TSTP Solution File: GRP167-2 by Metis---2.4

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP167-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n021.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 10:37:10 EDT 2022

% Result   : Unsatisfiable 6.76s 6.95s
% Output   : CNFRefutation 6.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   98
%            Number of leaves      :  241
% Syntax   : Number of clauses     : 1092 ( 571 unt;   0 nHn; 518 RR)
%            Number of literals    : 1834 (1833 equ; 744 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-2 aty)
%            Number of variables   : 1857 (  34 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_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(lat4_1,axiom,
    inverse(identity) = identity ).

cnf(lat4_2,axiom,
    inverse(inverse(X)) = X ).

cnf(lat4_3,axiom,
    inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ).

cnf(lat4_4,axiom,
    positive_part(X) = least_upper_bound(X,identity) ).

cnf(lat4_5,axiom,
    negative_part(X) = greatest_lower_bound(X,identity) ).

cnf(lat4_6,axiom,
    least_upper_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)) ).

cnf(lat4_7,axiom,
    greatest_lower_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z)) ).

cnf(prove_lat4,negated_conjecture,
    a != multiply(positive_part(a),negative_part(a)) ).

cnf(refute_0_0,plain,
    multiply(multiply(X_108,inverse(X_108)),X_110) = multiply(X_108,multiply(inverse(X_108),X_110)),
    inference(subst,[],[associativity:[bind(X,$fot(X_108)),bind(Y,$fot(inverse(X_108))),bind(Z,$fot(X_110))]]) ).

cnf(refute_0_1,plain,
    multiply(inverse(inverse(X_1)),inverse(X_1)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_1)))]]) ).

cnf(refute_0_2,plain,
    inverse(inverse(X_1)) = X_1,
    inference(subst,[],[lat4_2:[bind(X,$fot(X_1))]]) ).

cnf(refute_0_3,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_4,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_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    multiply(X_1,inverse(X_1)) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_1)),inverse(X_1)),identity) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    multiply(X_108,inverse(X_108)) = identity,
    inference(subst,[],[refute_0_5:[bind(X_1,$fot(X_108))]]) ).

cnf(refute_0_7,plain,
    ( multiply(X_108,inverse(X_108)) != identity
    | multiply(multiply(X_108,inverse(X_108)),X_110) != multiply(X_108,multiply(inverse(X_108),X_110))
    | multiply(identity,X_110) = multiply(X_108,multiply(inverse(X_108),X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_108,inverse(X_108)),X_110),multiply(X_108,multiply(inverse(X_108),X_110))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_8,plain,
    ( multiply(multiply(X_108,inverse(X_108)),X_110) != multiply(X_108,multiply(inverse(X_108),X_110))
    | multiply(identity,X_110) = multiply(X_108,multiply(inverse(X_108),X_110)) ),
    inference(resolve,[$cnf( $equal(multiply(X_108,inverse(X_108)),identity) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    multiply(identity,X_110) = multiply(X_108,multiply(inverse(X_108),X_110)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_108,inverse(X_108)),X_110),multiply(X_108,multiply(inverse(X_108),X_110))) )],[refute_0_0,refute_0_8]) ).

cnf(refute_0_10,plain,
    multiply(identity,X_110) = X_110,
    inference(subst,[],[left_identity:[bind(X,$fot(X_110))]]) ).

cnf(refute_0_11,plain,
    ( multiply(identity,X_110) != X_110
    | multiply(identity,X_110) != multiply(X_108,multiply(inverse(X_108),X_110))
    | X_110 = multiply(X_108,multiply(inverse(X_108),X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_110),multiply(X_108,multiply(inverse(X_108),X_110))) ),[0],$fot(X_110)]]) ).

cnf(refute_0_12,plain,
    ( multiply(identity,X_110) != multiply(X_108,multiply(inverse(X_108),X_110))
    | X_110 = multiply(X_108,multiply(inverse(X_108),X_110)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_110),X_110) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    X_110 = multiply(X_108,multiply(inverse(X_108),X_110)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_110),multiply(X_108,multiply(inverse(X_108),X_110))) )],[refute_0_9,refute_0_12]) ).

cnf(refute_0_14,plain,
    inverse(X) = multiply(X_111,multiply(inverse(X_111),inverse(X))),
    inference(subst,[],[refute_0_13:[bind(X_108,$fot(X_111)),bind(X_110,$fot(inverse(X)))]]) ).

cnf(refute_0_15,plain,
    inverse(multiply(X,X_111)) = multiply(inverse(X_111),inverse(X)),
    inference(subst,[],[lat4_3:[bind(Y,$fot(X_111))]]) ).

cnf(refute_0_16,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_17,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_18,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( inverse(multiply(X,X_111)) != multiply(inverse(X_111),inverse(X))
    | multiply(inverse(X_111),inverse(X)) = inverse(multiply(X,X_111)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(multiply(X,X_111)))),bind(Y0,$fot(multiply(inverse(X_111),inverse(X))))]]) ).

cnf(refute_0_20,plain,
    multiply(inverse(X_111),inverse(X)) = inverse(multiply(X,X_111)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,X_111)),multiply(inverse(X_111),inverse(X))) )],[refute_0_15,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( multiply(inverse(X_111),inverse(X)) != inverse(multiply(X,X_111))
    | inverse(X) != multiply(X_111,multiply(inverse(X_111),inverse(X)))
    | inverse(X) = multiply(X_111,inverse(multiply(X,X_111))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(X_111,multiply(inverse(X_111),inverse(X)))) ),[1,1],$fot(inverse(multiply(X,X_111)))]]) ).

cnf(refute_0_22,plain,
    ( inverse(X) != multiply(X_111,multiply(inverse(X_111),inverse(X)))
    | inverse(X) = multiply(X_111,inverse(multiply(X,X_111))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_111),inverse(X)),inverse(multiply(X,X_111))) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    inverse(X) = multiply(X_111,inverse(multiply(X,X_111))),
    inference(resolve,[$cnf( $equal(inverse(X),multiply(X_111,multiply(inverse(X_111),inverse(X)))) )],[refute_0_14,refute_0_22]) ).

cnf(refute_0_24,plain,
    inverse(inverse(X_134)) = multiply(positive_part(X_134),inverse(multiply(inverse(X_134),positive_part(X_134)))),
    inference(subst,[],[refute_0_23:[bind(X,$fot(inverse(X_134))),bind(X_111,$fot(positive_part(X_134)))]]) ).

cnf(refute_0_25,plain,
    multiply(X_119,least_upper_bound(X_120,identity)) = least_upper_bound(multiply(X_119,X_120),multiply(X_119,identity)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_119)),bind(Y,$fot(X_120)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_26,plain,
    inverse(multiply(identity,X_9)) = multiply(inverse(X_9),inverse(identity)),
    inference(subst,[],[lat4_3:[bind(X,$fot(identity)),bind(Y,$fot(X_9))]]) ).

cnf(refute_0_27,plain,
    ( inverse(multiply(identity,X_9)) != multiply(inverse(X_9),inverse(identity))
    | inverse(identity) != identity
    | inverse(multiply(identity,X_9)) = multiply(inverse(X_9),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_9)),multiply(inverse(X_9),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_28,plain,
    ( inverse(multiply(identity,X_9)) != multiply(inverse(X_9),inverse(identity))
    | inverse(multiply(identity,X_9)) = multiply(inverse(X_9),identity) ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[lat4_1,refute_0_27]) ).

cnf(refute_0_29,plain,
    inverse(multiply(identity,X_9)) = multiply(inverse(X_9),identity),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_9)),multiply(inverse(X_9),inverse(identity))) )],[refute_0_26,refute_0_28]) ).

cnf(refute_0_30,plain,
    multiply(identity,X_9) = X_9,
    inference(subst,[],[left_identity:[bind(X,$fot(X_9))]]) ).

cnf(refute_0_31,plain,
    inverse(multiply(identity,X_9)) = inverse(multiply(identity,X_9)),
    introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_9)))]]) ).

cnf(refute_0_32,plain,
    ( multiply(identity,X_9) != X_9
    | inverse(multiply(identity,X_9)) != inverse(multiply(identity,X_9))
    | inverse(multiply(identity,X_9)) = inverse(X_9) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_9)),inverse(multiply(identity,X_9))) ),[1,0],$fot(X_9)]]) ).

cnf(refute_0_33,plain,
    ( multiply(identity,X_9) != X_9
    | inverse(multiply(identity,X_9)) = inverse(X_9) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_9)),inverse(multiply(identity,X_9))) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    inverse(multiply(identity,X_9)) = inverse(X_9),
    inference(resolve,[$cnf( $equal(multiply(identity,X_9),X_9) )],[refute_0_30,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( inverse(multiply(identity,X_9)) != multiply(inverse(X_9),identity)
    | inverse(multiply(identity,X_9)) != inverse(X_9)
    | inverse(X_9) = multiply(inverse(X_9),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_9)),multiply(inverse(X_9),identity)) ),[0],$fot(inverse(X_9))]]) ).

cnf(refute_0_36,plain,
    ( inverse(multiply(identity,X_9)) != multiply(inverse(X_9),identity)
    | inverse(X_9) = multiply(inverse(X_9),identity) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_9)),inverse(X_9)) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    inverse(X_9) = multiply(inverse(X_9),identity),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_9)),multiply(inverse(X_9),identity)) )],[refute_0_29,refute_0_36]) ).

cnf(refute_0_38,plain,
    inverse(inverse(X)) = multiply(inverse(inverse(X)),identity),
    inference(subst,[],[refute_0_37:[bind(X_9,$fot(inverse(X)))]]) ).

cnf(refute_0_39,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_40,plain,
    ( inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
    | inverse(inverse(X)) = multiply(X,identity) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[lat4_2,refute_0_39]) ).

cnf(refute_0_41,plain,
    inverse(inverse(X)) = multiply(X,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) )],[refute_0_38,refute_0_40]) ).

cnf(refute_0_42,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_43,plain,
    ( inverse(inverse(X)) != multiply(X,identity)
    | X = multiply(X,identity) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[lat4_2,refute_0_42]) ).

cnf(refute_0_44,plain,
    X = multiply(X,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) )],[refute_0_41,refute_0_43]) ).

cnf(refute_0_45,plain,
    X_119 = multiply(X_119,identity),
    inference(subst,[],[refute_0_44:[bind(X,$fot(X_119))]]) ).

cnf(refute_0_46,plain,
    ( X_119 != multiply(X_119,identity)
    | multiply(X_119,identity) = X_119 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_119)),bind(Y0,$fot(multiply(X_119,identity)))]]) ).

cnf(refute_0_47,plain,
    multiply(X_119,identity) = X_119,
    inference(resolve,[$cnf( $equal(X_119,multiply(X_119,identity)) )],[refute_0_45,refute_0_46]) ).

cnf(refute_0_48,plain,
    ( multiply(X_119,identity) != X_119
    | multiply(X_119,least_upper_bound(X_120,identity)) != least_upper_bound(multiply(X_119,X_120),multiply(X_119,identity))
    | multiply(X_119,least_upper_bound(X_120,identity)) = least_upper_bound(multiply(X_119,X_120),X_119) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_119,least_upper_bound(X_120,identity)),least_upper_bound(multiply(X_119,X_120),multiply(X_119,identity))) ),[1,1],$fot(X_119)]]) ).

cnf(refute_0_49,plain,
    ( multiply(X_119,least_upper_bound(X_120,identity)) != least_upper_bound(multiply(X_119,X_120),multiply(X_119,identity))
    | multiply(X_119,least_upper_bound(X_120,identity)) = least_upper_bound(multiply(X_119,X_120),X_119) ),
    inference(resolve,[$cnf( $equal(multiply(X_119,identity),X_119) )],[refute_0_47,refute_0_48]) ).

cnf(refute_0_50,plain,
    multiply(X_119,least_upper_bound(X_120,identity)) = least_upper_bound(multiply(X_119,X_120),X_119),
    inference(resolve,[$cnf( $equal(multiply(X_119,least_upper_bound(X_120,identity)),least_upper_bound(multiply(X_119,X_120),multiply(X_119,identity))) )],[refute_0_25,refute_0_49]) ).

cnf(refute_0_51,plain,
    ( positive_part(X) != least_upper_bound(X,identity)
    | least_upper_bound(X,identity) = positive_part(X) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(positive_part(X))),bind(Y0,$fot(least_upper_bound(X,identity)))]]) ).

cnf(refute_0_52,plain,
    least_upper_bound(X,identity) = positive_part(X),
    inference(resolve,[$cnf( $equal(positive_part(X),least_upper_bound(X,identity)) )],[lat4_4,refute_0_51]) ).

cnf(refute_0_53,plain,
    least_upper_bound(X_120,identity) = positive_part(X_120),
    inference(subst,[],[refute_0_52:[bind(X,$fot(X_120))]]) ).

cnf(refute_0_54,plain,
    multiply(X_119,least_upper_bound(X_120,identity)) = multiply(X_119,least_upper_bound(X_120,identity)),
    introduced(tautology,[refl,[$fot(multiply(X_119,least_upper_bound(X_120,identity)))]]) ).

cnf(refute_0_55,plain,
    ( multiply(X_119,least_upper_bound(X_120,identity)) != multiply(X_119,least_upper_bound(X_120,identity))
    | least_upper_bound(X_120,identity) != positive_part(X_120)
    | multiply(X_119,least_upper_bound(X_120,identity)) = multiply(X_119,positive_part(X_120)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_119,least_upper_bound(X_120,identity)),multiply(X_119,least_upper_bound(X_120,identity))) ),[1,1],$fot(positive_part(X_120))]]) ).

cnf(refute_0_56,plain,
    ( least_upper_bound(X_120,identity) != positive_part(X_120)
    | multiply(X_119,least_upper_bound(X_120,identity)) = multiply(X_119,positive_part(X_120)) ),
    inference(resolve,[$cnf( $equal(multiply(X_119,least_upper_bound(X_120,identity)),multiply(X_119,least_upper_bound(X_120,identity))) )],[refute_0_54,refute_0_55]) ).

cnf(refute_0_57,plain,
    multiply(X_119,least_upper_bound(X_120,identity)) = multiply(X_119,positive_part(X_120)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_120,identity),positive_part(X_120)) )],[refute_0_53,refute_0_56]) ).

cnf(refute_0_58,plain,
    ( multiply(X_119,least_upper_bound(X_120,identity)) != multiply(X_119,positive_part(X_120))
    | multiply(X_119,least_upper_bound(X_120,identity)) != least_upper_bound(multiply(X_119,X_120),X_119)
    | multiply(X_119,positive_part(X_120)) = least_upper_bound(multiply(X_119,X_120),X_119) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_119,least_upper_bound(X_120,identity)),least_upper_bound(multiply(X_119,X_120),X_119)) ),[0],$fot(multiply(X_119,positive_part(X_120)))]]) ).

cnf(refute_0_59,plain,
    ( multiply(X_119,least_upper_bound(X_120,identity)) != least_upper_bound(multiply(X_119,X_120),X_119)
    | multiply(X_119,positive_part(X_120)) = least_upper_bound(multiply(X_119,X_120),X_119) ),
    inference(resolve,[$cnf( $equal(multiply(X_119,least_upper_bound(X_120,identity)),multiply(X_119,positive_part(X_120))) )],[refute_0_57,refute_0_58]) ).

cnf(refute_0_60,plain,
    least_upper_bound(X_22,greatest_lower_bound(X_22,X_23)) = X_22,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_22)),bind(Y,$fot(X_23))]]) ).

cnf(refute_0_61,plain,
    greatest_lower_bound(X_23,X_22) = greatest_lower_bound(X_22,X_23),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_23)),bind(Y,$fot(X_22))]]) ).

cnf(refute_0_62,plain,
    ( greatest_lower_bound(X_23,X_22) != greatest_lower_bound(X_22,X_23)
    | greatest_lower_bound(X_22,X_23) = greatest_lower_bound(X_23,X_22) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_23,X_22))),bind(Y0,$fot(greatest_lower_bound(X_22,X_23)))]]) ).

cnf(refute_0_63,plain,
    greatest_lower_bound(X_22,X_23) = greatest_lower_bound(X_23,X_22),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,X_22),greatest_lower_bound(X_22,X_23)) )],[refute_0_61,refute_0_62]) ).

cnf(refute_0_64,plain,
    ( greatest_lower_bound(X_22,X_23) != greatest_lower_bound(X_23,X_22)
    | least_upper_bound(X_22,greatest_lower_bound(X_22,X_23)) != X_22
    | least_upper_bound(X_22,greatest_lower_bound(X_23,X_22)) = X_22 ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,greatest_lower_bound(X_22,X_23)),X_22) ),[0,1],$fot(greatest_lower_bound(X_23,X_22))]]) ).

cnf(refute_0_65,plain,
    ( least_upper_bound(X_22,greatest_lower_bound(X_22,X_23)) != X_22
    | least_upper_bound(X_22,greatest_lower_bound(X_23,X_22)) = X_22 ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,X_23),greatest_lower_bound(X_23,X_22)) )],[refute_0_63,refute_0_64]) ).

cnf(refute_0_66,plain,
    least_upper_bound(X_22,greatest_lower_bound(X_23,X_22)) = X_22,
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,greatest_lower_bound(X_22,X_23)),X_22) )],[refute_0_60,refute_0_65]) ).

cnf(refute_0_67,plain,
    least_upper_bound(least_upper_bound(X_29,Y),greatest_lower_bound(X_29,least_upper_bound(X_29,Y))) = least_upper_bound(X_29,Y),
    inference(subst,[],[refute_0_66:[bind(X_22,$fot(least_upper_bound(X_29,Y))),bind(X_23,$fot(X_29))]]) ).

cnf(refute_0_68,plain,
    greatest_lower_bound(X_29,least_upper_bound(X_29,Y)) = X_29,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_29))]]) ).

cnf(refute_0_69,plain,
    ( greatest_lower_bound(X_29,least_upper_bound(X_29,Y)) != X_29
    | least_upper_bound(least_upper_bound(X_29,Y),greatest_lower_bound(X_29,least_upper_bound(X_29,Y))) != least_upper_bound(X_29,Y)
    | least_upper_bound(least_upper_bound(X_29,Y),X_29) = least_upper_bound(X_29,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,Y),greatest_lower_bound(X_29,least_upper_bound(X_29,Y))),least_upper_bound(X_29,Y)) ),[0,1],$fot(X_29)]]) ).

cnf(refute_0_70,plain,
    ( least_upper_bound(least_upper_bound(X_29,Y),greatest_lower_bound(X_29,least_upper_bound(X_29,Y))) != least_upper_bound(X_29,Y)
    | least_upper_bound(least_upper_bound(X_29,Y),X_29) = least_upper_bound(X_29,Y) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_29,least_upper_bound(X_29,Y)),X_29) )],[refute_0_68,refute_0_69]) ).

cnf(refute_0_71,plain,
    least_upper_bound(least_upper_bound(X_29,Y),X_29) = least_upper_bound(X_29,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,Y),greatest_lower_bound(X_29,least_upper_bound(X_29,Y))),least_upper_bound(X_29,Y)) )],[refute_0_67,refute_0_70]) ).

cnf(refute_0_72,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_18:[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_73,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_72]) ).

cnf(refute_0_74,plain,
    least_upper_bound(least_upper_bound(X_29,Y),X_29) = least_upper_bound(X_29,least_upper_bound(Y,X_29)),
    inference(subst,[],[refute_0_73:[bind(X,$fot(X_29)),bind(Z,$fot(X_29))]]) ).

cnf(refute_0_75,plain,
    ( least_upper_bound(least_upper_bound(X_29,Y),X_29) != least_upper_bound(X_29,Y)
    | least_upper_bound(least_upper_bound(X_29,Y),X_29) != least_upper_bound(X_29,least_upper_bound(Y,X_29))
    | least_upper_bound(X_29,least_upper_bound(Y,X_29)) = least_upper_bound(X_29,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,Y),X_29),least_upper_bound(X_29,Y)) ),[0],$fot(least_upper_bound(X_29,least_upper_bound(Y,X_29)))]]) ).

cnf(refute_0_76,plain,
    ( least_upper_bound(least_upper_bound(X_29,Y),X_29) != least_upper_bound(X_29,Y)
    | least_upper_bound(X_29,least_upper_bound(Y,X_29)) = least_upper_bound(X_29,Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,Y),X_29),least_upper_bound(X_29,least_upper_bound(Y,X_29))) )],[refute_0_74,refute_0_75]) ).

cnf(refute_0_77,plain,
    least_upper_bound(X_29,least_upper_bound(Y,X_29)) = least_upper_bound(X_29,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_29,Y),X_29),least_upper_bound(X_29,Y)) )],[refute_0_71,refute_0_76]) ).

cnf(refute_0_78,plain,
    least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) = least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y),
    inference(subst,[],[refute_0_77:[bind(X_29,$fot(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))))]]) ).

cnf(refute_0_79,plain,
    least_upper_bound(X_22,greatest_lower_bound(X_22,identity)) = X_22,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_22)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_80,plain,
    negative_part(X_22) = greatest_lower_bound(X_22,identity),
    inference(subst,[],[lat4_5:[bind(X,$fot(X_22))]]) ).

cnf(refute_0_81,plain,
    ( negative_part(X_22) != greatest_lower_bound(X_22,identity)
    | greatest_lower_bound(X_22,identity) = negative_part(X_22) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(X_22))),bind(Y0,$fot(greatest_lower_bound(X_22,identity)))]]) ).

cnf(refute_0_82,plain,
    greatest_lower_bound(X_22,identity) = negative_part(X_22),
    inference(resolve,[$cnf( $equal(negative_part(X_22),greatest_lower_bound(X_22,identity)) )],[refute_0_80,refute_0_81]) ).

cnf(refute_0_83,plain,
    ( greatest_lower_bound(X_22,identity) != negative_part(X_22)
    | least_upper_bound(X_22,greatest_lower_bound(X_22,identity)) != X_22
    | least_upper_bound(X_22,negative_part(X_22)) = X_22 ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,greatest_lower_bound(X_22,identity)),X_22) ),[0,1],$fot(negative_part(X_22))]]) ).

cnf(refute_0_84,plain,
    ( least_upper_bound(X_22,greatest_lower_bound(X_22,identity)) != X_22
    | least_upper_bound(X_22,negative_part(X_22)) = X_22 ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_22,identity),negative_part(X_22)) )],[refute_0_82,refute_0_83]) ).

cnf(refute_0_85,plain,
    least_upper_bound(X_22,negative_part(X_22)) = X_22,
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,greatest_lower_bound(X_22,identity)),X_22) )],[refute_0_79,refute_0_84]) ).

cnf(refute_0_86,plain,
    least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45))) = least_upper_bound(X_44,X_45),
    inference(subst,[],[refute_0_85:[bind(X_22,$fot(least_upper_bound(X_44,X_45)))]]) ).

cnf(refute_0_87,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45)))) = least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45))),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(negative_part(least_upper_bound(X_44,X_45))))]]) ).

cnf(refute_0_88,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45)))) != least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45)))
    | least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45))) = least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45)))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45)))))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45)))))]]) ).

cnf(refute_0_89,plain,
    least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45))) = least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45)))),least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45)))) )],[refute_0_87,refute_0_88]) ).

cnf(refute_0_90,plain,
    ( least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45))) != least_upper_bound(X_44,X_45)
    | least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45))) != least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45))))
    | least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45)))) = least_upper_bound(X_44,X_45) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45))),least_upper_bound(X_44,X_45)) ),[0],$fot(least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45)))))]]) ).

cnf(refute_0_91,plain,
    ( least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45))) != least_upper_bound(X_44,X_45)
    | least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45)))) = least_upper_bound(X_44,X_45) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45))),least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45))))) )],[refute_0_89,refute_0_90]) ).

cnf(refute_0_92,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,negative_part(least_upper_bound(X_44,X_45)))) = least_upper_bound(X_44,X_45),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_44,X_45),negative_part(least_upper_bound(X_44,X_45))),least_upper_bound(X_44,X_45)) )],[refute_0_86,refute_0_91]) ).

cnf(refute_0_93,plain,
    least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))) = least_upper_bound(Y,X_63),
    inference(subst,[],[refute_0_92:[bind(X_44,$fot(Y)),bind(X_45,$fot(X_63))]]) ).

cnf(refute_0_94,plain,
    ( least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))) != least_upper_bound(Y,X_63)
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) != least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) = least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))),least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)) ),[0,1],$fot(least_upper_bound(Y,X_63))]]) ).

cnf(refute_0_95,plain,
    ( least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) != least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) = least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))),least_upper_bound(Y,X_63)) )],[refute_0_93,refute_0_94]) ).

cnf(refute_0_96,plain,
    least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) = least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))),least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)) )],[refute_0_78,refute_0_95]) ).

cnf(refute_0_97,plain,
    least_upper_bound(X_32,least_upper_bound(X_31,X_32)) = least_upper_bound(X_32,X_31),
    inference(subst,[],[refute_0_77:[bind(Y,$fot(X_31)),bind(X_29,$fot(X_32))]]) ).

cnf(refute_0_98,plain,
    least_upper_bound(X_32,X_31) = least_upper_bound(X_31,X_32),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_32)),bind(Y,$fot(X_31))]]) ).

cnf(refute_0_99,plain,
    ( least_upper_bound(X_32,X_31) != least_upper_bound(X_31,X_32)
    | least_upper_bound(X_31,X_32) = least_upper_bound(X_32,X_31) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_32,X_31))),bind(Y0,$fot(least_upper_bound(X_31,X_32)))]]) ).

cnf(refute_0_100,plain,
    least_upper_bound(X_31,X_32) = least_upper_bound(X_32,X_31),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_32,X_31),least_upper_bound(X_31,X_32)) )],[refute_0_98,refute_0_99]) ).

cnf(refute_0_101,plain,
    ( least_upper_bound(X_31,X_32) != least_upper_bound(X_32,X_31)
    | least_upper_bound(X_32,least_upper_bound(X_31,X_32)) != least_upper_bound(X_32,X_31)
    | least_upper_bound(X_32,least_upper_bound(X_32,X_31)) = least_upper_bound(X_32,X_31) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_32,least_upper_bound(X_31,X_32)),least_upper_bound(X_32,X_31)) ),[0,1],$fot(least_upper_bound(X_32,X_31))]]) ).

cnf(refute_0_102,plain,
    ( least_upper_bound(X_32,least_upper_bound(X_31,X_32)) != least_upper_bound(X_32,X_31)
    | least_upper_bound(X_32,least_upper_bound(X_32,X_31)) = least_upper_bound(X_32,X_31) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,X_32),least_upper_bound(X_32,X_31)) )],[refute_0_100,refute_0_101]) ).

cnf(refute_0_103,plain,
    least_upper_bound(X_32,least_upper_bound(X_32,X_31)) = least_upper_bound(X_32,X_31),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_32,least_upper_bound(X_31,X_32)),least_upper_bound(X_32,X_31)) )],[refute_0_97,refute_0_102]) ).

cnf(refute_0_104,plain,
    least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))) = least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),
    inference(subst,[],[refute_0_103:[bind(X_31,$fot(negative_part(least_upper_bound(Y,X_63)))),bind(X_32,$fot(X_63))]]) ).

cnf(refute_0_105,plain,
    least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) = least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))))]]) ).

cnf(refute_0_106,plain,
    ( least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) != least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))))
    | least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))) != least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))
    | least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) = least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))),least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))))) ),[1,1],$fot(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))]]) ).

cnf(refute_0_107,plain,
    ( least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))) != least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))
    | least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) = least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))),least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))))) )],[refute_0_105,refute_0_106]) ).

cnf(refute_0_108,plain,
    least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) = least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))),least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))) )],[refute_0_104,refute_0_107]) ).

cnf(refute_0_109,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_110,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_18,refute_0_109]) ).

cnf(refute_0_111,plain,
    ( least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) != least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))
    | least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))) != least_upper_bound(Y,X_63)
    | least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) = least_upper_bound(Y,X_63) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))))),bind(Z0,$fot(least_upper_bound(Y,X_63)))]]) ).

cnf(refute_0_112,plain,
    ( least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))) != least_upper_bound(Y,X_63)
    | least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) = least_upper_bound(Y,X_63) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))),least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) )],[refute_0_108,refute_0_111]) ).

cnf(refute_0_113,plain,
    least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) = least_upper_bound(Y,X_63),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))),least_upper_bound(Y,X_63)) )],[refute_0_93,refute_0_112]) ).

cnf(refute_0_114,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,X_46)) = least_upper_bound(least_upper_bound(X_44,X_45),X_46),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(X_46))]]) ).

cnf(refute_0_115,plain,
    least_upper_bound(X_46,X_45) = least_upper_bound(X_45,X_46),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_46)),bind(Y,$fot(X_45))]]) ).

cnf(refute_0_116,plain,
    ( least_upper_bound(X_46,X_45) != least_upper_bound(X_45,X_46)
    | least_upper_bound(X_45,X_46) = least_upper_bound(X_46,X_45) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_46,X_45))),bind(Y0,$fot(least_upper_bound(X_45,X_46)))]]) ).

cnf(refute_0_117,plain,
    least_upper_bound(X_45,X_46) = least_upper_bound(X_46,X_45),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_46,X_45),least_upper_bound(X_45,X_46)) )],[refute_0_115,refute_0_116]) ).

cnf(refute_0_118,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,X_46)) != least_upper_bound(least_upper_bound(X_44,X_45),X_46)
    | least_upper_bound(X_45,X_46) != least_upper_bound(X_46,X_45)
    | least_upper_bound(X_44,least_upper_bound(X_46,X_45)) = least_upper_bound(least_upper_bound(X_44,X_45),X_46) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,X_46)),least_upper_bound(least_upper_bound(X_44,X_45),X_46)) ),[0,1],$fot(least_upper_bound(X_46,X_45))]]) ).

cnf(refute_0_119,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,X_46)) != least_upper_bound(least_upper_bound(X_44,X_45),X_46)
    | least_upper_bound(X_44,least_upper_bound(X_46,X_45)) = least_upper_bound(least_upper_bound(X_44,X_45),X_46) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,X_46),least_upper_bound(X_46,X_45)) )],[refute_0_117,refute_0_118]) ).

cnf(refute_0_120,plain,
    least_upper_bound(X_44,least_upper_bound(X_46,X_45)) = least_upper_bound(least_upper_bound(X_44,X_45),X_46),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,X_46)),least_upper_bound(least_upper_bound(X_44,X_45),X_46)) )],[refute_0_114,refute_0_119]) ).

cnf(refute_0_121,plain,
    least_upper_bound(least_upper_bound(X_44,X_45),X_46) = least_upper_bound(X_44,least_upper_bound(X_45,X_46)),
    inference(subst,[],[refute_0_73:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(X_46))]]) ).

cnf(refute_0_122,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_46,X_45)) != least_upper_bound(least_upper_bound(X_44,X_45),X_46)
    | least_upper_bound(least_upper_bound(X_44,X_45),X_46) != least_upper_bound(X_44,least_upper_bound(X_45,X_46))
    | least_upper_bound(X_44,least_upper_bound(X_46,X_45)) = least_upper_bound(X_44,least_upper_bound(X_45,X_46)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_44,least_upper_bound(X_46,X_45)),least_upper_bound(X_44,least_upper_bound(X_45,X_46))) ),[0],$fot(least_upper_bound(least_upper_bound(X_44,X_45),X_46))]]) ).

cnf(refute_0_123,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_46,X_45)) != least_upper_bound(least_upper_bound(X_44,X_45),X_46)
    | least_upper_bound(X_44,least_upper_bound(X_46,X_45)) = least_upper_bound(X_44,least_upper_bound(X_45,X_46)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_44,X_45),X_46),least_upper_bound(X_44,least_upper_bound(X_45,X_46))) )],[refute_0_121,refute_0_122]) ).

cnf(refute_0_124,plain,
    least_upper_bound(X_44,least_upper_bound(X_46,X_45)) = least_upper_bound(X_44,least_upper_bound(X_45,X_46)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_46,X_45)),least_upper_bound(least_upper_bound(X_44,X_45),X_46)) )],[refute_0_120,refute_0_123]) ).

cnf(refute_0_125,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_46,X_45)) != least_upper_bound(X_44,least_upper_bound(X_45,X_46))
    | least_upper_bound(X_44,least_upper_bound(X_45,X_46)) = least_upper_bound(X_44,least_upper_bound(X_46,X_45)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_44,least_upper_bound(X_46,X_45)))),bind(Y0,$fot(least_upper_bound(X_44,least_upper_bound(X_45,X_46))))]]) ).

cnf(refute_0_126,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,X_46)) = least_upper_bound(X_44,least_upper_bound(X_46,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_46,X_45)),least_upper_bound(X_44,least_upper_bound(X_45,X_46))) )],[refute_0_124,refute_0_125]) ).

cnf(refute_0_127,plain,
    least_upper_bound(Y,least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),X_63)) = least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))),
    inference(subst,[],[refute_0_126:[bind(X_44,$fot(Y)),bind(X_45,$fot(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))),bind(X_46,$fot(X_63))]]) ).

cnf(refute_0_128,plain,
    least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) = least_upper_bound(least_upper_bound(X_44,least_upper_bound(Y,X_44)),X_46),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_44)),bind(Y,$fot(least_upper_bound(Y,X_44))),bind(Z,$fot(X_46))]]) ).

cnf(refute_0_129,plain,
    least_upper_bound(X_44,least_upper_bound(Y,X_44)) = least_upper_bound(X_44,Y),
    inference(subst,[],[refute_0_77:[bind(X_29,$fot(X_44))]]) ).

cnf(refute_0_130,plain,
    ( least_upper_bound(X_44,least_upper_bound(Y,X_44)) != least_upper_bound(X_44,Y)
    | least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) != least_upper_bound(least_upper_bound(X_44,least_upper_bound(Y,X_44)),X_46)
    | least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) = least_upper_bound(least_upper_bound(X_44,Y),X_46) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)),least_upper_bound(least_upper_bound(X_44,least_upper_bound(Y,X_44)),X_46)) ),[1,0],$fot(least_upper_bound(X_44,Y))]]) ).

cnf(refute_0_131,plain,
    ( least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) != least_upper_bound(least_upper_bound(X_44,least_upper_bound(Y,X_44)),X_46)
    | least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) = least_upper_bound(least_upper_bound(X_44,Y),X_46) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(Y,X_44)),least_upper_bound(X_44,Y)) )],[refute_0_129,refute_0_130]) ).

cnf(refute_0_132,plain,
    least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) = least_upper_bound(least_upper_bound(X_44,Y),X_46),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)),least_upper_bound(least_upper_bound(X_44,least_upper_bound(Y,X_44)),X_46)) )],[refute_0_128,refute_0_131]) ).

cnf(refute_0_133,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,least_upper_bound(Y,X_45))) = least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(least_upper_bound(Y,X_45)))]]) ).

cnf(refute_0_134,plain,
    least_upper_bound(X_45,least_upper_bound(Y,X_45)) = least_upper_bound(X_45,Y),
    inference(subst,[],[refute_0_77:[bind(X_29,$fot(X_45))]]) ).

cnf(refute_0_135,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,least_upper_bound(Y,X_45))) != least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45))
    | least_upper_bound(X_45,least_upper_bound(Y,X_45)) != least_upper_bound(X_45,Y)
    | least_upper_bound(X_44,least_upper_bound(X_45,Y)) = least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,least_upper_bound(Y,X_45))),least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45))) ),[0,1],$fot(least_upper_bound(X_45,Y))]]) ).

cnf(refute_0_136,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,least_upper_bound(Y,X_45))) != least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45))
    | least_upper_bound(X_44,least_upper_bound(X_45,Y)) = least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(Y,X_45)),least_upper_bound(X_45,Y)) )],[refute_0_134,refute_0_135]) ).

cnf(refute_0_137,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,Y)) = least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,least_upper_bound(Y,X_45))),least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45))) )],[refute_0_133,refute_0_136]) ).

cnf(refute_0_138,plain,
    least_upper_bound(least_upper_bound(X_44,X_45),Y) = least_upper_bound(X_44,least_upper_bound(X_45,Y)),
    inference(subst,[],[refute_0_73:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_139,plain,
    least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)) = least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)))]]) ).

cnf(refute_0_140,plain,
    ( least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)) != least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y))
    | least_upper_bound(least_upper_bound(X_44,X_45),Y) != least_upper_bound(X_44,least_upper_bound(X_45,Y))
    | least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)) = least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)),least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y))) ),[1,1],$fot(least_upper_bound(X_44,least_upper_bound(X_45,Y)))]]) ).

cnf(refute_0_141,plain,
    ( least_upper_bound(least_upper_bound(X_44,X_45),Y) != least_upper_bound(X_44,least_upper_bound(X_45,Y))
    | least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)) = least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)),least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y))) )],[refute_0_139,refute_0_140]) ).

cnf(refute_0_142,plain,
    least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)) = least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_44,X_45),Y),least_upper_bound(X_44,least_upper_bound(X_45,Y))) )],[refute_0_138,refute_0_141]) ).

cnf(refute_0_143,plain,
    least_upper_bound(X,least_upper_bound(X_44,X_45)) = least_upper_bound(least_upper_bound(X_44,X_45),X),
    inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_44,X_45)))]]) ).

cnf(refute_0_144,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,X)) = least_upper_bound(least_upper_bound(X_44,X_45),X),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(X))]]) ).

cnf(refute_0_145,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,X)) != least_upper_bound(least_upper_bound(X_44,X_45),X)
    | least_upper_bound(least_upper_bound(X_44,X_45),X) = least_upper_bound(X_44,least_upper_bound(X_45,X)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_44,least_upper_bound(X_45,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_44,X_45),X)))]]) ).

cnf(refute_0_146,plain,
    least_upper_bound(least_upper_bound(X_44,X_45),X) = least_upper_bound(X_44,least_upper_bound(X_45,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,X)),least_upper_bound(least_upper_bound(X_44,X_45),X)) )],[refute_0_144,refute_0_145]) ).

cnf(refute_0_147,plain,
    ( least_upper_bound(X,least_upper_bound(X_44,X_45)) != least_upper_bound(least_upper_bound(X_44,X_45),X)
    | least_upper_bound(least_upper_bound(X_44,X_45),X) != least_upper_bound(X_44,least_upper_bound(X_45,X))
    | least_upper_bound(X,least_upper_bound(X_44,X_45)) = least_upper_bound(X_44,least_upper_bound(X_45,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_44,X_45)),least_upper_bound(X_44,least_upper_bound(X_45,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_44,X_45),X))]]) ).

cnf(refute_0_148,plain,
    ( least_upper_bound(X,least_upper_bound(X_44,X_45)) != least_upper_bound(least_upper_bound(X_44,X_45),X)
    | least_upper_bound(X,least_upper_bound(X_44,X_45)) = least_upper_bound(X_44,least_upper_bound(X_45,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_44,X_45),X),least_upper_bound(X_44,least_upper_bound(X_45,X))) )],[refute_0_146,refute_0_147]) ).

cnf(refute_0_149,plain,
    least_upper_bound(X,least_upper_bound(X_44,X_45)) = least_upper_bound(X_44,least_upper_bound(X_45,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_44,X_45)),least_upper_bound(least_upper_bound(X_44,X_45),X)) )],[refute_0_143,refute_0_148]) ).

