Metis---2.4.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP181-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n032.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 10:37:35 EDT 2022

% Result   : Unsatisfiable 30.57s 30.75s
% Output   : CNFRefutation 31.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :  174
%            Number of leaves      : 1315
% Syntax   : Number of clauses     : 6230 (3072 unt;   0 nHn;3902 RR)
%            Number of literals    : 10781 (10780 equ;4553 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   : 8655 (  56 sgn)

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

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

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

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

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

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

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

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

cnf(idempotence_of_gld,axiom,
    greatest_lower_bound(X,X) = X ).

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

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

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

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

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

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

cnf(p12x_1,hypothesis,
    greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ).

cnf(p12x_2,hypothesis,
    least_upper_bound(a,c) = least_upper_bound(b,c) ).

cnf(p12x_3,hypothesis,
    inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ).

cnf(p12x_4,hypothesis,
    inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) ).

cnf(prove_p12x,negated_conjecture,
    a != b ).

cnf(refute_0_0,plain,
    multiply(multiply(inverse(X_59),X_59),X_60) = multiply(inverse(X_59),multiply(X_59,X_60)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_59))),bind(Y,$fot(X_59)),bind(Z,$fot(X_60))]]) ).

cnf(refute_0_1,plain,
    multiply(inverse(X_59),X_59) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_59))]]) ).

cnf(refute_0_2,plain,
    ( multiply(multiply(inverse(X_59),X_59),X_60) != multiply(inverse(X_59),multiply(X_59,X_60))
    | multiply(inverse(X_59),X_59) != identity
    | multiply(identity,X_60) = multiply(inverse(X_59),multiply(X_59,X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_59),X_59),X_60),multiply(inverse(X_59),multiply(X_59,X_60))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_3,plain,
    ( multiply(multiply(inverse(X_59),X_59),X_60) != multiply(inverse(X_59),multiply(X_59,X_60))
    | multiply(identity,X_60) = multiply(inverse(X_59),multiply(X_59,X_60)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_59),X_59),identity) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    multiply(identity,X_60) = multiply(inverse(X_59),multiply(X_59,X_60)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_59),X_59),X_60),multiply(inverse(X_59),multiply(X_59,X_60))) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    multiply(identity,X_60) = X_60,
    inference(subst,[],[left_identity:[bind(X,$fot(X_60))]]) ).

cnf(refute_0_6,plain,
    ( multiply(identity,X_60) != X_60
    | multiply(identity,X_60) != multiply(inverse(X_59),multiply(X_59,X_60))
    | X_60 = multiply(inverse(X_59),multiply(X_59,X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_60),multiply(inverse(X_59),multiply(X_59,X_60))) ),[0],$fot(X_60)]]) ).

cnf(refute_0_7,plain,
    ( multiply(identity,X_60) != multiply(inverse(X_59),multiply(X_59,X_60))
    | X_60 = multiply(inverse(X_59),multiply(X_59,X_60)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_60),X_60) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    X_60 = multiply(inverse(X_59),multiply(X_59,X_60)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_60),multiply(inverse(X_59),multiply(X_59,X_60))) )],[refute_0_4,refute_0_7]) ).

cnf(refute_0_9,plain,
    X_62 = multiply(inverse(inverse(X_62)),multiply(inverse(X_62),X_62)),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(inverse(X_62))),bind(X_60,$fot(X_62))]]) ).

cnf(refute_0_10,plain,
    multiply(inverse(X_62),X_62) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_62))]]) ).

cnf(refute_0_11,plain,
    ( X_62 != multiply(inverse(inverse(X_62)),multiply(inverse(X_62),X_62))
    | multiply(inverse(X_62),X_62) != identity
    | X_62 = multiply(inverse(inverse(X_62)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(X_62,multiply(inverse(inverse(X_62)),multiply(inverse(X_62),X_62))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_12,plain,
    ( X_62 != multiply(inverse(inverse(X_62)),multiply(inverse(X_62),X_62))
    | X_62 = multiply(inverse(inverse(X_62)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_62),X_62),identity) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    X_62 = multiply(inverse(inverse(X_62)),identity),
    inference(resolve,[$cnf( $equal(X_62,multiply(inverse(inverse(X_62)),multiply(inverse(X_62),X_62))) )],[refute_0_9,refute_0_12]) ).

cnf(refute_0_14,plain,
    multiply(X_61,X_62) = multiply(inverse(inverse(X_61)),multiply(inverse(X_61),multiply(X_61,X_62))),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(inverse(X_61))),bind(X_60,$fot(multiply(X_61,X_62)))]]) ).

cnf(refute_0_15,plain,
    X_62 = multiply(inverse(X_61),multiply(X_61,X_62)),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(X_61)),bind(X_60,$fot(X_62))]]) ).

