_0_2065]) ).

cnf(refute_0_2067,plain,
    multiply(least_upper_bound(X_121,multiply(X_523,X_524)),multiply(inverse(X_524),X_525)) = multiply(least_upper_bound(X_523,multiply(X_121,inverse(X_524))),X_525),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_121,multiply(X_523,X_524)),inverse(multiply(inverse(X_525),X_524))),least_upper_bound(inverse(inverse(multiply(X_523,X_525))),multiply(X_121,inverse(multiply(inverse(multiply(X_523,X_525)),multiply(X_523,X_524)))))) )],[refute_0_2022,refute_0_2066]) ).

cnf(refute_0_2068,plain,
    multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) = multiply(least_upper_bound(inverse(X),multiply(identity,inverse(X_30))),X),
    inference(subst,[],[refute_0_2067:[bind(X_121,$fot(identity)),bind(X_523,$fot(inverse(X))),bind(X_524,$fot(X_30)),bind(X_525,$fot(X))]]) ).

cnf(refute_0_2069,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) != multiply(least_upper_bound(inverse(X),multiply(identity,inverse(X_30))),X)
    | multiply(least_upper_bound(inverse(X),multiply(identity,inverse(X_30))),X) != least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X))
    | multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) = least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(X),multiply(identity,inverse(X_30))),X))),bind(Z0,$fot(least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X))))]]) ).

cnf(refute_0_2070,plain,
    ( multiply(least_upper_bound(inverse(X),multiply(identity,inverse(X_30))),X) != least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X))
    | multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) = least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)),multiply(least_upper_bound(inverse(X),multiply(identity,inverse(X_30))),X)) )],[refute_0_2068,refute_0_2069]) ).

cnf(refute_0_2071,plain,
    multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) = least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X),multiply(identity,inverse(X_30))),X),least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X))) )],[refute_0_2004,refute_0_2070]) ).

cnf(refute_0_2072,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) != least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X))
    | least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)) != least_upper_bound(identity,multiply(inverse(X_30),X))
    | multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) = least_upper_bound(identity,multiply(inverse(X_30),X)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)))),bind(Y0,$fot(least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(X_30),X))))]]) ).

cnf(refute_0_2073,plain,
    ( least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)) != least_upper_bound(identity,multiply(inverse(X_30),X))
    | multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) = least_upper_bound(identity,multiply(inverse(X_30),X)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)),least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X))) )],[refute_0_2071,refute_0_2072]) ).

cnf(refute_0_2074,plain,
    multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) = least_upper_bound(identity,multiply(inverse(X_30),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(identity,inverse(X_30)),X)),least_upper_bound(identity,multiply(inverse(X_30),X))) )],[refute_0_2003,refute_0_2073]) ).

cnf(refute_0_2075,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) != inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30)))
    | multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) != least_upper_bound(identity,multiply(inverse(X_30),X))
    | least_upper_bound(identity,multiply(inverse(X_30),X)) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_30),X)))]]) ).

cnf(refute_0_2076,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)) != inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30)))
    | least_upper_bound(identity,multiply(inverse(X_30),X)) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)),least_upper_bound(identity,multiply(inverse(X_30),X))) )],[refute_0_2074,refute_0_2075]) ).

cnf(refute_0_2077,plain,
    least_upper_bound(identity,multiply(inverse(X_30),X)) = inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(X),X_30)),multiply(inverse(X_30),X)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30)))) )],[refute_0_1994,refute_0_2076]) ).

cnf(refute_0_2078,plain,
    ( least_upper_bound(identity,multiply(inverse(X_30),X)) != inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30)))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30))) = least_upper_bound(identity,multiply(inverse(X_30),X)) ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(X_30),X)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30)))))]]) ).

cnf(refute_0_2079,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30))) = least_upper_bound(identity,multiply(inverse(X_30),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_30),X)),inverse(greatest_lower_bound(identity,multiply(inverse(X),X_30)))) )],[refute_0_2077,refute_0_2078]) ).

cnf(refute_0_2080,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) = least_upper_bound(identity,multiply(inverse(X_83),X)),
    inference(subst,[],[refute_0_2079:[bind(X_30,$fot(X_83))]]) ).

cnf(refute_0_2081,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) != multiply(inverse(greatest_lower_bound(X_83,X)),X)
    | inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) != least_upper_bound(identity,multiply(inverse(X_83),X))
    | least_upper_bound(identity,multiply(inverse(X_83),X)) = multiply(inverse(greatest_lower_bound(X_83,X)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))),multiply(inverse(greatest_lower_bound(X_83,X)),X)) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_83),X)))]]) ).

cnf(refute_0_2082,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))) != multiply(inverse(greatest_lower_bound(X_83,X)),X)
    | least_upper_bound(identity,multiply(inverse(X_83),X)) = multiply(inverse(greatest_lower_bound(X_83,X)),X) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))),least_upper_bound(identity,multiply(inverse(X_83),X))) )],[refute_0_2080,refute_0_2081]) ).