cnf(refute_0_150,plain,
    ( least_upper_bound(X,least_upper_bound(X_44,X_45)) != least_upper_bound(X_44,least_upper_bound(X_45,X))
    | least_upper_bound(X_44,least_upper_bound(X_45,X)) = least_upper_bound(X,least_upper_bound(X_44,X_45)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_44,X_45)))),bind(Y0,$fot(least_upper_bound(X_44,least_upper_bound(X_45,X))))]]) ).

cnf(refute_0_151,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,X)) = least_upper_bound(X,least_upper_bound(X_44,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_44,X_45)),least_upper_bound(X_44,least_upper_bound(X_45,X))) )],[refute_0_149,refute_0_150]) ).

cnf(refute_0_152,plain,
    least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)) = least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)),
    inference(subst,[],[refute_0_151:[bind(X,$fot(X_45)),bind(X_44,$fot(least_upper_bound(X_44,X_45))),bind(X_45,$fot(Y))]]) ).

cnf(refute_0_153,plain,
    ( least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)) != least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y)))
    | least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)) != least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y))
    | least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)) = least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)))),bind(Y0,$fot(least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)))),bind(Z0,$fot(least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y)))))]]) ).

cnf(refute_0_154,plain,
    ( least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)) != least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y)))
    | least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)) = least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)),least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y))) )],[refute_0_152,refute_0_153]) ).

cnf(refute_0_155,plain,
    least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)) = least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(least_upper_bound(X_44,X_45),Y)),least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y)))) )],[refute_0_142,refute_0_154]) ).

cnf(refute_0_156,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,Y)) != least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45))
    | least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)) != least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y)))
    | least_upper_bound(X_44,least_upper_bound(X_45,Y)) = least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_44,least_upper_bound(X_45,Y)),least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)))]]) ).

cnf(refute_0_157,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,Y)) != least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45))
    | least_upper_bound(X_44,least_upper_bound(X_45,Y)) = least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45)),least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y)))) )],[refute_0_155,refute_0_156]) ).

cnf(refute_0_158,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,Y)) = least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,Y)),least_upper_bound(least_upper_bound(X_44,X_45),least_upper_bound(Y,X_45))) )],[refute_0_137,refute_0_157]) ).

cnf(refute_0_159,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,Y)) != least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y)))
    | least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y))) = least_upper_bound(X_44,least_upper_bound(X_45,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_44,least_upper_bound(X_45,Y)))),bind(Y0,$fot(least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y)))))]]) ).

cnf(refute_0_160,plain,
    least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y))) = least_upper_bound(X_44,least_upper_bound(X_45,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,Y)),least_upper_bound(X_45,least_upper_bound(X_44,least_upper_bound(X_45,Y)))) )],[refute_0_158,refute_0_159]) ).

cnf(refute_0_161,plain,
    least_upper_bound(X_44,least_upper_bound(Y,least_upper_bound(X_44,X_46))) = least_upper_bound(Y,least_upper_bound(X_44,X_46)),
    inference(subst,[],[refute_0_160:[bind(Y,$fot(X_46)),bind(X_44,$fot(Y)),bind(X_45,$fot(X_44))]]) ).

cnf(refute_0_162,plain,
    least_upper_bound(least_upper_bound(Y,X_44),X_46) = least_upper_bound(Y,least_upper_bound(X_44,X_46)),
    inference(subst,[],[refute_0_73:[bind(X,$fot(Y)),bind(Y,$fot(X_44)),bind(Z,$fot(X_46))]]) ).

cnf(refute_0_163,plain,
    least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) = least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)))]]) ).

cnf(refute_0_164,plain,
    ( least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) != least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46))
    | least_upper_bound(least_upper_bound(Y,X_44),X_46) != least_upper_bound(Y,least_upper_bound(X_44,X_46))
    | least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) = least_upper_bound(X_44,least_upper_bound(Y,least_upper_bound(X_44,X_46))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)),least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_44,X_46)))]]) ).

cnf(refute_0_165,plain,
    ( least_upper_bound(least_upper_bound(Y,X_44),X_46) != least_upper_bound(Y,least_upper_bound(X_44,X_46))
    | least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) = least_upper_bound(X_44,least_upper_bound(Y,least_upper_bound(X_44,X_46))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)),least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46))) )],[refute_0_163,refute_0_164]) ).

cnf(refute_0_166,plain,
    least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) = least_upper_bound(X_44,least_upper_bound(Y,least_upper_bound(X_44,X_46))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_44),X_46),least_upper_bound(Y,least_upper_bound(X_44,X_46))) )],[refute_0_162,refute_0_165]) ).

cnf(refute_0_167,plain,
    ( least_upper_bound(X_44,least_upper_bound(Y,least_upper_bound(X_44,X_46))) != least_upper_bound(Y,least_upper_bound(X_44,X_46))
    | least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) != least_upper_bound(X_44,least_upper_bound(Y,least_upper_bound(X_44,X_46)))
    | least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) = least_upper_bound(Y,least_upper_bound(X_44,X_46)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)))),bind(Y0,$fot(least_upper_bound(X_44,least_upper_bound(Y,least_upper_bound(X_44,X_46))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_44,X_46))))]]) ).

cnf(refute_0_168,plain,
    ( least_upper_bound(X_44,least_upper_bound(Y,least_upper_bound(X_44,X_46))) != least_upper_bound(Y,least_upper_bound(X_44,X_46))
    | least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) = least_upper_bound(Y,least_upper_bound(X_44,X_46)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)),least_upper_bound(X_44,least_upper_bound(Y,least_upper_bound(X_44,X_46)))) )],[refute_0_166,refute_0_167]) ).

cnf(refute_0_169,plain,
    least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) = least_upper_bound(Y,least_upper_bound(X_44,X_46)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(Y,least_upper_bound(X_44,X_46))),least_upper_bound(Y,least_upper_bound(X_44,X_46))) )],[refute_0_161,refute_0_168]) ).

cnf(refute_0_170,plain,
    ( least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) != least_upper_bound(Y,least_upper_bound(X_44,X_46))
    | least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) != least_upper_bound(least_upper_bound(X_44,Y),X_46)
    | least_upper_bound(Y,least_upper_bound(X_44,X_46)) = least_upper_bound(least_upper_bound(X_44,Y),X_46) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)),least_upper_bound(least_upper_bound(X_44,Y),X_46)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_44,X_46)))]]) ).

cnf(refute_0_171,plain,
    ( least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) != least_upper_bound(least_upper_bound(X_44,Y),X_46)
    | least_upper_bound(Y,least_upper_bound(X_44,X_46)) = least_upper_bound(least_upper_bound(X_44,Y),X_46) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)),least_upper_bound(Y,least_upper_bound(X_44,X_46))) )],[refute_0_169,refute_0_170]) ).

cnf(refute_0_172,plain,
    least_upper_bound(least_upper_bound(X_44,Y),X_46) = least_upper_bound(X_44,least_upper_bound(Y,X_46)),
    inference(subst,[],[refute_0_73:[bind(X,$fot(X_44)),bind(Z,$fot(X_46))]]) ).

cnf(refute_0_173,plain,
    ( least_upper_bound(Y,least_upper_bound(X_44,X_46)) != least_upper_bound(least_upper_bound(X_44,Y),X_46)
    | least_upper_bound(least_upper_bound(X_44,Y),X_46) != least_upper_bound(X_44,least_upper_bound(Y,X_46))
    | least_upper_bound(Y,least_upper_bound(X_44,X_46)) = least_upper_bound(X_44,least_upper_bound(Y,X_46)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_44,X_46)),least_upper_bound(X_44,least_upper_bound(Y,X_46))) ),[0],$fot(least_upper_bound(least_upper_bound(X_44,Y),X_46))]]) ).

cnf(refute_0_174,plain,
    ( least_upper_bound(Y,least_upper_bound(X_44,X_46)) != least_upper_bound(least_upper_bound(X_44,Y),X_46)
    | least_upper_bound(Y,least_upper_bound(X_44,X_46)) = least_upper_bound(X_44,least_upper_bound(Y,X_46)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_44,Y),X_46),least_upper_bound(X_44,least_upper_bound(Y,X_46))) )],[refute_0_172,refute_0_173]) ).

cnf(refute_0_175,plain,
    ( least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)) != least_upper_bound(least_upper_bound(X_44,Y),X_46)
    | least_upper_bound(Y,least_upper_bound(X_44,X_46)) = least_upper_bound(X_44,least_upper_bound(Y,X_46)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_44,X_46)),least_upper_bound(least_upper_bound(X_44,Y),X_46)) )],[refute_0_171,refute_0_174]) ).

cnf(refute_0_176,plain,
    least_upper_bound(Y,least_upper_bound(X_44,X_46)) = least_upper_bound(X_44,least_upper_bound(Y,X_46)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(least_upper_bound(Y,X_44),X_46)),least_upper_bound(least_upper_bound(X_44,Y),X_46)) )],[refute_0_132,refute_0_175]) ).

cnf(refute_0_177,plain,
    ( least_upper_bound(Y,least_upper_bound(X_44,X_46)) != least_upper_bound(X_44,least_upper_bound(Y,X_46))
    | least_upper_bound(X_44,least_upper_bound(Y,X_46)) = least_upper_bound(Y,least_upper_bound(X_44,X_46)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_44,X_46)))),bind(Y0,$fot(least_upper_bound(X_44,least_upper_bound(Y,X_46))))]]) ).

cnf(refute_0_178,plain,
    least_upper_bound(X_44,least_upper_bound(Y,X_46)) = least_upper_bound(Y,least_upper_bound(X_44,X_46)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_44,X_46)),least_upper_bound(X_44,least_upper_bound(Y,X_46))) )],[refute_0_176,refute_0_177]) ).

cnf(refute_0_179,plain,
    least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) = least_upper_bound(Y,least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),X_63)),
    inference(subst,[],[refute_0_178:[bind(X_44,$fot(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))),bind(X_46,$fot(X_63))]]) ).

cnf(refute_0_180,plain,
    ( least_upper_bound(Y,least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),X_63)) != least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))))
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) != least_upper_bound(Y,least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),X_63))
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) = least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),X_63)))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))))))]]) ).

cnf(refute_0_181,plain,
    ( least_upper_bound(Y,least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),X_63)) != least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))))
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) = least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)),least_upper_bound(Y,least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),X_63))) )],[refute_0_179,refute_0_180]) ).

cnf(refute_0_182,plain,
    least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) = least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),X_63)),least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))))) )],[refute_0_127,refute_0_181]) ).

cnf(refute_0_183,plain,
    ( least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) != least_upper_bound(Y,X_63)
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) != least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))))
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) = least_upper_bound(Y,X_63) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))))),bind(Z0,$fot(least_upper_bound(Y,X_63)))]]) ).

cnf(refute_0_184,plain,
    ( least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))) != least_upper_bound(Y,X_63)
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) = least_upper_bound(Y,X_63) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)),least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63)))))) )],[refute_0_182,refute_0_183]) ).

cnf(refute_0_185,plain,
    least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) = least_upper_bound(Y,X_63),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_63,least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))))),least_upper_bound(Y,X_63)) )],[refute_0_113,refute_0_184]) ).

cnf(refute_0_186,plain,
    ( least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) != least_upper_bound(Y,X_63)
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) != least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)
    | least_upper_bound(Y,X_63) = least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)),least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)) ),[0],$fot(least_upper_bound(Y,X_63))]]) ).

cnf(refute_0_187,plain,
    ( least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) != least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)
    | least_upper_bound(Y,X_63) = least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)),least_upper_bound(Y,X_63)) )],[refute_0_185,refute_0_186]) ).

cnf(refute_0_188,plain,
    least_upper_bound(X_63,least_upper_bound(negative_part(least_upper_bound(Y,X_63)),Y)) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))),
    inference(subst,[],[refute_0_126:[bind(X_44,$fot(X_63)),bind(X_45,$fot(negative_part(least_upper_bound(Y,X_63)))),bind(X_46,$fot(Y))]]) ).

cnf(refute_0_189,plain,
    least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y) = least_upper_bound(X_63,least_upper_bound(negative_part(least_upper_bound(Y,X_63)),Y)),
    inference(subst,[],[refute_0_73:[bind(X,$fot(X_63)),bind(Y,$fot(negative_part(least_upper_bound(Y,X_63)))),bind(Z,$fot(Y))]]) ).

cnf(refute_0_190,plain,
    ( least_upper_bound(X_63,least_upper_bound(negative_part(least_upper_bound(Y,X_63)),Y)) != least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y) != least_upper_bound(X_63,least_upper_bound(negative_part(least_upper_bound(Y,X_63)),Y))
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y))),bind(Y0,$fot(least_upper_bound(X_63,least_upper_bound(negative_part(least_upper_bound(Y,X_63)),Y)))),bind(Z0,$fot(least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))))]]) ).

cnf(refute_0_191,plain,
    ( least_upper_bound(X_63,least_upper_bound(negative_part(least_upper_bound(Y,X_63)),Y)) != least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y),least_upper_bound(X_63,least_upper_bound(negative_part(least_upper_bound(Y,X_63)),Y))) )],[refute_0_189,refute_0_190]) ).

cnf(refute_0_192,plain,
    least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_63,least_upper_bound(negative_part(least_upper_bound(Y,X_63)),Y)),least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))) )],[refute_0_188,refute_0_191]) ).

cnf(refute_0_193,plain,
    ( least_upper_bound(Y,X_63) != least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)
    | least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y) != least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))
    | least_upper_bound(Y,X_63) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,X_63),least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))) ),[0],$fot(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y))]]) ).

cnf(refute_0_194,plain,
    ( least_upper_bound(Y,X_63) != least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)
    | least_upper_bound(Y,X_63) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y),least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))) )],[refute_0_192,refute_0_193]) ).

cnf(refute_0_195,plain,
    ( least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)) != least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)
    | least_upper_bound(Y,X_63) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,X_63),least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)) )],[refute_0_187,refute_0_194]) ).

cnf(refute_0_196,plain,
    least_upper_bound(Y,X_63) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,X_63)),least_upper_bound(least_upper_bound(X_63,negative_part(least_upper_bound(Y,X_63))),Y)) )],[refute_0_96,refute_0_195]) ).

cnf(refute_0_197,plain,
    least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48))) = least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y),
    inference(subst,[],[refute_0_77:[bind(X_29,$fot(least_upper_bound(negative_part(Y),X_48)))]]) ).

cnf(refute_0_198,plain,
    least_upper_bound(X_44,least_upper_bound(negative_part(X_44),X_46)) = least_upper_bound(least_upper_bound(X_44,negative_part(X_44)),X_46),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_44)),bind(Y,$fot(negative_part(X_44))),bind(Z,$fot(X_46))]]) ).

cnf(refute_0_199,plain,
    least_upper_bound(X_44,negative_part(X_44)) = X_44,
    inference(subst,[],[refute_0_85:[bind(X_22,$fot(X_44))]]) ).

cnf(refute_0_200,plain,
    ( least_upper_bound(X_44,least_upper_bound(negative_part(X_44),X_46)) != least_upper_bound(least_upper_bound(X_44,negative_part(X_44)),X_46)
    | least_upper_bound(X_44,negative_part(X_44)) != X_44
    | least_upper_bound(X_44,least_upper_bound(negative_part(X_44),X_46)) = least_upper_bound(X_44,X_46) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(negative_part(X_44),X_46)),least_upper_bound(least_upper_bound(X_44,negative_part(X_44)),X_46)) ),[1,0],$fot(X_44)]]) ).

cnf(refute_0_201,plain,
    ( least_upper_bound(X_44,least_upper_bound(negative_part(X_44),X_46)) != least_upper_bound(least_upper_bound(X_44,negative_part(X_44)),X_46)
    | least_upper_bound(X_44,least_upper_bound(negative_part(X_44),X_46)) = least_upper_bound(X_44,X_46) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,negative_part(X_44)),X_44) )],[refute_0_199,refute_0_200]) ).

cnf(refute_0_202,plain,
    least_upper_bound(X_44,least_upper_bound(negative_part(X_44),X_46)) = least_upper_bound(X_44,X_46),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(negative_part(X_44),X_46)),least_upper_bound(least_upper_bound(X_44,negative_part(X_44)),X_46)) )],[refute_0_198,refute_0_201]) ).

cnf(refute_0_203,plain,
    least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48)) = least_upper_bound(Y,X_48),
    inference(subst,[],[refute_0_202:[bind(X_44,$fot(Y)),bind(X_46,$fot(X_48))]]) ).

cnf(refute_0_204,plain,
    ( least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48)) != least_upper_bound(Y,X_48)
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48))) != least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) = least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48))),least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)) ),[0,1],$fot(least_upper_bound(Y,X_48))]]) ).

cnf(refute_0_205,plain,
    ( least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48))) != least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) = least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48)),least_upper_bound(Y,X_48)) )],[refute_0_203,refute_0_204]) ).

cnf(refute_0_206,plain,
    least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) = least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48))),least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)) )],[refute_0_197,refute_0_205]) ).

cnf(refute_0_207,plain,
    least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)) = least_upper_bound(X_48,negative_part(Y)),
    inference(subst,[],[refute_0_77:[bind(Y,$fot(negative_part(Y))),bind(X_29,$fot(X_48))]]) ).

cnf(refute_0_208,plain,
    least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))) = least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))),
    introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))))]]) ).

cnf(refute_0_209,plain,
    ( least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))) != least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)))
    | least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)) != least_upper_bound(X_48,negative_part(Y))
    | least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))) = least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))),least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)))) ),[1,1],$fot(least_upper_bound(X_48,negative_part(Y)))]]) ).

cnf(refute_0_210,plain,
    ( least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)) != least_upper_bound(X_48,negative_part(Y))
    | least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))) = least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))),least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)))) )],[refute_0_208,refute_0_209]) ).

cnf(refute_0_211,plain,
    least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))) = least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)),least_upper_bound(X_48,negative_part(Y))) )],[refute_0_207,refute_0_210]) ).

cnf(refute_0_212,plain,
    least_upper_bound(Y,least_upper_bound(least_upper_bound(negative_part(Y),X_48),X_48)) = least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))),
    inference(subst,[],[refute_0_126:[bind(X_44,$fot(Y)),bind(X_45,$fot(least_upper_bound(negative_part(Y),X_48))),bind(X_46,$fot(X_48))]]) ).

cnf(refute_0_213,plain,
    least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) = least_upper_bound(Y,least_upper_bound(least_upper_bound(negative_part(Y),X_48),X_48)),
    inference(subst,[],[refute_0_178:[bind(X_44,$fot(least_upper_bound(negative_part(Y),X_48))),bind(X_46,$fot(X_48))]]) ).

cnf(refute_0_214,plain,
    ( least_upper_bound(Y,least_upper_bound(least_upper_bound(negative_part(Y),X_48),X_48)) != least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)))
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) != least_upper_bound(Y,least_upper_bound(least_upper_bound(negative_part(Y),X_48),X_48))
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) = least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(negative_part(Y),X_48),X_48)))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)))))]]) ).

cnf(refute_0_215,plain,
    ( least_upper_bound(Y,least_upper_bound(least_upper_bound(negative_part(Y),X_48),X_48)) != least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)))
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) = least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)),least_upper_bound(Y,least_upper_bound(least_upper_bound(negative_part(Y),X_48),X_48))) )],[refute_0_213,refute_0_214]) ).

cnf(refute_0_216,plain,
    least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) = least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(negative_part(Y),X_48),X_48)),least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)))) )],[refute_0_212,refute_0_215]) ).

cnf(refute_0_217,plain,
    ( least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))) != least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y)))
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) != least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)))
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) = least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y)))))]]) ).

cnf(refute_0_218,plain,
    ( least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))) != least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y)))
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) = least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)),least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48)))) )],[refute_0_216,refute_0_217]) ).

cnf(refute_0_219,plain,
    least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) = least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_48,least_upper_bound(negative_part(Y),X_48))),least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y)))) )],[refute_0_211,refute_0_218]) ).

cnf(refute_0_220,plain,
    ( least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) != least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y)))
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) != least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)
    | least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) = least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)),least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))))]]) ).

cnf(refute_0_221,plain,
    ( least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) != least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)
    | least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) = least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)),least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y)))) )],[refute_0_219,refute_0_220]) ).

cnf(refute_0_222,plain,
    least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)) = least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48)),
    inference(subst,[],[refute_0_151:[bind(X,$fot(Y)),bind(X_44,$fot(negative_part(Y))),bind(X_45,$fot(X_48))]]) ).

cnf(refute_0_223,plain,
    ( least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48)) != least_upper_bound(Y,X_48)
    | least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)) != least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48))
    | least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)) = least_upper_bound(Y,X_48) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48)))),bind(Z0,$fot(least_upper_bound(Y,X_48)))]]) ).

cnf(refute_0_224,plain,
    ( least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48)) != least_upper_bound(Y,X_48)
    | least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)) = least_upper_bound(Y,X_48) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)),least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48))) )],[refute_0_222,refute_0_223]) ).

cnf(refute_0_225,plain,
    least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)) = least_upper_bound(Y,X_48),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(negative_part(Y),X_48)),least_upper_bound(Y,X_48)) )],[refute_0_203,refute_0_224]) ).

cnf(refute_0_226,plain,
    least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y) = least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)),
    inference(subst,[],[refute_0_73:[bind(X,$fot(negative_part(Y))),bind(Y,$fot(X_48)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_227,plain,
    ( least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y) != least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y))
    | least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)) != least_upper_bound(Y,X_48)
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y) = least_upper_bound(Y,X_48) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y))),bind(Y0,$fot(least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)))),bind(Z0,$fot(least_upper_bound(Y,X_48)))]]) ).

cnf(refute_0_228,plain,
    ( least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)) != least_upper_bound(Y,X_48)
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y) = least_upper_bound(Y,X_48) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y),least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y))) )],[refute_0_226,refute_0_227]) ).

cnf(refute_0_229,plain,
    least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y) = least_upper_bound(Y,X_48),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(Y),least_upper_bound(X_48,Y)),least_upper_bound(Y,X_48)) )],[refute_0_225,refute_0_228]) ).

cnf(refute_0_230,plain,
    ( least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) != least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)
    | least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y) != least_upper_bound(Y,X_48)
    | least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) = least_upper_bound(Y,X_48) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))),least_upper_bound(Y,X_48)) ),[0],$fot(least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y))]]) ).

cnf(refute_0_231,plain,
    ( least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) != least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)
    | least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) = least_upper_bound(Y,X_48) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y),least_upper_bound(Y,X_48)) )],[refute_0_229,refute_0_230]) ).

cnf(refute_0_232,plain,
    ( least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)) != least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)
    | least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) = least_upper_bound(Y,X_48) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))),least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)) )],[refute_0_221,refute_0_231]) ).

cnf(refute_0_233,plain,
    least_upper_bound(Y,least_upper_bound(X_48,negative_part(Y))) = least_upper_bound(Y,X_48),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(negative_part(Y),X_48),least_upper_bound(Y,X_48)),least_upper_bound(least_upper_bound(negative_part(Y),X_48),Y)) )],[refute_0_206,refute_0_232]) ).

cnf(refute_0_234,plain,
    least_upper_bound(X_63,least_upper_bound(Y,negative_part(X_63))) = least_upper_bound(X_63,Y),
    inference(subst,[],[refute_0_233:[bind(Y,$fot(X_63)),bind(X_48,$fot(Y))]]) ).

cnf(refute_0_235,plain,
    greatest_lower_bound(X_16,least_upper_bound(X_16,X_17)) = X_16,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_16)),bind(Y,$fot(X_17))]]) ).

cnf(refute_0_236,plain,
    least_upper_bound(X_17,X_16) = least_upper_bound(X_16,X_17),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_17)),bind(Y,$fot(X_16))]]) ).

cnf(refute_0_237,plain,
    ( least_upper_bound(X_17,X_16) != least_upper_bound(X_16,X_17)
    | least_upper_bound(X_16,X_17) = least_upper_bound(X_17,X_16) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_17,X_16))),bind(Y0,$fot(least_upper_bound(X_16,X_17)))]]) ).

cnf(refute_0_238,plain,
    least_upper_bound(X_16,X_17) = least_upper_bound(X_17,X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_17,X_16),least_upper_bound(X_16,X_17)) )],[refute_0_236,refute_0_237]) ).

cnf(refute_0_239,plain,
    ( greatest_lower_bound(X_16,least_upper_bound(X_16,X_17)) != X_16
    | least_upper_bound(X_16,X_17) != least_upper_bound(X_17,X_16)
    | greatest_lower_bound(X_16,least_upper_bound(X_17,X_16)) = X_16 ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_16,least_upper_bound(X_16,X_17)),X_16) ),[0,1],$fot(least_upper_bound(X_17,X_16))]]) ).

cnf(refute_0_240,plain,
    ( greatest_lower_bound(X_16,least_upper_bound(X_16,X_17)) != X_16
    | greatest_lower_bound(X_16,least_upper_bound(X_17,X_16)) = X_16 ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_16,X_17),least_upper_bound(X_17,X_16)) )],[refute_0_238,refute_0_239]) ).

cnf(refute_0_241,plain,
    greatest_lower_bound(X_16,least_upper_bound(X_17,X_16)) = X_16,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,least_upper_bound(X_16,X_17)),X_16) )],[refute_0_235,refute_0_240]) ).

cnf(refute_0_242,plain,
    greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))))) = least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),
    inference(subst,[],[refute_0_241:[bind(X_16,$fot(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))))]]) ).

cnf(refute_0_243,plain,
    least_upper_bound(X_98,X_17) = least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))),
    inference(subst,[],[refute_0_196:[bind(Y,$fot(X_98)),bind(X_63,$fot(X_17))]]) ).

cnf(refute_0_244,plain,
    ( least_upper_bound(X_98,X_17) != least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))))
    | least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))) = least_upper_bound(X_98,X_17) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_98,X_17))),bind(Y0,$fot(least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))))))]]) ).

cnf(refute_0_245,plain,
    least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))) = least_upper_bound(X_98,X_17),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_98,X_17),least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))))) )],[refute_0_243,refute_0_244]) ).

cnf(refute_0_246,plain,
    ( greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))))) != least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))
    | least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))) != least_upper_bound(X_98,X_17)
    | greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)) = least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))))),least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))) ),[0,1],$fot(least_upper_bound(X_98,X_17))]]) ).

cnf(refute_0_247,plain,
    ( greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))))) != least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))
    | greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)) = least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))),least_upper_bound(X_98,X_17)) )],[refute_0_245,refute_0_246]) ).

cnf(refute_0_248,plain,
    greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)) = least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_17,least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))))),least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))) )],[refute_0_242,refute_0_247]) ).

cnf(refute_0_249,plain,
    greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)) = X_17,
    inference(subst,[],[refute_0_241:[bind(X_16,$fot(X_17)),bind(X_17,$fot(X_98))]]) ).

cnf(refute_0_250,plain,
    negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))) = negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))),
    introduced(tautology,[refl,[$fot(negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))))]]) ).

cnf(refute_0_251,plain,
    ( greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)) != X_17
    | negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))) != negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)))
    | negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))) = negative_part(X_17) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))),negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)))) ),[1,0],$fot(X_17)]]) ).

cnf(refute_0_252,plain,
    ( greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)) != X_17
    | negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))) = negative_part(X_17) ),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))),negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)))) )],[refute_0_250,refute_0_251]) ).

cnf(refute_0_253,plain,
    negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))) = negative_part(X_17),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)),X_17) )],[refute_0_249,refute_0_252]) ).

cnf(refute_0_254,plain,
    greatest_lower_bound(X,identity) = greatest_lower_bound(identity,X),
    inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(identity))]]) ).

cnf(refute_0_255,plain,
    ( greatest_lower_bound(X,identity) != greatest_lower_bound(identity,X)
    | negative_part(X) != greatest_lower_bound(X,identity)
    | negative_part(X) = greatest_lower_bound(identity,X) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(X),greatest_lower_bound(X,identity)) ),[1],$fot(greatest_lower_bound(identity,X))]]) ).

cnf(refute_0_256,plain,
    ( negative_part(X) != greatest_lower_bound(X,identity)
    | negative_part(X) = greatest_lower_bound(identity,X) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,identity),greatest_lower_bound(identity,X)) )],[refute_0_254,refute_0_255]) ).

cnf(refute_0_257,plain,
    negative_part(X) = greatest_lower_bound(identity,X),
    inference(resolve,[$cnf( $equal(negative_part(X),greatest_lower_bound(X,identity)) )],[lat4_5,refute_0_256]) ).

cnf(refute_0_258,plain,
    negative_part(greatest_lower_bound(X_90,X_88)) = greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88)),
    inference(subst,[],[refute_0_257:[bind(X,$fot(greatest_lower_bound(X_90,X_88)))]]) ).

cnf(refute_0_259,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(greatest_lower_bound(X_35,X_36),X),
    inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_35,X_36)))]]) ).

cnf(refute_0_260,plain,
    greatest_lower_bound(X_35,greatest_lower_bound(X_36,X)) = greatest_lower_bound(greatest_lower_bound(X_35,X_36),X),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_35)),bind(Y,$fot(X_36)),bind(Z,$fot(X))]]) ).

cnf(refute_0_261,plain,
    ( greatest_lower_bound(X_35,greatest_lower_bound(X_36,X)) != greatest_lower_bound(greatest_lower_bound(X_35,X_36),X)
    | greatest_lower_bound(greatest_lower_bound(X_35,X_36),X) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,X)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_35,greatest_lower_bound(X_36,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_35,X_36),X)))]]) ).

cnf(refute_0_262,plain,
    greatest_lower_bound(greatest_lower_bound(X_35,X_36),X) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_35,greatest_lower_bound(X_36,X)),greatest_lower_bound(greatest_lower_bound(X_35,X_36),X)) )],[refute_0_260,refute_0_261]) ).

cnf(refute_0_263,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(greatest_lower_bound(X_35,X_36),X)
    | greatest_lower_bound(greatest_lower_bound(X_35,X_36),X) != greatest_lower_bound(X_35,greatest_lower_bound(X_36,X))
    | greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)),greatest_lower_bound(X_35,greatest_lower_bound(X_36,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_35,X_36),X))]]) ).

cnf(refute_0_264,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(greatest_lower_bound(X_35,X_36),X)
    | greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_35,X_36),X),greatest_lower_bound(X_35,greatest_lower_bound(X_36,X))) )],[refute_0_262,refute_0_263]) ).

cnf(refute_0_265,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)),greatest_lower_bound(greatest_lower_bound(X_35,X_36),X)) )],[refute_0_259,refute_0_264]) ).

cnf(refute_0_266,plain,
    greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) = greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88)),
    inference(subst,[],[refute_0_265:[bind(X,$fot(X_88)),bind(X_35,$fot(identity)),bind(X_36,$fot(X_90))]]) ).

cnf(refute_0_267,plain,
    ( greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) != greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88))
    | greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88)) = greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88))))]]) ).

cnf(refute_0_268,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88)) = greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)),greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88))) )],[refute_0_266,refute_0_267]) ).

cnf(refute_0_269,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88)) != greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90))
    | negative_part(greatest_lower_bound(X_90,X_88)) != greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88))
    | negative_part(greatest_lower_bound(X_90,X_88)) = greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(greatest_lower_bound(X_90,X_88)),greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88))) ),[1],$fot(greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)))]]) ).

cnf(refute_0_270,plain,
    ( negative_part(greatest_lower_bound(X_90,X_88)) != greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88))
    | negative_part(greatest_lower_bound(X_90,X_88)) = greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88)),greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90))) )],[refute_0_268,refute_0_269]) ).

cnf(refute_0_271,plain,
    negative_part(greatest_lower_bound(X_90,X_88)) = greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(X_90,X_88)),greatest_lower_bound(identity,greatest_lower_bound(X_90,X_88))) )],[refute_0_258,refute_0_270]) ).

cnf(refute_0_272,plain,
    negative_part(greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity),
    inference(subst,[],[lat4_5:[bind(X,$fot(greatest_lower_bound(X_35,X_36)))]]) ).

cnf(refute_0_273,plain,
    greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_35)),bind(Y,$fot(X_36)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_274,plain,
    ( greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)) != greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity)
    | greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity)))]]) ).

cnf(refute_0_275,plain,
    greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)),greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity)) )],[refute_0_273,refute_0_274]) ).

cnf(refute_0_276,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity) != greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity))
    | negative_part(greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity)
    | negative_part(greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(greatest_lower_bound(X_35,X_36)),greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity)) ),[1],$fot(greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)))]]) ).

cnf(refute_0_277,plain,
    ( negative_part(greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity)
    | negative_part(greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity),greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity))) )],[refute_0_275,refute_0_276]) ).

cnf(refute_0_278,plain,
    negative_part(greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(X_35,X_36)),greatest_lower_bound(greatest_lower_bound(X_35,X_36),identity)) )],[refute_0_272,refute_0_277]) ).

cnf(refute_0_279,plain,
    ( negative_part(X) != greatest_lower_bound(X,identity)
    | greatest_lower_bound(X,identity) = negative_part(X) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(X))),bind(Y0,$fot(greatest_lower_bound(X,identity)))]]) ).

cnf(refute_0_280,plain,
    greatest_lower_bound(X,identity) = negative_part(X),
    inference(resolve,[$cnf( $equal(negative_part(X),greatest_lower_bound(X,identity)) )],[lat4_5,refute_0_279]) ).

cnf(refute_0_281,plain,
    greatest_lower_bound(X_36,identity) = negative_part(X_36),
    inference(subst,[],[refute_0_280:[bind(X,$fot(X_36))]]) ).

cnf(refute_0_282,plain,
    greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)))]]) ).

cnf(refute_0_283,plain,
    ( greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)) != greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity))
    | greatest_lower_bound(X_36,identity) != negative_part(X_36)
    | greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(X_35,negative_part(X_36)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)),greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity))) ),[1,1],$fot(negative_part(X_36))]]) ).

cnf(refute_0_284,plain,
    ( greatest_lower_bound(X_36,identity) != negative_part(X_36)
    | greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(X_35,negative_part(X_36)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)),greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity))) )],[refute_0_282,refute_0_283]) ).

cnf(refute_0_285,plain,
    greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)) = greatest_lower_bound(X_35,negative_part(X_36)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,identity),negative_part(X_36)) )],[refute_0_281,refute_0_284]) ).

cnf(refute_0_286,plain,
    ( greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)) != greatest_lower_bound(X_35,negative_part(X_36))
    | negative_part(greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity))
    | negative_part(greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(X_35,negative_part(X_36)) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(greatest_lower_bound(X_35,X_36)),greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity))) ),[1],$fot(greatest_lower_bound(X_35,negative_part(X_36)))]]) ).

cnf(refute_0_287,plain,
    ( negative_part(greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity))
    | negative_part(greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(X_35,negative_part(X_36)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity)),greatest_lower_bound(X_35,negative_part(X_36))) )],[refute_0_285,refute_0_286]) ).

cnf(refute_0_288,plain,
    negative_part(greatest_lower_bound(X_35,X_36)) = greatest_lower_bound(X_35,negative_part(X_36)),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(X_35,X_36)),greatest_lower_bound(X_35,greatest_lower_bound(X_36,identity))) )],[refute_0_278,refute_0_287]) ).

cnf(refute_0_289,plain,
    ( negative_part(greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(X_35,negative_part(X_36))
    | greatest_lower_bound(X_35,negative_part(X_36)) = negative_part(greatest_lower_bound(X_35,X_36)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(greatest_lower_bound(X_35,X_36)))),bind(Y0,$fot(greatest_lower_bound(X_35,negative_part(X_36))))]]) ).

cnf(refute_0_290,plain,
    greatest_lower_bound(X_35,negative_part(X_36)) = negative_part(greatest_lower_bound(X_35,X_36)),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(X_35,X_36)),greatest_lower_bound(X_35,negative_part(X_36))) )],[refute_0_288,refute_0_289]) ).

cnf(refute_0_291,plain,
    greatest_lower_bound(X_88,negative_part(X_90)) = negative_part(greatest_lower_bound(X_88,X_90)),
    inference(subst,[],[refute_0_290:[bind(X_35,$fot(X_88)),bind(X_36,$fot(X_90))]]) ).

cnf(refute_0_292,plain,
    ( negative_part(X) != greatest_lower_bound(identity,X)
    | greatest_lower_bound(identity,X) = negative_part(X) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(X))),bind(Y0,$fot(greatest_lower_bound(identity,X)))]]) ).

cnf(refute_0_293,plain,
    greatest_lower_bound(identity,X) = negative_part(X),
    inference(resolve,[$cnf( $equal(negative_part(X),greatest_lower_bound(identity,X)) )],[refute_0_257,refute_0_292]) ).

cnf(refute_0_294,plain,
    greatest_lower_bound(identity,X_90) = negative_part(X_90),
    inference(subst,[],[refute_0_293:[bind(X,$fot(X_90))]]) ).

cnf(refute_0_295,plain,
    greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) = greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)))]]) ).

cnf(refute_0_296,plain,
    ( greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) != greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90))
    | greatest_lower_bound(identity,X_90) != negative_part(X_90)
    | greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) = greatest_lower_bound(X_88,negative_part(X_90)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)),greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90))) ),[1,1],$fot(negative_part(X_90))]]) ).

cnf(refute_0_297,plain,
    ( greatest_lower_bound(identity,X_90) != negative_part(X_90)
    | greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) = greatest_lower_bound(X_88,negative_part(X_90)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)),greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90))) )],[refute_0_295,refute_0_296]) ).

cnf(refute_0_298,plain,
    greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) = greatest_lower_bound(X_88,negative_part(X_90)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_90),negative_part(X_90)) )],[refute_0_294,refute_0_297]) ).

cnf(refute_0_299,plain,
    ( greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) != greatest_lower_bound(X_88,negative_part(X_90))
    | greatest_lower_bound(X_88,negative_part(X_90)) != negative_part(greatest_lower_bound(X_88,X_90))
    | greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) = negative_part(greatest_lower_bound(X_88,X_90)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)))),bind(Y0,$fot(greatest_lower_bound(X_88,negative_part(X_90)))),bind(Z0,$fot(negative_part(greatest_lower_bound(X_88,X_90))))]]) ).

cnf(refute_0_300,plain,
    ( greatest_lower_bound(X_88,negative_part(X_90)) != negative_part(greatest_lower_bound(X_88,X_90))
    | greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) = negative_part(greatest_lower_bound(X_88,X_90)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)),greatest_lower_bound(X_88,negative_part(X_90))) )],[refute_0_298,refute_0_299]) ).

cnf(refute_0_301,plain,
    greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) = negative_part(greatest_lower_bound(X_88,X_90)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_88,negative_part(X_90)),negative_part(greatest_lower_bound(X_88,X_90))) )],[refute_0_291,refute_0_300]) ).