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,
    ( X_62 != multiply(inverse(X_61),multiply(X_61,X_62))
    | multiply(inverse(X_61),multiply(X_61,X_62)) = X_62 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_62)),bind(Y0,$fot(multiply(inverse(X_61),multiply(X_61,X_62))))]]) ).

cnf(refute_0_20,plain,
    multiply(inverse(X_61),multiply(X_61,X_62)) = X_62,
    inference(resolve,[$cnf( $equal(X_62,multiply(inverse(X_61),multiply(X_61,X_62))) )],[refute_0_15,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( multiply(X_61,X_62) != multiply(inverse(inverse(X_61)),multiply(inverse(X_61),multiply(X_61,X_62)))
    | multiply(inverse(X_61),multiply(X_61,X_62)) != X_62
    | multiply(X_61,X_62) = multiply(inverse(inverse(X_61)),X_62) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_61,X_62),multiply(inverse(inverse(X_61)),multiply(inverse(X_61),multiply(X_61,X_62)))) ),[1,1],$fot(X_62)]]) ).

cnf(refute_0_22,plain,
    ( multiply(X_61,X_62) != multiply(inverse(inverse(X_61)),multiply(inverse(X_61),multiply(X_61,X_62)))
    | multiply(X_61,X_62) = multiply(inverse(inverse(X_61)),X_62) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_61),multiply(X_61,X_62)),X_62) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    multiply(X_61,X_62) = multiply(inverse(inverse(X_61)),X_62),
    inference(resolve,[$cnf( $equal(multiply(X_61,X_62),multiply(inverse(inverse(X_61)),multiply(inverse(X_61),multiply(X_61,X_62)))) )],[refute_0_14,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( multiply(X_61,X_62) != multiply(inverse(inverse(X_61)),X_62)
    | multiply(inverse(inverse(X_61)),X_62) = multiply(X_61,X_62) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_61,X_62))),bind(Y0,$fot(multiply(inverse(inverse(X_61)),X_62)))]]) ).

cnf(refute_0_25,plain,
    multiply(inverse(inverse(X_61)),X_62) = multiply(X_61,X_62),
    inference(resolve,[$cnf( $equal(multiply(X_61,X_62),multiply(inverse(inverse(X_61)),X_62)) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    multiply(inverse(inverse(X_62)),identity) = multiply(X_62,identity),
    inference(subst,[],[refute_0_25:[bind(X_61,$fot(X_62)),bind(X_62,$fot(identity))]]) ).

cnf(refute_0_27,plain,
    ( X_62 != multiply(inverse(inverse(X_62)),identity)
    | multiply(inverse(inverse(X_62)),identity) != multiply(X_62,identity)
    | X_62 = multiply(X_62,identity) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_62,multiply(X_62,identity)) ),[0],$fot(multiply(inverse(inverse(X_62)),identity))]]) ).

cnf(refute_0_28,plain,
    ( X_62 != multiply(inverse(inverse(X_62)),identity)
    | X_62 = multiply(X_62,identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_62)),identity),multiply(X_62,identity)) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    X_62 = multiply(X_62,identity),
    inference(resolve,[$cnf( $equal(X_62,multiply(inverse(inverse(X_62)),identity)) )],[refute_0_13,refute_0_28]) ).

cnf(refute_0_30,plain,
    inverse(inverse(X_87)) = multiply(inverse(inverse(X_87)),identity),
    inference(subst,[],[refute_0_29:[bind(X_62,$fot(inverse(inverse(X_87))))]]) ).

cnf(refute_0_31,plain,
    multiply(X_87,identity) = multiply(inverse(inverse(X_87)),identity),
    inference(subst,[],[refute_0_23:[bind(X_61,$fot(X_87)),bind(X_62,$fot(identity))]]) ).