cnf(refute_0_2083,plain,
    least_upper_bound(identity,multiply(inverse(X_83),X)) = multiply(inverse(greatest_lower_bound(X_83,X)),X),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X),X_83))),multiply(inverse(greatest_lower_bound(X_83,X)),X)) )],[refute_0_58,refute_0_2082]) ).

cnf(refute_0_2084,plain,
    least_upper_bound(identity,multiply(inverse(X_775),X_68)) = multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68),
    inference(subst,[],[refute_0_2083:[bind(X,$fot(X_68)),bind(X_83,$fot(X_775))]]) ).

cnf(refute_0_2085,plain,
    ( multiply(inverse(inverse(X_775)),least_upper_bound(identity,multiply(inverse(X_775),X_68))) != least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)
    | least_upper_bound(identity,multiply(inverse(X_775),X_68)) != multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)
    | multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_775)),least_upper_bound(identity,multiply(inverse(X_775),X_68))),least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)) ),[0,1],$fot(multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68))]]) ).

cnf(refute_0_2086,plain,
    ( multiply(inverse(inverse(X_775)),least_upper_bound(identity,multiply(inverse(X_775),X_68))) != least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)
    | multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_775),X_68)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) )],[refute_0_2084,refute_0_2085]) ).

cnf(refute_0_2087,plain,
    multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_775)),least_upper_bound(identity,multiply(inverse(X_775),X_68))),least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)) )],[refute_0_18,refute_0_2086]) ).

cnf(refute_0_2088,plain,
    multiply(multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))),X_68) = multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)),
    inference(subst,[],[associativity:[bind(X,$fot(X_775)),bind(Y,$fot(inverse(greatest_lower_bound(X_775,X_68)))),bind(Z,$fot(X_68))]]) ).

cnf(refute_0_2089,plain,
    inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))) = multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))),
    inference(subst,[],[refute_0_293:[bind(X,$fot(X_775)),bind(X_29,$fot(greatest_lower_bound(X_775,X_68)))]]) ).

cnf(refute_0_2090,plain,
    multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68) = multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68),
    introduced(tautology,[refl,[$fot(multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68))]]) ).

cnf(refute_0_2091,plain,
    ( multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68) != multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68)
    | inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))) != multiply(X_775,inverse(greatest_lower_bound(X_775,X_68)))
    | multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68) = multiply(multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))),X_68) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68),multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68)) ),[1,0],$fot(multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))))]]) ).

cnf(refute_0_2092,plain,
    ( inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))) != multiply(X_775,inverse(greatest_lower_bound(X_775,X_68)))
    | multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68) = multiply(multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))),X_68) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68),multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68)) )],[refute_0_2090,refute_0_2091]) ).

cnf(refute_0_2093,plain,
    multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68) = multiply(multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))),X_68),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),multiply(X_775,inverse(greatest_lower_bound(X_775,X_68)))) )],[refute_0_2089,refute_0_2092]) ).

cnf(refute_0_2094,plain,
    ( multiply(multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))),X_68) != multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68))
    | multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68) != multiply(multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))),X_68)
    | multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68) = multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68))),bind(Y0,$fot(multiply(multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))),X_68))),bind(Z0,$fot(multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68))))]]) ).

cnf(refute_0_2095,plain,
    ( multiply(multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))),X_68) != multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68))
    | multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68) = multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68),multiply(multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))),X_68)) )],[refute_0_2093,refute_0_2094]) ).

cnf(refute_0_2096,plain,
    multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68) = multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_775,inverse(greatest_lower_bound(X_775,X_68))),X_68),multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68))) )],[refute_0_2088,refute_0_2095]) ).

cnf(refute_0_2097,plain,
    multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68),
    inference(subst,[],[refute_0_1415:[bind(X_30,$fot(inverse(X_775))),bind(X_36,$fot(greatest_lower_bound(X_775,X_68))),bind(X_37,$fot(X_68))]]) ).

cnf(refute_0_2098,plain,
    ( multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68) != multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68))
    | multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) != multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68)
    | multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)))),bind(Y0,$fot(multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68))),bind(Z0,$fot(multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68))))]]) ).

cnf(refute_0_2099,plain,
    ( multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68) != multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68))
    | multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)),multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68)) )],[refute_0_2097,refute_0_2098]) ).

cnf(refute_0_2100,plain,
    multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(greatest_lower_bound(X_775,X_68),inverse(X_775))),X_68),multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68))) )],[refute_0_2096,refute_0_2099]) ).

cnf(refute_0_2101,plain,
    ( multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) != multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68))
    | multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) != least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)
    | multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)),least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)) ),[0],$fot(multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)))]]) ).

cnf(refute_0_2102,plain,
    ( multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) != least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)
    | multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)),multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68))) )],[refute_0_2100,refute_0_2101]) ).