cnf(refute_0_302,plain,
    ( greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)) != negative_part(greatest_lower_bound(X_88,X_90))
    | negative_part(greatest_lower_bound(X_90,X_88)) != greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90))
    | negative_part(greatest_lower_bound(X_90,X_88)) = negative_part(greatest_lower_bound(X_88,X_90)) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(greatest_lower_bound(X_90,X_88)),greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90))) ),[1],$fot(negative_part(greatest_lower_bound(X_88,X_90)))]]) ).

cnf(refute_0_303,plain,
    ( negative_part(greatest_lower_bound(X_90,X_88)) != greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90))
    | negative_part(greatest_lower_bound(X_90,X_88)) = negative_part(greatest_lower_bound(X_88,X_90)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90)),negative_part(greatest_lower_bound(X_88,X_90))) )],[refute_0_301,refute_0_302]) ).

cnf(refute_0_304,plain,
    negative_part(greatest_lower_bound(X_90,X_88)) = negative_part(greatest_lower_bound(X_88,X_90)),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(X_90,X_88)),greatest_lower_bound(X_88,greatest_lower_bound(identity,X_90))) )],[refute_0_271,refute_0_303]) ).

cnf(refute_0_305,plain,
    ( negative_part(greatest_lower_bound(X_90,X_88)) != negative_part(greatest_lower_bound(X_88,X_90))
    | negative_part(greatest_lower_bound(X_88,X_90)) = negative_part(greatest_lower_bound(X_90,X_88)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(greatest_lower_bound(X_90,X_88)))),bind(Y0,$fot(negative_part(greatest_lower_bound(X_88,X_90))))]]) ).

cnf(refute_0_306,plain,
    negative_part(greatest_lower_bound(X_88,X_90)) = negative_part(greatest_lower_bound(X_90,X_88)),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(X_90,X_88)),negative_part(greatest_lower_bound(X_88,X_90))) )],[refute_0_304,refute_0_305]) ).

cnf(refute_0_307,plain,
    negative_part(greatest_lower_bound(least_upper_bound(X_98,X_17),X_17)) = negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))),
    inference(subst,[],[refute_0_306:[bind(X_88,$fot(least_upper_bound(X_98,X_17))),bind(X_90,$fot(X_17))]]) ).

cnf(refute_0_308,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(greatest_lower_bound(identity,X_36),X_37),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_36)),bind(Z,$fot(X_37))]]) ).

cnf(refute_0_309,plain,
    negative_part(X_36) = greatest_lower_bound(identity,X_36),
    inference(subst,[],[refute_0_257:[bind(X,$fot(X_36))]]) ).

cnf(refute_0_310,plain,
    ( negative_part(X_36) != greatest_lower_bound(identity,X_36)
    | greatest_lower_bound(identity,X_36) = negative_part(X_36) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(X_36))),bind(Y0,$fot(greatest_lower_bound(identity,X_36)))]]) ).

cnf(refute_0_311,plain,
    greatest_lower_bound(identity,X_36) = negative_part(X_36),
    inference(resolve,[$cnf( $equal(negative_part(X_36),greatest_lower_bound(identity,X_36)) )],[refute_0_309,refute_0_310]) ).

cnf(refute_0_312,plain,
    ( greatest_lower_bound(identity,X_36) != negative_part(X_36)
    | greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(identity,X_36),X_37)
    | greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(negative_part(X_36),X_37) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(greatest_lower_bound(identity,X_36),X_37)) ),[1,0],$fot(negative_part(X_36))]]) ).

cnf(refute_0_313,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(identity,X_36),X_37)
    | greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(negative_part(X_36),X_37) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_36),negative_part(X_36)) )],[refute_0_311,refute_0_312]) ).

cnf(refute_0_314,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(negative_part(X_36),X_37),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(greatest_lower_bound(identity,X_36),X_37)) )],[refute_0_308,refute_0_313]) ).

cnf(refute_0_315,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)) = negative_part(greatest_lower_bound(X_36,X_37)),
    inference(subst,[],[refute_0_293:[bind(X,$fot(greatest_lower_bound(X_36,X_37)))]]) ).

cnf(refute_0_316,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(negative_part(X_36),X_37)
    | greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)) != negative_part(greatest_lower_bound(X_36,X_37))
    | negative_part(greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(negative_part(X_36),X_37) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(negative_part(X_36),X_37)) ),[0],$fot(negative_part(greatest_lower_bound(X_36,X_37)))]]) ).

cnf(refute_0_317,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(negative_part(X_36),X_37)
    | negative_part(greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(negative_part(X_36),X_37) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)),negative_part(greatest_lower_bound(X_36,X_37))) )],[refute_0_315,refute_0_316]) ).

cnf(refute_0_318,plain,
    negative_part(greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(negative_part(X_36),X_37),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(negative_part(X_36),X_37)) )],[refute_0_314,refute_0_317]) ).

cnf(refute_0_319,plain,
    ( negative_part(greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(negative_part(X_36),X_37)
    | greatest_lower_bound(negative_part(X_36),X_37) = negative_part(greatest_lower_bound(X_36,X_37)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(greatest_lower_bound(X_36,X_37)))),bind(Y0,$fot(greatest_lower_bound(negative_part(X_36),X_37)))]]) ).

cnf(refute_0_320,plain,
    greatest_lower_bound(negative_part(X_36),X_37) = negative_part(greatest_lower_bound(X_36,X_37)),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(X_36,X_37)),greatest_lower_bound(negative_part(X_36),X_37)) )],[refute_0_318,refute_0_319]) ).

cnf(refute_0_321,plain,
    greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17) = negative_part(greatest_lower_bound(least_upper_bound(X_98,X_17),X_17)),
    inference(subst,[],[refute_0_320:[bind(X_36,$fot(least_upper_bound(X_98,X_17))),bind(X_37,$fot(X_17))]]) ).

cnf(refute_0_322,plain,
    ( greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17) != negative_part(greatest_lower_bound(least_upper_bound(X_98,X_17),X_17))
    | negative_part(greatest_lower_bound(least_upper_bound(X_98,X_17),X_17)) != negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)))
    | greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17) = negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17))),bind(Y0,$fot(negative_part(greatest_lower_bound(least_upper_bound(X_98,X_17),X_17)))),bind(Z0,$fot(negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)))))]]) ).

cnf(refute_0_323,plain,
    ( negative_part(greatest_lower_bound(least_upper_bound(X_98,X_17),X_17)) != negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)))
    | greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17) = negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17),negative_part(greatest_lower_bound(least_upper_bound(X_98,X_17),X_17))) )],[refute_0_321,refute_0_322]) ).

cnf(refute_0_324,plain,
    greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17) = negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(least_upper_bound(X_98,X_17),X_17)),negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)))) )],[refute_0_307,refute_0_323]) ).

cnf(refute_0_325,plain,
    ( greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17) != negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)))
    | negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))) != negative_part(X_17)
    | greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17) = negative_part(X_17) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17))),bind(Y0,$fot(negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))))),bind(Z0,$fot(negative_part(X_17)))]]) ).

cnf(refute_0_326,plain,
    ( negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))) != negative_part(X_17)
    | greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17) = negative_part(X_17) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17),negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17)))) )],[refute_0_324,refute_0_325]) ).

cnf(refute_0_327,plain,
    greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17) = negative_part(X_17),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(X_17,least_upper_bound(X_98,X_17))),negative_part(X_17)) )],[refute_0_253,refute_0_326]) ).

cnf(refute_0_328,plain,
    least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)) = least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)))]]) ).

cnf(refute_0_329,plain,
    ( greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17) != negative_part(X_17)
    | least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)) != least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17))
    | least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)) = least_upper_bound(X_98,negative_part(X_17)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)),least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17))) ),[1,1],$fot(negative_part(X_17))]]) ).

cnf(refute_0_330,plain,
    ( greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17) != negative_part(X_17)
    | least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)) = least_upper_bound(X_98,negative_part(X_17)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)),least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17))) )],[refute_0_328,refute_0_329]) ).

cnf(refute_0_331,plain,
    least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)) = least_upper_bound(X_98,negative_part(X_17)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17),negative_part(X_17)) )],[refute_0_327,refute_0_330]) ).

cnf(refute_0_332,plain,
    ( least_upper_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z))
    | greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)) = least_upper_bound(X,greatest_lower_bound(Y,Z)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z))))]]) ).

cnf(refute_0_333,plain,
    greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)) = least_upper_bound(X,greatest_lower_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z))) )],[lat4_6,refute_0_332]) ).

cnf(refute_0_334,plain,
    greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)) = least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)),
    inference(subst,[],[refute_0_333:[bind(X,$fot(X_98)),bind(Y,$fot(negative_part(least_upper_bound(X_98,X_17)))),bind(Z,$fot(X_17))]]) ).

cnf(refute_0_335,plain,
    ( greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)) != least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17))
    | least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)) != least_upper_bound(X_98,negative_part(X_17))
    | greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)) = least_upper_bound(X_98,negative_part(X_17)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)))),bind(Y0,$fot(least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)))),bind(Z0,$fot(least_upper_bound(X_98,negative_part(X_17))))]]) ).

cnf(refute_0_336,plain,
    ( least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)) != least_upper_bound(X_98,negative_part(X_17))
    | greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)) = least_upper_bound(X_98,negative_part(X_17)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)),least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17))) )],[refute_0_334,refute_0_335]) ).

cnf(refute_0_337,plain,
    greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)) = least_upper_bound(X_98,negative_part(X_17)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_98,greatest_lower_bound(negative_part(least_upper_bound(X_98,X_17)),X_17)),least_upper_bound(X_98,negative_part(X_17))) )],[refute_0_331,refute_0_336]) ).

cnf(refute_0_338,plain,
    ( greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)) != least_upper_bound(X_98,negative_part(X_17))
    | greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)) != least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))
    | least_upper_bound(X_98,negative_part(X_17)) = least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)),least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))) ),[0],$fot(least_upper_bound(X_98,negative_part(X_17)))]]) ).

cnf(refute_0_339,plain,
    ( greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)) != least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))
    | least_upper_bound(X_98,negative_part(X_17)) = least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)),least_upper_bound(X_98,negative_part(X_17))) )],[refute_0_337,refute_0_338]) ).

cnf(refute_0_340,plain,
    least_upper_bound(X_98,negative_part(X_17)) = least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))),least_upper_bound(X_98,X_17)),least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))) )],[refute_0_248,refute_0_339]) ).

cnf(refute_0_341,plain,
    ( least_upper_bound(X_98,negative_part(X_17)) != least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))
    | least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))) = least_upper_bound(X_98,negative_part(X_17)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_98,negative_part(X_17)))),bind(Y0,$fot(least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))))]]) ).

cnf(refute_0_342,plain,
    least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17))) = least_upper_bound(X_98,negative_part(X_17)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_98,negative_part(X_17)),least_upper_bound(X_98,negative_part(least_upper_bound(X_98,X_17)))) )],[refute_0_340,refute_0_341]) ).

cnf(refute_0_343,plain,
    least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))) = least_upper_bound(Y,negative_part(X_63)),
    inference(subst,[],[refute_0_342:[bind(X_17,$fot(X_63)),bind(X_98,$fot(Y))]]) ).

cnf(refute_0_344,plain,
    least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))))]]) ).

cnf(refute_0_345,plain,
    ( least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))) != least_upper_bound(Y,negative_part(X_63))
    | least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) != least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))
    | least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(X_63))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))),least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))) ),[1,1],$fot(least_upper_bound(Y,negative_part(X_63)))]]) ).

cnf(refute_0_346,plain,
    ( least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))) != least_upper_bound(Y,negative_part(X_63))
    | least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(X_63))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))),least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))) )],[refute_0_344,refute_0_345]) ).

cnf(refute_0_347,plain,
    least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) = least_upper_bound(X_63,least_upper_bound(Y,negative_part(X_63))),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))),least_upper_bound(Y,negative_part(X_63))) )],[refute_0_343,refute_0_346]) ).

cnf(refute_0_348,plain,
    ( least_upper_bound(X_63,least_upper_bound(Y,negative_part(X_63))) != least_upper_bound(X_63,Y)
    | least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) != least_upper_bound(X_63,least_upper_bound(Y,negative_part(X_63)))
    | least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) = least_upper_bound(X_63,Y) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))))),bind(Y0,$fot(least_upper_bound(X_63,least_upper_bound(Y,negative_part(X_63))))),bind(Z0,$fot(least_upper_bound(X_63,Y)))]]) ).

cnf(refute_0_349,plain,
    ( least_upper_bound(X_63,least_upper_bound(Y,negative_part(X_63))) != least_upper_bound(X_63,Y)
    | least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) = least_upper_bound(X_63,Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))),least_upper_bound(X_63,least_upper_bound(Y,negative_part(X_63)))) )],[refute_0_347,refute_0_348]) ).

cnf(refute_0_350,plain,
    least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) = least_upper_bound(X_63,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_63,least_upper_bound(Y,negative_part(X_63))),least_upper_bound(X_63,Y)) )],[refute_0_234,refute_0_349]) ).

cnf(refute_0_351,plain,
    ( least_upper_bound(Y,X_63) != least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))
    | least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))) != least_upper_bound(X_63,Y)
    | least_upper_bound(Y,X_63) = least_upper_bound(X_63,Y) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,X_63),least_upper_bound(X_63,Y)) ),[0],$fot(least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))))]]) ).

cnf(refute_0_352,plain,
    ( least_upper_bound(Y,X_63) != least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))
    | least_upper_bound(Y,X_63) = least_upper_bound(X_63,Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63)))),least_upper_bound(X_63,Y)) )],[refute_0_350,refute_0_351]) ).

cnf(refute_0_353,plain,
    least_upper_bound(Y,X_63) = least_upper_bound(X_63,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,X_63),least_upper_bound(X_63,least_upper_bound(Y,negative_part(least_upper_bound(Y,X_63))))) )],[refute_0_196,refute_0_352]) ).

cnf(refute_0_354,plain,
    ( least_upper_bound(Y,X_63) != least_upper_bound(X_63,Y)
    | least_upper_bound(X_63,Y) = least_upper_bound(Y,X_63) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(Y,X_63))),bind(Y0,$fot(least_upper_bound(X_63,Y)))]]) ).

cnf(refute_0_355,plain,
    least_upper_bound(X_63,Y) = least_upper_bound(Y,X_63),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,X_63),least_upper_bound(X_63,Y)) )],[refute_0_353,refute_0_354]) ).

cnf(refute_0_356,plain,
    least_upper_bound(multiply(X_119,X_120),X_119) = least_upper_bound(X_119,multiply(X_119,X_120)),
    inference(subst,[],[refute_0_355:[bind(Y,$fot(X_119)),bind(X_63,$fot(multiply(X_119,X_120)))]]) ).

cnf(refute_0_357,plain,
    ( multiply(X_119,positive_part(X_120)) != least_upper_bound(multiply(X_119,X_120),X_119)
    | least_upper_bound(multiply(X_119,X_120),X_119) != least_upper_bound(X_119,multiply(X_119,X_120))
    | multiply(X_119,positive_part(X_120)) = least_upper_bound(X_119,multiply(X_119,X_120)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_119,positive_part(X_120)),least_upper_bound(X_119,multiply(X_119,X_120))) ),[0],$fot(least_upper_bound(multiply(X_119,X_120),X_119))]]) ).

cnf(refute_0_358,plain,
    ( multiply(X_119,positive_part(X_120)) != least_upper_bound(multiply(X_119,X_120),X_119)
    | multiply(X_119,positive_part(X_120)) = least_upper_bound(X_119,multiply(X_119,X_120)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_119,X_120),X_119),least_upper_bound(X_119,multiply(X_119,X_120))) )],[refute_0_356,refute_0_357]) ).

cnf(refute_0_359,plain,
    ( multiply(X_119,least_upper_bound(X_120,identity)) != least_upper_bound(multiply(X_119,X_120),X_119)
    | multiply(X_119,positive_part(X_120)) = least_upper_bound(X_119,multiply(X_119,X_120)) ),
    inference(resolve,[$cnf( $equal(multiply(X_119,positive_part(X_120)),least_upper_bound(multiply(X_119,X_120),X_119)) )],[refute_0_59,refute_0_358]) ).

cnf(refute_0_360,plain,
    multiply(X_119,positive_part(X_120)) = least_upper_bound(X_119,multiply(X_119,X_120)),
    inference(resolve,[$cnf( $equal(multiply(X_119,least_upper_bound(X_120,identity)),least_upper_bound(multiply(X_119,X_120),X_119)) )],[refute_0_50,refute_0_359]) ).

cnf(refute_0_361,plain,
    multiply(inverse(X_123),positive_part(X_123)) = least_upper_bound(inverse(X_123),multiply(inverse(X_123),X_123)),
    inference(subst,[],[refute_0_360:[bind(X_119,$fot(inverse(X_123))),bind(X_120,$fot(X_123))]]) ).

cnf(refute_0_362,plain,
    multiply(inverse(X_123),X_123) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_123))]]) ).

cnf(refute_0_363,plain,
    ( multiply(inverse(X_123),X_123) != identity
    | multiply(inverse(X_123),positive_part(X_123)) != least_upper_bound(inverse(X_123),multiply(inverse(X_123),X_123))
    | multiply(inverse(X_123),positive_part(X_123)) = least_upper_bound(inverse(X_123),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_123),positive_part(X_123)),least_upper_bound(inverse(X_123),multiply(inverse(X_123),X_123))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_364,plain,
    ( multiply(inverse(X_123),positive_part(X_123)) != least_upper_bound(inverse(X_123),multiply(inverse(X_123),X_123))
    | multiply(inverse(X_123),positive_part(X_123)) = least_upper_bound(inverse(X_123),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_123),X_123),identity) )],[refute_0_362,refute_0_363]) ).

cnf(refute_0_365,plain,
    multiply(inverse(X_123),positive_part(X_123)) = least_upper_bound(inverse(X_123),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_123),positive_part(X_123)),least_upper_bound(inverse(X_123),multiply(inverse(X_123),X_123))) )],[refute_0_361,refute_0_364]) ).

cnf(refute_0_366,plain,
    least_upper_bound(X,identity) = least_upper_bound(identity,X),
    inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(identity))]]) ).

cnf(refute_0_367,plain,
    ( least_upper_bound(X,identity) != least_upper_bound(identity,X)
    | positive_part(X) != least_upper_bound(X,identity)
    | positive_part(X) = least_upper_bound(identity,X) ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(X),least_upper_bound(X,identity)) ),[1],$fot(least_upper_bound(identity,X))]]) ).

cnf(refute_0_368,plain,
    ( positive_part(X) != least_upper_bound(X,identity)
    | positive_part(X) = least_upper_bound(identity,X) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,identity),least_upper_bound(identity,X)) )],[refute_0_366,refute_0_367]) ).

cnf(refute_0_369,plain,
    positive_part(X) = least_upper_bound(identity,X),
    inference(resolve,[$cnf( $equal(positive_part(X),least_upper_bound(X,identity)) )],[lat4_4,refute_0_368]) ).

cnf(refute_0_370,plain,
    ( positive_part(X) != least_upper_bound(identity,X)
    | least_upper_bound(identity,X) = positive_part(X) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(positive_part(X))),bind(Y0,$fot(least_upper_bound(identity,X)))]]) ).

cnf(refute_0_371,plain,
    least_upper_bound(identity,X) = positive_part(X),
    inference(resolve,[$cnf( $equal(positive_part(X),least_upper_bound(identity,X)) )],[refute_0_369,refute_0_370]) ).

cnf(refute_0_372,plain,
    least_upper_bound(identity,inverse(X_123)) = positive_part(inverse(X_123)),
    inference(subst,[],[refute_0_371:[bind(X,$fot(inverse(X_123)))]]) ).

cnf(refute_0_373,plain,
    least_upper_bound(inverse(X_123),identity) = least_upper_bound(identity,inverse(X_123)),
    inference(subst,[],[refute_0_355:[bind(Y,$fot(identity)),bind(X_63,$fot(inverse(X_123)))]]) ).

cnf(refute_0_374,plain,
    ( least_upper_bound(identity,inverse(X_123)) != positive_part(inverse(X_123))
    | least_upper_bound(inverse(X_123),identity) != least_upper_bound(identity,inverse(X_123))
    | least_upper_bound(inverse(X_123),identity) = positive_part(inverse(X_123)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(inverse(X_123),identity))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_123)))),bind(Z0,$fot(positive_part(inverse(X_123))))]]) ).

cnf(refute_0_375,plain,
    ( least_upper_bound(identity,inverse(X_123)) != positive_part(inverse(X_123))
    | least_upper_bound(inverse(X_123),identity) = positive_part(inverse(X_123)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_123),identity),least_upper_bound(identity,inverse(X_123))) )],[refute_0_373,refute_0_374]) ).

cnf(refute_0_376,plain,
    least_upper_bound(inverse(X_123),identity) = positive_part(inverse(X_123)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_123)),positive_part(inverse(X_123))) )],[refute_0_372,refute_0_375]) ).

cnf(refute_0_377,plain,
    ( multiply(inverse(X_123),positive_part(X_123)) != least_upper_bound(inverse(X_123),identity)
    | least_upper_bound(inverse(X_123),identity) != positive_part(inverse(X_123))
    | multiply(inverse(X_123),positive_part(X_123)) = positive_part(inverse(X_123)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_123),positive_part(X_123)),positive_part(inverse(X_123))) ),[0],$fot(least_upper_bound(inverse(X_123),identity))]]) ).

cnf(refute_0_378,plain,
    ( multiply(inverse(X_123),positive_part(X_123)) != least_upper_bound(inverse(X_123),identity)
    | multiply(inverse(X_123),positive_part(X_123)) = positive_part(inverse(X_123)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_123),identity),positive_part(inverse(X_123))) )],[refute_0_376,refute_0_377]) ).

cnf(refute_0_379,plain,
    multiply(inverse(X_123),positive_part(X_123)) = positive_part(inverse(X_123)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_123),positive_part(X_123)),least_upper_bound(inverse(X_123),identity)) )],[refute_0_365,refute_0_378]) ).

cnf(refute_0_380,plain,
    multiply(inverse(X_134),positive_part(X_134)) = positive_part(inverse(X_134)),
    inference(subst,[],[refute_0_379:[bind(X_123,$fot(X_134))]]) ).

cnf(refute_0_381,plain,
    ( multiply(inverse(X_134),positive_part(X_134)) != positive_part(inverse(X_134))
    | inverse(inverse(X_134)) != multiply(positive_part(X_134),inverse(multiply(inverse(X_134),positive_part(X_134))))
    | inverse(inverse(X_134)) = multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_134)),multiply(positive_part(X_134),inverse(multiply(inverse(X_134),positive_part(X_134))))) ),[1,1,0],$fot(positive_part(inverse(X_134)))]]) ).

cnf(refute_0_382,plain,
    ( inverse(inverse(X_134)) != multiply(positive_part(X_134),inverse(multiply(inverse(X_134),positive_part(X_134))))
    | inverse(inverse(X_134)) = multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_134),positive_part(X_134)),positive_part(inverse(X_134))) )],[refute_0_380,refute_0_381]) ).

cnf(refute_0_383,plain,
    inverse(inverse(X_134)) = multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_134)),multiply(positive_part(X_134),inverse(multiply(inverse(X_134),positive_part(X_134))))) )],[refute_0_24,refute_0_382]) ).

cnf(refute_0_384,plain,
    inverse(inverse(X_134)) = X_134,
    inference(subst,[],[lat4_2:[bind(X,$fot(X_134))]]) ).

cnf(refute_0_385,plain,
    ( inverse(inverse(X_134)) != X_134
    | inverse(inverse(X_134)) != multiply(positive_part(X_134),inverse(positive_part(inverse(X_134))))
    | X_134 = multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_134)),multiply(positive_part(X_134),inverse(positive_part(inverse(X_134))))) ),[0],$fot(X_134)]]) ).

cnf(refute_0_386,plain,
    ( inverse(inverse(X_134)) != multiply(positive_part(X_134),inverse(positive_part(inverse(X_134))))
    | X_134 = multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_134)),X_134) )],[refute_0_384,refute_0_385]) ).

cnf(refute_0_387,plain,
    X_134 = multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_134)),multiply(positive_part(X_134),inverse(positive_part(inverse(X_134))))) )],[refute_0_383,refute_0_386]) ).

cnf(refute_0_388,plain,
    multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))) = greatest_lower_bound(multiply(X_155,X_156),multiply(X_155,inverse(X_155))),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_155)),bind(Y,$fot(X_156)),bind(Z,$fot(inverse(X_155)))]]) ).

cnf(refute_0_389,plain,
    multiply(X_155,inverse(X_155)) = identity,
    inference(subst,[],[refute_0_5:[bind(X_1,$fot(X_155))]]) ).

cnf(refute_0_390,plain,
    ( multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))) != greatest_lower_bound(multiply(X_155,X_156),multiply(X_155,inverse(X_155)))
    | multiply(X_155,inverse(X_155)) != identity
    | multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))) = greatest_lower_bound(multiply(X_155,X_156),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))),greatest_lower_bound(multiply(X_155,X_156),multiply(X_155,inverse(X_155)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_391,plain,
    ( multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))) != greatest_lower_bound(multiply(X_155,X_156),multiply(X_155,inverse(X_155)))
    | multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))) = greatest_lower_bound(multiply(X_155,X_156),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_155,inverse(X_155)),identity) )],[refute_0_389,refute_0_390]) ).

cnf(refute_0_392,plain,
    multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))) = greatest_lower_bound(multiply(X_155,X_156),identity),
    inference(resolve,[$cnf( $equal(multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))),greatest_lower_bound(multiply(X_155,X_156),multiply(X_155,inverse(X_155)))) )],[refute_0_388,refute_0_391]) ).

cnf(refute_0_393,plain,
    greatest_lower_bound(multiply(X_155,X_156),identity) = negative_part(multiply(X_155,X_156)),
    inference(subst,[],[refute_0_280:[bind(X,$fot(multiply(X_155,X_156)))]]) ).

cnf(refute_0_394,plain,
    ( multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))) != greatest_lower_bound(multiply(X_155,X_156),identity)
    | greatest_lower_bound(multiply(X_155,X_156),identity) != negative_part(multiply(X_155,X_156))
    | multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))) = negative_part(multiply(X_155,X_156)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))),negative_part(multiply(X_155,X_156))) ),[0],$fot(greatest_lower_bound(multiply(X_155,X_156),identity))]]) ).

cnf(refute_0_395,plain,
    ( multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))) != greatest_lower_bound(multiply(X_155,X_156),identity)
    | multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))) = negative_part(multiply(X_155,X_156)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_155,X_156),identity),negative_part(multiply(X_155,X_156))) )],[refute_0_393,refute_0_394]) ).

cnf(refute_0_396,plain,
    multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))) = negative_part(multiply(X_155,X_156)),
    inference(resolve,[$cnf( $equal(multiply(X_155,greatest_lower_bound(X_156,inverse(X_155))),greatest_lower_bound(multiply(X_155,X_156),identity)) )],[refute_0_392,refute_0_395]) ).

cnf(refute_0_397,plain,
    multiply(X_158,greatest_lower_bound(identity,inverse(X_158))) = negative_part(multiply(X_158,identity)),
    inference(subst,[],[refute_0_396:[bind(X_155,$fot(X_158)),bind(X_156,$fot(identity))]]) ).

cnf(refute_0_398,plain,
    negative_part(inverse(X_158)) = greatest_lower_bound(identity,inverse(X_158)),
    inference(subst,[],[refute_0_257:[bind(X,$fot(inverse(X_158)))]]) ).

cnf(refute_0_399,plain,
    ( negative_part(inverse(X_158)) != greatest_lower_bound(identity,inverse(X_158))
    | greatest_lower_bound(identity,inverse(X_158)) = negative_part(inverse(X_158)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(inverse(X_158)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_158))))]]) ).

cnf(refute_0_400,plain,
    greatest_lower_bound(identity,inverse(X_158)) = negative_part(inverse(X_158)),
    inference(resolve,[$cnf( $equal(negative_part(inverse(X_158)),greatest_lower_bound(identity,inverse(X_158))) )],[refute_0_398,refute_0_399]) ).

cnf(refute_0_401,plain,
    ( multiply(X_158,greatest_lower_bound(identity,inverse(X_158))) != negative_part(multiply(X_158,identity))
    | greatest_lower_bound(identity,inverse(X_158)) != negative_part(inverse(X_158))
    | multiply(X_158,negative_part(inverse(X_158))) = negative_part(multiply(X_158,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_158,greatest_lower_bound(identity,inverse(X_158))),negative_part(multiply(X_158,identity))) ),[0,1],$fot(negative_part(inverse(X_158)))]]) ).

cnf(refute_0_402,plain,
    ( multiply(X_158,greatest_lower_bound(identity,inverse(X_158))) != negative_part(multiply(X_158,identity))
    | multiply(X_158,negative_part(inverse(X_158))) = negative_part(multiply(X_158,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_158)),negative_part(inverse(X_158))) )],[refute_0_400,refute_0_401]) ).

cnf(refute_0_403,plain,
    multiply(X_158,negative_part(inverse(X_158))) = negative_part(multiply(X_158,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_158,greatest_lower_bound(identity,inverse(X_158))),negative_part(multiply(X_158,identity))) )],[refute_0_397,refute_0_402]) ).

cnf(refute_0_404,plain,
    ( X != multiply(X,identity)
    | multiply(X,identity) = X ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,identity)))]]) ).

cnf(refute_0_405,plain,
    multiply(X,identity) = X,
    inference(resolve,[$cnf( $equal(X,multiply(X,identity)) )],[refute_0_44,refute_0_404]) ).

cnf(refute_0_406,plain,
    multiply(X_158,identity) = X_158,
    inference(subst,[],[refute_0_405:[bind(X,$fot(X_158))]]) ).

cnf(refute_0_407,plain,
    negative_part(multiply(X_158,identity)) = negative_part(multiply(X_158,identity)),
    introduced(tautology,[refl,[$fot(negative_part(multiply(X_158,identity)))]]) ).

cnf(refute_0_408,plain,
    ( multiply(X_158,identity) != X_158
    | negative_part(multiply(X_158,identity)) != negative_part(multiply(X_158,identity))
    | negative_part(multiply(X_158,identity)) = negative_part(X_158) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(multiply(X_158,identity)),negative_part(multiply(X_158,identity))) ),[1,0],$fot(X_158)]]) ).

cnf(refute_0_409,plain,
    ( multiply(X_158,identity) != X_158
    | negative_part(multiply(X_158,identity)) = negative_part(X_158) ),
    inference(resolve,[$cnf( $equal(negative_part(multiply(X_158,identity)),negative_part(multiply(X_158,identity))) )],[refute_0_407,refute_0_408]) ).

cnf(refute_0_410,plain,
    negative_part(multiply(X_158,identity)) = negative_part(X_158),
    inference(resolve,[$cnf( $equal(multiply(X_158,identity),X_158) )],[refute_0_406,refute_0_409]) ).

cnf(refute_0_411,plain,
    ( multiply(X_158,negative_part(inverse(X_158))) != negative_part(multiply(X_158,identity))
    | negative_part(multiply(X_158,identity)) != negative_part(X_158)
    | multiply(X_158,negative_part(inverse(X_158))) = negative_part(X_158) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_158,negative_part(inverse(X_158))),negative_part(X_158)) ),[0],$fot(negative_part(multiply(X_158,identity)))]]) ).

cnf(refute_0_412,plain,
    ( multiply(X_158,negative_part(inverse(X_158))) != negative_part(multiply(X_158,identity))
    | multiply(X_158,negative_part(inverse(X_158))) = negative_part(X_158) ),
    inference(resolve,[$cnf( $equal(negative_part(multiply(X_158,identity)),negative_part(X_158)) )],[refute_0_410,refute_0_411]) ).

cnf(refute_0_413,plain,
    multiply(X_158,negative_part(inverse(X_158))) = negative_part(X_158),
    inference(resolve,[$cnf( $equal(multiply(X_158,negative_part(inverse(X_158))),negative_part(multiply(X_158,identity))) )],[refute_0_403,refute_0_412]) ).

cnf(refute_0_414,plain,
    inverse(multiply(X_8,inverse(X))) = multiply(inverse(inverse(X)),inverse(X_8)),
    inference(subst,[],[lat4_3:[bind(X,$fot(X_8)),bind(Y,$fot(inverse(X)))]]) ).

cnf(refute_0_415,plain,
    ( inverse(multiply(X_8,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_8))
    | inverse(inverse(X)) != X
    | inverse(multiply(X_8,inverse(X))) = multiply(X,inverse(X_8)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_8,inverse(X))),multiply(inverse(inverse(X)),inverse(X_8))) ),[1,0],$fot(X)]]) ).

cnf(refute_0_416,plain,
    ( inverse(multiply(X_8,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_8))
    | inverse(multiply(X_8,inverse(X))) = multiply(X,inverse(X_8)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[lat4_2,refute_0_415]) ).

cnf(refute_0_417,plain,
    inverse(multiply(X_8,inverse(X))) = multiply(X,inverse(X_8)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_8,inverse(X))),multiply(inverse(inverse(X)),inverse(X_8))) )],[refute_0_414,refute_0_416]) ).

cnf(refute_0_418,plain,
    inverse(multiply(positive_part(inverse(inverse(X))),inverse(X))) = multiply(X,inverse(positive_part(inverse(inverse(X))))),
    inference(subst,[],[refute_0_417:[bind(X_8,$fot(positive_part(inverse(inverse(X)))))]]) ).

cnf(refute_0_419,plain,
    multiply(least_upper_bound(X_167,identity),X_166) = least_upper_bound(multiply(X_167,X_166),multiply(identity,X_166)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_166)),bind(Y,$fot(X_167)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_420,plain,
    multiply(identity,X_166) = X_166,
    inference(subst,[],[left_identity:[bind(X,$fot(X_166))]]) ).

cnf(refute_0_421,plain,
    ( multiply(identity,X_166) != X_166
    | multiply(least_upper_bound(X_167,identity),X_166) != least_upper_bound(multiply(X_167,X_166),multiply(identity,X_166))
    | multiply(least_upper_bound(X_167,identity),X_166) = least_upper_bound(multiply(X_167,X_166),X_166) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_167,identity),X_166),least_upper_bound(multiply(X_167,X_166),multiply(identity,X_166))) ),[1,1],$fot(X_166)]]) ).

cnf(refute_0_422,plain,
    ( multiply(least_upper_bound(X_167,identity),X_166) != least_upper_bound(multiply(X_167,X_166),multiply(identity,X_166))
    | multiply(least_upper_bound(X_167,identity),X_166) = least_upper_bound(multiply(X_167,X_166),X_166) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_166),X_166) )],[refute_0_420,refute_0_421]) ).

cnf(refute_0_423,plain,
    multiply(least_upper_bound(X_167,identity),X_166) = least_upper_bound(multiply(X_167,X_166),X_166),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_167,identity),X_166),least_upper_bound(multiply(X_167,X_166),multiply(identity,X_166))) )],[refute_0_419,refute_0_422]) ).

cnf(refute_0_424,plain,
    least_upper_bound(X_167,identity) = positive_part(X_167),
    inference(subst,[],[refute_0_52:[bind(X,$fot(X_167))]]) ).

cnf(refute_0_425,plain,
    multiply(least_upper_bound(X_167,identity),X_166) = multiply(least_upper_bound(X_167,identity),X_166),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_167,identity),X_166))]]) ).

cnf(refute_0_426,plain,
    ( multiply(least_upper_bound(X_167,identity),X_166) != multiply(least_upper_bound(X_167,identity),X_166)
    | least_upper_bound(X_167,identity) != positive_part(X_167)
    | multiply(least_upper_bound(X_167,identity),X_166) = multiply(positive_part(X_167),X_166) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_167,identity),X_166),multiply(least_upper_bound(X_167,identity),X_166)) ),[1,0],$fot(positive_part(X_167))]]) ).

cnf(refute_0_427,plain,
    ( least_upper_bound(X_167,identity) != positive_part(X_167)
    | multiply(least_upper_bound(X_167,identity),X_166) = multiply(positive_part(X_167),X_166) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_167,identity),X_166),multiply(least_upper_bound(X_167,identity),X_166)) )],[refute_0_425,refute_0_426]) ).

cnf(refute_0_428,plain,
    multiply(least_upper_bound(X_167,identity),X_166) = multiply(positive_part(X_167),X_166),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_167,identity),positive_part(X_167)) )],[refute_0_424,refute_0_427]) ).

cnf(refute_0_429,plain,
    ( multiply(least_upper_bound(X_167,identity),X_166) != multiply(positive_part(X_167),X_166)
    | multiply(least_upper_bound(X_167,identity),X_166) != least_upper_bound(multiply(X_167,X_166),X_166)
    | multiply(positive_part(X_167),X_166) = least_upper_bound(multiply(X_167,X_166),X_166) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_167,identity),X_166),least_upper_bound(multiply(X_167,X_166),X_166)) ),[0],$fot(multiply(positive_part(X_167),X_166))]]) ).

cnf(refute_0_430,plain,
    ( multiply(least_upper_bound(X_167,identity),X_166) != least_upper_bound(multiply(X_167,X_166),X_166)
    | multiply(positive_part(X_167),X_166) = least_upper_bound(multiply(X_167,X_166),X_166) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_167,identity),X_166),multiply(positive_part(X_167),X_166)) )],[refute_0_428,refute_0_429]) ).

cnf(refute_0_431,plain,
    least_upper_bound(multiply(X_167,X_166),X_166) = least_upper_bound(X_166,multiply(X_167,X_166)),
    inference(subst,[],[refute_0_355:[bind(Y,$fot(X_166)),bind(X_63,$fot(multiply(X_167,X_166)))]]) ).

cnf(refute_0_432,plain,
    ( multiply(positive_part(X_167),X_166) != least_upper_bound(multiply(X_167,X_166),X_166)
    | least_upper_bound(multiply(X_167,X_166),X_166) != least_upper_bound(X_166,multiply(X_167,X_166))
    | multiply(positive_part(X_167),X_166) = least_upper_bound(X_166,multiply(X_167,X_166)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(positive_part(X_167),X_166),least_upper_bound(X_166,multiply(X_167,X_166))) ),[0],$fot(least_upper_bound(multiply(X_167,X_166),X_166))]]) ).

cnf(refute_0_433,plain,
    ( multiply(positive_part(X_167),X_166) != least_upper_bound(multiply(X_167,X_166),X_166)
    | multiply(positive_part(X_167),X_166) = least_upper_bound(X_166,multiply(X_167,X_166)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_167,X_166),X_166),least_upper_bound(X_166,multiply(X_167,X_166))) )],[refute_0_431,refute_0_432]) ).

cnf(refute_0_434,plain,
    ( multiply(least_upper_bound(X_167,identity),X_166) != least_upper_bound(multiply(X_167,X_166),X_166)
    | multiply(positive_part(X_167),X_166) = least_upper_bound(X_166,multiply(X_167,X_166)) ),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_167),X_166),least_upper_bound(multiply(X_167,X_166),X_166)) )],[refute_0_430,refute_0_433]) ).