cnf(refute_0_32,plain,
    ( multiply(X_87,identity) != multiply(inverse(inverse(X_87)),identity)
    | multiply(inverse(inverse(X_87)),identity) = multiply(X_87,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_87,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_87)),identity)))]]) ).

cnf(refute_0_33,plain,
    multiply(inverse(inverse(X_87)),identity) = multiply(X_87,identity),
    inference(resolve,[$cnf( $equal(multiply(X_87,identity),multiply(inverse(inverse(X_87)),identity)) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    ( multiply(inverse(inverse(X_87)),identity) != multiply(X_87,identity)
    | inverse(inverse(X_87)) != multiply(inverse(inverse(X_87)),identity)
    | inverse(inverse(X_87)) = multiply(X_87,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_87)),multiply(inverse(inverse(X_87)),identity)) ),[1],$fot(multiply(X_87,identity))]]) ).

cnf(refute_0_35,plain,
    ( inverse(inverse(X_87)) != multiply(inverse(inverse(X_87)),identity)
    | inverse(inverse(X_87)) = multiply(X_87,identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_87)),identity),multiply(X_87,identity)) )],[refute_0_33,refute_0_34]) ).

cnf(refute_0_36,plain,
    inverse(inverse(X_87)) = multiply(X_87,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_87)),multiply(inverse(inverse(X_87)),identity)) )],[refute_0_30,refute_0_35]) ).

cnf(refute_0_37,plain,
    ( X_62 != multiply(X_62,identity)
    | multiply(X_62,identity) = X_62 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_62)),bind(Y0,$fot(multiply(X_62,identity)))]]) ).

cnf(refute_0_38,plain,
    multiply(X_62,identity) = X_62,
    inference(resolve,[$cnf( $equal(X_62,multiply(X_62,identity)) )],[refute_0_29,refute_0_37]) ).

cnf(refute_0_39,plain,
    multiply(X_87,identity) = X_87,
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(X_87))]]) ).

cnf(refute_0_40,plain,
    ( multiply(X_87,identity) != X_87
    | inverse(inverse(X_87)) != multiply(X_87,identity)
    | inverse(inverse(X_87)) = X_87 ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_87)),multiply(X_87,identity)) ),[1],$fot(X_87)]]) ).

cnf(refute_0_41,plain,
    ( inverse(inverse(X_87)) != multiply(X_87,identity)
    | inverse(inverse(X_87)) = X_87 ),
    inference(resolve,[$cnf( $equal(multiply(X_87,identity),X_87) )],[refute_0_39,refute_0_40]) ).

cnf(refute_0_42,plain,
    inverse(inverse(X_87)) = X_87,
    inference(resolve,[$cnf( $equal(inverse(inverse(X_87)),multiply(X_87,identity)) )],[refute_0_36,refute_0_41]) ).

cnf(refute_0_43,plain,
    inverse(inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) = greatest_lower_bound(a,least_upper_bound(b,identity)),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_44,plain,
    multiply(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)),X_60) = multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(least_upper_bound(X_16,X_17)))),bind(Y,$fot(least_upper_bound(X_17,X_16))),bind(Z,$fot(X_60))]]) ).

cnf(refute_0_45,plain,
    multiply(inverse(least_upper_bound(X_17,X_16)),least_upper_bound(X_17,X_16)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(X_17,X_16)))]]) ).

cnf(refute_0_46,plain,
    greatest_lower_bound(inverse(X_15),inverse(X_14)) = greatest_lower_bound(inverse(X_14),inverse(X_15)),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(inverse(X_15))),bind(Y,$fot(inverse(X_14)))]]) ).

cnf(refute_0_47,plain,
    inverse(least_upper_bound(X_14,X_15)) = greatest_lower_bound(inverse(X_14),inverse(X_15)),
    inference(subst,[],[p12x_4:[bind(X,$fot(X_14)),bind(Y,$fot(X_15))]]) ).

cnf(refute_0_48,plain,
    ( inverse(least_upper_bound(X_14,X_15)) != greatest_lower_bound(inverse(X_14),inverse(X_15))
    | greatest_lower_bound(inverse(X_14),inverse(X_15)) = inverse(least_upper_bound(X_14,X_15)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(least_upper_bound(X_14,X_15)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_14),inverse(X_15))))]]) ).