cnf(refute_0_2103,plain,
    inverse(inverse(X_775)) = X_775,
    inference(subst,[],[p11_2:[bind(X,$fot(X_775))]]) ).

cnf(refute_0_2104,plain,
    multiply(inverse(inverse(X_775)),identity) = inverse(inverse(X_775)),
    inference(subst,[],[refute_0_942:[bind(X,$fot(inverse(inverse(X_775))))]]) ).

cnf(refute_0_2105,plain,
    ( multiply(inverse(inverse(X_775)),identity) != inverse(inverse(X_775))
    | inverse(inverse(X_775)) != X_775
    | multiply(inverse(inverse(X_775)),identity) = X_775 ),
    inference(subst,[],[refute_0_140:[bind(X0,$fot(multiply(inverse(inverse(X_775)),identity))),bind(Y0,$fot(inverse(inverse(X_775)))),bind(Z0,$fot(X_775))]]) ).

cnf(refute_0_2106,plain,
    ( inverse(inverse(X_775)) != X_775
    | multiply(inverse(inverse(X_775)),identity) = X_775 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_775)),identity),inverse(inverse(X_775))) )],[refute_0_2104,refute_0_2105]) ).

cnf(refute_0_2107,plain,
    multiply(inverse(inverse(X_775)),identity) = X_775,
    inference(resolve,[$cnf( $equal(inverse(inverse(X_775)),X_775) )],[refute_0_2103,refute_0_2106]) ).

cnf(refute_0_2108,plain,
    least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68) = least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68),
    introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68))]]) ).

cnf(refute_0_2109,plain,
    ( multiply(inverse(inverse(X_775)),identity) != X_775
    | least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68) != least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)
    | least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68) = least_upper_bound(X_775,X_68) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68),least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)) ),[1,0],$fot(X_775)]]) ).

cnf(refute_0_2110,plain,
    ( multiply(inverse(inverse(X_775)),identity) != X_775
    | least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68) = least_upper_bound(X_775,X_68) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68),least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)) )],[refute_0_2108,refute_0_2109]) ).

cnf(refute_0_2111,plain,
    least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68) = least_upper_bound(X_775,X_68),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_775)),identity),X_775) )],[refute_0_2107,refute_0_2110]) ).

cnf(refute_0_2112,plain,
    ( multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) != least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)
    | least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68) != least_upper_bound(X_775,X_68)
    | multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = least_upper_bound(X_775,X_68) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)),least_upper_bound(X_775,X_68)) ),[0],$fot(least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68))]]) ).

cnf(refute_0_2113,plain,
    ( multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) != least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)
    | multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = least_upper_bound(X_775,X_68) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68),least_upper_bound(X_775,X_68)) )],[refute_0_2111,refute_0_2112]) ).

cnf(refute_0_2114,plain,
    ( multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) != least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)
    | multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = least_upper_bound(X_775,X_68) ),
    inference(resolve,[$cnf( $equal(multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)),least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)) )],[refute_0_2102,refute_0_2113]) ).

cnf(refute_0_2115,plain,
    multiply(X_775,multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)) = least_upper_bound(X_775,X_68),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_775)),multiply(inverse(greatest_lower_bound(X_775,X_68)),X_68)),least_upper_bound(multiply(inverse(inverse(X_775)),identity),X_68)) )],[refute_0_2087,refute_0_2114]) ).

cnf(refute_0_2116,plain,
    multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) = least_upper_bound(a,b),
    inference(subst,[],[refute_0_2115:[bind(X_68,$fot(b)),bind(X_775,$fot(a))]]) ).

cnf(refute_0_2117,plain,
    ( multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != least_upper_bound(a,b)
    | least_upper_bound(a,b) != least_upper_bound(a,b)
    | multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) = least_upper_bound(a,b) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),least_upper_bound(a,b)) ),[0],$fot(least_upper_bound(a,b))]]) ).

cnf(refute_0_2118,plain,
    ( least_upper_bound(a,b) != least_upper_bound(a,b)
    | multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) = least_upper_bound(a,b) ),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),least_upper_bound(a,b)) )],[refute_0_2116,refute_0_2117]) ).

cnf(refute_0_2119,plain,
    least_upper_bound(a,b) != least_upper_bound(a,b),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)),least_upper_bound(a,b)) )],[refute_0_2118,prove_p11]) ).

cnf(refute_0_2120,plain,
    least_upper_bound(a,b) = least_upper_bound(a,b),
    introduced(tautology,[refl,[$fot(least_upper_bound(a,b))]]) ).

cnf(refute_0_2121,plain,
    $false,
    inference(resolve,[$cnf( $equal(least_upper_bound(a,b),least_upper_bound(a,b)) )],[refute_0_2120,refute_0_2119]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP180-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun 14 04:42:39 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 205.27/205.50  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 205.27/205.50  
% 205.27/205.50  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 205.56/205.74  
%------------------------------------------------------------------------------