cnf(refute_0_435,plain,
    multiply(positive_part(X_167),X_166) = least_upper_bound(X_166,multiply(X_167,X_166)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_167,identity),X_166),least_upper_bound(multiply(X_167,X_166),X_166)) )],[refute_0_423,refute_0_434]) ).

cnf(refute_0_436,plain,
    multiply(positive_part(inverse(X_169)),X_169) = least_upper_bound(X_169,multiply(inverse(X_169),X_169)),
    inference(subst,[],[refute_0_435:[bind(X_166,$fot(X_169)),bind(X_167,$fot(inverse(X_169)))]]) ).

cnf(refute_0_437,plain,
    multiply(inverse(X_169),X_169) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_169))]]) ).

cnf(refute_0_438,plain,
    ( multiply(inverse(X_169),X_169) != identity
    | multiply(positive_part(inverse(X_169)),X_169) != least_upper_bound(X_169,multiply(inverse(X_169),X_169))
    | multiply(positive_part(inverse(X_169)),X_169) = least_upper_bound(X_169,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(inverse(X_169)),X_169),least_upper_bound(X_169,multiply(inverse(X_169),X_169))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_439,plain,
    ( multiply(positive_part(inverse(X_169)),X_169) != least_upper_bound(X_169,multiply(inverse(X_169),X_169))
    | multiply(positive_part(inverse(X_169)),X_169) = least_upper_bound(X_169,identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_169),X_169),identity) )],[refute_0_437,refute_0_438]) ).

cnf(refute_0_440,plain,
    multiply(positive_part(inverse(X_169)),X_169) = least_upper_bound(X_169,identity),
    inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_169)),X_169),least_upper_bound(X_169,multiply(inverse(X_169),X_169))) )],[refute_0_436,refute_0_439]) ).

cnf(refute_0_441,plain,
    least_upper_bound(X_169,identity) = positive_part(X_169),
    inference(subst,[],[refute_0_52:[bind(X,$fot(X_169))]]) ).

cnf(refute_0_442,plain,
    ( multiply(positive_part(inverse(X_169)),X_169) != least_upper_bound(X_169,identity)
    | least_upper_bound(X_169,identity) != positive_part(X_169)
    | multiply(positive_part(inverse(X_169)),X_169) = positive_part(X_169) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(positive_part(inverse(X_169)),X_169),positive_part(X_169)) ),[0],$fot(least_upper_bound(X_169,identity))]]) ).

cnf(refute_0_443,plain,
    ( multiply(positive_part(inverse(X_169)),X_169) != least_upper_bound(X_169,identity)
    | multiply(positive_part(inverse(X_169)),X_169) = positive_part(X_169) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_169,identity),positive_part(X_169)) )],[refute_0_441,refute_0_442]) ).

cnf(refute_0_444,plain,
    multiply(positive_part(inverse(X_169)),X_169) = positive_part(X_169),
    inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_169)),X_169),least_upper_bound(X_169,identity)) )],[refute_0_440,refute_0_443]) ).

cnf(refute_0_445,plain,
    multiply(positive_part(inverse(inverse(X))),inverse(X)) = positive_part(inverse(X)),
    inference(subst,[],[refute_0_444:[bind(X_169,$fot(inverse(X)))]]) ).

cnf(refute_0_446,plain,
    ( multiply(positive_part(inverse(inverse(X))),inverse(X)) != positive_part(inverse(X))
    | inverse(multiply(positive_part(inverse(inverse(X))),inverse(X))) != multiply(X,inverse(positive_part(inverse(inverse(X)))))
    | inverse(positive_part(inverse(X))) = multiply(X,inverse(positive_part(inverse(inverse(X))))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(positive_part(inverse(inverse(X))),inverse(X))),multiply(X,inverse(positive_part(inverse(inverse(X)))))) ),[0,0],$fot(positive_part(inverse(X)))]]) ).

cnf(refute_0_447,plain,
    ( inverse(multiply(positive_part(inverse(inverse(X))),inverse(X))) != multiply(X,inverse(positive_part(inverse(inverse(X)))))
    | inverse(positive_part(inverse(X))) = multiply(X,inverse(positive_part(inverse(inverse(X))))) ),
    inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(inverse(X))),inverse(X)),positive_part(inverse(X))) )],[refute_0_445,refute_0_446]) ).

cnf(refute_0_448,plain,
    inverse(positive_part(inverse(X))) = multiply(X,inverse(positive_part(inverse(inverse(X))))),
    inference(resolve,[$cnf( $equal(inverse(multiply(positive_part(inverse(inverse(X))),inverse(X))),multiply(X,inverse(positive_part(inverse(inverse(X)))))) )],[refute_0_418,refute_0_447]) ).

cnf(refute_0_449,plain,
    positive_part(inverse(inverse(X))) = positive_part(inverse(inverse(X))),
    introduced(tautology,[refl,[$fot(positive_part(inverse(inverse(X))))]]) ).

cnf(refute_0_450,plain,
    ( inverse(inverse(X)) != X
    | positive_part(inverse(inverse(X))) != positive_part(inverse(inverse(X)))
    | positive_part(inverse(inverse(X))) = positive_part(X) ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(inverse(inverse(X))),positive_part(inverse(inverse(X)))) ),[1,0],$fot(X)]]) ).

cnf(refute_0_451,plain,
    ( inverse(inverse(X)) != X
    | positive_part(inverse(inverse(X))) = positive_part(X) ),
    inference(resolve,[$cnf( $equal(positive_part(inverse(inverse(X))),positive_part(inverse(inverse(X)))) )],[refute_0_449,refute_0_450]) ).

cnf(refute_0_452,plain,
    positive_part(inverse(inverse(X))) = positive_part(X),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[lat4_2,refute_0_451]) ).

cnf(refute_0_453,plain,
    inverse(positive_part(inverse(inverse(X)))) = inverse(positive_part(inverse(inverse(X)))),
    introduced(tautology,[refl,[$fot(inverse(positive_part(inverse(inverse(X)))))]]) ).

cnf(refute_0_454,plain,
    ( inverse(positive_part(inverse(inverse(X)))) != inverse(positive_part(inverse(inverse(X))))
    | positive_part(inverse(inverse(X))) != positive_part(X)
    | inverse(positive_part(inverse(inverse(X)))) = inverse(positive_part(X)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(positive_part(inverse(inverse(X)))),inverse(positive_part(inverse(inverse(X))))) ),[1,0],$fot(positive_part(X))]]) ).

cnf(refute_0_455,plain,
    ( positive_part(inverse(inverse(X))) != positive_part(X)
    | inverse(positive_part(inverse(inverse(X)))) = inverse(positive_part(X)) ),
    inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(inverse(X)))),inverse(positive_part(inverse(inverse(X))))) )],[refute_0_453,refute_0_454]) ).

cnf(refute_0_456,plain,
    inverse(positive_part(inverse(inverse(X)))) = inverse(positive_part(X)),
    inference(resolve,[$cnf( $equal(positive_part(inverse(inverse(X))),positive_part(X)) )],[refute_0_452,refute_0_455]) ).

cnf(refute_0_457,plain,
    multiply(X,inverse(positive_part(inverse(inverse(X))))) = multiply(X,inverse(positive_part(inverse(inverse(X))))),
    introduced(tautology,[refl,[$fot(multiply(X,inverse(positive_part(inverse(inverse(X))))))]]) ).

cnf(refute_0_458,plain,
    ( multiply(X,inverse(positive_part(inverse(inverse(X))))) != multiply(X,inverse(positive_part(inverse(inverse(X)))))
    | inverse(positive_part(inverse(inverse(X)))) != inverse(positive_part(X))
    | multiply(X,inverse(positive_part(inverse(inverse(X))))) = multiply(X,inverse(positive_part(X))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,inverse(positive_part(inverse(inverse(X))))),multiply(X,inverse(positive_part(inverse(inverse(X)))))) ),[1,1],$fot(inverse(positive_part(X)))]]) ).

cnf(refute_0_459,plain,
    ( inverse(positive_part(inverse(inverse(X)))) != inverse(positive_part(X))
    | multiply(X,inverse(positive_part(inverse(inverse(X))))) = multiply(X,inverse(positive_part(X))) ),
    inference(resolve,[$cnf( $equal(multiply(X,inverse(positive_part(inverse(inverse(X))))),multiply(X,inverse(positive_part(inverse(inverse(X)))))) )],[refute_0_457,refute_0_458]) ).

cnf(refute_0_460,plain,
    multiply(X,inverse(positive_part(inverse(inverse(X))))) = multiply(X,inverse(positive_part(X))),
    inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(inverse(X)))),inverse(positive_part(X))) )],[refute_0_456,refute_0_459]) ).

cnf(refute_0_461,plain,
    ( multiply(X,inverse(positive_part(inverse(inverse(X))))) != multiply(X,inverse(positive_part(X)))
    | inverse(positive_part(inverse(X))) != multiply(X,inverse(positive_part(inverse(inverse(X)))))
    | inverse(positive_part(inverse(X))) = multiply(X,inverse(positive_part(X))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(positive_part(inverse(X))),multiply(X,inverse(positive_part(inverse(inverse(X)))))) ),[1],$fot(multiply(X,inverse(positive_part(X))))]]) ).

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

cnf(refute_0_463,plain,
    inverse(positive_part(inverse(X))) = multiply(X,inverse(positive_part(X))),
    inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(X))),multiply(X,inverse(positive_part(inverse(inverse(X)))))) )],[refute_0_448,refute_0_462]) ).

cnf(refute_0_464,plain,
    ( inverse(positive_part(inverse(X))) != multiply(X,inverse(positive_part(X)))
    | multiply(X,inverse(positive_part(X))) = inverse(positive_part(inverse(X))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(positive_part(inverse(X))))),bind(Y0,$fot(multiply(X,inverse(positive_part(X)))))]]) ).

cnf(refute_0_465,plain,
    multiply(X,inverse(positive_part(X))) = inverse(positive_part(inverse(X))),
    inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(X))),multiply(X,inverse(positive_part(X)))) )],[refute_0_463,refute_0_464]) ).

cnf(refute_0_466,plain,
    multiply(X_158,inverse(positive_part(X_158))) = inverse(positive_part(inverse(X_158))),
    inference(subst,[],[refute_0_465:[bind(X,$fot(X_158))]]) ).

cnf(refute_0_467,plain,
    multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186) = greatest_lower_bound(multiply(X_187,X_186),multiply(positive_part(inverse(X_186)),X_186)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_186)),bind(Y,$fot(X_187)),bind(Z,$fot(positive_part(inverse(X_186))))]]) ).

cnf(refute_0_468,plain,
    multiply(positive_part(inverse(X_186)),X_186) = positive_part(X_186),
    inference(subst,[],[refute_0_444:[bind(X_169,$fot(X_186))]]) ).

cnf(refute_0_469,plain,
    ( multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186) != greatest_lower_bound(multiply(X_187,X_186),multiply(positive_part(inverse(X_186)),X_186))
    | multiply(positive_part(inverse(X_186)),X_186) != positive_part(X_186)
    | multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186) = greatest_lower_bound(multiply(X_187,X_186),positive_part(X_186)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186),greatest_lower_bound(multiply(X_187,X_186),multiply(positive_part(inverse(X_186)),X_186))) ),[1,1],$fot(positive_part(X_186))]]) ).

cnf(refute_0_470,plain,
    ( multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186) != greatest_lower_bound(multiply(X_187,X_186),multiply(positive_part(inverse(X_186)),X_186))
    | multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186) = greatest_lower_bound(multiply(X_187,X_186),positive_part(X_186)) ),
    inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_186)),X_186),positive_part(X_186)) )],[refute_0_468,refute_0_469]) ).

cnf(refute_0_471,plain,
    multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186) = greatest_lower_bound(multiply(X_187,X_186),positive_part(X_186)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186),greatest_lower_bound(multiply(X_187,X_186),multiply(positive_part(inverse(X_186)),X_186))) )],[refute_0_467,refute_0_470]) ).

cnf(refute_0_472,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_18:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).

cnf(refute_0_473,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_472]) ).

cnf(refute_0_474,plain,
    greatest_lower_bound(multiply(X_187,X_186),positive_part(X_186)) = greatest_lower_bound(positive_part(X_186),multiply(X_187,X_186)),
    inference(subst,[],[refute_0_473:[bind(X,$fot(positive_part(X_186))),bind(Y,$fot(multiply(X_187,X_186)))]]) ).

cnf(refute_0_475,plain,
    ( multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186) != greatest_lower_bound(multiply(X_187,X_186),positive_part(X_186))
    | greatest_lower_bound(multiply(X_187,X_186),positive_part(X_186)) != greatest_lower_bound(positive_part(X_186),multiply(X_187,X_186))
    | multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186) = greatest_lower_bound(positive_part(X_186),multiply(X_187,X_186)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186),greatest_lower_bound(positive_part(X_186),multiply(X_187,X_186))) ),[0],$fot(greatest_lower_bound(multiply(X_187,X_186),positive_part(X_186)))]]) ).

cnf(refute_0_476,plain,
    ( multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186) != greatest_lower_bound(multiply(X_187,X_186),positive_part(X_186))
    | multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186) = greatest_lower_bound(positive_part(X_186),multiply(X_187,X_186)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_187,X_186),positive_part(X_186)),greatest_lower_bound(positive_part(X_186),multiply(X_187,X_186))) )],[refute_0_474,refute_0_475]) ).

cnf(refute_0_477,plain,
    multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186) = greatest_lower_bound(positive_part(X_186),multiply(X_187,X_186)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_187,positive_part(inverse(X_186))),X_186),greatest_lower_bound(multiply(X_187,X_186),positive_part(X_186))) )],[refute_0_471,refute_0_476]) ).

cnf(refute_0_478,plain,
    multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) = greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230)))),
    inference(subst,[],[refute_0_477:[bind(X_186,$fot(inverse(positive_part(X_230)))),bind(X_187,$fot(positive_part(inverse(X_230))))]]) ).

cnf(refute_0_479,plain,
    inverse(X) = multiply(positive_part(inverse(X)),inverse(multiply(X,positive_part(inverse(X))))),
    inference(subst,[],[refute_0_23:[bind(X_111,$fot(positive_part(inverse(X))))]]) ).

cnf(refute_0_480,plain,
    multiply(X_122,positive_part(inverse(X_122))) = least_upper_bound(X_122,multiply(X_122,inverse(X_122))),
    inference(subst,[],[refute_0_360:[bind(X_119,$fot(X_122)),bind(X_120,$fot(inverse(X_122)))]]) ).

cnf(refute_0_481,plain,
    multiply(X_122,inverse(X_122)) = identity,
    inference(subst,[],[refute_0_5:[bind(X_1,$fot(X_122))]]) ).

cnf(refute_0_482,plain,
    ( multiply(X_122,inverse(X_122)) != identity
    | multiply(X_122,positive_part(inverse(X_122))) != least_upper_bound(X_122,multiply(X_122,inverse(X_122)))
    | multiply(X_122,positive_part(inverse(X_122))) = least_upper_bound(X_122,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_122,positive_part(inverse(X_122))),least_upper_bound(X_122,multiply(X_122,inverse(X_122)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_483,plain,
    ( multiply(X_122,positive_part(inverse(X_122))) != least_upper_bound(X_122,multiply(X_122,inverse(X_122)))
    | multiply(X_122,positive_part(inverse(X_122))) = least_upper_bound(X_122,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_122,inverse(X_122)),identity) )],[refute_0_481,refute_0_482]) ).

cnf(refute_0_484,plain,
    multiply(X_122,positive_part(inverse(X_122))) = least_upper_bound(X_122,identity),
    inference(resolve,[$cnf( $equal(multiply(X_122,positive_part(inverse(X_122))),least_upper_bound(X_122,multiply(X_122,inverse(X_122)))) )],[refute_0_480,refute_0_483]) ).

cnf(refute_0_485,plain,
    least_upper_bound(X_122,identity) = positive_part(X_122),
    inference(subst,[],[refute_0_52:[bind(X,$fot(X_122))]]) ).

cnf(refute_0_486,plain,
    ( multiply(X_122,positive_part(inverse(X_122))) != least_upper_bound(X_122,identity)
    | least_upper_bound(X_122,identity) != positive_part(X_122)
    | multiply(X_122,positive_part(inverse(X_122))) = positive_part(X_122) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_122,positive_part(inverse(X_122))),positive_part(X_122)) ),[0],$fot(least_upper_bound(X_122,identity))]]) ).

cnf(refute_0_487,plain,
    ( multiply(X_122,positive_part(inverse(X_122))) != least_upper_bound(X_122,identity)
    | multiply(X_122,positive_part(inverse(X_122))) = positive_part(X_122) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_122,identity),positive_part(X_122)) )],[refute_0_485,refute_0_486]) ).

cnf(refute_0_488,plain,
    multiply(X_122,positive_part(inverse(X_122))) = positive_part(X_122),
    inference(resolve,[$cnf( $equal(multiply(X_122,positive_part(inverse(X_122))),least_upper_bound(X_122,identity)) )],[refute_0_484,refute_0_487]) ).

cnf(refute_0_489,plain,
    multiply(X,positive_part(inverse(X))) = positive_part(X),
    inference(subst,[],[refute_0_488:[bind(X_122,$fot(X))]]) ).

cnf(refute_0_490,plain,
    ( multiply(X,positive_part(inverse(X))) != positive_part(X)
    | inverse(X) != multiply(positive_part(inverse(X)),inverse(multiply(X,positive_part(inverse(X)))))
    | inverse(X) = multiply(positive_part(inverse(X)),inverse(positive_part(X))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(X),multiply(positive_part(inverse(X)),inverse(multiply(X,positive_part(inverse(X)))))) ),[1,1,0],$fot(positive_part(X))]]) ).

cnf(refute_0_491,plain,
    ( inverse(X) != multiply(positive_part(inverse(X)),inverse(multiply(X,positive_part(inverse(X)))))
    | inverse(X) = multiply(positive_part(inverse(X)),inverse(positive_part(X))) ),
    inference(resolve,[$cnf( $equal(multiply(X,positive_part(inverse(X))),positive_part(X)) )],[refute_0_489,refute_0_490]) ).

cnf(refute_0_492,plain,
    inverse(X) = multiply(positive_part(inverse(X)),inverse(positive_part(X))),
    inference(resolve,[$cnf( $equal(inverse(X),multiply(positive_part(inverse(X)),inverse(multiply(X,positive_part(inverse(X)))))) )],[refute_0_479,refute_0_491]) ).

cnf(refute_0_493,plain,
    inverse(X_230) = multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230))),
    inference(subst,[],[refute_0_492:[bind(X,$fot(X_230))]]) ).

cnf(refute_0_494,plain,
    ( inverse(X_230) != multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230)))
    | multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230))) = inverse(X_230) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(X_230))),bind(Y0,$fot(multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230)))))]]) ).

cnf(refute_0_495,plain,
    multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230))) = inverse(X_230),
    inference(resolve,[$cnf( $equal(inverse(X_230),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230)))) )],[refute_0_493,refute_0_494]) ).

cnf(refute_0_496,plain,
    ( multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) != greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230))))
    | multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230))) != inverse(X_230)
    | multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) = greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))),greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230))))) ),[1,1],$fot(inverse(X_230))]]) ).

cnf(refute_0_497,plain,
    ( multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) != greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230))))
    | multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) = greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)) ),
    inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230))),inverse(X_230)) )],[refute_0_495,refute_0_496]) ).

cnf(refute_0_498,plain,
    multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) = greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))),greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230))))) )],[refute_0_478,refute_0_497]) ).

cnf(refute_0_499,plain,
    multiply(greatest_lower_bound(X_187,identity),X_186) = greatest_lower_bound(multiply(X_187,X_186),multiply(identity,X_186)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_186)),bind(Y,$fot(X_187)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_500,plain,
    multiply(identity,X_186) = X_186,
    inference(subst,[],[left_identity:[bind(X,$fot(X_186))]]) ).

cnf(refute_0_501,plain,
    ( multiply(greatest_lower_bound(X_187,identity),X_186) != greatest_lower_bound(multiply(X_187,X_186),multiply(identity,X_186))
    | multiply(identity,X_186) != X_186
    | multiply(greatest_lower_bound(X_187,identity),X_186) = greatest_lower_bound(multiply(X_187,X_186),X_186) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_187,identity),X_186),greatest_lower_bound(multiply(X_187,X_186),multiply(identity,X_186))) ),[1,1],$fot(X_186)]]) ).

cnf(refute_0_502,plain,
    ( multiply(greatest_lower_bound(X_187,identity),X_186) != greatest_lower_bound(multiply(X_187,X_186),multiply(identity,X_186))
    | multiply(greatest_lower_bound(X_187,identity),X_186) = greatest_lower_bound(multiply(X_187,X_186),X_186) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_186),X_186) )],[refute_0_500,refute_0_501]) ).

cnf(refute_0_503,plain,
    multiply(greatest_lower_bound(X_187,identity),X_186) = greatest_lower_bound(multiply(X_187,X_186),X_186),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_187,identity),X_186),greatest_lower_bound(multiply(X_187,X_186),multiply(identity,X_186))) )],[refute_0_499,refute_0_502]) ).

cnf(refute_0_504,plain,
    greatest_lower_bound(X_187,identity) = negative_part(X_187),
    inference(subst,[],[refute_0_280:[bind(X,$fot(X_187))]]) ).

cnf(refute_0_505,plain,
    multiply(greatest_lower_bound(X_187,identity),X_186) = multiply(greatest_lower_bound(X_187,identity),X_186),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_187,identity),X_186))]]) ).

cnf(refute_0_506,plain,
    ( multiply(greatest_lower_bound(X_187,identity),X_186) != multiply(greatest_lower_bound(X_187,identity),X_186)
    | greatest_lower_bound(X_187,identity) != negative_part(X_187)
    | multiply(greatest_lower_bound(X_187,identity),X_186) = multiply(negative_part(X_187),X_186) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_187,identity),X_186),multiply(greatest_lower_bound(X_187,identity),X_186)) ),[1,0],$fot(negative_part(X_187))]]) ).

cnf(refute_0_507,plain,
    ( greatest_lower_bound(X_187,identity) != negative_part(X_187)
    | multiply(greatest_lower_bound(X_187,identity),X_186) = multiply(negative_part(X_187),X_186) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_187,identity),X_186),multiply(greatest_lower_bound(X_187,identity),X_186)) )],[refute_0_505,refute_0_506]) ).

cnf(refute_0_508,plain,
    multiply(greatest_lower_bound(X_187,identity),X_186) = multiply(negative_part(X_187),X_186),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_187,identity),negative_part(X_187)) )],[refute_0_504,refute_0_507]) ).

cnf(refute_0_509,plain,
    ( multiply(greatest_lower_bound(X_187,identity),X_186) != multiply(negative_part(X_187),X_186)
    | multiply(greatest_lower_bound(X_187,identity),X_186) != greatest_lower_bound(multiply(X_187,X_186),X_186)
    | multiply(negative_part(X_187),X_186) = greatest_lower_bound(multiply(X_187,X_186),X_186) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_187,identity),X_186),greatest_lower_bound(multiply(X_187,X_186),X_186)) ),[0],$fot(multiply(negative_part(X_187),X_186))]]) ).

cnf(refute_0_510,plain,
    ( multiply(greatest_lower_bound(X_187,identity),X_186) != greatest_lower_bound(multiply(X_187,X_186),X_186)
    | multiply(negative_part(X_187),X_186) = greatest_lower_bound(multiply(X_187,X_186),X_186) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_187,identity),X_186),multiply(negative_part(X_187),X_186)) )],[refute_0_508,refute_0_509]) ).

cnf(refute_0_511,plain,
    greatest_lower_bound(multiply(X_187,X_186),X_186) = greatest_lower_bound(X_186,multiply(X_187,X_186)),
    inference(subst,[],[refute_0_473:[bind(X,$fot(X_186)),bind(Y,$fot(multiply(X_187,X_186)))]]) ).

cnf(refute_0_512,plain,
    ( multiply(negative_part(X_187),X_186) != greatest_lower_bound(multiply(X_187,X_186),X_186)
    | greatest_lower_bound(multiply(X_187,X_186),X_186) != greatest_lower_bound(X_186,multiply(X_187,X_186))
    | multiply(negative_part(X_187),X_186) = greatest_lower_bound(X_186,multiply(X_187,X_186)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(X_187),X_186),greatest_lower_bound(X_186,multiply(X_187,X_186))) ),[0],$fot(greatest_lower_bound(multiply(X_187,X_186),X_186))]]) ).

cnf(refute_0_513,plain,
    ( multiply(negative_part(X_187),X_186) != greatest_lower_bound(multiply(X_187,X_186),X_186)
    | multiply(negative_part(X_187),X_186) = greatest_lower_bound(X_186,multiply(X_187,X_186)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_187,X_186),X_186),greatest_lower_bound(X_186,multiply(X_187,X_186))) )],[refute_0_511,refute_0_512]) ).

cnf(refute_0_514,plain,
    ( multiply(greatest_lower_bound(X_187,identity),X_186) != greatest_lower_bound(multiply(X_187,X_186),X_186)
    | multiply(negative_part(X_187),X_186) = greatest_lower_bound(X_186,multiply(X_187,X_186)) ),
    inference(resolve,[$cnf( $equal(multiply(negative_part(X_187),X_186),greatest_lower_bound(multiply(X_187,X_186),X_186)) )],[refute_0_510,refute_0_513]) ).

cnf(refute_0_515,plain,
    multiply(negative_part(X_187),X_186) = greatest_lower_bound(X_186,multiply(X_187,X_186)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_187,identity),X_186),greatest_lower_bound(multiply(X_187,X_186),X_186)) )],[refute_0_503,refute_0_514]) ).

cnf(refute_0_516,plain,
    multiply(negative_part(inverse(X_123)),positive_part(X_123)) = greatest_lower_bound(positive_part(X_123),multiply(inverse(X_123),positive_part(X_123))),
    inference(subst,[],[refute_0_515:[bind(X_186,$fot(positive_part(X_123))),bind(X_187,$fot(inverse(X_123)))]]) ).

cnf(refute_0_517,plain,
    ( multiply(inverse(X_123),positive_part(X_123)) != positive_part(inverse(X_123))
    | multiply(negative_part(inverse(X_123)),positive_part(X_123)) != greatest_lower_bound(positive_part(X_123),multiply(inverse(X_123),positive_part(X_123)))
    | multiply(negative_part(inverse(X_123)),positive_part(X_123)) = greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X_123)),positive_part(X_123)),greatest_lower_bound(positive_part(X_123),multiply(inverse(X_123),positive_part(X_123)))) ),[1,1],$fot(positive_part(inverse(X_123)))]]) ).

cnf(refute_0_518,plain,
    ( multiply(negative_part(inverse(X_123)),positive_part(X_123)) != greatest_lower_bound(positive_part(X_123),multiply(inverse(X_123),positive_part(X_123)))
    | multiply(negative_part(inverse(X_123)),positive_part(X_123)) = greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_123),positive_part(X_123)),positive_part(inverse(X_123))) )],[refute_0_379,refute_0_517]) ).

cnf(refute_0_519,plain,
    multiply(negative_part(inverse(X_123)),positive_part(X_123)) = greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))),
    inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_123)),positive_part(X_123)),greatest_lower_bound(positive_part(X_123),multiply(inverse(X_123),positive_part(X_123)))) )],[refute_0_516,refute_0_518]) ).

cnf(refute_0_520,plain,
    multiply(negative_part(X_190),positive_part(inverse(X_190))) = greatest_lower_bound(positive_part(inverse(X_190)),multiply(X_190,positive_part(inverse(X_190)))),
    inference(subst,[],[refute_0_515:[bind(X_186,$fot(positive_part(inverse(X_190)))),bind(X_187,$fot(X_190))]]) ).

cnf(refute_0_521,plain,
    multiply(X_190,positive_part(inverse(X_190))) = positive_part(X_190),
    inference(subst,[],[refute_0_488:[bind(X_122,$fot(X_190))]]) ).

cnf(refute_0_522,plain,
    ( multiply(X_190,positive_part(inverse(X_190))) != positive_part(X_190)
    | multiply(negative_part(X_190),positive_part(inverse(X_190))) != greatest_lower_bound(positive_part(inverse(X_190)),multiply(X_190,positive_part(inverse(X_190))))
    | multiply(negative_part(X_190),positive_part(inverse(X_190))) = greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(X_190),positive_part(inverse(X_190))),greatest_lower_bound(positive_part(inverse(X_190)),multiply(X_190,positive_part(inverse(X_190))))) ),[1,1],$fot(positive_part(X_190))]]) ).

cnf(refute_0_523,plain,
    ( multiply(negative_part(X_190),positive_part(inverse(X_190))) != greatest_lower_bound(positive_part(inverse(X_190)),multiply(X_190,positive_part(inverse(X_190))))
    | multiply(negative_part(X_190),positive_part(inverse(X_190))) = greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)) ),
    inference(resolve,[$cnf( $equal(multiply(X_190,positive_part(inverse(X_190))),positive_part(X_190)) )],[refute_0_521,refute_0_522]) ).

cnf(refute_0_524,plain,
    multiply(negative_part(X_190),positive_part(inverse(X_190))) = greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)),
    inference(resolve,[$cnf( $equal(multiply(negative_part(X_190),positive_part(inverse(X_190))),greatest_lower_bound(positive_part(inverse(X_190)),multiply(X_190,positive_part(inverse(X_190))))) )],[refute_0_520,refute_0_523]) ).

cnf(refute_0_525,plain,
    ( multiply(negative_part(inverse(X_123)),positive_part(X_123)) != greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))
    | greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) = multiply(negative_part(inverse(X_123)),positive_part(X_123)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(negative_part(inverse(X_123)),positive_part(X_123)))),bind(Y0,$fot(greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))))]]) ).

cnf(refute_0_526,plain,
    greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) = multiply(negative_part(inverse(X_123)),positive_part(X_123)),
    inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_123)),positive_part(X_123)),greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))) )],[refute_0_519,refute_0_525]) ).

cnf(refute_0_527,plain,
    greatest_lower_bound(positive_part(X_190),positive_part(inverse(X_190))) = multiply(negative_part(inverse(X_190)),positive_part(X_190)),
    inference(subst,[],[refute_0_526:[bind(X_123,$fot(X_190))]]) ).

cnf(refute_0_528,plain,
    greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)) = greatest_lower_bound(positive_part(X_190),positive_part(inverse(X_190))),
    inference(subst,[],[refute_0_473:[bind(X,$fot(positive_part(X_190))),bind(Y,$fot(positive_part(inverse(X_190))))]]) ).

cnf(refute_0_529,plain,
    ( greatest_lower_bound(positive_part(X_190),positive_part(inverse(X_190))) != multiply(negative_part(inverse(X_190)),positive_part(X_190))
    | greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)) != greatest_lower_bound(positive_part(X_190),positive_part(inverse(X_190)))
    | greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)) = multiply(negative_part(inverse(X_190)),positive_part(X_190)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)))),bind(Y0,$fot(greatest_lower_bound(positive_part(X_190),positive_part(inverse(X_190))))),bind(Z0,$fot(multiply(negative_part(inverse(X_190)),positive_part(X_190))))]]) ).

cnf(refute_0_530,plain,
    ( greatest_lower_bound(positive_part(X_190),positive_part(inverse(X_190))) != multiply(negative_part(inverse(X_190)),positive_part(X_190))
    | greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)) = multiply(negative_part(inverse(X_190)),positive_part(X_190)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)),greatest_lower_bound(positive_part(X_190),positive_part(inverse(X_190)))) )],[refute_0_528,refute_0_529]) ).

cnf(refute_0_531,plain,
    greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)) = multiply(negative_part(inverse(X_190)),positive_part(X_190)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_190),positive_part(inverse(X_190))),multiply(negative_part(inverse(X_190)),positive_part(X_190))) )],[refute_0_527,refute_0_530]) ).

cnf(refute_0_532,plain,
    ( multiply(negative_part(X_190),positive_part(inverse(X_190))) != greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190))
    | greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)) != multiply(negative_part(inverse(X_190)),positive_part(X_190))
    | multiply(negative_part(X_190),positive_part(inverse(X_190))) = multiply(negative_part(inverse(X_190)),positive_part(X_190)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(X_190),positive_part(inverse(X_190))),multiply(negative_part(inverse(X_190)),positive_part(X_190))) ),[0],$fot(greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)))]]) ).

cnf(refute_0_533,plain,
    ( multiply(negative_part(X_190),positive_part(inverse(X_190))) != greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190))
    | multiply(negative_part(X_190),positive_part(inverse(X_190))) = multiply(negative_part(inverse(X_190)),positive_part(X_190)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190)),multiply(negative_part(inverse(X_190)),positive_part(X_190))) )],[refute_0_531,refute_0_532]) ).

cnf(refute_0_534,plain,
    multiply(negative_part(X_190),positive_part(inverse(X_190))) = multiply(negative_part(inverse(X_190)),positive_part(X_190)),
    inference(resolve,[$cnf( $equal(multiply(negative_part(X_190),positive_part(inverse(X_190))),greatest_lower_bound(positive_part(inverse(X_190)),positive_part(X_190))) )],[refute_0_524,refute_0_533]) ).

cnf(refute_0_535,plain,
    ( multiply(negative_part(X_190),positive_part(inverse(X_190))) != multiply(negative_part(inverse(X_190)),positive_part(X_190))
    | multiply(negative_part(inverse(X_190)),positive_part(X_190)) = multiply(negative_part(X_190),positive_part(inverse(X_190))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(negative_part(X_190),positive_part(inverse(X_190))))),bind(Y0,$fot(multiply(negative_part(inverse(X_190)),positive_part(X_190))))]]) ).

cnf(refute_0_536,plain,
    multiply(negative_part(inverse(X_190)),positive_part(X_190)) = multiply(negative_part(X_190),positive_part(inverse(X_190))),
    inference(resolve,[$cnf( $equal(multiply(negative_part(X_190),positive_part(inverse(X_190))),multiply(negative_part(inverse(X_190)),positive_part(X_190))) )],[refute_0_534,refute_0_535]) ).

cnf(refute_0_537,plain,
    multiply(negative_part(inverse(X_123)),positive_part(X_123)) = multiply(negative_part(X_123),positive_part(inverse(X_123))),
    inference(subst,[],[refute_0_536:[bind(X_190,$fot(X_123))]]) ).

cnf(refute_0_538,plain,
    ( multiply(negative_part(inverse(X_123)),positive_part(X_123)) != multiply(negative_part(X_123),positive_part(inverse(X_123)))
    | multiply(negative_part(inverse(X_123)),positive_part(X_123)) != greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))
    | multiply(negative_part(X_123),positive_part(inverse(X_123))) = greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X_123)),positive_part(X_123)),greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))) ),[0],$fot(multiply(negative_part(X_123),positive_part(inverse(X_123))))]]) ).

cnf(refute_0_539,plain,
    ( multiply(negative_part(inverse(X_123)),positive_part(X_123)) != greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))
    | multiply(negative_part(X_123),positive_part(inverse(X_123))) = greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) ),
    inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_123)),positive_part(X_123)),multiply(negative_part(X_123),positive_part(inverse(X_123)))) )],[refute_0_537,refute_0_538]) ).

cnf(refute_0_540,plain,
    multiply(negative_part(X_123),positive_part(inverse(X_123))) = greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))),
    inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_123)),positive_part(X_123)),greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))) )],[refute_0_519,refute_0_539]) ).

cnf(refute_0_541,plain,
    multiply(positive_part(inverse(X_109)),negative_part(X_109)) = least_upper_bound(negative_part(X_109),multiply(inverse(X_109),negative_part(X_109))),
    inference(subst,[],[refute_0_435:[bind(X_166,$fot(negative_part(X_109))),bind(X_167,$fot(inverse(X_109)))]]) ).

cnf(refute_0_542,plain,
    multiply(multiply(inverse(X_109),X_109),X_110) = multiply(inverse(X_109),multiply(X_109,X_110)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_109))),bind(Y,$fot(X_109)),bind(Z,$fot(X_110))]]) ).

cnf(refute_0_543,plain,
    multiply(inverse(X_109),X_109) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_109))]]) ).

cnf(refute_0_544,plain,
    ( multiply(multiply(inverse(X_109),X_109),X_110) != multiply(inverse(X_109),multiply(X_109,X_110))
    | multiply(inverse(X_109),X_109) != identity
    | multiply(identity,X_110) = multiply(inverse(X_109),multiply(X_109,X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_109),X_109),X_110),multiply(inverse(X_109),multiply(X_109,X_110))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_545,plain,
    ( multiply(multiply(inverse(X_109),X_109),X_110) != multiply(inverse(X_109),multiply(X_109,X_110))
    | multiply(identity,X_110) = multiply(inverse(X_109),multiply(X_109,X_110)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_109),X_109),identity) )],[refute_0_543,refute_0_544]) ).

cnf(refute_0_546,plain,
    multiply(identity,X_110) = multiply(inverse(X_109),multiply(X_109,X_110)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_109),X_109),X_110),multiply(inverse(X_109),multiply(X_109,X_110))) )],[refute_0_542,refute_0_545]) ).

cnf(refute_0_547,plain,
    ( multiply(identity,X_110) != X_110
    | multiply(identity,X_110) != multiply(inverse(X_109),multiply(X_109,X_110))
    | X_110 = multiply(inverse(X_109),multiply(X_109,X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_110),multiply(inverse(X_109),multiply(X_109,X_110))) ),[0],$fot(X_110)]]) ).

cnf(refute_0_548,plain,
    ( multiply(identity,X_110) != multiply(inverse(X_109),multiply(X_109,X_110))
    | X_110 = multiply(inverse(X_109),multiply(X_109,X_110)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_110),X_110) )],[refute_0_10,refute_0_547]) ).

cnf(refute_0_549,plain,
    X_110 = multiply(inverse(X_109),multiply(X_109,X_110)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_110),multiply(inverse(X_109),multiply(X_109,X_110))) )],[refute_0_546,refute_0_548]) ).

cnf(refute_0_550,plain,
    negative_part(inverse(X_109)) = multiply(inverse(X_109),multiply(X_109,negative_part(inverse(X_109)))),
    inference(subst,[],[refute_0_549:[bind(X_110,$fot(negative_part(inverse(X_109))))]]) ).

cnf(refute_0_551,plain,
    multiply(X_109,negative_part(inverse(X_109))) = negative_part(X_109),
    inference(subst,[],[refute_0_413:[bind(X_158,$fot(X_109))]]) ).

cnf(refute_0_552,plain,
    ( multiply(X_109,negative_part(inverse(X_109))) != negative_part(X_109)
    | negative_part(inverse(X_109)) != multiply(inverse(X_109),multiply(X_109,negative_part(inverse(X_109))))
    | negative_part(inverse(X_109)) = multiply(inverse(X_109),negative_part(X_109)) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(inverse(X_109)),multiply(inverse(X_109),multiply(X_109,negative_part(inverse(X_109))))) ),[1,1],$fot(negative_part(X_109))]]) ).