cnf(refute_0_49,plain,
    greatest_lower_bound(inverse(X_14),inverse(X_15)) = inverse(least_upper_bound(X_14,X_15)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_14,X_15)),greatest_lower_bound(inverse(X_14),inverse(X_15))) )],[refute_0_47,refute_0_48]) ).

cnf(refute_0_50,plain,
    ( greatest_lower_bound(inverse(X_14),inverse(X_15)) != inverse(least_upper_bound(X_14,X_15))
    | greatest_lower_bound(inverse(X_15),inverse(X_14)) != greatest_lower_bound(inverse(X_14),inverse(X_15))
    | greatest_lower_bound(inverse(X_15),inverse(X_14)) = inverse(least_upper_bound(X_14,X_15)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(X_15),inverse(X_14)),greatest_lower_bound(inverse(X_14),inverse(X_15))) ),[1],$fot(inverse(least_upper_bound(X_14,X_15)))]]) ).

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

cnf(refute_0_52,plain,
    greatest_lower_bound(inverse(X_15),inverse(X_14)) = inverse(least_upper_bound(X_14,X_15)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_15),inverse(X_14)),greatest_lower_bound(inverse(X_14),inverse(X_15))) )],[refute_0_46,refute_0_51]) ).

cnf(refute_0_53,plain,
    ( inverse(least_upper_bound(X,Y)) != greatest_lower_bound(inverse(X),inverse(Y))
    | greatest_lower_bound(inverse(X),inverse(Y)) = inverse(least_upper_bound(X,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(least_upper_bound(X,Y)))),bind(Y0,$fot(greatest_lower_bound(inverse(X),inverse(Y))))]]) ).

cnf(refute_0_54,plain,
    greatest_lower_bound(inverse(X),inverse(Y)) = inverse(least_upper_bound(X,Y)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X,Y)),greatest_lower_bound(inverse(X),inverse(Y))) )],[p12x_4,refute_0_53]) ).

cnf(refute_0_55,plain,
    greatest_lower_bound(inverse(X_15),inverse(X_14)) = inverse(least_upper_bound(X_15,X_14)),
    inference(subst,[],[refute_0_54:[bind(X,$fot(X_15)),bind(Y,$fot(X_14))]]) ).

cnf(refute_0_56,plain,
    ( greatest_lower_bound(inverse(X_15),inverse(X_14)) != inverse(least_upper_bound(X_14,X_15))
    | greatest_lower_bound(inverse(X_15),inverse(X_14)) != inverse(least_upper_bound(X_15,X_14))
    | inverse(least_upper_bound(X_15,X_14)) = inverse(least_upper_bound(X_14,X_15)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(X_15),inverse(X_14)),inverse(least_upper_bound(X_14,X_15))) ),[0],$fot(inverse(least_upper_bound(X_15,X_14)))]]) ).

cnf(refute_0_57,plain,
    ( greatest_lower_bound(inverse(X_15),inverse(X_14)) != inverse(least_upper_bound(X_14,X_15))
    | inverse(least_upper_bound(X_15,X_14)) = inverse(least_upper_bound(X_14,X_15)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_15),inverse(X_14)),inverse(least_upper_bound(X_15,X_14))) )],[refute_0_55,refute_0_56]) ).

cnf(refute_0_58,plain,
    inverse(least_upper_bound(X_15,X_14)) = inverse(least_upper_bound(X_14,X_15)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_15),inverse(X_14)),inverse(least_upper_bound(X_14,X_15))) )],[refute_0_52,refute_0_57]) ).

cnf(refute_0_59,plain,
    inverse(least_upper_bound(X_17,X_16)) = inverse(least_upper_bound(X_16,X_17)),
    inference(subst,[],[refute_0_58:[bind(X_14,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).

cnf(refute_0_60,plain,
    ( multiply(inverse(least_upper_bound(X_17,X_16)),least_upper_bound(X_17,X_16)) != identity
    | inverse(least_upper_bound(X_17,X_16)) != inverse(least_upper_bound(X_16,X_17))
    | multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_17,X_16)),least_upper_bound(X_17,X_16)),identity) ),[0,0],$fot(inverse(least_upper_bound(X_16,X_17)))]]) ).