cnf(refute_0_553,plain,
    ( negative_part(inverse(X_109)) != multiply(inverse(X_109),multiply(X_109,negative_part(inverse(X_109))))
    | negative_part(inverse(X_109)) = multiply(inverse(X_109),negative_part(X_109)) ),
    inference(resolve,[$cnf( $equal(multiply(X_109,negative_part(inverse(X_109))),negative_part(X_109)) )],[refute_0_551,refute_0_552]) ).

cnf(refute_0_554,plain,
    negative_part(inverse(X_109)) = multiply(inverse(X_109),negative_part(X_109)),
    inference(resolve,[$cnf( $equal(negative_part(inverse(X_109)),multiply(inverse(X_109),multiply(X_109,negative_part(inverse(X_109))))) )],[refute_0_550,refute_0_553]) ).

cnf(refute_0_555,plain,
    ( negative_part(inverse(X_109)) != multiply(inverse(X_109),negative_part(X_109))
    | multiply(inverse(X_109),negative_part(X_109)) = negative_part(inverse(X_109)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(inverse(X_109)))),bind(Y0,$fot(multiply(inverse(X_109),negative_part(X_109))))]]) ).

cnf(refute_0_556,plain,
    multiply(inverse(X_109),negative_part(X_109)) = negative_part(inverse(X_109)),
    inference(resolve,[$cnf( $equal(negative_part(inverse(X_109)),multiply(inverse(X_109),negative_part(X_109))) )],[refute_0_554,refute_0_555]) ).

cnf(refute_0_557,plain,
    ( multiply(inverse(X_109),negative_part(X_109)) != negative_part(inverse(X_109))
    | multiply(positive_part(inverse(X_109)),negative_part(X_109)) != least_upper_bound(negative_part(X_109),multiply(inverse(X_109),negative_part(X_109)))
    | multiply(positive_part(inverse(X_109)),negative_part(X_109)) = least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(inverse(X_109)),negative_part(X_109)),least_upper_bound(negative_part(X_109),multiply(inverse(X_109),negative_part(X_109)))) ),[1,1],$fot(negative_part(inverse(X_109)))]]) ).

cnf(refute_0_558,plain,
    ( multiply(positive_part(inverse(X_109)),negative_part(X_109)) != least_upper_bound(negative_part(X_109),multiply(inverse(X_109),negative_part(X_109)))
    | multiply(positive_part(inverse(X_109)),negative_part(X_109)) = least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_109),negative_part(X_109)),negative_part(inverse(X_109))) )],[refute_0_556,refute_0_557]) ).

cnf(refute_0_559,plain,
    multiply(positive_part(inverse(X_109)),negative_part(X_109)) = least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))),
    inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_109)),negative_part(X_109)),least_upper_bound(negative_part(X_109),multiply(inverse(X_109),negative_part(X_109)))) )],[refute_0_541,refute_0_558]) ).

cnf(refute_0_560,plain,
    multiply(positive_part(X_170),negative_part(inverse(X_170))) = least_upper_bound(negative_part(inverse(X_170)),multiply(X_170,negative_part(inverse(X_170)))),
    inference(subst,[],[refute_0_435:[bind(X_166,$fot(negative_part(inverse(X_170)))),bind(X_167,$fot(X_170))]]) ).

cnf(refute_0_561,plain,
    multiply(X_170,negative_part(inverse(X_170))) = negative_part(X_170),
    inference(subst,[],[refute_0_413:[bind(X_158,$fot(X_170))]]) ).

cnf(refute_0_562,plain,
    ( multiply(X_170,negative_part(inverse(X_170))) != negative_part(X_170)
    | multiply(positive_part(X_170),negative_part(inverse(X_170))) != least_upper_bound(negative_part(inverse(X_170)),multiply(X_170,negative_part(inverse(X_170))))
    | multiply(positive_part(X_170),negative_part(inverse(X_170))) = least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(X_170),negative_part(inverse(X_170))),least_upper_bound(negative_part(inverse(X_170)),multiply(X_170,negative_part(inverse(X_170))))) ),[1,1],$fot(negative_part(X_170))]]) ).

cnf(refute_0_563,plain,
    ( multiply(positive_part(X_170),negative_part(inverse(X_170))) != least_upper_bound(negative_part(inverse(X_170)),multiply(X_170,negative_part(inverse(X_170))))
    | multiply(positive_part(X_170),negative_part(inverse(X_170))) = least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)) ),
    inference(resolve,[$cnf( $equal(multiply(X_170,negative_part(inverse(X_170))),negative_part(X_170)) )],[refute_0_561,refute_0_562]) ).

cnf(refute_0_564,plain,
    multiply(positive_part(X_170),negative_part(inverse(X_170))) = least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_170),negative_part(inverse(X_170))),least_upper_bound(negative_part(inverse(X_170)),multiply(X_170,negative_part(inverse(X_170))))) )],[refute_0_560,refute_0_563]) ).

cnf(refute_0_565,plain,
    ( multiply(positive_part(inverse(X_109)),negative_part(X_109)) != least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))
    | least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) = multiply(positive_part(inverse(X_109)),negative_part(X_109)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(positive_part(inverse(X_109)),negative_part(X_109)))),bind(Y0,$fot(least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))))]]) ).

cnf(refute_0_566,plain,
    least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) = multiply(positive_part(inverse(X_109)),negative_part(X_109)),
    inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_109)),negative_part(X_109)),least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))) )],[refute_0_559,refute_0_565]) ).

cnf(refute_0_567,plain,
    least_upper_bound(negative_part(X_170),negative_part(inverse(X_170))) = multiply(positive_part(inverse(X_170)),negative_part(X_170)),
    inference(subst,[],[refute_0_566:[bind(X_109,$fot(X_170))]]) ).

cnf(refute_0_568,plain,
    least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)) = least_upper_bound(negative_part(X_170),negative_part(inverse(X_170))),
    inference(subst,[],[refute_0_355:[bind(Y,$fot(negative_part(X_170))),bind(X_63,$fot(negative_part(inverse(X_170))))]]) ).

cnf(refute_0_569,plain,
    ( least_upper_bound(negative_part(X_170),negative_part(inverse(X_170))) != multiply(positive_part(inverse(X_170)),negative_part(X_170))
    | least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)) != least_upper_bound(negative_part(X_170),negative_part(inverse(X_170)))
    | least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)) = multiply(positive_part(inverse(X_170)),negative_part(X_170)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)))),bind(Y0,$fot(least_upper_bound(negative_part(X_170),negative_part(inverse(X_170))))),bind(Z0,$fot(multiply(positive_part(inverse(X_170)),negative_part(X_170))))]]) ).

cnf(refute_0_570,plain,
    ( least_upper_bound(negative_part(X_170),negative_part(inverse(X_170))) != multiply(positive_part(inverse(X_170)),negative_part(X_170))
    | least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)) = multiply(positive_part(inverse(X_170)),negative_part(X_170)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)),least_upper_bound(negative_part(X_170),negative_part(inverse(X_170)))) )],[refute_0_568,refute_0_569]) ).

cnf(refute_0_571,plain,
    least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)) = multiply(positive_part(inverse(X_170)),negative_part(X_170)),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_170),negative_part(inverse(X_170))),multiply(positive_part(inverse(X_170)),negative_part(X_170))) )],[refute_0_567,refute_0_570]) ).

cnf(refute_0_572,plain,
    ( multiply(positive_part(X_170),negative_part(inverse(X_170))) != least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170))
    | least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)) != multiply(positive_part(inverse(X_170)),negative_part(X_170))
    | multiply(positive_part(X_170),negative_part(inverse(X_170))) = multiply(positive_part(inverse(X_170)),negative_part(X_170)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(positive_part(X_170),negative_part(inverse(X_170))),multiply(positive_part(inverse(X_170)),negative_part(X_170))) ),[0],$fot(least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)))]]) ).

cnf(refute_0_573,plain,
    ( multiply(positive_part(X_170),negative_part(inverse(X_170))) != least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170))
    | multiply(positive_part(X_170),negative_part(inverse(X_170))) = multiply(positive_part(inverse(X_170)),negative_part(X_170)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170)),multiply(positive_part(inverse(X_170)),negative_part(X_170))) )],[refute_0_571,refute_0_572]) ).

cnf(refute_0_574,plain,
    multiply(positive_part(X_170),negative_part(inverse(X_170))) = multiply(positive_part(inverse(X_170)),negative_part(X_170)),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_170),negative_part(inverse(X_170))),least_upper_bound(negative_part(inverse(X_170)),negative_part(X_170))) )],[refute_0_564,refute_0_573]) ).

cnf(refute_0_575,plain,
    ( multiply(positive_part(X_170),negative_part(inverse(X_170))) != multiply(positive_part(inverse(X_170)),negative_part(X_170))
    | multiply(positive_part(inverse(X_170)),negative_part(X_170)) = multiply(positive_part(X_170),negative_part(inverse(X_170))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(positive_part(X_170),negative_part(inverse(X_170))))),bind(Y0,$fot(multiply(positive_part(inverse(X_170)),negative_part(X_170))))]]) ).

cnf(refute_0_576,plain,
    multiply(positive_part(inverse(X_170)),negative_part(X_170)) = multiply(positive_part(X_170),negative_part(inverse(X_170))),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_170),negative_part(inverse(X_170))),multiply(positive_part(inverse(X_170)),negative_part(X_170))) )],[refute_0_574,refute_0_575]) ).

cnf(refute_0_577,plain,
    multiply(positive_part(inverse(X_109)),negative_part(X_109)) = multiply(positive_part(X_109),negative_part(inverse(X_109))),
    inference(subst,[],[refute_0_576:[bind(X_170,$fot(X_109))]]) ).

cnf(refute_0_578,plain,
    ( multiply(positive_part(inverse(X_109)),negative_part(X_109)) != multiply(positive_part(X_109),negative_part(inverse(X_109)))
    | multiply(positive_part(inverse(X_109)),negative_part(X_109)) != least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))
    | multiply(positive_part(X_109),negative_part(inverse(X_109))) = least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(inverse(X_109)),negative_part(X_109)),least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))) ),[0],$fot(multiply(positive_part(X_109),negative_part(inverse(X_109))))]]) ).

cnf(refute_0_579,plain,
    ( multiply(positive_part(inverse(X_109)),negative_part(X_109)) != least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))
    | multiply(positive_part(X_109),negative_part(inverse(X_109))) = least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) ),
    inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_109)),negative_part(X_109)),multiply(positive_part(X_109),negative_part(inverse(X_109)))) )],[refute_0_577,refute_0_578]) ).

cnf(refute_0_580,plain,
    multiply(positive_part(X_109),negative_part(inverse(X_109))) = least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))),
    inference(resolve,[$cnf( $equal(multiply(positive_part(inverse(X_109)),negative_part(X_109)),least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))) )],[refute_0_559,refute_0_579]) ).

cnf(refute_0_581,plain,
    multiply(negative_part(inverse(X_120)),positive_part(X_120)) = least_upper_bound(negative_part(inverse(X_120)),multiply(negative_part(inverse(X_120)),X_120)),
    inference(subst,[],[refute_0_360:[bind(X_119,$fot(negative_part(inverse(X_120))))]]) ).

cnf(refute_0_582,plain,
    multiply(negative_part(inverse(X_189)),X_189) = greatest_lower_bound(X_189,multiply(inverse(X_189),X_189)),
    inference(subst,[],[refute_0_515:[bind(X_186,$fot(X_189)),bind(X_187,$fot(inverse(X_189)))]]) ).

cnf(refute_0_583,plain,
    multiply(inverse(X_189),X_189) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_189))]]) ).

cnf(refute_0_584,plain,
    ( multiply(inverse(X_189),X_189) != identity
    | multiply(negative_part(inverse(X_189)),X_189) != greatest_lower_bound(X_189,multiply(inverse(X_189),X_189))
    | multiply(negative_part(inverse(X_189)),X_189) = greatest_lower_bound(X_189,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X_189)),X_189),greatest_lower_bound(X_189,multiply(inverse(X_189),X_189))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_585,plain,
    ( multiply(negative_part(inverse(X_189)),X_189) != greatest_lower_bound(X_189,multiply(inverse(X_189),X_189))
    | multiply(negative_part(inverse(X_189)),X_189) = greatest_lower_bound(X_189,identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_189),X_189),identity) )],[refute_0_583,refute_0_584]) ).

cnf(refute_0_586,plain,
    multiply(negative_part(inverse(X_189)),X_189) = greatest_lower_bound(X_189,identity),
    inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_189)),X_189),greatest_lower_bound(X_189,multiply(inverse(X_189),X_189))) )],[refute_0_582,refute_0_585]) ).

cnf(refute_0_587,plain,
    greatest_lower_bound(X_189,identity) = negative_part(X_189),
    inference(subst,[],[refute_0_280:[bind(X,$fot(X_189))]]) ).

cnf(refute_0_588,plain,
    ( multiply(negative_part(inverse(X_189)),X_189) != greatest_lower_bound(X_189,identity)
    | greatest_lower_bound(X_189,identity) != negative_part(X_189)
    | multiply(negative_part(inverse(X_189)),X_189) = negative_part(X_189) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(inverse(X_189)),X_189),negative_part(X_189)) ),[0],$fot(greatest_lower_bound(X_189,identity))]]) ).

cnf(refute_0_589,plain,
    ( multiply(negative_part(inverse(X_189)),X_189) != greatest_lower_bound(X_189,identity)
    | multiply(negative_part(inverse(X_189)),X_189) = negative_part(X_189) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_189,identity),negative_part(X_189)) )],[refute_0_587,refute_0_588]) ).

cnf(refute_0_590,plain,
    multiply(negative_part(inverse(X_189)),X_189) = negative_part(X_189),
    inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_189)),X_189),greatest_lower_bound(X_189,identity)) )],[refute_0_586,refute_0_589]) ).

cnf(refute_0_591,plain,
    multiply(negative_part(inverse(X_120)),X_120) = negative_part(X_120),
    inference(subst,[],[refute_0_590:[bind(X_189,$fot(X_120))]]) ).

cnf(refute_0_592,plain,
    ( multiply(negative_part(inverse(X_120)),X_120) != negative_part(X_120)
    | multiply(negative_part(inverse(X_120)),positive_part(X_120)) != least_upper_bound(negative_part(inverse(X_120)),multiply(negative_part(inverse(X_120)),X_120))
    | multiply(negative_part(inverse(X_120)),positive_part(X_120)) = least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X_120)),positive_part(X_120)),least_upper_bound(negative_part(inverse(X_120)),multiply(negative_part(inverse(X_120)),X_120))) ),[1,1],$fot(negative_part(X_120))]]) ).

cnf(refute_0_593,plain,
    ( multiply(negative_part(inverse(X_120)),positive_part(X_120)) != least_upper_bound(negative_part(inverse(X_120)),multiply(negative_part(inverse(X_120)),X_120))
    | multiply(negative_part(inverse(X_120)),positive_part(X_120)) = least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)) ),
    inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_120)),X_120),negative_part(X_120)) )],[refute_0_591,refute_0_592]) ).

cnf(refute_0_594,plain,
    multiply(negative_part(inverse(X_120)),positive_part(X_120)) = least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)),
    inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_120)),positive_part(X_120)),least_upper_bound(negative_part(inverse(X_120)),multiply(negative_part(inverse(X_120)),X_120))) )],[refute_0_581,refute_0_593]) ).

cnf(refute_0_595,plain,
    multiply(negative_part(inverse(X_120)),positive_part(X_120)) = multiply(negative_part(X_120),positive_part(inverse(X_120))),
    inference(subst,[],[refute_0_536:[bind(X_190,$fot(X_120))]]) ).

cnf(refute_0_596,plain,
    ( multiply(negative_part(inverse(X_120)),positive_part(X_120)) != multiply(negative_part(X_120),positive_part(inverse(X_120)))
    | multiply(negative_part(inverse(X_120)),positive_part(X_120)) != least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120))
    | multiply(negative_part(X_120),positive_part(inverse(X_120))) = least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(inverse(X_120)),positive_part(X_120)),least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120))) ),[0],$fot(multiply(negative_part(X_120),positive_part(inverse(X_120))))]]) ).

cnf(refute_0_597,plain,
    ( multiply(negative_part(inverse(X_120)),positive_part(X_120)) != least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120))
    | multiply(negative_part(X_120),positive_part(inverse(X_120))) = least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)) ),
    inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_120)),positive_part(X_120)),multiply(negative_part(X_120),positive_part(inverse(X_120)))) )],[refute_0_595,refute_0_596]) ).

cnf(refute_0_598,plain,
    ( multiply(positive_part(X_109),negative_part(inverse(X_109))) != least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))
    | least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) = multiply(positive_part(X_109),negative_part(inverse(X_109))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(positive_part(X_109),negative_part(inverse(X_109))))),bind(Y0,$fot(least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))))]]) ).

cnf(refute_0_599,plain,
    least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) = multiply(positive_part(X_109),negative_part(inverse(X_109))),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_109),negative_part(inverse(X_109))),least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))) )],[refute_0_580,refute_0_598]) ).

cnf(refute_0_600,plain,
    least_upper_bound(negative_part(X_120),negative_part(inverse(X_120))) = multiply(positive_part(X_120),negative_part(inverse(X_120))),
    inference(subst,[],[refute_0_599:[bind(X_109,$fot(X_120))]]) ).

cnf(refute_0_601,plain,
    least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)) = least_upper_bound(negative_part(X_120),negative_part(inverse(X_120))),
    inference(subst,[],[refute_0_355:[bind(Y,$fot(negative_part(X_120))),bind(X_63,$fot(negative_part(inverse(X_120))))]]) ).

cnf(refute_0_602,plain,
    ( least_upper_bound(negative_part(X_120),negative_part(inverse(X_120))) != multiply(positive_part(X_120),negative_part(inverse(X_120)))
    | least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)) != least_upper_bound(negative_part(X_120),negative_part(inverse(X_120)))
    | least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)) = multiply(positive_part(X_120),negative_part(inverse(X_120))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)))),bind(Y0,$fot(least_upper_bound(negative_part(X_120),negative_part(inverse(X_120))))),bind(Z0,$fot(multiply(positive_part(X_120),negative_part(inverse(X_120)))))]]) ).

cnf(refute_0_603,plain,
    ( least_upper_bound(negative_part(X_120),negative_part(inverse(X_120))) != multiply(positive_part(X_120),negative_part(inverse(X_120)))
    | least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)) = multiply(positive_part(X_120),negative_part(inverse(X_120))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)),least_upper_bound(negative_part(X_120),negative_part(inverse(X_120)))) )],[refute_0_601,refute_0_602]) ).

cnf(refute_0_604,plain,
    least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)) = multiply(positive_part(X_120),negative_part(inverse(X_120))),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_120),negative_part(inverse(X_120))),multiply(positive_part(X_120),negative_part(inverse(X_120)))) )],[refute_0_600,refute_0_603]) ).

cnf(refute_0_605,plain,
    ( multiply(negative_part(X_120),positive_part(inverse(X_120))) != least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120))
    | least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)) != multiply(positive_part(X_120),negative_part(inverse(X_120)))
    | multiply(negative_part(X_120),positive_part(inverse(X_120))) = multiply(positive_part(X_120),negative_part(inverse(X_120))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(X_120),positive_part(inverse(X_120))),multiply(positive_part(X_120),negative_part(inverse(X_120)))) ),[0],$fot(least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)))]]) ).

cnf(refute_0_606,plain,
    ( multiply(negative_part(X_120),positive_part(inverse(X_120))) != least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120))
    | multiply(negative_part(X_120),positive_part(inverse(X_120))) = multiply(positive_part(X_120),negative_part(inverse(X_120))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120)),multiply(positive_part(X_120),negative_part(inverse(X_120)))) )],[refute_0_604,refute_0_605]) ).

cnf(refute_0_607,plain,
    ( multiply(negative_part(inverse(X_120)),positive_part(X_120)) != least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120))
    | multiply(negative_part(X_120),positive_part(inverse(X_120))) = multiply(positive_part(X_120),negative_part(inverse(X_120))) ),
    inference(resolve,[$cnf( $equal(multiply(negative_part(X_120),positive_part(inverse(X_120))),least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120))) )],[refute_0_597,refute_0_606]) ).

cnf(refute_0_608,plain,
    multiply(negative_part(X_120),positive_part(inverse(X_120))) = multiply(positive_part(X_120),negative_part(inverse(X_120))),
    inference(resolve,[$cnf( $equal(multiply(negative_part(inverse(X_120)),positive_part(X_120)),least_upper_bound(negative_part(inverse(X_120)),negative_part(X_120))) )],[refute_0_594,refute_0_607]) ).

cnf(refute_0_609,plain,
    ( multiply(negative_part(X_120),positive_part(inverse(X_120))) != multiply(positive_part(X_120),negative_part(inverse(X_120)))
    | multiply(positive_part(X_120),negative_part(inverse(X_120))) = multiply(negative_part(X_120),positive_part(inverse(X_120))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(negative_part(X_120),positive_part(inverse(X_120))))),bind(Y0,$fot(multiply(positive_part(X_120),negative_part(inverse(X_120)))))]]) ).

cnf(refute_0_610,plain,
    multiply(positive_part(X_120),negative_part(inverse(X_120))) = multiply(negative_part(X_120),positive_part(inverse(X_120))),
    inference(resolve,[$cnf( $equal(multiply(negative_part(X_120),positive_part(inverse(X_120))),multiply(positive_part(X_120),negative_part(inverse(X_120)))) )],[refute_0_608,refute_0_609]) ).

cnf(refute_0_611,plain,
    multiply(positive_part(X_109),negative_part(inverse(X_109))) = multiply(negative_part(X_109),positive_part(inverse(X_109))),
    inference(subst,[],[refute_0_610:[bind(X_120,$fot(X_109))]]) ).

cnf(refute_0_612,plain,
    ( multiply(positive_part(X_109),negative_part(inverse(X_109))) != multiply(negative_part(X_109),positive_part(inverse(X_109)))
    | multiply(positive_part(X_109),negative_part(inverse(X_109))) != least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))
    | multiply(negative_part(X_109),positive_part(inverse(X_109))) = least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(X_109),negative_part(inverse(X_109))),least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))) ),[0],$fot(multiply(negative_part(X_109),positive_part(inverse(X_109))))]]) ).

cnf(refute_0_613,plain,
    ( multiply(positive_part(X_109),negative_part(inverse(X_109))) != least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))
    | multiply(negative_part(X_109),positive_part(inverse(X_109))) = least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) ),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_109),negative_part(inverse(X_109))),multiply(negative_part(X_109),positive_part(inverse(X_109)))) )],[refute_0_611,refute_0_612]) ).

cnf(refute_0_614,plain,
    multiply(negative_part(X_109),positive_part(inverse(X_109))) = least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_109),negative_part(inverse(X_109))),least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))) )],[refute_0_580,refute_0_613]) ).

cnf(refute_0_615,plain,
    greatest_lower_bound(identity,least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(identity,X_200),greatest_lower_bound(identity,X_201)),
    inference(subst,[],[lat4_7:[bind(X,$fot(identity)),bind(Y,$fot(X_200)),bind(Z,$fot(X_201))]]) ).

cnf(refute_0_616,plain,
    negative_part(X_201) = greatest_lower_bound(identity,X_201),
    inference(subst,[],[refute_0_257:[bind(X,$fot(X_201))]]) ).

cnf(refute_0_617,plain,
    ( negative_part(X_201) != greatest_lower_bound(identity,X_201)
    | greatest_lower_bound(identity,X_201) = negative_part(X_201) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(X_201))),bind(Y0,$fot(greatest_lower_bound(identity,X_201)))]]) ).

cnf(refute_0_618,plain,
    greatest_lower_bound(identity,X_201) = negative_part(X_201),
    inference(resolve,[$cnf( $equal(negative_part(X_201),greatest_lower_bound(identity,X_201)) )],[refute_0_616,refute_0_617]) ).

cnf(refute_0_619,plain,
    ( greatest_lower_bound(identity,X_201) != negative_part(X_201)
    | greatest_lower_bound(identity,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(identity,X_200),greatest_lower_bound(identity,X_201))
    | greatest_lower_bound(identity,least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(identity,X_200),greatest_lower_bound(identity,X_201))) ),[1,1],$fot(negative_part(X_201))]]) ).

cnf(refute_0_620,plain,
    ( greatest_lower_bound(identity,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(identity,X_200),greatest_lower_bound(identity,X_201))
    | greatest_lower_bound(identity,least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_201),negative_part(X_201)) )],[refute_0_618,refute_0_619]) ).

cnf(refute_0_621,plain,
    greatest_lower_bound(identity,least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(identity,X_200),greatest_lower_bound(identity,X_201))) )],[refute_0_615,refute_0_620]) ).

cnf(refute_0_622,plain,
    greatest_lower_bound(identity,least_upper_bound(X_200,X_201)) = negative_part(least_upper_bound(X_200,X_201)),
    inference(subst,[],[refute_0_293:[bind(X,$fot(least_upper_bound(X_200,X_201)))]]) ).

cnf(refute_0_623,plain,
    ( greatest_lower_bound(identity,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))
    | greatest_lower_bound(identity,least_upper_bound(X_200,X_201)) != negative_part(least_upper_bound(X_200,X_201))
    | negative_part(least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))) ),[0],$fot(negative_part(least_upper_bound(X_200,X_201)))]]) ).

cnf(refute_0_624,plain,
    ( greatest_lower_bound(identity,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))
    | negative_part(least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_200,X_201)),negative_part(least_upper_bound(X_200,X_201))) )],[refute_0_622,refute_0_623]) ).

cnf(refute_0_625,plain,
    greatest_lower_bound(identity,X_200) = negative_part(X_200),
    inference(subst,[],[refute_0_293:[bind(X,$fot(X_200))]]) ).

cnf(refute_0_626,plain,
    least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)) = least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)),
    introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)))]]) ).

cnf(refute_0_627,plain,
    ( greatest_lower_bound(identity,X_200) != negative_part(X_200)
    | least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)) != least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))
    | least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)) = least_upper_bound(negative_part(X_200),negative_part(X_201)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)),least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))) ),[1,0],$fot(negative_part(X_200))]]) ).

cnf(refute_0_628,plain,
    ( greatest_lower_bound(identity,X_200) != negative_part(X_200)
    | least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)) = least_upper_bound(negative_part(X_200),negative_part(X_201)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)),least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))) )],[refute_0_626,refute_0_627]) ).

cnf(refute_0_629,plain,
    least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)) = least_upper_bound(negative_part(X_200),negative_part(X_201)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_200),negative_part(X_200)) )],[refute_0_625,refute_0_628]) ).

cnf(refute_0_630,plain,
    ( least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)) != least_upper_bound(negative_part(X_200),negative_part(X_201))
    | negative_part(least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))
    | negative_part(least_upper_bound(X_200,X_201)) = least_upper_bound(negative_part(X_200),negative_part(X_201)) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))) ),[1],$fot(least_upper_bound(negative_part(X_200),negative_part(X_201)))]]) ).

cnf(refute_0_631,plain,
    ( negative_part(least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))
    | negative_part(least_upper_bound(X_200,X_201)) = least_upper_bound(negative_part(X_200),negative_part(X_201)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201)),least_upper_bound(negative_part(X_200),negative_part(X_201))) )],[refute_0_629,refute_0_630]) ).

cnf(refute_0_632,plain,
    ( greatest_lower_bound(identity,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))
    | negative_part(least_upper_bound(X_200,X_201)) = least_upper_bound(negative_part(X_200),negative_part(X_201)) ),
    inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))) )],[refute_0_624,refute_0_631]) ).

cnf(refute_0_633,plain,
    negative_part(least_upper_bound(X_200,X_201)) = least_upper_bound(negative_part(X_200),negative_part(X_201)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(identity,X_200),negative_part(X_201))) )],[refute_0_621,refute_0_632]) ).

cnf(refute_0_634,plain,
    ( negative_part(least_upper_bound(X_200,X_201)) != least_upper_bound(negative_part(X_200),negative_part(X_201))
    | least_upper_bound(negative_part(X_200),negative_part(X_201)) = negative_part(least_upper_bound(X_200,X_201)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(least_upper_bound(X_200,X_201)))),bind(Y0,$fot(least_upper_bound(negative_part(X_200),negative_part(X_201))))]]) ).

cnf(refute_0_635,plain,
    least_upper_bound(negative_part(X_200),negative_part(X_201)) = negative_part(least_upper_bound(X_200,X_201)),
    inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_200,X_201)),least_upper_bound(negative_part(X_200),negative_part(X_201))) )],[refute_0_633,refute_0_634]) ).

cnf(refute_0_636,plain,
    least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) = negative_part(least_upper_bound(X_109,inverse(X_109))),
    inference(subst,[],[refute_0_635:[bind(X_200,$fot(X_109)),bind(X_201,$fot(inverse(X_109)))]]) ).

cnf(refute_0_637,plain,
    ( multiply(negative_part(X_109),positive_part(inverse(X_109))) != least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))
    | least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))) != negative_part(least_upper_bound(X_109,inverse(X_109)))
    | multiply(negative_part(X_109),positive_part(inverse(X_109))) = negative_part(least_upper_bound(X_109,inverse(X_109))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(X_109),positive_part(inverse(X_109))),negative_part(least_upper_bound(X_109,inverse(X_109)))) ),[0],$fot(least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))))]]) ).

cnf(refute_0_638,plain,
    ( multiply(negative_part(X_109),positive_part(inverse(X_109))) != least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))
    | multiply(negative_part(X_109),positive_part(inverse(X_109))) = negative_part(least_upper_bound(X_109,inverse(X_109))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_109),negative_part(inverse(X_109))),negative_part(least_upper_bound(X_109,inverse(X_109)))) )],[refute_0_636,refute_0_637]) ).

cnf(refute_0_639,plain,
    multiply(negative_part(X_109),positive_part(inverse(X_109))) = negative_part(least_upper_bound(X_109,inverse(X_109))),
    inference(resolve,[$cnf( $equal(multiply(negative_part(X_109),positive_part(inverse(X_109))),least_upper_bound(negative_part(X_109),negative_part(inverse(X_109)))) )],[refute_0_614,refute_0_638]) ).

cnf(refute_0_640,plain,
    multiply(negative_part(X_123),positive_part(inverse(X_123))) = negative_part(least_upper_bound(X_123,inverse(X_123))),
    inference(subst,[],[refute_0_639:[bind(X_109,$fot(X_123))]]) ).

cnf(refute_0_641,plain,
    ( multiply(negative_part(X_123),positive_part(inverse(X_123))) != greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))
    | multiply(negative_part(X_123),positive_part(inverse(X_123))) != negative_part(least_upper_bound(X_123,inverse(X_123)))
    | negative_part(least_upper_bound(X_123,inverse(X_123))) = greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(X_123),positive_part(inverse(X_123))),greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))) ),[0],$fot(negative_part(least_upper_bound(X_123,inverse(X_123))))]]) ).

cnf(refute_0_642,plain,
    ( multiply(negative_part(X_123),positive_part(inverse(X_123))) != greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))
    | negative_part(least_upper_bound(X_123,inverse(X_123))) = greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) ),
    inference(resolve,[$cnf( $equal(multiply(negative_part(X_123),positive_part(inverse(X_123))),negative_part(least_upper_bound(X_123,inverse(X_123)))) )],[refute_0_640,refute_0_641]) ).

cnf(refute_0_643,plain,
    negative_part(least_upper_bound(X_123,inverse(X_123))) = greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))),
    inference(resolve,[$cnf( $equal(multiply(negative_part(X_123),positive_part(inverse(X_123))),greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))) )],[refute_0_540,refute_0_642]) ).

cnf(refute_0_644,plain,
    ( negative_part(least_upper_bound(X_123,inverse(X_123))) != greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))
    | greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) = negative_part(least_upper_bound(X_123,inverse(X_123))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(least_upper_bound(X_123,inverse(X_123))))),bind(Y0,$fot(greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))))]]) ).

cnf(refute_0_645,plain,
    greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) = negative_part(least_upper_bound(X_123,inverse(X_123))),
    inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_123,inverse(X_123))),greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))) )],[refute_0_643,refute_0_644]) ).

cnf(refute_0_646,plain,
    greatest_lower_bound(positive_part(X_230),positive_part(inverse(X_230))) = negative_part(least_upper_bound(X_230,inverse(X_230))),
    inference(subst,[],[refute_0_645:[bind(X_123,$fot(X_230))]]) ).

cnf(refute_0_647,plain,
    least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(greatest_lower_bound(positive_part(X_104),X_105))) = greatest_lower_bound(positive_part(X_104),X_105),
    inference(subst,[],[refute_0_85:[bind(X_22,$fot(greatest_lower_bound(positive_part(X_104),X_105)))]]) ).

cnf(refute_0_648,plain,
    negative_part(greatest_lower_bound(positive_part(X_17),X_41)) = greatest_lower_bound(negative_part(positive_part(X_17)),X_41),
    inference(subst,[],[refute_0_318:[bind(X_36,$fot(positive_part(X_17))),bind(X_37,$fot(X_41))]]) ).

cnf(refute_0_649,plain,
    negative_part(least_upper_bound(identity,X_17)) = greatest_lower_bound(identity,least_upper_bound(identity,X_17)),
    inference(subst,[],[refute_0_257:[bind(X,$fot(least_upper_bound(identity,X_17)))]]) ).

cnf(refute_0_650,plain,
    greatest_lower_bound(identity,least_upper_bound(identity,X_17)) = identity,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_17))]]) ).

cnf(refute_0_651,plain,
    ( greatest_lower_bound(identity,least_upper_bound(identity,X_17)) != identity
    | negative_part(least_upper_bound(identity,X_17)) != greatest_lower_bound(identity,least_upper_bound(identity,X_17))
    | negative_part(least_upper_bound(identity,X_17)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(identity,X_17)),greatest_lower_bound(identity,least_upper_bound(identity,X_17))) ),[1],$fot(identity)]]) ).

cnf(refute_0_652,plain,
    ( negative_part(least_upper_bound(identity,X_17)) != greatest_lower_bound(identity,least_upper_bound(identity,X_17))
    | negative_part(least_upper_bound(identity,X_17)) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,X_17)),identity) )],[refute_0_650,refute_0_651]) ).

cnf(refute_0_653,plain,
    negative_part(least_upper_bound(identity,X_17)) = identity,
    inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(identity,X_17)),greatest_lower_bound(identity,least_upper_bound(identity,X_17))) )],[refute_0_649,refute_0_652]) ).

cnf(refute_0_654,plain,
    least_upper_bound(identity,X_17) = positive_part(X_17),
    inference(subst,[],[refute_0_371:[bind(X,$fot(X_17))]]) ).

cnf(refute_0_655,plain,
    negative_part(least_upper_bound(identity,X_17)) = negative_part(least_upper_bound(identity,X_17)),
    introduced(tautology,[refl,[$fot(negative_part(least_upper_bound(identity,X_17)))]]) ).

cnf(refute_0_656,plain,
    ( least_upper_bound(identity,X_17) != positive_part(X_17)
    | negative_part(least_upper_bound(identity,X_17)) != negative_part(least_upper_bound(identity,X_17))
    | negative_part(least_upper_bound(identity,X_17)) = negative_part(positive_part(X_17)) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(identity,X_17)),negative_part(least_upper_bound(identity,X_17))) ),[1,0],$fot(positive_part(X_17))]]) ).

cnf(refute_0_657,plain,
    ( least_upper_bound(identity,X_17) != positive_part(X_17)
    | negative_part(least_upper_bound(identity,X_17)) = negative_part(positive_part(X_17)) ),
    inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(identity,X_17)),negative_part(least_upper_bound(identity,X_17))) )],[refute_0_655,refute_0_656]) ).

cnf(refute_0_658,plain,
    negative_part(least_upper_bound(identity,X_17)) = negative_part(positive_part(X_17)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_17),positive_part(X_17)) )],[refute_0_654,refute_0_657]) ).

cnf(refute_0_659,plain,
    ( negative_part(least_upper_bound(identity,X_17)) != identity
    | negative_part(least_upper_bound(identity,X_17)) != negative_part(positive_part(X_17))
    | negative_part(positive_part(X_17)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(identity,X_17)),identity) ),[0],$fot(negative_part(positive_part(X_17)))]]) ).

cnf(refute_0_660,plain,
    ( negative_part(least_upper_bound(identity,X_17)) != identity
    | negative_part(positive_part(X_17)) = identity ),
    inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(identity,X_17)),negative_part(positive_part(X_17))) )],[refute_0_658,refute_0_659]) ).

cnf(refute_0_661,plain,
    negative_part(positive_part(X_17)) = identity,
    inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(identity,X_17)),identity) )],[refute_0_653,refute_0_660]) ).

cnf(refute_0_662,plain,
    ( negative_part(greatest_lower_bound(positive_part(X_17),X_41)) != greatest_lower_bound(negative_part(positive_part(X_17)),X_41)
    | negative_part(positive_part(X_17)) != identity
    | negative_part(greatest_lower_bound(positive_part(X_17),X_41)) = greatest_lower_bound(identity,X_41) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_17),X_41)),greatest_lower_bound(negative_part(positive_part(X_17)),X_41)) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_663,plain,
    ( negative_part(greatest_lower_bound(positive_part(X_17),X_41)) != greatest_lower_bound(negative_part(positive_part(X_17)),X_41)
    | negative_part(greatest_lower_bound(positive_part(X_17),X_41)) = greatest_lower_bound(identity,X_41) ),
    inference(resolve,[$cnf( $equal(negative_part(positive_part(X_17)),identity) )],[refute_0_661,refute_0_662]) ).

cnf(refute_0_664,plain,
    negative_part(greatest_lower_bound(positive_part(X_17),X_41)) = greatest_lower_bound(identity,X_41),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_17),X_41)),greatest_lower_bound(negative_part(positive_part(X_17)),X_41)) )],[refute_0_648,refute_0_663]) ).

cnf(refute_0_665,plain,
    greatest_lower_bound(identity,X_41) = negative_part(X_41),
    inference(subst,[],[refute_0_293:[bind(X,$fot(X_41))]]) ).

cnf(refute_0_666,plain,
    ( greatest_lower_bound(identity,X_41) != negative_part(X_41)
    | negative_part(greatest_lower_bound(positive_part(X_17),X_41)) != greatest_lower_bound(identity,X_41)
    | negative_part(greatest_lower_bound(positive_part(X_17),X_41)) = negative_part(X_41) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_17),X_41)),greatest_lower_bound(identity,X_41)) ),[1],$fot(negative_part(X_41))]]) ).

cnf(refute_0_667,plain,
    ( negative_part(greatest_lower_bound(positive_part(X_17),X_41)) != greatest_lower_bound(identity,X_41)
    | negative_part(greatest_lower_bound(positive_part(X_17),X_41)) = negative_part(X_41) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_41),negative_part(X_41)) )],[refute_0_665,refute_0_666]) ).