cnf(refute_0_61,plain,
    ( multiply(inverse(least_upper_bound(X_17,X_16)),least_upper_bound(X_17,X_16)) != identity
    | multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) = identity ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_17,X_16)),inverse(least_upper_bound(X_16,X_17))) )],[refute_0_59,refute_0_60]) ).

cnf(refute_0_62,plain,
    multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_17,X_16)),least_upper_bound(X_17,X_16)),identity) )],[refute_0_45,refute_0_61]) ).

cnf(refute_0_63,plain,
    ( multiply(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)),X_60) != multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))
    | multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) != identity
    | multiply(identity,X_60) = multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)),X_60),multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_64,plain,
    ( multiply(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)),X_60) != multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))
    | multiply(identity,X_60) = multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)),identity) )],[refute_0_62,refute_0_63]) ).

cnf(refute_0_65,plain,
    multiply(identity,X_60) = multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)),X_60),multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))) )],[refute_0_44,refute_0_64]) ).

cnf(refute_0_66,plain,
    ( multiply(identity,X_60) != X_60
    | multiply(identity,X_60) != multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))
    | X_60 = multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_60),multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))) ),[0],$fot(X_60)]]) ).

cnf(refute_0_67,plain,
    ( multiply(identity,X_60) != multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))
    | X_60 = multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_60),X_60) )],[refute_0_5,refute_0_66]) ).

cnf(refute_0_68,plain,
    X_60 = multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_60),multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))) )],[refute_0_65,refute_0_67]) ).

cnf(refute_0_69,plain,
    X_60 = multiply(inverse(least_upper_bound(inverse(X_60),X_17)),multiply(least_upper_bound(X_17,inverse(X_60)),X_60)),
    inference(subst,[],[refute_0_68:[bind(X_16,$fot(inverse(X_60)))]]) ).

cnf(refute_0_70,plain,
    multiply(least_upper_bound(X_111,inverse(X_110)),X_110) = least_upper_bound(multiply(X_111,X_110),multiply(inverse(X_110),X_110)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_110)),bind(Y,$fot(X_111)),bind(Z,$fot(inverse(X_110)))]]) ).

cnf(refute_0_71,plain,
    multiply(inverse(X_110),X_110) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_110))]]) ).

cnf(refute_0_72,plain,
    ( multiply(inverse(X_110),X_110) != identity
    | multiply(least_upper_bound(X_111,inverse(X_110)),X_110) != least_upper_bound(multiply(X_111,X_110),multiply(inverse(X_110),X_110))
    | multiply(least_upper_bound(X_111,inverse(X_110)),X_110) = least_upper_bound(multiply(X_111,X_110),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_111,inverse(X_110)),X_110),least_upper_bound(multiply(X_111,X_110),multiply(inverse(X_110),X_110))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_73,plain,
    ( multiply(least_upper_bound(X_111,inverse(X_110)),X_110) != least_upper_bound(multiply(X_111,X_110),multiply(inverse(X_110),X_110))
    | multiply(least_upper_bound(X_111,inverse(X_110)),X_110) = least_upper_bound(multiply(X_111,X_110),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_110),X_110),identity) )],[refute_0_71,refute_0_72]) ).

cnf(refute_0_74,plain,
    multiply(least_upper_bound(X_111,inverse(X_110)),X_110) = least_upper_bound(multiply(X_111,X_110),identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,inverse(X_110)),X_110),least_upper_bound(multiply(X_111,X_110),multiply(inverse(X_110),X_110))) )],[refute_0_70,refute_0_73]) ).

cnf(refute_0_75,plain,
    least_upper_bound(X_17,X_16) = multiply(inverse(inverse(least_upper_bound(X_16,X_17))),multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16))),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(inverse(least_upper_bound(X_16,X_17)))),bind(X_60,$fot(least_upper_bound(X_17,X_16)))]]) ).

cnf(refute_0_76,plain,
    ( multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)) != identity
    | least_upper_bound(X_17,X_16) != multiply(inverse(inverse(least_upper_bound(X_16,X_17))),multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)))
    | least_upper_bound(X_17,X_16) = multiply(inverse(inverse(least_upper_bound(X_16,X_17))),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,X_16),multiply(inverse(inverse(least_upper_bound(X_16,X_17))),multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_77,plain,
    ( least_upper_bound(X_17,X_16) != multiply(inverse(inverse(least_upper_bound(X_16,X_17))),multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)))
    | least_upper_bound(X_17,X_16) = multiply(inverse(inverse(least_upper_bound(X_16,X_17))),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)),identity) )],[refute_0_62,refute_0_76]) ).