cnf(refute_0_668,plain,
    negative_part(greatest_lower_bound(positive_part(X_17),X_41)) = negative_part(X_41),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_17),X_41)),greatest_lower_bound(identity,X_41)) )],[refute_0_664,refute_0_667]) ).

cnf(refute_0_669,plain,
    negative_part(greatest_lower_bound(positive_part(X_104),X_105)) = negative_part(X_105),
    inference(subst,[],[refute_0_668:[bind(X_17,$fot(X_104)),bind(X_41,$fot(X_105))]]) ).

cnf(refute_0_670,plain,
    ( least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(greatest_lower_bound(positive_part(X_104),X_105))) != greatest_lower_bound(positive_part(X_104),X_105)
    | negative_part(greatest_lower_bound(positive_part(X_104),X_105)) != negative_part(X_105)
    | least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(X_105)) = greatest_lower_bound(positive_part(X_104),X_105) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(greatest_lower_bound(positive_part(X_104),X_105))),greatest_lower_bound(positive_part(X_104),X_105)) ),[0,1],$fot(negative_part(X_105))]]) ).

cnf(refute_0_671,plain,
    ( least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(greatest_lower_bound(positive_part(X_104),X_105))) != greatest_lower_bound(positive_part(X_104),X_105)
    | least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(X_105)) = greatest_lower_bound(positive_part(X_104),X_105) ),
    inference(resolve,[$cnf( $equal(negative_part(greatest_lower_bound(positive_part(X_104),X_105)),negative_part(X_105)) )],[refute_0_669,refute_0_670]) ).

cnf(refute_0_672,plain,
    least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(X_105)) = greatest_lower_bound(positive_part(X_104),X_105),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(greatest_lower_bound(positive_part(X_104),X_105))),greatest_lower_bound(positive_part(X_104),X_105)) )],[refute_0_647,refute_0_671]) ).

cnf(refute_0_673,plain,
    least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(X_105)) = least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)),
    inference(subst,[],[refute_0_355:[bind(Y,$fot(negative_part(X_105))),bind(X_63,$fot(greatest_lower_bound(positive_part(X_104),X_105)))]]) ).

cnf(refute_0_674,plain,
    ( least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(X_105)) != greatest_lower_bound(positive_part(X_104),X_105)
    | least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(X_105)) != least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105))
    | least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)) = greatest_lower_bound(positive_part(X_104),X_105) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(X_105)),greatest_lower_bound(positive_part(X_104),X_105)) ),[0],$fot(least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)))]]) ).

cnf(refute_0_675,plain,
    ( least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(X_105)) != greatest_lower_bound(positive_part(X_104),X_105)
    | least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)) = greatest_lower_bound(positive_part(X_104),X_105) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(X_105)),least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105))) )],[refute_0_673,refute_0_674]) ).

cnf(refute_0_676,plain,
    least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)) = greatest_lower_bound(positive_part(X_104),X_105),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(positive_part(X_104),X_105),negative_part(X_105)),greatest_lower_bound(positive_part(X_104),X_105)) )],[refute_0_672,refute_0_675]) ).

cnf(refute_0_677,plain,
    least_upper_bound(identity,least_upper_bound(X_45,X_46)) = least_upper_bound(least_upper_bound(identity,X_45),X_46),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_45)),bind(Z,$fot(X_46))]]) ).

cnf(refute_0_678,plain,
    positive_part(X_45) = least_upper_bound(identity,X_45),
    inference(subst,[],[refute_0_369:[bind(X,$fot(X_45))]]) ).

cnf(refute_0_679,plain,
    ( positive_part(X_45) != least_upper_bound(identity,X_45)
    | least_upper_bound(identity,X_45) = positive_part(X_45) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(positive_part(X_45))),bind(Y0,$fot(least_upper_bound(identity,X_45)))]]) ).

cnf(refute_0_680,plain,
    least_upper_bound(identity,X_45) = positive_part(X_45),
    inference(resolve,[$cnf( $equal(positive_part(X_45),least_upper_bound(identity,X_45)) )],[refute_0_678,refute_0_679]) ).

cnf(refute_0_681,plain,
    ( least_upper_bound(identity,X_45) != positive_part(X_45)
    | least_upper_bound(identity,least_upper_bound(X_45,X_46)) != least_upper_bound(least_upper_bound(identity,X_45),X_46)
    | least_upper_bound(identity,least_upper_bound(X_45,X_46)) = least_upper_bound(positive_part(X_45),X_46) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_45,X_46)),least_upper_bound(least_upper_bound(identity,X_45),X_46)) ),[1,0],$fot(positive_part(X_45))]]) ).

cnf(refute_0_682,plain,
    ( least_upper_bound(identity,least_upper_bound(X_45,X_46)) != least_upper_bound(least_upper_bound(identity,X_45),X_46)
    | least_upper_bound(identity,least_upper_bound(X_45,X_46)) = least_upper_bound(positive_part(X_45),X_46) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_45),positive_part(X_45)) )],[refute_0_680,refute_0_681]) ).

cnf(refute_0_683,plain,
    least_upper_bound(identity,least_upper_bound(X_45,X_46)) = least_upper_bound(positive_part(X_45),X_46),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_45,X_46)),least_upper_bound(least_upper_bound(identity,X_45),X_46)) )],[refute_0_677,refute_0_682]) ).

cnf(refute_0_684,plain,
    least_upper_bound(identity,least_upper_bound(X_45,X_46)) = positive_part(least_upper_bound(X_45,X_46)),
    inference(subst,[],[refute_0_371:[bind(X,$fot(least_upper_bound(X_45,X_46)))]]) ).

cnf(refute_0_685,plain,
    ( least_upper_bound(identity,least_upper_bound(X_45,X_46)) != least_upper_bound(positive_part(X_45),X_46)
    | least_upper_bound(identity,least_upper_bound(X_45,X_46)) != positive_part(least_upper_bound(X_45,X_46))
    | positive_part(least_upper_bound(X_45,X_46)) = least_upper_bound(positive_part(X_45),X_46) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_45,X_46)),least_upper_bound(positive_part(X_45),X_46)) ),[0],$fot(positive_part(least_upper_bound(X_45,X_46)))]]) ).

cnf(refute_0_686,plain,
    ( least_upper_bound(identity,least_upper_bound(X_45,X_46)) != least_upper_bound(positive_part(X_45),X_46)
    | positive_part(least_upper_bound(X_45,X_46)) = least_upper_bound(positive_part(X_45),X_46) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_45,X_46)),positive_part(least_upper_bound(X_45,X_46))) )],[refute_0_684,refute_0_685]) ).

cnf(refute_0_687,plain,
    positive_part(least_upper_bound(X_45,X_46)) = least_upper_bound(positive_part(X_45),X_46),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_45,X_46)),least_upper_bound(positive_part(X_45),X_46)) )],[refute_0_683,refute_0_686]) ).

cnf(refute_0_688,plain,
    positive_part(least_upper_bound(negative_part(X_23),X_83)) = least_upper_bound(positive_part(negative_part(X_23)),X_83),
    inference(subst,[],[refute_0_687:[bind(X_45,$fot(negative_part(X_23))),bind(X_46,$fot(X_83))]]) ).

cnf(refute_0_689,plain,
    positive_part(greatest_lower_bound(identity,X_23)) = least_upper_bound(identity,greatest_lower_bound(identity,X_23)),
    inference(subst,[],[refute_0_369:[bind(X,$fot(greatest_lower_bound(identity,X_23)))]]) ).

cnf(refute_0_690,plain,
    least_upper_bound(identity,greatest_lower_bound(identity,X_23)) = identity,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_23))]]) ).

cnf(refute_0_691,plain,
    ( least_upper_bound(identity,greatest_lower_bound(identity,X_23)) != identity
    | positive_part(greatest_lower_bound(identity,X_23)) != least_upper_bound(identity,greatest_lower_bound(identity,X_23))
    | positive_part(greatest_lower_bound(identity,X_23)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_23)),least_upper_bound(identity,greatest_lower_bound(identity,X_23))) ),[1],$fot(identity)]]) ).

cnf(refute_0_692,plain,
    ( positive_part(greatest_lower_bound(identity,X_23)) != least_upper_bound(identity,greatest_lower_bound(identity,X_23))
    | positive_part(greatest_lower_bound(identity,X_23)) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_23)),identity) )],[refute_0_690,refute_0_691]) ).

cnf(refute_0_693,plain,
    positive_part(greatest_lower_bound(identity,X_23)) = identity,
    inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_23)),least_upper_bound(identity,greatest_lower_bound(identity,X_23))) )],[refute_0_689,refute_0_692]) ).

cnf(refute_0_694,plain,
    greatest_lower_bound(identity,X_23) = negative_part(X_23),
    inference(subst,[],[refute_0_293:[bind(X,$fot(X_23))]]) ).

cnf(refute_0_695,plain,
    positive_part(greatest_lower_bound(identity,X_23)) = positive_part(greatest_lower_bound(identity,X_23)),
    introduced(tautology,[refl,[$fot(positive_part(greatest_lower_bound(identity,X_23)))]]) ).

cnf(refute_0_696,plain,
    ( greatest_lower_bound(identity,X_23) != negative_part(X_23)
    | positive_part(greatest_lower_bound(identity,X_23)) != positive_part(greatest_lower_bound(identity,X_23))
    | positive_part(greatest_lower_bound(identity,X_23)) = positive_part(negative_part(X_23)) ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_23)),positive_part(greatest_lower_bound(identity,X_23))) ),[1,0],$fot(negative_part(X_23))]]) ).

cnf(refute_0_697,plain,
    ( greatest_lower_bound(identity,X_23) != negative_part(X_23)
    | positive_part(greatest_lower_bound(identity,X_23)) = positive_part(negative_part(X_23)) ),
    inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_23)),positive_part(greatest_lower_bound(identity,X_23))) )],[refute_0_695,refute_0_696]) ).

cnf(refute_0_698,plain,
    positive_part(greatest_lower_bound(identity,X_23)) = positive_part(negative_part(X_23)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_23),negative_part(X_23)) )],[refute_0_694,refute_0_697]) ).

cnf(refute_0_699,plain,
    ( positive_part(greatest_lower_bound(identity,X_23)) != identity
    | positive_part(greatest_lower_bound(identity,X_23)) != positive_part(negative_part(X_23))
    | positive_part(negative_part(X_23)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_23)),identity) ),[0],$fot(positive_part(negative_part(X_23)))]]) ).

cnf(refute_0_700,plain,
    ( positive_part(greatest_lower_bound(identity,X_23)) != identity
    | positive_part(negative_part(X_23)) = identity ),
    inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_23)),positive_part(negative_part(X_23))) )],[refute_0_698,refute_0_699]) ).

cnf(refute_0_701,plain,
    positive_part(negative_part(X_23)) = identity,
    inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(identity,X_23)),identity) )],[refute_0_693,refute_0_700]) ).

cnf(refute_0_702,plain,
    ( positive_part(least_upper_bound(negative_part(X_23),X_83)) != least_upper_bound(positive_part(negative_part(X_23)),X_83)
    | positive_part(negative_part(X_23)) != identity
    | positive_part(least_upper_bound(negative_part(X_23),X_83)) = least_upper_bound(identity,X_83) ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(least_upper_bound(negative_part(X_23),X_83)),least_upper_bound(positive_part(negative_part(X_23)),X_83)) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_703,plain,
    ( positive_part(least_upper_bound(negative_part(X_23),X_83)) != least_upper_bound(positive_part(negative_part(X_23)),X_83)
    | positive_part(least_upper_bound(negative_part(X_23),X_83)) = least_upper_bound(identity,X_83) ),
    inference(resolve,[$cnf( $equal(positive_part(negative_part(X_23)),identity) )],[refute_0_701,refute_0_702]) ).

cnf(refute_0_704,plain,
    positive_part(least_upper_bound(negative_part(X_23),X_83)) = least_upper_bound(identity,X_83),
    inference(resolve,[$cnf( $equal(positive_part(least_upper_bound(negative_part(X_23),X_83)),least_upper_bound(positive_part(negative_part(X_23)),X_83)) )],[refute_0_688,refute_0_703]) ).

cnf(refute_0_705,plain,
    least_upper_bound(identity,X_83) = positive_part(X_83),
    inference(subst,[],[refute_0_371:[bind(X,$fot(X_83))]]) ).

cnf(refute_0_706,plain,
    ( least_upper_bound(identity,X_83) != positive_part(X_83)
    | positive_part(least_upper_bound(negative_part(X_23),X_83)) != least_upper_bound(identity,X_83)
    | positive_part(least_upper_bound(negative_part(X_23),X_83)) = positive_part(X_83) ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(least_upper_bound(negative_part(X_23),X_83)),least_upper_bound(identity,X_83)) ),[1],$fot(positive_part(X_83))]]) ).

cnf(refute_0_707,plain,
    ( positive_part(least_upper_bound(negative_part(X_23),X_83)) != least_upper_bound(identity,X_83)
    | positive_part(least_upper_bound(negative_part(X_23),X_83)) = positive_part(X_83) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_83),positive_part(X_83)) )],[refute_0_705,refute_0_706]) ).

cnf(refute_0_708,plain,
    positive_part(least_upper_bound(negative_part(X_23),X_83)) = positive_part(X_83),
    inference(resolve,[$cnf( $equal(positive_part(least_upper_bound(negative_part(X_23),X_83)),least_upper_bound(identity,X_83)) )],[refute_0_704,refute_0_707]) ).

cnf(refute_0_709,plain,
    positive_part(least_upper_bound(negative_part(X_105),X_104)) = positive_part(X_104),
    inference(subst,[],[refute_0_708:[bind(X_23,$fot(X_105)),bind(X_83,$fot(X_104))]]) ).

cnf(refute_0_710,plain,
    positive_part(least_upper_bound(X_44,X_45)) = least_upper_bound(least_upper_bound(X_44,X_45),identity),
    inference(subst,[],[lat4_4:[bind(X,$fot(least_upper_bound(X_44,X_45)))]]) ).

cnf(refute_0_711,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(least_upper_bound(X_44,X_45),identity),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_712,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,identity)) != least_upper_bound(least_upper_bound(X_44,X_45),identity)
    | least_upper_bound(least_upper_bound(X_44,X_45),identity) = least_upper_bound(X_44,least_upper_bound(X_45,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_44,least_upper_bound(X_45,identity)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_44,X_45),identity)))]]) ).

cnf(refute_0_713,plain,
    least_upper_bound(least_upper_bound(X_44,X_45),identity) = least_upper_bound(X_44,least_upper_bound(X_45,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,identity)),least_upper_bound(least_upper_bound(X_44,X_45),identity)) )],[refute_0_711,refute_0_712]) ).

cnf(refute_0_714,plain,
    ( least_upper_bound(least_upper_bound(X_44,X_45),identity) != least_upper_bound(X_44,least_upper_bound(X_45,identity))
    | positive_part(least_upper_bound(X_44,X_45)) != least_upper_bound(least_upper_bound(X_44,X_45),identity)
    | positive_part(least_upper_bound(X_44,X_45)) = least_upper_bound(X_44,least_upper_bound(X_45,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(least_upper_bound(X_44,X_45)),least_upper_bound(least_upper_bound(X_44,X_45),identity)) ),[1],$fot(least_upper_bound(X_44,least_upper_bound(X_45,identity)))]]) ).

cnf(refute_0_715,plain,
    ( positive_part(least_upper_bound(X_44,X_45)) != least_upper_bound(least_upper_bound(X_44,X_45),identity)
    | positive_part(least_upper_bound(X_44,X_45)) = least_upper_bound(X_44,least_upper_bound(X_45,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_44,X_45),identity),least_upper_bound(X_44,least_upper_bound(X_45,identity))) )],[refute_0_713,refute_0_714]) ).

cnf(refute_0_716,plain,
    positive_part(least_upper_bound(X_44,X_45)) = least_upper_bound(X_44,least_upper_bound(X_45,identity)),
    inference(resolve,[$cnf( $equal(positive_part(least_upper_bound(X_44,X_45)),least_upper_bound(least_upper_bound(X_44,X_45),identity)) )],[refute_0_710,refute_0_715]) ).

cnf(refute_0_717,plain,
    least_upper_bound(X_45,identity) = positive_part(X_45),
    inference(subst,[],[refute_0_52:[bind(X,$fot(X_45))]]) ).

cnf(refute_0_718,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(X_44,least_upper_bound(X_45,identity)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_44,least_upper_bound(X_45,identity)))]]) ).

cnf(refute_0_719,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,identity)) != least_upper_bound(X_44,least_upper_bound(X_45,identity))
    | least_upper_bound(X_45,identity) != positive_part(X_45)
    | least_upper_bound(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(X_44,positive_part(X_45)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,identity)),least_upper_bound(X_44,least_upper_bound(X_45,identity))) ),[1,1],$fot(positive_part(X_45))]]) ).

cnf(refute_0_720,plain,
    ( least_upper_bound(X_45,identity) != positive_part(X_45)
    | least_upper_bound(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(X_44,positive_part(X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,identity)),least_upper_bound(X_44,least_upper_bound(X_45,identity))) )],[refute_0_718,refute_0_719]) ).

cnf(refute_0_721,plain,
    least_upper_bound(X_44,least_upper_bound(X_45,identity)) = least_upper_bound(X_44,positive_part(X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,identity),positive_part(X_45)) )],[refute_0_717,refute_0_720]) ).

cnf(refute_0_722,plain,
    ( least_upper_bound(X_44,least_upper_bound(X_45,identity)) != least_upper_bound(X_44,positive_part(X_45))
    | positive_part(least_upper_bound(X_44,X_45)) != least_upper_bound(X_44,least_upper_bound(X_45,identity))
    | positive_part(least_upper_bound(X_44,X_45)) = least_upper_bound(X_44,positive_part(X_45)) ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(least_upper_bound(X_44,X_45)),least_upper_bound(X_44,least_upper_bound(X_45,identity))) ),[1],$fot(least_upper_bound(X_44,positive_part(X_45)))]]) ).

cnf(refute_0_723,plain,
    ( positive_part(least_upper_bound(X_44,X_45)) != least_upper_bound(X_44,least_upper_bound(X_45,identity))
    | positive_part(least_upper_bound(X_44,X_45)) = least_upper_bound(X_44,positive_part(X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_45,identity)),least_upper_bound(X_44,positive_part(X_45))) )],[refute_0_721,refute_0_722]) ).

cnf(refute_0_724,plain,
    positive_part(least_upper_bound(X_44,X_45)) = least_upper_bound(X_44,positive_part(X_45)),
    inference(resolve,[$cnf( $equal(positive_part(least_upper_bound(X_44,X_45)),least_upper_bound(X_44,least_upper_bound(X_45,identity))) )],[refute_0_716,refute_0_723]) ).

cnf(refute_0_725,plain,
    ( positive_part(least_upper_bound(X_44,X_45)) != least_upper_bound(X_44,positive_part(X_45))
    | least_upper_bound(X_44,positive_part(X_45)) = positive_part(least_upper_bound(X_44,X_45)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(positive_part(least_upper_bound(X_44,X_45)))),bind(Y0,$fot(least_upper_bound(X_44,positive_part(X_45))))]]) ).

cnf(refute_0_726,plain,
    least_upper_bound(X_44,positive_part(X_45)) = positive_part(least_upper_bound(X_44,X_45)),
    inference(resolve,[$cnf( $equal(positive_part(least_upper_bound(X_44,X_45)),least_upper_bound(X_44,positive_part(X_45))) )],[refute_0_724,refute_0_725]) ).

cnf(refute_0_727,plain,
    least_upper_bound(negative_part(X_105),positive_part(X_104)) = positive_part(least_upper_bound(negative_part(X_105),X_104)),
    inference(subst,[],[refute_0_726:[bind(X_44,$fot(negative_part(X_105))),bind(X_45,$fot(X_104))]]) ).

cnf(refute_0_728,plain,
    ( least_upper_bound(negative_part(X_105),positive_part(X_104)) != positive_part(least_upper_bound(negative_part(X_105),X_104))
    | positive_part(least_upper_bound(negative_part(X_105),X_104)) != positive_part(X_104)
    | least_upper_bound(negative_part(X_105),positive_part(X_104)) = positive_part(X_104) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(negative_part(X_105),positive_part(X_104)))),bind(Y0,$fot(positive_part(least_upper_bound(negative_part(X_105),X_104)))),bind(Z0,$fot(positive_part(X_104)))]]) ).

cnf(refute_0_729,plain,
    ( positive_part(least_upper_bound(negative_part(X_105),X_104)) != positive_part(X_104)
    | least_upper_bound(negative_part(X_105),positive_part(X_104)) = positive_part(X_104) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_105),positive_part(X_104)),positive_part(least_upper_bound(negative_part(X_105),X_104))) )],[refute_0_727,refute_0_728]) ).

cnf(refute_0_730,plain,
    least_upper_bound(negative_part(X_105),positive_part(X_104)) = positive_part(X_104),
    inference(resolve,[$cnf( $equal(positive_part(least_upper_bound(negative_part(X_105),X_104)),positive_part(X_104)) )],[refute_0_709,refute_0_729]) ).

cnf(refute_0_731,plain,
    greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))) = greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))))]]) ).

cnf(refute_0_732,plain,
    ( greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))) != greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104)))
    | least_upper_bound(negative_part(X_105),positive_part(X_104)) != positive_part(X_104)
    | greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))) = greatest_lower_bound(X_105,positive_part(X_104)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))),greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104)))) ),[1,1],$fot(positive_part(X_104))]]) ).

cnf(refute_0_733,plain,
    ( least_upper_bound(negative_part(X_105),positive_part(X_104)) != positive_part(X_104)
    | greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))) = greatest_lower_bound(X_105,positive_part(X_104)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))),greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104)))) )],[refute_0_731,refute_0_732]) ).

cnf(refute_0_734,plain,
    greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))) = greatest_lower_bound(X_105,positive_part(X_104)),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_105),positive_part(X_104)),positive_part(X_104)) )],[refute_0_730,refute_0_733]) ).

cnf(refute_0_735,plain,
    greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,least_upper_bound(negative_part(X_50),X_46))) = least_upper_bound(negative_part(X_50),X_46),
    inference(subst,[],[refute_0_241:[bind(X_16,$fot(least_upper_bound(negative_part(X_50),X_46))),bind(X_17,$fot(X_50))]]) ).

cnf(refute_0_736,plain,
    least_upper_bound(X_50,least_upper_bound(negative_part(X_50),X_46)) = least_upper_bound(X_50,X_46),
    inference(subst,[],[refute_0_202:[bind(X_44,$fot(X_50))]]) ).

cnf(refute_0_737,plain,
    ( greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,least_upper_bound(negative_part(X_50),X_46))) != least_upper_bound(negative_part(X_50),X_46)
    | least_upper_bound(X_50,least_upper_bound(negative_part(X_50),X_46)) != least_upper_bound(X_50,X_46)
    | greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,X_46)) = least_upper_bound(negative_part(X_50),X_46) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,least_upper_bound(negative_part(X_50),X_46))),least_upper_bound(negative_part(X_50),X_46)) ),[0,1],$fot(least_upper_bound(X_50,X_46))]]) ).

cnf(refute_0_738,plain,
    ( greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,least_upper_bound(negative_part(X_50),X_46))) != least_upper_bound(negative_part(X_50),X_46)
    | greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,X_46)) = least_upper_bound(negative_part(X_50),X_46) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(negative_part(X_50),X_46)),least_upper_bound(X_50,X_46)) )],[refute_0_736,refute_0_737]) ).

cnf(refute_0_739,plain,
    greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,X_46)) = least_upper_bound(negative_part(X_50),X_46),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,least_upper_bound(negative_part(X_50),X_46))),least_upper_bound(negative_part(X_50),X_46)) )],[refute_0_735,refute_0_738]) ).

cnf(refute_0_740,plain,
    greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,X_46)) = greatest_lower_bound(least_upper_bound(X_50,X_46),least_upper_bound(negative_part(X_50),X_46)),
    inference(subst,[],[refute_0_473:[bind(X,$fot(least_upper_bound(X_50,X_46))),bind(Y,$fot(least_upper_bound(negative_part(X_50),X_46)))]]) ).

cnf(refute_0_741,plain,
    ( greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,X_46)) != greatest_lower_bound(least_upper_bound(X_50,X_46),least_upper_bound(negative_part(X_50),X_46))
    | greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,X_46)) != least_upper_bound(negative_part(X_50),X_46)
    | greatest_lower_bound(least_upper_bound(X_50,X_46),least_upper_bound(negative_part(X_50),X_46)) = least_upper_bound(negative_part(X_50),X_46) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,X_46)),least_upper_bound(negative_part(X_50),X_46)) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_50,X_46),least_upper_bound(negative_part(X_50),X_46)))]]) ).

cnf(refute_0_742,plain,
    ( greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,X_46)) != least_upper_bound(negative_part(X_50),X_46)
    | greatest_lower_bound(least_upper_bound(X_50,X_46),least_upper_bound(negative_part(X_50),X_46)) = least_upper_bound(negative_part(X_50),X_46) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,X_46)),greatest_lower_bound(least_upper_bound(X_50,X_46),least_upper_bound(negative_part(X_50),X_46))) )],[refute_0_740,refute_0_741]) ).

cnf(refute_0_743,plain,
    greatest_lower_bound(least_upper_bound(X_50,X_46),least_upper_bound(negative_part(X_50),X_46)) = least_upper_bound(negative_part(X_50),X_46),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(negative_part(X_50),X_46),least_upper_bound(X_50,X_46)),least_upper_bound(negative_part(X_50),X_46)) )],[refute_0_739,refute_0_742]) ).

cnf(refute_0_744,plain,
    greatest_lower_bound(least_upper_bound(X_87,greatest_lower_bound(X_23,X_87)),least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) = least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87)),
    inference(subst,[],[refute_0_743:[bind(X_46,$fot(greatest_lower_bound(X_23,X_87))),bind(X_50,$fot(X_87))]]) ).

cnf(refute_0_745,plain,
    least_upper_bound(X_87,greatest_lower_bound(X_23,X_87)) = X_87,
    inference(subst,[],[refute_0_66:[bind(X_22,$fot(X_87))]]) ).

cnf(refute_0_746,plain,
    ( greatest_lower_bound(least_upper_bound(X_87,greatest_lower_bound(X_23,X_87)),least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) != least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))
    | least_upper_bound(X_87,greatest_lower_bound(X_23,X_87)) != X_87
    | greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) = least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_87,greatest_lower_bound(X_23,X_87)),least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))),least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) ),[0,0],$fot(X_87)]]) ).

cnf(refute_0_747,plain,
    ( greatest_lower_bound(least_upper_bound(X_87,greatest_lower_bound(X_23,X_87)),least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) != least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))
    | greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) = least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_87,greatest_lower_bound(X_23,X_87)),X_87) )],[refute_0_745,refute_0_746]) ).

cnf(refute_0_748,plain,
    greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) = least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_87,greatest_lower_bound(X_23,X_87)),least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))),least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) )],[refute_0_744,refute_0_747]) ).

cnf(refute_0_749,plain,
    greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,X_201)),
    inference(subst,[],[lat4_7:[bind(X,$fot(X_199)),bind(Y,$fot(X_200)),bind(Z,$fot(X_201))]]) ).

cnf(refute_0_750,plain,
    greatest_lower_bound(X_201,X_199) = greatest_lower_bound(X_199,X_201),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_201)),bind(Y,$fot(X_199))]]) ).

cnf(refute_0_751,plain,
    ( greatest_lower_bound(X_201,X_199) != greatest_lower_bound(X_199,X_201)
    | greatest_lower_bound(X_199,X_201) = greatest_lower_bound(X_201,X_199) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_201,X_199))),bind(Y0,$fot(greatest_lower_bound(X_199,X_201)))]]) ).

cnf(refute_0_752,plain,
    greatest_lower_bound(X_199,X_201) = greatest_lower_bound(X_201,X_199),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_201,X_199),greatest_lower_bound(X_199,X_201)) )],[refute_0_750,refute_0_751]) ).

cnf(refute_0_753,plain,
    ( greatest_lower_bound(X_199,X_201) != greatest_lower_bound(X_201,X_199)
    | greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,X_201))
    | greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_201,X_199)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,X_201))) ),[1,1],$fot(greatest_lower_bound(X_201,X_199))]]) ).

cnf(refute_0_754,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,X_201))
    | greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_201,X_199)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,X_201),greatest_lower_bound(X_201,X_199)) )],[refute_0_752,refute_0_753]) ).

cnf(refute_0_755,plain,
    greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_201,X_199)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,X_201))) )],[refute_0_749,refute_0_754]) ).

cnf(refute_0_756,plain,
    greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))) = least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199))),
    inference(subst,[],[lat4_7:[bind(X,$fot(X_199)),bind(Y,$fot(X_200)),bind(Z,$fot(greatest_lower_bound(X_36,X_199)))]]) ).

cnf(refute_0_757,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(greatest_lower_bound(X_36,X_37))),bind(Y,$fot(X_36)),bind(Z,$fot(X_37))]]) ).

cnf(refute_0_758,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,X_37),
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(greatest_lower_bound(X_36,X_37)))]]) ).

cnf(refute_0_759,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,X_37)
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37)
    | greatest_lower_bound(X_36,X_37) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37)) ),[0],$fot(greatest_lower_bound(X_36,X_37))]]) ).

cnf(refute_0_760,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37)
    | greatest_lower_bound(X_36,X_37) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,X_37)) )],[refute_0_758,refute_0_759]) ).

cnf(refute_0_761,plain,
    greatest_lower_bound(X_36,X_37) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37)) )],[refute_0_757,refute_0_760]) ).

cnf(refute_0_762,plain,
    greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_35)),bind(Y,$fot(X_36)),bind(Z,$fot(X_37))]]) ).

cnf(refute_0_763,plain,
    greatest_lower_bound(X_37,X_36) = greatest_lower_bound(X_36,X_37),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_37)),bind(Y,$fot(X_36))]]) ).

cnf(refute_0_764,plain,
    ( greatest_lower_bound(X_37,X_36) != greatest_lower_bound(X_36,X_37)
    | greatest_lower_bound(X_36,X_37) = greatest_lower_bound(X_37,X_36) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_37,X_36))),bind(Y0,$fot(greatest_lower_bound(X_36,X_37)))]]) ).

cnf(refute_0_765,plain,
    greatest_lower_bound(X_36,X_37) = greatest_lower_bound(X_37,X_36),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,X_36),greatest_lower_bound(X_36,X_37)) )],[refute_0_763,refute_0_764]) ).

cnf(refute_0_766,plain,
    ( greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37)
    | greatest_lower_bound(X_36,X_37) != greatest_lower_bound(X_37,X_36)
    | greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)) = greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37)) ),[0,1],$fot(greatest_lower_bound(X_37,X_36))]]) ).

cnf(refute_0_767,plain,
    ( greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37)
    | greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)) = greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_37,X_36)) )],[refute_0_765,refute_0_766]) ).

cnf(refute_0_768,plain,
    greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)) = greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37)) )],[refute_0_762,refute_0_767]) ).

cnf(refute_0_769,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_18:[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_770,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_769]) ).

cnf(refute_0_771,plain,
    greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37)),
    inference(subst,[],[refute_0_770:[bind(X,$fot(X_35)),bind(Y,$fot(X_36)),bind(Z,$fot(X_37))]]) ).

cnf(refute_0_772,plain,
    ( greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)) != greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37)
    | greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37) != greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37))
    | greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)),greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37))]]) ).

cnf(refute_0_773,plain,
    ( greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)) != greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37)
    | greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37),greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37))) )],[refute_0_771,refute_0_772]) ).

cnf(refute_0_774,plain,
    greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)) = greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)),greatest_lower_bound(greatest_lower_bound(X_35,X_36),X_37)) )],[refute_0_768,refute_0_773]) ).

cnf(refute_0_775,plain,
    ( greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)) != greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37))
    | greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)))),bind(Y0,$fot(greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37))))]]) ).

cnf(refute_0_776,plain,
    greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_35,greatest_lower_bound(X_37,X_36)),greatest_lower_bound(X_35,greatest_lower_bound(X_36,X_37))) )],[refute_0_774,refute_0_775]) ).

cnf(refute_0_777,plain,
    greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))),
    inference(subst,[],[refute_0_776:[bind(X_35,$fot(X_37)),bind(X_36,$fot(greatest_lower_bound(X_36,X_37))),bind(X_37,$fot(X_36))]]) ).

cnf(refute_0_778,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)) != greatest_lower_bound(X_35,greatest_lower_bound(X_36,X))
    | greatest_lower_bound(X_35,greatest_lower_bound(X_36,X)) = greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)))),bind(Y0,$fot(greatest_lower_bound(X_35,greatest_lower_bound(X_36,X))))]]) ).

cnf(refute_0_779,plain,
    greatest_lower_bound(X_35,greatest_lower_bound(X_36,X)) = greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_35,X_36)),greatest_lower_bound(X_35,greatest_lower_bound(X_36,X))) )],[refute_0_265,refute_0_778]) ).

cnf(refute_0_780,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36)),
    inference(subst,[],[refute_0_779:[bind(X,$fot(X_37)),bind(X_35,$fot(greatest_lower_bound(X_36,X_37)))]]) ).

cnf(refute_0_781,plain,
    ( greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36))
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)))),bind(Y0,$fot(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36)))),bind(Z0,$fot(greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))))]]) ).

cnf(refute_0_782,plain,
    ( greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36))) )],[refute_0_780,refute_0_781]) ).

cnf(refute_0_783,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36)),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))) )],[refute_0_777,refute_0_782]) ).

cnf(refute_0_784,plain,
    greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)),
    inference(subst,[],[refute_0_770:[bind(X,$fot(greatest_lower_bound(X_36,X_37))),bind(Y,$fot(X_36)),bind(Z,$fot(X_37))]]) ).

cnf(refute_0_785,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))
    | greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37))
    | greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,X_37)))),bind(Z0,$fot(greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))))]]) ).

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

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

cnf(refute_0_788,plain,
    ( greatest_lower_bound(X_36,X_37) != greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37)
    | greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))
    | greatest_lower_bound(X_36,X_37) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37))]]) ).

cnf(refute_0_789,plain,
    ( greatest_lower_bound(X_36,X_37) != greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37)
    | greatest_lower_bound(X_36,X_37) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))) )],[refute_0_787,refute_0_788]) ).

cnf(refute_0_790,plain,
    greatest_lower_bound(X_36,X_37) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,X_37),greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_36),X_37)) )],[refute_0_761,refute_0_789]) ).

cnf(refute_0_791,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(greatest_lower_bound(X_36,X_36),X_37),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(X_36)),bind(Z,$fot(X_37))]]) ).

cnf(refute_0_792,plain,
    greatest_lower_bound(X_36,X_36) = X_36,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_36))]]) ).

cnf(refute_0_793,plain,
    ( greatest_lower_bound(X_36,X_36) != X_36
    | greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(X_36,X_36),X_37)
    | greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,X_37) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(greatest_lower_bound(X_36,X_36),X_37)) ),[1,0],$fot(X_36)]]) ).

cnf(refute_0_794,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(X_36,X_36),X_37)
    | greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,X_37) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,X_36),X_36) )],[refute_0_792,refute_0_793]) ).

cnf(refute_0_795,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,X_37),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(greatest_lower_bound(X_36,X_36),X_37)) )],[refute_0_791,refute_0_794]) ).

cnf(refute_0_796,plain,
    greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))))]]) ).

cnf(refute_0_797,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,X_37)
    | greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))
    | greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,X_37)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))) ),[1,1],$fot(greatest_lower_bound(X_36,X_37))]]) ).

cnf(refute_0_798,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,X_37)
    | greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,X_37)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))) )],[refute_0_796,refute_0_797]) ).

cnf(refute_0_799,plain,
    greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,X_37)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,X_37)) )],[refute_0_795,refute_0_798]) ).

cnf(refute_0_800,plain,
    ( greatest_lower_bound(X_36,X_37) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))
    | greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,X_37))
    | greatest_lower_bound(X_36,X_37) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,X_37)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_37,greatest_lower_bound(X_36,X_37))) ),[0],$fot(greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))))]]) ).

cnf(refute_0_801,plain,
    ( greatest_lower_bound(X_36,X_37) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))
    | greatest_lower_bound(X_36,X_37) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,X_37)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37))),greatest_lower_bound(X_37,greatest_lower_bound(X_36,X_37))) )],[refute_0_799,refute_0_800]) ).

cnf(refute_0_802,plain,
    greatest_lower_bound(X_36,X_37) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,X_37)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_36,X_37)))) )],[refute_0_790,refute_0_801]) ).

cnf(refute_0_803,plain,
    greatest_lower_bound(X_36,X_199) = greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)),
    inference(subst,[],[refute_0_802:[bind(X_37,$fot(X_199))]]) ).

cnf(refute_0_804,plain,
    ( greatest_lower_bound(X_36,X_199) != greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199))
    | greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)) = greatest_lower_bound(X_36,X_199) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_36,X_199))),bind(Y0,$fot(greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199))))]]) ).

cnf(refute_0_805,plain,
    greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)) = greatest_lower_bound(X_36,X_199),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,X_199),greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199))) )],[refute_0_803,refute_0_804]) ).

cnf(refute_0_806,plain,
    ( greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)) != greatest_lower_bound(X_36,X_199)
    | greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))) != least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)))
    | greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))) = least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_36,X_199)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))),least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)))) ),[1,1],$fot(greatest_lower_bound(X_36,X_199))]]) ).

cnf(refute_0_807,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))) != least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)))
    | greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))) = least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_36,X_199)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)),greatest_lower_bound(X_36,X_199)) )],[refute_0_805,refute_0_806]) ).

cnf(refute_0_808,plain,
    greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))) = least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_36,X_199)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))),least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)))) )],[refute_0_756,refute_0_807]) ).

cnf(refute_0_809,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))) != least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_36,X_199))
    | least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_36,X_199)) = greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_36,X_199))))]]) ).

cnf(refute_0_810,plain,
    least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_36,X_199)) = greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_36,X_199))),least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_36,X_199))) )],[refute_0_808,refute_0_809]) ).

cnf(refute_0_811,plain,
    least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_201,X_199)) = greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199))),
    inference(subst,[],[refute_0_810:[bind(X_36,$fot(X_201))]]) ).

cnf(refute_0_812,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_201,X_199))
    | least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_201,X_199)) != greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199)))
    | greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_201,X_199)))]]) ).

cnf(refute_0_813,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_201,X_199))
    | greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_201,X_199)),greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199)))) )],[refute_0_811,refute_0_812]) ).

cnf(refute_0_814,plain,
    greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_201,X_199))) )],[refute_0_755,refute_0_813]) ).

cnf(refute_0_815,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) != greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199)))
    | greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199))) = greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)))),bind(Y0,$fot(greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199)))))]]) ).

cnf(refute_0_816,plain,
    greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199))) = greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),greatest_lower_bound(X_199,least_upper_bound(X_200,greatest_lower_bound(X_201,X_199)))) )],[refute_0_814,refute_0_815]) ).

cnf(refute_0_817,plain,
    greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) = greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23)),
    inference(subst,[],[refute_0_816:[bind(X_199,$fot(X_87)),bind(X_200,$fot(negative_part(X_87))),bind(X_201,$fot(X_23))]]) ).

cnf(refute_0_818,plain,
    ( greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) != greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23))
    | greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) != least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))
    | greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23)) = least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))),least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) ),[0],$fot(greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23)))]]) ).

cnf(refute_0_819,plain,
    ( greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) != least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))
    | greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23)) = least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))),greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23))) )],[refute_0_817,refute_0_818]) ).

cnf(refute_0_820,plain,
    greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23)) = least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))),least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) )],[refute_0_748,refute_0_819]) ).

cnf(refute_0_821,plain,
    ( greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23)) != least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))
    | least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87)) = greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23)))),bind(Y0,$fot(least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))))]]) ).

cnf(refute_0_822,plain,
    least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87)) = greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_87,least_upper_bound(negative_part(X_87),X_23)),least_upper_bound(negative_part(X_87),greatest_lower_bound(X_23,X_87))) )],[refute_0_820,refute_0_821]) ).

cnf(refute_0_823,plain,
    least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)) = greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))),
    inference(subst,[],[refute_0_822:[bind(X_23,$fot(positive_part(X_104))),bind(X_87,$fot(X_105))]]) ).

cnf(refute_0_824,plain,
    ( greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))) != greatest_lower_bound(X_105,positive_part(X_104))
    | least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)) != greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104)))
    | least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)) = greatest_lower_bound(X_105,positive_part(X_104)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)))),bind(Y0,$fot(greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))))),bind(Z0,$fot(greatest_lower_bound(X_105,positive_part(X_104))))]]) ).

cnf(refute_0_825,plain,
    ( greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))) != greatest_lower_bound(X_105,positive_part(X_104))
    | least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)) = greatest_lower_bound(X_105,positive_part(X_104)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)),greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104)))) )],[refute_0_823,refute_0_824]) ).

cnf(refute_0_826,plain,
    least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)) = greatest_lower_bound(X_105,positive_part(X_104)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_105,least_upper_bound(negative_part(X_105),positive_part(X_104))),greatest_lower_bound(X_105,positive_part(X_104))) )],[refute_0_734,refute_0_825]) ).

cnf(refute_0_827,plain,
    ( least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)) != greatest_lower_bound(X_105,positive_part(X_104))
    | least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)) != greatest_lower_bound(positive_part(X_104),X_105)
    | greatest_lower_bound(X_105,positive_part(X_104)) = greatest_lower_bound(positive_part(X_104),X_105) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)),greatest_lower_bound(positive_part(X_104),X_105)) ),[0],$fot(greatest_lower_bound(X_105,positive_part(X_104)))]]) ).

cnf(refute_0_828,plain,
    ( least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)) != greatest_lower_bound(positive_part(X_104),X_105)
    | greatest_lower_bound(X_105,positive_part(X_104)) = greatest_lower_bound(positive_part(X_104),X_105) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)),greatest_lower_bound(X_105,positive_part(X_104))) )],[refute_0_826,refute_0_827]) ).

cnf(refute_0_829,plain,
    greatest_lower_bound(X_105,positive_part(X_104)) = greatest_lower_bound(positive_part(X_104),X_105),
    inference(resolve,[$cnf( $equal(least_upper_bound(negative_part(X_105),greatest_lower_bound(positive_part(X_104),X_105)),greatest_lower_bound(positive_part(X_104),X_105)) )],[refute_0_676,refute_0_828]) ).

cnf(refute_0_830,plain,
    greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)) = greatest_lower_bound(positive_part(X_230),positive_part(inverse(X_230))),
    inference(subst,[],[refute_0_829:[bind(X_104,$fot(X_230)),bind(X_105,$fot(positive_part(inverse(X_230))))]]) ).

cnf(refute_0_831,plain,
    ( greatest_lower_bound(positive_part(X_230),positive_part(inverse(X_230))) != negative_part(least_upper_bound(X_230,inverse(X_230)))
    | greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)) != greatest_lower_bound(positive_part(X_230),positive_part(inverse(X_230)))
    | greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)) = negative_part(least_upper_bound(X_230,inverse(X_230))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)))),bind(Y0,$fot(greatest_lower_bound(positive_part(X_230),positive_part(inverse(X_230))))),bind(Z0,$fot(negative_part(least_upper_bound(X_230,inverse(X_230)))))]]) ).

cnf(refute_0_832,plain,
    ( greatest_lower_bound(positive_part(X_230),positive_part(inverse(X_230))) != negative_part(least_upper_bound(X_230,inverse(X_230)))
    | greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)) = negative_part(least_upper_bound(X_230,inverse(X_230))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)),greatest_lower_bound(positive_part(X_230),positive_part(inverse(X_230)))) )],[refute_0_830,refute_0_831]) ).

cnf(refute_0_833,plain,
    greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)) = negative_part(least_upper_bound(X_230,inverse(X_230))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_230),positive_part(inverse(X_230))),negative_part(least_upper_bound(X_230,inverse(X_230)))) )],[refute_0_646,refute_0_832]) ).

cnf(refute_0_834,plain,
    least_upper_bound(positive_part(X_17),negative_part(positive_part(X_17))) = positive_part(X_17),
    inference(subst,[],[refute_0_85:[bind(X_22,$fot(positive_part(X_17)))]]) ).

cnf(refute_0_835,plain,
    ( least_upper_bound(positive_part(X_17),negative_part(positive_part(X_17))) != positive_part(X_17)
    | negative_part(positive_part(X_17)) != identity
    | least_upper_bound(positive_part(X_17),identity) = positive_part(X_17) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(positive_part(X_17),negative_part(positive_part(X_17))),positive_part(X_17)) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_836,plain,
    ( least_upper_bound(positive_part(X_17),negative_part(positive_part(X_17))) != positive_part(X_17)
    | least_upper_bound(positive_part(X_17),identity) = positive_part(X_17) ),
    inference(resolve,[$cnf( $equal(negative_part(positive_part(X_17)),identity) )],[refute_0_661,refute_0_835]) ).

cnf(refute_0_837,plain,
    least_upper_bound(positive_part(X_17),identity) = positive_part(X_17),
    inference(resolve,[$cnf( $equal(least_upper_bound(positive_part(X_17),negative_part(positive_part(X_17))),positive_part(X_17)) )],[refute_0_834,refute_0_836]) ).

cnf(refute_0_838,plain,
    least_upper_bound(positive_part(X_17),identity) = positive_part(positive_part(X_17)),
    inference(subst,[],[refute_0_52:[bind(X,$fot(positive_part(X_17)))]]) ).

cnf(refute_0_839,plain,
    ( least_upper_bound(positive_part(X_17),identity) != positive_part(X_17)
    | least_upper_bound(positive_part(X_17),identity) != positive_part(positive_part(X_17))
    | positive_part(positive_part(X_17)) = positive_part(X_17) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(positive_part(X_17),identity),positive_part(X_17)) ),[0],$fot(positive_part(positive_part(X_17)))]]) ).

cnf(refute_0_840,plain,
    ( least_upper_bound(positive_part(X_17),identity) != positive_part(X_17)
    | positive_part(positive_part(X_17)) = positive_part(X_17) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(positive_part(X_17),identity),positive_part(positive_part(X_17))) )],[refute_0_838,refute_0_839]) ).

cnf(refute_0_841,plain,
    positive_part(positive_part(X_17)) = positive_part(X_17),
    inference(resolve,[$cnf( $equal(least_upper_bound(positive_part(X_17),identity),positive_part(X_17)) )],[refute_0_837,refute_0_840]) ).

cnf(refute_0_842,plain,
    positive_part(positive_part(X_230)) = positive_part(X_230),
    inference(subst,[],[refute_0_841:[bind(X_17,$fot(X_230))]]) ).

cnf(refute_0_843,plain,
    greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))) = greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))))]]) ).

cnf(refute_0_844,plain,
    ( greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))) != greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230)))
    | positive_part(positive_part(X_230)) != positive_part(X_230)
    | greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))) = greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230)))) ),[1,1],$fot(positive_part(X_230))]]) ).

cnf(refute_0_845,plain,
    ( positive_part(positive_part(X_230)) != positive_part(X_230)
    | greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))) = greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230)))) )],[refute_0_843,refute_0_844]) ).

cnf(refute_0_846,plain,
    greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))) = greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)),
    inference(resolve,[$cnf( $equal(positive_part(positive_part(X_230)),positive_part(X_230)) )],[refute_0_842,refute_0_845]) ).

cnf(refute_0_847,plain,
    ( greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)) != negative_part(least_upper_bound(X_230,inverse(X_230)))
    | greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))) != greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230))
    | greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))) = negative_part(least_upper_bound(X_230,inverse(X_230))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))))),bind(Y0,$fot(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)))),bind(Z0,$fot(negative_part(least_upper_bound(X_230,inverse(X_230)))))]]) ).

cnf(refute_0_848,plain,
    ( greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)) != negative_part(least_upper_bound(X_230,inverse(X_230)))
    | greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))) = negative_part(least_upper_bound(X_230,inverse(X_230))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230))) )],[refute_0_846,refute_0_847]) ).

cnf(refute_0_849,plain,
    greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))) = negative_part(least_upper_bound(X_230,inverse(X_230))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(X_230)),negative_part(least_upper_bound(X_230,inverse(X_230)))) )],[refute_0_833,refute_0_848]) ).

cnf(refute_0_850,plain,
    multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))) = multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))))]]) ).

cnf(refute_0_851,plain,
    ( multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))) != multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230)))
    | greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))) != negative_part(least_upper_bound(X_230,inverse(X_230)))
    | multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))) = multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))),multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230)))) ),[1,0],$fot(negative_part(least_upper_bound(X_230,inverse(X_230))))]]) ).

cnf(refute_0_852,plain,
    ( greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))) != negative_part(least_upper_bound(X_230,inverse(X_230)))
    | multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))) = multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))),multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230)))) )],[refute_0_850,refute_0_851]) ).

cnf(refute_0_853,plain,
    multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))) = multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),negative_part(least_upper_bound(X_230,inverse(X_230)))) )],[refute_0_849,refute_0_852]) ).

cnf(refute_0_854,plain,
    multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) = greatest_lower_bound(multiply(X_187,inverse(X_170)),multiply(positive_part(X_170),inverse(X_170))),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_170))),bind(Y,$fot(X_187)),bind(Z,$fot(positive_part(X_170)))]]) ).

cnf(refute_0_855,plain,
    multiply(positive_part(X_170),inverse(X_170)) = least_upper_bound(inverse(X_170),multiply(X_170,inverse(X_170))),
    inference(subst,[],[refute_0_435:[bind(X_166,$fot(inverse(X_170))),bind(X_167,$fot(X_170))]]) ).

cnf(refute_0_856,plain,
    multiply(X_170,inverse(X_170)) = identity,
    inference(subst,[],[refute_0_5:[bind(X_1,$fot(X_170))]]) ).

cnf(refute_0_857,plain,
    ( multiply(X_170,inverse(X_170)) != identity
    | multiply(positive_part(X_170),inverse(X_170)) != least_upper_bound(inverse(X_170),multiply(X_170,inverse(X_170)))
    | multiply(positive_part(X_170),inverse(X_170)) = least_upper_bound(inverse(X_170),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(X_170),inverse(X_170)),least_upper_bound(inverse(X_170),multiply(X_170,inverse(X_170)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_858,plain,
    ( multiply(positive_part(X_170),inverse(X_170)) != least_upper_bound(inverse(X_170),multiply(X_170,inverse(X_170)))
    | multiply(positive_part(X_170),inverse(X_170)) = least_upper_bound(inverse(X_170),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_170,inverse(X_170)),identity) )],[refute_0_856,refute_0_857]) ).

cnf(refute_0_859,plain,
    multiply(positive_part(X_170),inverse(X_170)) = least_upper_bound(inverse(X_170),identity),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_170),inverse(X_170)),least_upper_bound(inverse(X_170),multiply(X_170,inverse(X_170)))) )],[refute_0_855,refute_0_858]) ).

cnf(refute_0_860,plain,
    least_upper_bound(identity,inverse(X_170)) = positive_part(inverse(X_170)),
    inference(subst,[],[refute_0_371:[bind(X,$fot(inverse(X_170)))]]) ).

cnf(refute_0_861,plain,
    least_upper_bound(inverse(X_170),identity) = least_upper_bound(identity,inverse(X_170)),
    inference(subst,[],[refute_0_355:[bind(Y,$fot(identity)),bind(X_63,$fot(inverse(X_170)))]]) ).

cnf(refute_0_862,plain,
    ( least_upper_bound(identity,inverse(X_170)) != positive_part(inverse(X_170))
    | least_upper_bound(inverse(X_170),identity) != least_upper_bound(identity,inverse(X_170))
    | least_upper_bound(inverse(X_170),identity) = positive_part(inverse(X_170)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(inverse(X_170),identity))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_170)))),bind(Z0,$fot(positive_part(inverse(X_170))))]]) ).

cnf(refute_0_863,plain,
    ( least_upper_bound(identity,inverse(X_170)) != positive_part(inverse(X_170))
    | least_upper_bound(inverse(X_170),identity) = positive_part(inverse(X_170)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_170),identity),least_upper_bound(identity,inverse(X_170))) )],[refute_0_861,refute_0_862]) ).

cnf(refute_0_864,plain,
    least_upper_bound(inverse(X_170),identity) = positive_part(inverse(X_170)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_170)),positive_part(inverse(X_170))) )],[refute_0_860,refute_0_863]) ).

cnf(refute_0_865,plain,
    ( multiply(positive_part(X_170),inverse(X_170)) != least_upper_bound(inverse(X_170),identity)
    | least_upper_bound(inverse(X_170),identity) != positive_part(inverse(X_170))
    | multiply(positive_part(X_170),inverse(X_170)) = positive_part(inverse(X_170)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(positive_part(X_170),inverse(X_170)),positive_part(inverse(X_170))) ),[0],$fot(least_upper_bound(inverse(X_170),identity))]]) ).

cnf(refute_0_866,plain,
    ( multiply(positive_part(X_170),inverse(X_170)) != least_upper_bound(inverse(X_170),identity)
    | multiply(positive_part(X_170),inverse(X_170)) = positive_part(inverse(X_170)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_170),identity),positive_part(inverse(X_170))) )],[refute_0_864,refute_0_865]) ).

cnf(refute_0_867,plain,
    multiply(positive_part(X_170),inverse(X_170)) = positive_part(inverse(X_170)),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_170),inverse(X_170)),least_upper_bound(inverse(X_170),identity)) )],[refute_0_859,refute_0_866]) ).

cnf(refute_0_868,plain,
    ( multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) != greatest_lower_bound(multiply(X_187,inverse(X_170)),multiply(positive_part(X_170),inverse(X_170)))
    | multiply(positive_part(X_170),inverse(X_170)) != positive_part(inverse(X_170))
    | multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) = greatest_lower_bound(multiply(X_187,inverse(X_170)),positive_part(inverse(X_170))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)),greatest_lower_bound(multiply(X_187,inverse(X_170)),multiply(positive_part(X_170),inverse(X_170)))) ),[1,1],$fot(positive_part(inverse(X_170)))]]) ).

cnf(refute_0_869,plain,
    ( multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) != greatest_lower_bound(multiply(X_187,inverse(X_170)),multiply(positive_part(X_170),inverse(X_170)))
    | multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) = greatest_lower_bound(multiply(X_187,inverse(X_170)),positive_part(inverse(X_170))) ),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_170),inverse(X_170)),positive_part(inverse(X_170))) )],[refute_0_867,refute_0_868]) ).

cnf(refute_0_870,plain,
    multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) = greatest_lower_bound(multiply(X_187,inverse(X_170)),positive_part(inverse(X_170))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)),greatest_lower_bound(multiply(X_187,inverse(X_170)),multiply(positive_part(X_170),inverse(X_170)))) )],[refute_0_854,refute_0_869]) ).

cnf(refute_0_871,plain,
    greatest_lower_bound(multiply(X_187,inverse(X_170)),positive_part(inverse(X_170))) = greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170))),
    inference(subst,[],[refute_0_473:[bind(X,$fot(positive_part(inverse(X_170)))),bind(Y,$fot(multiply(X_187,inverse(X_170))))]]) ).

cnf(refute_0_872,plain,
    ( multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) != greatest_lower_bound(multiply(X_187,inverse(X_170)),positive_part(inverse(X_170)))
    | greatest_lower_bound(multiply(X_187,inverse(X_170)),positive_part(inverse(X_170))) != greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170)))
    | multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) = greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)),greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170)))) ),[0],$fot(greatest_lower_bound(multiply(X_187,inverse(X_170)),positive_part(inverse(X_170))))]]) ).

cnf(refute_0_873,plain,
    ( multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) != greatest_lower_bound(multiply(X_187,inverse(X_170)),positive_part(inverse(X_170)))
    | multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) = greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_187,inverse(X_170)),positive_part(inverse(X_170))),greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170)))) )],[refute_0_871,refute_0_872]) ).

cnf(refute_0_874,plain,
    multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) = greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)),greatest_lower_bound(multiply(X_187,inverse(X_170)),positive_part(inverse(X_170)))) )],[refute_0_870,refute_0_873]) ).

cnf(refute_0_875,plain,
    ( multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) != greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170)))
    | greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170))) = multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)))),bind(Y0,$fot(greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170)))))]]) ).

cnf(refute_0_876,plain,
    greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170))) = multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_187,positive_part(X_170)),inverse(X_170)),greatest_lower_bound(positive_part(inverse(X_170)),multiply(X_187,inverse(X_170)))) )],[refute_0_874,refute_0_875]) ).

cnf(refute_0_877,plain,
    greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230)))) = multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))),
    inference(subst,[],[refute_0_876:[bind(X_170,$fot(positive_part(X_230))),bind(X_187,$fot(positive_part(inverse(X_230))))]]) ).

cnf(refute_0_878,plain,
    ( multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) != greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230))))
    | greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230)))) != multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230)))
    | multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) = multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))))),bind(Y0,$fot(greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230)))))),bind(Z0,$fot(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230)))))]]) ).

cnf(refute_0_879,plain,
    ( greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230)))) != multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230)))
    | multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) = multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))),greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230))))) )],[refute_0_478,refute_0_878]) ).

cnf(refute_0_880,plain,
    multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) = multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(inverse(positive_part(X_230))),multiply(positive_part(inverse(X_230)),inverse(positive_part(X_230)))),multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230)))) )],[refute_0_877,refute_0_879]) ).

cnf(refute_0_881,plain,
    ( multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) != multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230)))
    | multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))) != multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230)))
    | multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) = multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))))),bind(Y0,$fot(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))))),bind(Z0,$fot(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230)))))]]) ).

cnf(refute_0_882,plain,
    ( multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))) != multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230)))
    | multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) = multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))),multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230)))) )],[refute_0_880,refute_0_881]) ).

cnf(refute_0_883,plain,
    multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) = multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(positive_part(X_230))),inverse(positive_part(X_230))),multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230)))) )],[refute_0_853,refute_0_882]) ).

cnf(refute_0_884,plain,
    ( multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) != multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230)))
    | multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) != greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230))
    | multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))),greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230))) ),[0],$fot(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))))]]) ).

cnf(refute_0_885,plain,
    ( multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) != greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230))
    | multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))),multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230)))) )],[refute_0_883,refute_0_884]) ).

cnf(refute_0_886,plain,
    greatest_lower_bound(identity,inverse(X_230)) = negative_part(inverse(X_230)),
    inference(subst,[],[refute_0_293:[bind(X,$fot(inverse(X_230)))]]) ).

cnf(refute_0_887,plain,
    least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88))) = greatest_lower_bound(X_90,X_88),
    inference(subst,[],[refute_0_66:[bind(X_22,$fot(greatest_lower_bound(X_90,X_88)))]]) ).

cnf(refute_0_888,plain,
    greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90)) = greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88)),
    inference(subst,[],[refute_0_265:[bind(X,$fot(X_88)),bind(X_35,$fot(X_23)),bind(X_36,$fot(X_90))]]) ).

cnf(refute_0_889,plain,
    ( greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90)) != greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88))
    | greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88)) = greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90)))),bind(Y0,$fot(greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88))))]]) ).

cnf(refute_0_890,plain,
    greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88)) = greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90)),greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88))) )],[refute_0_888,refute_0_889]) ).

cnf(refute_0_891,plain,
    ( greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88)) != greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))
    | least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88))) != greatest_lower_bound(X_90,X_88)
    | least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_90,X_88) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88))),greatest_lower_bound(X_90,X_88)) ),[0,1],$fot(greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90)))]]) ).

cnf(refute_0_892,plain,
    ( least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88))) != greatest_lower_bound(X_90,X_88)
    | least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_90,X_88) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88)),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) )],[refute_0_890,refute_0_891]) ).

cnf(refute_0_893,plain,
    least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_90,X_88),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,greatest_lower_bound(X_90,X_88))),greatest_lower_bound(X_90,X_88)) )],[refute_0_887,refute_0_892]) ).

cnf(refute_0_894,plain,
    least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)) = X_90,
    inference(subst,[],[refute_0_66:[bind(X_22,$fot(X_90))]]) ).

cnf(refute_0_895,plain,
    greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))))]]) ).

cnf(refute_0_896,plain,
    ( greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))) != greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)))
    | least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)) != X_90
    | greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,X_90) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))),greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)))) ),[1,1],$fot(X_90)]]) ).

cnf(refute_0_897,plain,
    ( least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)) != X_90
    | greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,X_90) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))),greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)))) )],[refute_0_895,refute_0_896]) ).

cnf(refute_0_898,plain,
    greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,X_90),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)),X_90) )],[refute_0_894,refute_0_897]) ).

cnf(refute_0_899,plain,
    greatest_lower_bound(X_200,X_199) = greatest_lower_bound(X_199,X_200),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_200)),bind(Y,$fot(X_199))]]) ).

cnf(refute_0_900,plain,
    ( greatest_lower_bound(X_200,X_199) != greatest_lower_bound(X_199,X_200)
    | greatest_lower_bound(X_199,X_200) = greatest_lower_bound(X_200,X_199) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_200,X_199))),bind(Y0,$fot(greatest_lower_bound(X_199,X_200)))]]) ).

cnf(refute_0_901,plain,
    greatest_lower_bound(X_199,X_200) = greatest_lower_bound(X_200,X_199),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_200,X_199),greatest_lower_bound(X_199,X_200)) )],[refute_0_899,refute_0_900]) ).

cnf(refute_0_902,plain,
    ( greatest_lower_bound(X_199,X_200) != greatest_lower_bound(X_200,X_199)
    | greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,X_201))
    | greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(X_200,X_199),greatest_lower_bound(X_199,X_201)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,X_201))) ),[1,0],$fot(greatest_lower_bound(X_200,X_199))]]) ).

cnf(refute_0_903,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,X_201))
    | greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(X_200,X_199),greatest_lower_bound(X_199,X_201)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_200,X_199)) )],[refute_0_901,refute_0_902]) ).

cnf(refute_0_904,plain,
    greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = least_upper_bound(greatest_lower_bound(X_200,X_199),greatest_lower_bound(X_199,X_201)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(X_199,X_200),greatest_lower_bound(X_199,X_201))) )],[refute_0_749,refute_0_903]) ).

cnf(refute_0_905,plain,
    greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)) = least_upper_bound(greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)),greatest_lower_bound(X_199,X_201)),
    inference(subst,[],[lat4_7:[bind(X,$fot(X_199)),bind(Y,$fot(greatest_lower_bound(X_36,X_199))),bind(Z,$fot(X_201))]]) ).

cnf(refute_0_906,plain,
    ( greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)) != greatest_lower_bound(X_36,X_199)
    | greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)) != least_upper_bound(greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)),greatest_lower_bound(X_199,X_201))
    | greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)) = least_upper_bound(greatest_lower_bound(X_36,X_199),greatest_lower_bound(X_199,X_201)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)),least_upper_bound(greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)),greatest_lower_bound(X_199,X_201))) ),[1,0],$fot(greatest_lower_bound(X_36,X_199))]]) ).

cnf(refute_0_907,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)) != least_upper_bound(greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)),greatest_lower_bound(X_199,X_201))
    | greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)) = least_upper_bound(greatest_lower_bound(X_36,X_199),greatest_lower_bound(X_199,X_201)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)),greatest_lower_bound(X_36,X_199)) )],[refute_0_805,refute_0_906]) ).

cnf(refute_0_908,plain,
    greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)) = least_upper_bound(greatest_lower_bound(X_36,X_199),greatest_lower_bound(X_199,X_201)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)),least_upper_bound(greatest_lower_bound(X_199,greatest_lower_bound(X_36,X_199)),greatest_lower_bound(X_199,X_201))) )],[refute_0_905,refute_0_907]) ).

cnf(refute_0_909,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)) != least_upper_bound(greatest_lower_bound(X_36,X_199),greatest_lower_bound(X_199,X_201))
    | least_upper_bound(greatest_lower_bound(X_36,X_199),greatest_lower_bound(X_199,X_201)) = greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_36,X_199),greatest_lower_bound(X_199,X_201))))]]) ).

cnf(refute_0_910,plain,
    least_upper_bound(greatest_lower_bound(X_36,X_199),greatest_lower_bound(X_199,X_201)) = greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_36,X_199),X_201)),least_upper_bound(greatest_lower_bound(X_36,X_199),greatest_lower_bound(X_199,X_201))) )],[refute_0_908,refute_0_909]) ).

cnf(refute_0_911,plain,
    least_upper_bound(greatest_lower_bound(X_200,X_199),greatest_lower_bound(X_199,X_201)) = greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201)),
    inference(subst,[],[refute_0_910:[bind(X_36,$fot(X_200))]]) ).

cnf(refute_0_912,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(X_200,X_199),greatest_lower_bound(X_199,X_201))
    | least_upper_bound(greatest_lower_bound(X_200,X_199),greatest_lower_bound(X_199,X_201)) != greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201))
    | greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_200,X_199),greatest_lower_bound(X_199,X_201)))]]) ).

cnf(refute_0_913,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) != least_upper_bound(greatest_lower_bound(X_200,X_199),greatest_lower_bound(X_199,X_201))
    | greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_200,X_199),greatest_lower_bound(X_199,X_201)),greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201))) )],[refute_0_911,refute_0_912]) ).

cnf(refute_0_914,plain,
    greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) = greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),least_upper_bound(greatest_lower_bound(X_200,X_199),greatest_lower_bound(X_199,X_201))) )],[refute_0_904,refute_0_913]) ).

cnf(refute_0_915,plain,
    ( greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) != greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201))
    | greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201)) = greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)))),bind(Y0,$fot(greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201))))]]) ).

cnf(refute_0_916,plain,
    greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201)) = greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_199,least_upper_bound(X_200,X_201)),greatest_lower_bound(X_199,least_upper_bound(greatest_lower_bound(X_200,X_199),X_201))) )],[refute_0_914,refute_0_915]) ).

cnf(refute_0_917,plain,
    greatest_lower_bound(X_88,least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))),
    inference(subst,[],[refute_0_916:[bind(X_199,$fot(X_88)),bind(X_200,$fot(X_90)),bind(X_201,$fot(greatest_lower_bound(X_23,X_90)))]]) ).

cnf(refute_0_918,plain,
    least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,X_90))),
    inference(subst,[],[refute_0_910:[bind(X_199,$fot(X_88)),bind(X_201,$fot(greatest_lower_bound(X_23,X_90))),bind(X_36,$fot(X_90))]]) ).

cnf(refute_0_919,plain,
    ( greatest_lower_bound(X_88,least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,X_90))) != greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)))
    | least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) != greatest_lower_bound(X_88,least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,X_90)))
    | least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))))),bind(Y0,$fot(greatest_lower_bound(X_88,least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,X_90))))),bind(Z0,$fot(greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)))))]]) ).

cnf(refute_0_920,plain,
    ( greatest_lower_bound(X_88,least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,X_90))) != greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)))
    | least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))),greatest_lower_bound(X_88,least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,X_90)))) )],[refute_0_918,refute_0_919]) ).

cnf(refute_0_921,plain,
    least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_88,least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_23,X_90))),greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)))) )],[refute_0_917,refute_0_920]) ).

cnf(refute_0_922,plain,
    ( greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))) != greatest_lower_bound(X_88,X_90)
    | least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) != greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)))
    | least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,X_90) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))))),bind(Y0,$fot(greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))))),bind(Z0,$fot(greatest_lower_bound(X_88,X_90)))]]) ).

cnf(refute_0_923,plain,
    ( greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))) != greatest_lower_bound(X_88,X_90)
    | least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,X_90) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))),greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90)))) )],[refute_0_921,refute_0_922]) ).

cnf(refute_0_924,plain,
    least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) = greatest_lower_bound(X_88,X_90),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_88,least_upper_bound(X_90,greatest_lower_bound(X_23,X_90))),greatest_lower_bound(X_88,X_90)) )],[refute_0_898,refute_0_923]) ).

cnf(refute_0_925,plain,
    ( least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) != greatest_lower_bound(X_88,X_90)
    | least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) != greatest_lower_bound(X_90,X_88)
    | greatest_lower_bound(X_88,X_90) = greatest_lower_bound(X_90,X_88) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))),greatest_lower_bound(X_90,X_88)) ),[0],$fot(greatest_lower_bound(X_88,X_90))]]) ).

cnf(refute_0_926,plain,
    ( least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))) != greatest_lower_bound(X_90,X_88)
    | greatest_lower_bound(X_88,X_90) = greatest_lower_bound(X_90,X_88) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))),greatest_lower_bound(X_88,X_90)) )],[refute_0_924,refute_0_925]) ).

cnf(refute_0_927,plain,
    greatest_lower_bound(X_88,X_90) = greatest_lower_bound(X_90,X_88),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_90,X_88),greatest_lower_bound(X_88,greatest_lower_bound(X_23,X_90))),greatest_lower_bound(X_90,X_88)) )],[refute_0_893,refute_0_926]) ).

cnf(refute_0_928,plain,
    ( greatest_lower_bound(X_88,X_90) != greatest_lower_bound(X_90,X_88)
    | greatest_lower_bound(X_90,X_88) = greatest_lower_bound(X_88,X_90) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_88,X_90))),bind(Y0,$fot(greatest_lower_bound(X_90,X_88)))]]) ).

cnf(refute_0_929,plain,
    greatest_lower_bound(X_90,X_88) = greatest_lower_bound(X_88,X_90),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_88,X_90),greatest_lower_bound(X_90,X_88)) )],[refute_0_927,refute_0_928]) ).

cnf(refute_0_930,plain,
    greatest_lower_bound(inverse(X_230),identity) = greatest_lower_bound(identity,inverse(X_230)),
    inference(subst,[],[refute_0_929:[bind(X_88,$fot(identity)),bind(X_90,$fot(inverse(X_230)))]]) ).

cnf(refute_0_931,plain,
    ( greatest_lower_bound(identity,inverse(X_230)) != negative_part(inverse(X_230))
    | greatest_lower_bound(inverse(X_230),identity) != greatest_lower_bound(identity,inverse(X_230))
    | greatest_lower_bound(inverse(X_230),identity) = negative_part(inverse(X_230)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(inverse(X_230),identity))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_230)))),bind(Z0,$fot(negative_part(inverse(X_230))))]]) ).

cnf(refute_0_932,plain,
    ( greatest_lower_bound(identity,inverse(X_230)) != negative_part(inverse(X_230))
    | greatest_lower_bound(inverse(X_230),identity) = negative_part(inverse(X_230)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_230),identity),greatest_lower_bound(identity,inverse(X_230))) )],[refute_0_930,refute_0_931]) ).

cnf(refute_0_933,plain,
    greatest_lower_bound(inverse(X_230),identity) = negative_part(inverse(X_230)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_230)),negative_part(inverse(X_230))) )],[refute_0_886,refute_0_932]) ).

cnf(refute_0_934,plain,
    multiply(X_119,least_upper_bound(inverse(X_119),X_121)) = least_upper_bound(multiply(X_119,inverse(X_119)),multiply(X_119,X_121)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_119)),bind(Y,$fot(inverse(X_119))),bind(Z,$fot(X_121))]]) ).

cnf(refute_0_935,plain,
    multiply(X_119,inverse(X_119)) = identity,
    inference(subst,[],[refute_0_5:[bind(X_1,$fot(X_119))]]) ).

cnf(refute_0_936,plain,
    ( multiply(X_119,inverse(X_119)) != identity
    | multiply(X_119,least_upper_bound(inverse(X_119),X_121)) != least_upper_bound(multiply(X_119,inverse(X_119)),multiply(X_119,X_121))
    | multiply(X_119,least_upper_bound(inverse(X_119),X_121)) = least_upper_bound(identity,multiply(X_119,X_121)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_119,least_upper_bound(inverse(X_119),X_121)),least_upper_bound(multiply(X_119,inverse(X_119)),multiply(X_119,X_121))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_937,plain,
    ( multiply(X_119,least_upper_bound(inverse(X_119),X_121)) != least_upper_bound(multiply(X_119,inverse(X_119)),multiply(X_119,X_121))
    | multiply(X_119,least_upper_bound(inverse(X_119),X_121)) = least_upper_bound(identity,multiply(X_119,X_121)) ),
    inference(resolve,[$cnf( $equal(multiply(X_119,inverse(X_119)),identity) )],[refute_0_935,refute_0_936]) ).

cnf(refute_0_938,plain,
    multiply(X_119,least_upper_bound(inverse(X_119),X_121)) = least_upper_bound(identity,multiply(X_119,X_121)),
    inference(resolve,[$cnf( $equal(multiply(X_119,least_upper_bound(inverse(X_119),X_121)),least_upper_bound(multiply(X_119,inverse(X_119)),multiply(X_119,X_121))) )],[refute_0_934,refute_0_937]) ).

cnf(refute_0_939,plain,
    least_upper_bound(identity,multiply(X_119,X_121)) = positive_part(multiply(X_119,X_121)),
    inference(subst,[],[refute_0_371:[bind(X,$fot(multiply(X_119,X_121)))]]) ).

cnf(refute_0_940,plain,
    ( multiply(X_119,least_upper_bound(inverse(X_119),X_121)) != least_upper_bound(identity,multiply(X_119,X_121))
    | least_upper_bound(identity,multiply(X_119,X_121)) != positive_part(multiply(X_119,X_121))
    | multiply(X_119,least_upper_bound(inverse(X_119),X_121)) = positive_part(multiply(X_119,X_121)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_119,least_upper_bound(inverse(X_119),X_121)),positive_part(multiply(X_119,X_121))) ),[0],$fot(least_upper_bound(identity,multiply(X_119,X_121)))]]) ).

cnf(refute_0_941,plain,
    ( multiply(X_119,least_upper_bound(inverse(X_119),X_121)) != least_upper_bound(identity,multiply(X_119,X_121))
    | multiply(X_119,least_upper_bound(inverse(X_119),X_121)) = positive_part(multiply(X_119,X_121)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_119,X_121)),positive_part(multiply(X_119,X_121))) )],[refute_0_939,refute_0_940]) ).

cnf(refute_0_942,plain,
    multiply(X_119,least_upper_bound(inverse(X_119),X_121)) = positive_part(multiply(X_119,X_121)),
    inference(resolve,[$cnf( $equal(multiply(X_119,least_upper_bound(inverse(X_119),X_121)),least_upper_bound(identity,multiply(X_119,X_121))) )],[refute_0_938,refute_0_941]) ).

cnf(refute_0_943,plain,
    multiply(X_125,least_upper_bound(inverse(X_125),negative_part(inverse(X_125)))) = positive_part(multiply(X_125,negative_part(inverse(X_125)))),
    inference(subst,[],[refute_0_942:[bind(X_119,$fot(X_125)),bind(X_121,$fot(negative_part(inverse(X_125))))]]) ).

cnf(refute_0_944,plain,
    least_upper_bound(inverse(X_125),negative_part(inverse(X_125))) = inverse(X_125),
    inference(subst,[],[refute_0_85:[bind(X_22,$fot(inverse(X_125)))]]) ).

cnf(refute_0_945,plain,
    ( multiply(X_125,least_upper_bound(inverse(X_125),negative_part(inverse(X_125)))) != positive_part(multiply(X_125,negative_part(inverse(X_125))))
    | least_upper_bound(inverse(X_125),negative_part(inverse(X_125))) != inverse(X_125)
    | multiply(X_125,inverse(X_125)) = positive_part(multiply(X_125,negative_part(inverse(X_125)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_125,least_upper_bound(inverse(X_125),negative_part(inverse(X_125)))),positive_part(multiply(X_125,negative_part(inverse(X_125))))) ),[0,1],$fot(inverse(X_125))]]) ).

cnf(refute_0_946,plain,
    ( multiply(X_125,least_upper_bound(inverse(X_125),negative_part(inverse(X_125)))) != positive_part(multiply(X_125,negative_part(inverse(X_125))))
    | multiply(X_125,inverse(X_125)) = positive_part(multiply(X_125,negative_part(inverse(X_125)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_125),negative_part(inverse(X_125))),inverse(X_125)) )],[refute_0_944,refute_0_945]) ).

cnf(refute_0_947,plain,
    multiply(X_125,inverse(X_125)) = positive_part(multiply(X_125,negative_part(inverse(X_125)))),
    inference(resolve,[$cnf( $equal(multiply(X_125,least_upper_bound(inverse(X_125),negative_part(inverse(X_125)))),positive_part(multiply(X_125,negative_part(inverse(X_125))))) )],[refute_0_943,refute_0_946]) ).

cnf(refute_0_948,plain,
    multiply(X_125,inverse(X_125)) = identity,
    inference(subst,[],[refute_0_5:[bind(X_1,$fot(X_125))]]) ).

cnf(refute_0_949,plain,
    ( multiply(X_125,inverse(X_125)) != identity
    | multiply(X_125,inverse(X_125)) != positive_part(multiply(X_125,negative_part(inverse(X_125))))
    | identity = positive_part(multiply(X_125,negative_part(inverse(X_125)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_125,inverse(X_125)),positive_part(multiply(X_125,negative_part(inverse(X_125))))) ),[0],$fot(identity)]]) ).

cnf(refute_0_950,plain,
    ( multiply(X_125,inverse(X_125)) != positive_part(multiply(X_125,negative_part(inverse(X_125))))
    | identity = positive_part(multiply(X_125,negative_part(inverse(X_125)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_125,inverse(X_125)),identity) )],[refute_0_948,refute_0_949]) ).

cnf(refute_0_951,plain,
    identity = positive_part(multiply(X_125,negative_part(inverse(X_125)))),
    inference(resolve,[$cnf( $equal(multiply(X_125,inverse(X_125)),positive_part(multiply(X_125,negative_part(inverse(X_125))))) )],[refute_0_947,refute_0_950]) ).

cnf(refute_0_952,plain,
    identity = positive_part(multiply(inverse(X),negative_part(inverse(inverse(X))))),
    inference(subst,[],[refute_0_951:[bind(X_125,$fot(inverse(X)))]]) ).

cnf(refute_0_953,plain,
    ( identity != positive_part(multiply(inverse(X),negative_part(inverse(inverse(X)))))
    | inverse(inverse(X)) != X
    | identity = positive_part(multiply(inverse(X),negative_part(X))) ),
    introduced(tautology,[equality,[$cnf( $equal(identity,positive_part(multiply(inverse(X),negative_part(inverse(inverse(X)))))) ),[1,0,1,0],$fot(X)]]) ).

cnf(refute_0_954,plain,
    ( identity != positive_part(multiply(inverse(X),negative_part(inverse(inverse(X)))))
    | identity = positive_part(multiply(inverse(X),negative_part(X))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[lat4_2,refute_0_953]) ).

cnf(refute_0_955,plain,
    identity = positive_part(multiply(inverse(X),negative_part(X))),
    inference(resolve,[$cnf( $equal(identity,positive_part(multiply(inverse(X),negative_part(inverse(inverse(X)))))) )],[refute_0_952,refute_0_954]) ).

cnf(refute_0_956,plain,
    identity = positive_part(multiply(inverse(positive_part(X_17)),negative_part(positive_part(X_17)))),
    inference(subst,[],[refute_0_955:[bind(X,$fot(positive_part(X_17)))]]) ).

cnf(refute_0_957,plain,
    ( identity != positive_part(multiply(inverse(positive_part(X_17)),negative_part(positive_part(X_17))))
    | negative_part(positive_part(X_17)) != identity
    | identity = positive_part(multiply(inverse(positive_part(X_17)),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(identity,positive_part(multiply(inverse(positive_part(X_17)),negative_part(positive_part(X_17))))) ),[1,0,1],$fot(identity)]]) ).

cnf(refute_0_958,plain,
    ( identity != positive_part(multiply(inverse(positive_part(X_17)),negative_part(positive_part(X_17))))
    | identity = positive_part(multiply(inverse(positive_part(X_17)),identity)) ),
    inference(resolve,[$cnf( $equal(negative_part(positive_part(X_17)),identity) )],[refute_0_661,refute_0_957]) ).

cnf(refute_0_959,plain,
    identity = positive_part(multiply(inverse(positive_part(X_17)),identity)),
    inference(resolve,[$cnf( $equal(identity,positive_part(multiply(inverse(positive_part(X_17)),negative_part(positive_part(X_17))))) )],[refute_0_956,refute_0_958]) ).

cnf(refute_0_960,plain,
    multiply(inverse(positive_part(X_17)),identity) = inverse(positive_part(X_17)),
    inference(subst,[],[refute_0_405:[bind(X,$fot(inverse(positive_part(X_17))))]]) ).

cnf(refute_0_961,plain,
    positive_part(multiply(inverse(positive_part(X_17)),identity)) = positive_part(multiply(inverse(positive_part(X_17)),identity)),
    introduced(tautology,[refl,[$fot(positive_part(multiply(inverse(positive_part(X_17)),identity)))]]) ).

cnf(refute_0_962,plain,
    ( multiply(inverse(positive_part(X_17)),identity) != inverse(positive_part(X_17))
    | positive_part(multiply(inverse(positive_part(X_17)),identity)) != positive_part(multiply(inverse(positive_part(X_17)),identity))
    | positive_part(multiply(inverse(positive_part(X_17)),identity)) = positive_part(inverse(positive_part(X_17))) ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(multiply(inverse(positive_part(X_17)),identity)),positive_part(multiply(inverse(positive_part(X_17)),identity))) ),[1,0],$fot(inverse(positive_part(X_17)))]]) ).

cnf(refute_0_963,plain,
    ( multiply(inverse(positive_part(X_17)),identity) != inverse(positive_part(X_17))
    | positive_part(multiply(inverse(positive_part(X_17)),identity)) = positive_part(inverse(positive_part(X_17))) ),
    inference(resolve,[$cnf( $equal(positive_part(multiply(inverse(positive_part(X_17)),identity)),positive_part(multiply(inverse(positive_part(X_17)),identity))) )],[refute_0_961,refute_0_962]) ).

cnf(refute_0_964,plain,
    positive_part(multiply(inverse(positive_part(X_17)),identity)) = positive_part(inverse(positive_part(X_17))),
    inference(resolve,[$cnf( $equal(multiply(inverse(positive_part(X_17)),identity),inverse(positive_part(X_17))) )],[refute_0_960,refute_0_963]) ).

cnf(refute_0_965,plain,
    ( identity != positive_part(multiply(inverse(positive_part(X_17)),identity))
    | positive_part(multiply(inverse(positive_part(X_17)),identity)) != positive_part(inverse(positive_part(X_17)))
    | identity = positive_part(inverse(positive_part(X_17))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(identity,positive_part(inverse(positive_part(X_17)))) ),[0],$fot(positive_part(multiply(inverse(positive_part(X_17)),identity)))]]) ).

cnf(refute_0_966,plain,
    ( identity != positive_part(multiply(inverse(positive_part(X_17)),identity))
    | identity = positive_part(inverse(positive_part(X_17))) ),
    inference(resolve,[$cnf( $equal(positive_part(multiply(inverse(positive_part(X_17)),identity)),positive_part(inverse(positive_part(X_17)))) )],[refute_0_964,refute_0_965]) ).

cnf(refute_0_967,plain,
    identity = positive_part(inverse(positive_part(X_17))),
    inference(resolve,[$cnf( $equal(identity,positive_part(multiply(inverse(positive_part(X_17)),identity))) )],[refute_0_959,refute_0_966]) ).

cnf(refute_0_968,plain,
    ( identity != positive_part(inverse(positive_part(X_17)))
    | positive_part(inverse(positive_part(X_17))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(positive_part(inverse(positive_part(X_17)))))]]) ).

cnf(refute_0_969,plain,
    positive_part(inverse(positive_part(X_17))) = identity,
    inference(resolve,[$cnf( $equal(identity,positive_part(inverse(positive_part(X_17)))) )],[refute_0_967,refute_0_968]) ).

cnf(refute_0_970,plain,
    positive_part(inverse(positive_part(X_230))) = identity,
    inference(subst,[],[refute_0_969:[bind(X_17,$fot(X_230))]]) ).

cnf(refute_0_971,plain,
    greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))) = greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))))]]) ).

cnf(refute_0_972,plain,
    ( greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))) != greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230))))
    | positive_part(inverse(positive_part(X_230))) != identity
    | greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))) = greatest_lower_bound(inverse(X_230),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))),greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_973,plain,
    ( positive_part(inverse(positive_part(X_230))) != identity
    | greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))) = greatest_lower_bound(inverse(X_230),identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))),greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230))))) )],[refute_0_971,refute_0_972]) ).

cnf(refute_0_974,plain,
    greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))) = greatest_lower_bound(inverse(X_230),identity),
    inference(resolve,[$cnf( $equal(positive_part(inverse(positive_part(X_230))),identity) )],[refute_0_970,refute_0_973]) ).

cnf(refute_0_975,plain,
    ( greatest_lower_bound(inverse(X_230),identity) != negative_part(inverse(X_230))
    | greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))) != greatest_lower_bound(inverse(X_230),identity)
    | greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))) = negative_part(inverse(X_230)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))))),bind(Y0,$fot(greatest_lower_bound(inverse(X_230),identity))),bind(Z0,$fot(negative_part(inverse(X_230))))]]) ).

cnf(refute_0_976,plain,
    ( greatest_lower_bound(inverse(X_230),identity) != negative_part(inverse(X_230))
    | greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))) = negative_part(inverse(X_230)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))),greatest_lower_bound(inverse(X_230),identity)) )],[refute_0_974,refute_0_975]) ).

cnf(refute_0_977,plain,
    greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))) = negative_part(inverse(X_230)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_230),identity),negative_part(inverse(X_230))) )],[refute_0_933,refute_0_976]) ).

cnf(refute_0_978,plain,
    ( greatest_lower_bound(X_105,positive_part(X_104)) != greatest_lower_bound(positive_part(X_104),X_105)
    | greatest_lower_bound(positive_part(X_104),X_105) = greatest_lower_bound(X_105,positive_part(X_104)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_105,positive_part(X_104)))),bind(Y0,$fot(greatest_lower_bound(positive_part(X_104),X_105)))]]) ).

cnf(refute_0_979,plain,
    greatest_lower_bound(positive_part(X_104),X_105) = greatest_lower_bound(X_105,positive_part(X_104)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_105,positive_part(X_104)),greatest_lower_bound(positive_part(X_104),X_105)) )],[refute_0_829,refute_0_978]) ).

cnf(refute_0_980,plain,
    greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)) = greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))),
    inference(subst,[],[refute_0_979:[bind(X_104,$fot(inverse(positive_part(X_230)))),bind(X_105,$fot(inverse(X_230)))]]) ).

cnf(refute_0_981,plain,
    ( greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))) != negative_part(inverse(X_230))
    | greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)) != greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230))))
    | greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)) = negative_part(inverse(X_230)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))))),bind(Z0,$fot(negative_part(inverse(X_230))))]]) ).

cnf(refute_0_982,plain,
    ( greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))) != negative_part(inverse(X_230))
    | greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)) = negative_part(inverse(X_230)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)),greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230))))) )],[refute_0_980,refute_0_981]) ).

cnf(refute_0_983,plain,
    greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)) = negative_part(inverse(X_230)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_230),positive_part(inverse(positive_part(X_230)))),negative_part(inverse(X_230))) )],[refute_0_977,refute_0_982]) ).

cnf(refute_0_984,plain,
    ( multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) != greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230))
    | greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)) != negative_part(inverse(X_230))
    | multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = negative_part(inverse(X_230)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))),negative_part(inverse(X_230))) ),[0],$fot(greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)))]]) ).

cnf(refute_0_985,plain,
    ( multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) != greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230))
    | multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = negative_part(inverse(X_230)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230)),negative_part(inverse(X_230))) )],[refute_0_983,refute_0_984]) ).

cnf(refute_0_986,plain,
    ( multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))) != greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230))
    | multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = negative_part(inverse(X_230)) ),
    inference(resolve,[$cnf( $equal(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))),greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230))) )],[refute_0_885,refute_0_985]) ).

cnf(refute_0_987,plain,
    multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = negative_part(inverse(X_230)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(positive_part(inverse(X_230)),positive_part(inverse(inverse(positive_part(X_230))))),inverse(positive_part(X_230))),greatest_lower_bound(positive_part(inverse(positive_part(X_230))),inverse(X_230))) )],[refute_0_498,refute_0_986]) ).

cnf(refute_0_988,plain,
    multiply(identity,inverse(positive_part(X_230))) = inverse(positive_part(X_230)),
    inference(subst,[],[left_identity:[bind(X,$fot(inverse(positive_part(X_230))))]]) ).

cnf(refute_0_989,plain,
    positive_part(positive_part(greatest_lower_bound(X_361,inverse(X_361)))) = positive_part(greatest_lower_bound(X_361,inverse(X_361))),
    inference(subst,[],[refute_0_841:[bind(X_17,$fot(greatest_lower_bound(X_361,inverse(X_361))))]]) ).

cnf(refute_0_990,plain,
    least_upper_bound(identity,greatest_lower_bound(X_284,X_285)) = greatest_lower_bound(least_upper_bound(identity,X_284),least_upper_bound(identity,X_285)),
    inference(subst,[],[lat4_6:[bind(X,$fot(identity)),bind(Y,$fot(X_284)),bind(Z,$fot(X_285))]]) ).

cnf(refute_0_991,plain,
    positive_part(X_285) = least_upper_bound(identity,X_285),
    inference(subst,[],[refute_0_369:[bind(X,$fot(X_285))]]) ).

cnf(refute_0_992,plain,
    ( positive_part(X_285) != least_upper_bound(identity,X_285)
    | least_upper_bound(identity,X_285) = positive_part(X_285) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(positive_part(X_285))),bind(Y0,$fot(least_upper_bound(identity,X_285)))]]) ).

cnf(refute_0_993,plain,
    least_upper_bound(identity,X_285) = positive_part(X_285),
    inference(resolve,[$cnf( $equal(positive_part(X_285),least_upper_bound(identity,X_285)) )],[refute_0_991,refute_0_992]) ).

cnf(refute_0_994,plain,
    ( least_upper_bound(identity,X_285) != positive_part(X_285)
    | least_upper_bound(identity,greatest_lower_bound(X_284,X_285)) != greatest_lower_bound(least_upper_bound(identity,X_284),least_upper_bound(identity,X_285))
    | least_upper_bound(identity,greatest_lower_bound(X_284,X_285)) = greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_284,X_285)),greatest_lower_bound(least_upper_bound(identity,X_284),least_upper_bound(identity,X_285))) ),[1,1],$fot(positive_part(X_285))]]) ).

cnf(refute_0_995,plain,
    ( least_upper_bound(identity,greatest_lower_bound(X_284,X_285)) != greatest_lower_bound(least_upper_bound(identity,X_284),least_upper_bound(identity,X_285))
    | least_upper_bound(identity,greatest_lower_bound(X_284,X_285)) = greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_285),positive_part(X_285)) )],[refute_0_993,refute_0_994]) ).

cnf(refute_0_996,plain,
    least_upper_bound(identity,greatest_lower_bound(X_284,X_285)) = greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_284,X_285)),greatest_lower_bound(least_upper_bound(identity,X_284),least_upper_bound(identity,X_285))) )],[refute_0_990,refute_0_995]) ).

cnf(refute_0_997,plain,
    least_upper_bound(identity,greatest_lower_bound(X_284,X_285)) = positive_part(greatest_lower_bound(X_284,X_285)),
    inference(subst,[],[refute_0_371:[bind(X,$fot(greatest_lower_bound(X_284,X_285)))]]) ).

cnf(refute_0_998,plain,
    ( least_upper_bound(identity,greatest_lower_bound(X_284,X_285)) != greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))
    | least_upper_bound(identity,greatest_lower_bound(X_284,X_285)) != positive_part(greatest_lower_bound(X_284,X_285))
    | positive_part(greatest_lower_bound(X_284,X_285)) = greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_284,X_285)),greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))) ),[0],$fot(positive_part(greatest_lower_bound(X_284,X_285)))]]) ).

cnf(refute_0_999,plain,
    ( least_upper_bound(identity,greatest_lower_bound(X_284,X_285)) != greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))
    | positive_part(greatest_lower_bound(X_284,X_285)) = greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_284,X_285)),positive_part(greatest_lower_bound(X_284,X_285))) )],[refute_0_997,refute_0_998]) ).

cnf(refute_0_1000,plain,
    least_upper_bound(identity,X_284) = positive_part(X_284),
    inference(subst,[],[refute_0_371:[bind(X,$fot(X_284))]]) ).

cnf(refute_0_1001,plain,
    greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)) = greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)))]]) ).

cnf(refute_0_1002,plain,
    ( greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)) != greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))
    | least_upper_bound(identity,X_284) != positive_part(X_284)
    | greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)) = greatest_lower_bound(positive_part(X_284),positive_part(X_285)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)),greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))) ),[1,0],$fot(positive_part(X_284))]]) ).

cnf(refute_0_1003,plain,
    ( least_upper_bound(identity,X_284) != positive_part(X_284)
    | greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)) = greatest_lower_bound(positive_part(X_284),positive_part(X_285)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)),greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))) )],[refute_0_1001,refute_0_1002]) ).

cnf(refute_0_1004,plain,
    greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)) = greatest_lower_bound(positive_part(X_284),positive_part(X_285)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_284),positive_part(X_284)) )],[refute_0_1000,refute_0_1003]) ).

cnf(refute_0_1005,plain,
    ( greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)) != greatest_lower_bound(positive_part(X_284),positive_part(X_285))
    | positive_part(greatest_lower_bound(X_284,X_285)) != greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))
    | positive_part(greatest_lower_bound(X_284,X_285)) = greatest_lower_bound(positive_part(X_284),positive_part(X_285)) ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(greatest_lower_bound(X_284,X_285)),greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))) ),[1],$fot(greatest_lower_bound(positive_part(X_284),positive_part(X_285)))]]) ).

cnf(refute_0_1006,plain,
    ( positive_part(greatest_lower_bound(X_284,X_285)) != greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))
    | positive_part(greatest_lower_bound(X_284,X_285)) = greatest_lower_bound(positive_part(X_284),positive_part(X_285)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285)),greatest_lower_bound(positive_part(X_284),positive_part(X_285))) )],[refute_0_1004,refute_0_1005]) ).

cnf(refute_0_1007,plain,
    ( least_upper_bound(identity,greatest_lower_bound(X_284,X_285)) != greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))
    | positive_part(greatest_lower_bound(X_284,X_285)) = greatest_lower_bound(positive_part(X_284),positive_part(X_285)) ),
    inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(X_284,X_285)),greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))) )],[refute_0_999,refute_0_1006]) ).

cnf(refute_0_1008,plain,
    positive_part(greatest_lower_bound(X_284,X_285)) = greatest_lower_bound(positive_part(X_284),positive_part(X_285)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_284,X_285)),greatest_lower_bound(least_upper_bound(identity,X_284),positive_part(X_285))) )],[refute_0_996,refute_0_1007]) ).

cnf(refute_0_1009,plain,
    ( positive_part(greatest_lower_bound(X_284,X_285)) != greatest_lower_bound(positive_part(X_284),positive_part(X_285))
    | greatest_lower_bound(positive_part(X_284),positive_part(X_285)) = positive_part(greatest_lower_bound(X_284,X_285)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(positive_part(greatest_lower_bound(X_284,X_285)))),bind(Y0,$fot(greatest_lower_bound(positive_part(X_284),positive_part(X_285))))]]) ).

cnf(refute_0_1010,plain,
    greatest_lower_bound(positive_part(X_284),positive_part(X_285)) = positive_part(greatest_lower_bound(X_284,X_285)),
    inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(X_284,X_285)),greatest_lower_bound(positive_part(X_284),positive_part(X_285))) )],[refute_0_1008,refute_0_1009]) ).

cnf(refute_0_1011,plain,
    greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) = positive_part(greatest_lower_bound(X_123,inverse(X_123))),
    inference(subst,[],[refute_0_1010:[bind(X_284,$fot(X_123)),bind(X_285,$fot(inverse(X_123)))]]) ).

cnf(refute_0_1012,plain,
    ( greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))) != positive_part(greatest_lower_bound(X_123,inverse(X_123)))
    | negative_part(least_upper_bound(X_123,inverse(X_123))) != greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))
    | negative_part(least_upper_bound(X_123,inverse(X_123))) = positive_part(greatest_lower_bound(X_123,inverse(X_123))) ),
    introduced(tautology,[equality,[$cnf( $equal(negative_part(least_upper_bound(X_123,inverse(X_123))),greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))) ),[1],$fot(positive_part(greatest_lower_bound(X_123,inverse(X_123))))]]) ).

cnf(refute_0_1013,plain,
    ( negative_part(least_upper_bound(X_123,inverse(X_123))) != greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))
    | negative_part(least_upper_bound(X_123,inverse(X_123))) = positive_part(greatest_lower_bound(X_123,inverse(X_123))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123))),positive_part(greatest_lower_bound(X_123,inverse(X_123)))) )],[refute_0_1011,refute_0_1012]) ).

cnf(refute_0_1014,plain,
    negative_part(least_upper_bound(X_123,inverse(X_123))) = positive_part(greatest_lower_bound(X_123,inverse(X_123))),
    inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_123,inverse(X_123))),greatest_lower_bound(positive_part(X_123),positive_part(inverse(X_123)))) )],[refute_0_643,refute_0_1013]) ).

cnf(refute_0_1015,plain,
    negative_part(least_upper_bound(X_361,inverse(X_361))) = positive_part(greatest_lower_bound(X_361,inverse(X_361))),
    inference(subst,[],[refute_0_1014:[bind(X_123,$fot(X_361))]]) ).

cnf(refute_0_1016,plain,
    ( negative_part(least_upper_bound(X_361,inverse(X_361))) != positive_part(greatest_lower_bound(X_361,inverse(X_361)))
    | positive_part(greatest_lower_bound(X_361,inverse(X_361))) = negative_part(least_upper_bound(X_361,inverse(X_361))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(negative_part(least_upper_bound(X_361,inverse(X_361))))),bind(Y0,$fot(positive_part(greatest_lower_bound(X_361,inverse(X_361)))))]]) ).

cnf(refute_0_1017,plain,
    positive_part(greatest_lower_bound(X_361,inverse(X_361))) = negative_part(least_upper_bound(X_361,inverse(X_361))),
    inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_361,inverse(X_361))),positive_part(greatest_lower_bound(X_361,inverse(X_361)))) )],[refute_0_1015,refute_0_1016]) ).

cnf(refute_0_1018,plain,
    ( positive_part(greatest_lower_bound(X_361,inverse(X_361))) != negative_part(least_upper_bound(X_361,inverse(X_361)))
    | positive_part(positive_part(greatest_lower_bound(X_361,inverse(X_361)))) != positive_part(greatest_lower_bound(X_361,inverse(X_361)))
    | positive_part(negative_part(least_upper_bound(X_361,inverse(X_361)))) = positive_part(greatest_lower_bound(X_361,inverse(X_361))) ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(positive_part(greatest_lower_bound(X_361,inverse(X_361)))),positive_part(greatest_lower_bound(X_361,inverse(X_361)))) ),[0,0],$fot(negative_part(least_upper_bound(X_361,inverse(X_361))))]]) ).

cnf(refute_0_1019,plain,
    ( positive_part(positive_part(greatest_lower_bound(X_361,inverse(X_361)))) != positive_part(greatest_lower_bound(X_361,inverse(X_361)))
    | positive_part(negative_part(least_upper_bound(X_361,inverse(X_361)))) = positive_part(greatest_lower_bound(X_361,inverse(X_361))) ),
    inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(X_361,inverse(X_361))),negative_part(least_upper_bound(X_361,inverse(X_361)))) )],[refute_0_1017,refute_0_1018]) ).

cnf(refute_0_1020,plain,
    positive_part(negative_part(least_upper_bound(X_361,inverse(X_361)))) = positive_part(greatest_lower_bound(X_361,inverse(X_361))),
    inference(resolve,[$cnf( $equal(positive_part(positive_part(greatest_lower_bound(X_361,inverse(X_361)))),positive_part(greatest_lower_bound(X_361,inverse(X_361)))) )],[refute_0_989,refute_0_1019]) ).

cnf(refute_0_1021,plain,
    positive_part(negative_part(least_upper_bound(X_361,inverse(X_361)))) = identity,
    inference(subst,[],[refute_0_701:[bind(X_23,$fot(least_upper_bound(X_361,inverse(X_361))))]]) ).

cnf(refute_0_1022,plain,
    ( positive_part(negative_part(least_upper_bound(X_361,inverse(X_361)))) != identity
    | positive_part(negative_part(least_upper_bound(X_361,inverse(X_361)))) != positive_part(greatest_lower_bound(X_361,inverse(X_361)))
    | identity = positive_part(greatest_lower_bound(X_361,inverse(X_361))) ),
    introduced(tautology,[equality,[$cnf( $equal(positive_part(negative_part(least_upper_bound(X_361,inverse(X_361)))),positive_part(greatest_lower_bound(X_361,inverse(X_361)))) ),[0],$fot(identity)]]) ).

cnf(refute_0_1023,plain,
    ( positive_part(negative_part(least_upper_bound(X_361,inverse(X_361)))) != positive_part(greatest_lower_bound(X_361,inverse(X_361)))
    | identity = positive_part(greatest_lower_bound(X_361,inverse(X_361))) ),
    inference(resolve,[$cnf( $equal(positive_part(negative_part(least_upper_bound(X_361,inverse(X_361)))),identity) )],[refute_0_1021,refute_0_1022]) ).

cnf(refute_0_1024,plain,
    ( identity != positive_part(greatest_lower_bound(X_361,inverse(X_361)))
    | positive_part(greatest_lower_bound(X_361,inverse(X_361))) != negative_part(least_upper_bound(X_361,inverse(X_361)))
    | identity = negative_part(least_upper_bound(X_361,inverse(X_361))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(identity,negative_part(least_upper_bound(X_361,inverse(X_361)))) ),[0],$fot(positive_part(greatest_lower_bound(X_361,inverse(X_361))))]]) ).

cnf(refute_0_1025,plain,
    ( identity != positive_part(greatest_lower_bound(X_361,inverse(X_361)))
    | identity = negative_part(least_upper_bound(X_361,inverse(X_361))) ),
    inference(resolve,[$cnf( $equal(positive_part(greatest_lower_bound(X_361,inverse(X_361))),negative_part(least_upper_bound(X_361,inverse(X_361)))) )],[refute_0_1017,refute_0_1024]) ).

cnf(refute_0_1026,plain,
    ( positive_part(negative_part(least_upper_bound(X_361,inverse(X_361)))) != positive_part(greatest_lower_bound(X_361,inverse(X_361)))
    | identity = negative_part(least_upper_bound(X_361,inverse(X_361))) ),
    inference(resolve,[$cnf( $equal(identity,positive_part(greatest_lower_bound(X_361,inverse(X_361)))) )],[refute_0_1023,refute_0_1025]) ).

cnf(refute_0_1027,plain,
    identity = negative_part(least_upper_bound(X_361,inverse(X_361))),
    inference(resolve,[$cnf( $equal(positive_part(negative_part(least_upper_bound(X_361,inverse(X_361)))),positive_part(greatest_lower_bound(X_361,inverse(X_361)))) )],[refute_0_1020,refute_0_1026]) ).

cnf(refute_0_1028,plain,
    ( identity != negative_part(least_upper_bound(X_361,inverse(X_361)))
    | negative_part(least_upper_bound(X_361,inverse(X_361))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(negative_part(least_upper_bound(X_361,inverse(X_361)))))]]) ).

cnf(refute_0_1029,plain,
    negative_part(least_upper_bound(X_361,inverse(X_361))) = identity,
    inference(resolve,[$cnf( $equal(identity,negative_part(least_upper_bound(X_361,inverse(X_361)))) )],[refute_0_1027,refute_0_1028]) ).

cnf(refute_0_1030,plain,
    negative_part(least_upper_bound(X_230,inverse(X_230))) = identity,
    inference(subst,[],[refute_0_1029:[bind(X_361,$fot(X_230))]]) ).

cnf(refute_0_1031,plain,
    multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))),
    introduced(tautology,[refl,[$fot(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))))]]) ).

cnf(refute_0_1032,plain,
    ( multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) != multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230)))
    | negative_part(least_upper_bound(X_230,inverse(X_230))) != identity
    | multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = multiply(identity,inverse(positive_part(X_230))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))),multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1033,plain,
    ( negative_part(least_upper_bound(X_230,inverse(X_230))) != identity
    | multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = multiply(identity,inverse(positive_part(X_230))) ),
    inference(resolve,[$cnf( $equal(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))),multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230)))) )],[refute_0_1031,refute_0_1032]) ).

cnf(refute_0_1034,plain,
    multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = multiply(identity,inverse(positive_part(X_230))),
    inference(resolve,[$cnf( $equal(negative_part(least_upper_bound(X_230,inverse(X_230))),identity) )],[refute_0_1030,refute_0_1033]) ).

cnf(refute_0_1035,plain,
    ( multiply(identity,inverse(positive_part(X_230))) != inverse(positive_part(X_230))
    | multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) != multiply(identity,inverse(positive_part(X_230)))
    | multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = inverse(positive_part(X_230)) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))))),bind(Y0,$fot(multiply(identity,inverse(positive_part(X_230))))),bind(Z0,$fot(inverse(positive_part(X_230))))]]) ).

cnf(refute_0_1036,plain,
    ( multiply(identity,inverse(positive_part(X_230))) != inverse(positive_part(X_230))
    | multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = inverse(positive_part(X_230)) ),
    inference(resolve,[$cnf( $equal(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))),multiply(identity,inverse(positive_part(X_230)))) )],[refute_0_1034,refute_0_1035]) ).

cnf(refute_0_1037,plain,
    multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) = inverse(positive_part(X_230)),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(positive_part(X_230))),inverse(positive_part(X_230))) )],[refute_0_988,refute_0_1036]) ).

cnf(refute_0_1038,plain,
    ( multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) != inverse(positive_part(X_230))
    | multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) != negative_part(inverse(X_230))
    | inverse(positive_part(X_230)) = negative_part(inverse(X_230)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))),negative_part(inverse(X_230))) ),[0],$fot(inverse(positive_part(X_230)))]]) ).

cnf(refute_0_1039,plain,
    ( multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))) != negative_part(inverse(X_230))
    | inverse(positive_part(X_230)) = negative_part(inverse(X_230)) ),
    inference(resolve,[$cnf( $equal(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))),inverse(positive_part(X_230))) )],[refute_0_1037,refute_0_1038]) ).

cnf(refute_0_1040,plain,
    inverse(positive_part(X_230)) = negative_part(inverse(X_230)),
    inference(resolve,[$cnf( $equal(multiply(negative_part(least_upper_bound(X_230,inverse(X_230))),inverse(positive_part(X_230))),negative_part(inverse(X_230))) )],[refute_0_987,refute_0_1039]) ).

cnf(refute_0_1041,plain,
    ( inverse(positive_part(X_230)) != negative_part(inverse(X_230))
    | negative_part(inverse(X_230)) = inverse(positive_part(X_230)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(positive_part(X_230)))),bind(Y0,$fot(negative_part(inverse(X_230))))]]) ).

cnf(refute_0_1042,plain,
    negative_part(inverse(X_230)) = inverse(positive_part(X_230)),
    inference(resolve,[$cnf( $equal(inverse(positive_part(X_230)),negative_part(inverse(X_230))) )],[refute_0_1040,refute_0_1041]) ).

cnf(refute_0_1043,plain,
    negative_part(inverse(X_158)) = inverse(positive_part(X_158)),
    inference(subst,[],[refute_0_1042:[bind(X_230,$fot(X_158))]]) ).

cnf(refute_0_1044,plain,
    multiply(X_158,negative_part(inverse(X_158))) = multiply(X_158,negative_part(inverse(X_158))),
    introduced(tautology,[refl,[$fot(multiply(X_158,negative_part(inverse(X_158))))]]) ).

cnf(refute_0_1045,plain,
    ( multiply(X_158,negative_part(inverse(X_158))) != multiply(X_158,negative_part(inverse(X_158)))
    | negative_part(inverse(X_158)) != inverse(positive_part(X_158))
    | multiply(X_158,negative_part(inverse(X_158))) = multiply(X_158,inverse(positive_part(X_158))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_158,negative_part(inverse(X_158))),multiply(X_158,negative_part(inverse(X_158)))) ),[1,1],$fot(inverse(positive_part(X_158)))]]) ).

cnf(refute_0_1046,plain,
    ( negative_part(inverse(X_158)) != inverse(positive_part(X_158))
    | multiply(X_158,negative_part(inverse(X_158))) = multiply(X_158,inverse(positive_part(X_158))) ),
    inference(resolve,[$cnf( $equal(multiply(X_158,negative_part(inverse(X_158))),multiply(X_158,negative_part(inverse(X_158)))) )],[refute_0_1044,refute_0_1045]) ).

cnf(refute_0_1047,plain,
    multiply(X_158,negative_part(inverse(X_158))) = multiply(X_158,inverse(positive_part(X_158))),
    inference(resolve,[$cnf( $equal(negative_part(inverse(X_158)),inverse(positive_part(X_158))) )],[refute_0_1043,refute_0_1046]) ).

cnf(refute_0_1048,plain,
    ( multiply(X_158,inverse(positive_part(X_158))) != inverse(positive_part(inverse(X_158)))
    | multiply(X_158,negative_part(inverse(X_158))) != multiply(X_158,inverse(positive_part(X_158)))
    | multiply(X_158,negative_part(inverse(X_158))) = inverse(positive_part(inverse(X_158))) ),
    inference(subst,[],[refute_0_110:[bind(X0,$fot(multiply(X_158,negative_part(inverse(X_158))))),bind(Y0,$fot(multiply(X_158,inverse(positive_part(X_158))))),bind(Z0,$fot(inverse(positive_part(inverse(X_158)))))]]) ).

cnf(refute_0_1049,plain,
    ( multiply(X_158,inverse(positive_part(X_158))) != inverse(positive_part(inverse(X_158)))
    | multiply(X_158,negative_part(inverse(X_158))) = inverse(positive_part(inverse(X_158))) ),
    inference(resolve,[$cnf( $equal(multiply(X_158,negative_part(inverse(X_158))),multiply(X_158,inverse(positive_part(X_158)))) )],[refute_0_1047,refute_0_1048]) ).

cnf(refute_0_1050,plain,
    multiply(X_158,negative_part(inverse(X_158))) = inverse(positive_part(inverse(X_158))),
    inference(resolve,[$cnf( $equal(multiply(X_158,inverse(positive_part(X_158))),inverse(positive_part(inverse(X_158)))) )],[refute_0_466,refute_0_1049]) ).

cnf(refute_0_1051,plain,
    ( multiply(X_158,negative_part(inverse(X_158))) != inverse(positive_part(inverse(X_158)))
    | multiply(X_158,negative_part(inverse(X_158))) != negative_part(X_158)
    | inverse(positive_part(inverse(X_158))) = negative_part(X_158) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_158,negative_part(inverse(X_158))),negative_part(X_158)) ),[0],$fot(inverse(positive_part(inverse(X_158))))]]) ).

cnf(refute_0_1052,plain,
    ( multiply(X_158,negative_part(inverse(X_158))) != negative_part(X_158)
    | inverse(positive_part(inverse(X_158))) = negative_part(X_158) ),
    inference(resolve,[$cnf( $equal(multiply(X_158,negative_part(inverse(X_158))),inverse(positive_part(inverse(X_158)))) )],[refute_0_1050,refute_0_1051]) ).

cnf(refute_0_1053,plain,
    inverse(positive_part(inverse(X_158))) = negative_part(X_158),
    inference(resolve,[$cnf( $equal(multiply(X_158,negative_part(inverse(X_158))),negative_part(X_158)) )],[refute_0_413,refute_0_1052]) ).

cnf(refute_0_1054,plain,
    inverse(positive_part(inverse(X_134))) = negative_part(X_134),
    inference(subst,[],[refute_0_1053:[bind(X_158,$fot(X_134))]]) ).

cnf(refute_0_1055,plain,
    multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))) = multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))),
    introduced(tautology,[refl,[$fot(multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))))]]) ).

cnf(refute_0_1056,plain,
    ( multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))) != multiply(positive_part(X_134),inverse(positive_part(inverse(X_134))))
    | inverse(positive_part(inverse(X_134))) != negative_part(X_134)
    | multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))) = multiply(positive_part(X_134),negative_part(X_134)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))),multiply(positive_part(X_134),inverse(positive_part(inverse(X_134))))) ),[1,1],$fot(negative_part(X_134))]]) ).

cnf(refute_0_1057,plain,
    ( inverse(positive_part(inverse(X_134))) != negative_part(X_134)
    | multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))) = multiply(positive_part(X_134),negative_part(X_134)) ),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))),multiply(positive_part(X_134),inverse(positive_part(inverse(X_134))))) )],[refute_0_1055,refute_0_1056]) ).

cnf(refute_0_1058,plain,
    multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))) = multiply(positive_part(X_134),negative_part(X_134)),
    inference(resolve,[$cnf( $equal(inverse(positive_part(inverse(X_134))),negative_part(X_134)) )],[refute_0_1054,refute_0_1057]) ).

cnf(refute_0_1059,plain,
    ( X_134 != multiply(positive_part(X_134),inverse(positive_part(inverse(X_134))))
    | multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))) != multiply(positive_part(X_134),negative_part(X_134))
    | X_134 = multiply(positive_part(X_134),negative_part(X_134)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_134,multiply(positive_part(X_134),negative_part(X_134))) ),[0],$fot(multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))))]]) ).

cnf(refute_0_1060,plain,
    ( X_134 != multiply(positive_part(X_134),inverse(positive_part(inverse(X_134))))
    | X_134 = multiply(positive_part(X_134),negative_part(X_134)) ),
    inference(resolve,[$cnf( $equal(multiply(positive_part(X_134),inverse(positive_part(inverse(X_134)))),multiply(positive_part(X_134),negative_part(X_134))) )],[refute_0_1058,refute_0_1059]) ).

cnf(refute_0_1061,plain,
    X_134 = multiply(positive_part(X_134),negative_part(X_134)),
    inference(resolve,[$cnf( $equal(X_134,multiply(positive_part(X_134),inverse(positive_part(inverse(X_134))))) )],[refute_0_387,refute_0_1060]) ).

cnf(refute_0_1062,plain,
    ( X_134 != multiply(positive_part(X_134),negative_part(X_134))
    | multiply(positive_part(X_134),negative_part(X_134)) = X_134 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_134)),bind(Y0,$fot(multiply(positive_part(X_134),negative_part(X_134))))]]) ).

cnf(refute_0_1063,plain,
    multiply(positive_part(X_134),negative_part(X_134)) = X_134,
    inference(resolve,[$cnf( $equal(X_134,multiply(positive_part(X_134),negative_part(X_134))) )],[refute_0_1061,refute_0_1062]) ).

cnf(refute_0_1064,plain,
    multiply(positive_part(a),negative_part(a)) = a,
    inference(subst,[],[refute_0_1063:[bind(X_134,$fot(a))]]) ).

cnf(refute_0_1065,plain,
    ( multiply(positive_part(a),negative_part(a)) != a
    | a != a
    | a = multiply(positive_part(a),negative_part(a)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(a,multiply(positive_part(a),negative_part(a))) ),[1],$fot(a)]]) ).

cnf(refute_0_1066,plain,
    ( a != a
    | a = multiply(positive_part(a),negative_part(a)) ),
    inference(resolve,[$cnf( $equal(multiply(positive_part(a),negative_part(a)),a) )],[refute_0_1064,refute_0_1065]) ).

cnf(refute_0_1067,plain,
    a != a,
    inference(resolve,[$cnf( $equal(a,multiply(positive_part(a),negative_part(a))) )],[refute_0_1066,prove_lat4]) ).

cnf(refute_0_1068,plain,
    a = a,
    introduced(tautology,[refl,[$fot(a)]]) ).

cnf(refute_0_1069,plain,
    $false,
    inference(resolve,[$cnf( $equal(a,a) )],[refute_0_1068,refute_0_1067]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP167-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jun 13 03:58:56 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.76/6.95  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.76/6.95  
% 6.76/6.95  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.84/7.05  
%------------------------------------------------------------------------------