cnf(refute_0_78,plain,
    least_upper_bound(X_17,X_16) = multiply(inverse(inverse(least_upper_bound(X_16,X_17))),identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_17,X_16),multiply(inverse(inverse(least_upper_bound(X_16,X_17))),multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_17,X_16)))) )],[refute_0_75,refute_0_77]) ).

cnf(refute_0_79,plain,
    multiply(inverse(inverse(least_upper_bound(X_16,X_17))),identity) = multiply(least_upper_bound(X_16,X_17),identity),
    inference(subst,[],[refute_0_25:[bind(X_61,$fot(least_upper_bound(X_16,X_17))),bind(X_62,$fot(identity))]]) ).

cnf(refute_0_80,plain,
    ( multiply(inverse(inverse(least_upper_bound(X_16,X_17))),identity) != multiply(least_upper_bound(X_16,X_17),identity)
    | least_upper_bound(X_17,X_16) != multiply(inverse(inverse(least_upper_bound(X_16,X_17))),identity)
    | least_upper_bound(X_17,X_16) = multiply(least_upper_bound(X_16,X_17),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,X_16),multiply(inverse(inverse(least_upper_bound(X_16,X_17))),identity)) ),[1],$fot(multiply(least_upper_bound(X_16,X_17),identity))]]) ).

cnf(refute_0_81,plain,
    ( least_upper_bound(X_17,X_16) != multiply(inverse(inverse(least_upper_bound(X_16,X_17))),identity)
    | least_upper_bound(X_17,X_16) = multiply(least_upper_bound(X_16,X_17),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X_16,X_17))),identity),multiply(least_upper_bound(X_16,X_17),identity)) )],[refute_0_79,refute_0_80]) ).

cnf(refute_0_82,plain,
    least_upper_bound(X_17,X_16) = multiply(least_upper_bound(X_16,X_17),identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_17,X_16),multiply(inverse(inverse(least_upper_bound(X_16,X_17))),identity)) )],[refute_0_78,refute_0_81]) ).

cnf(refute_0_83,plain,
    multiply(least_upper_bound(X_16,X_17),identity) = least_upper_bound(X_16,X_17),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(least_upper_bound(X_16,X_17)))]]) ).

cnf(refute_0_84,plain,
    ( multiply(least_upper_bound(X_16,X_17),identity) != least_upper_bound(X_16,X_17)
    | least_upper_bound(X_17,X_16) != multiply(least_upper_bound(X_16,X_17),identity)
    | least_upper_bound(X_17,X_16) = least_upper_bound(X_16,X_17) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_17,X_16),multiply(least_upper_bound(X_16,X_17),identity)) ),[1],$fot(least_upper_bound(X_16,X_17))]]) ).

cnf(refute_0_85,plain,
    ( least_upper_bound(X_17,X_16) != multiply(least_upper_bound(X_16,X_17),identity)
    | least_upper_bound(X_17,X_16) = least_upper_bound(X_16,X_17) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_16,X_17),identity),least_upper_bound(X_16,X_17)) )],[refute_0_83,refute_0_84]) ).

cnf(refute_0_86,plain,
    least_upper_bound(X_17,X_16) = least_upper_bound(X_16,X_17),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_17,X_16),multiply(least_upper_bound(X_16,X_17),identity)) )],[refute_0_82,refute_0_85]) ).

cnf(refute_0_87,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_88,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_86,refute_0_87]) ).

cnf(refute_0_89,plain,
    least_upper_bound(multiply(X_111,X_110),identity) = least_upper_bound(identity,multiply(X_111,X_110)),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(multiply(X_111,X_110))),bind(X_17,$fot(identity))]]) ).

cnf(refute_0_90,plain,
    ( multiply(least_upper_bound(X_111,inverse(X_110)),X_110) != least_upper_bound(multiply(X_111,X_110),identity)
    | least_upper_bound(multiply(X_111,X_110),identity) != least_upper_bound(identity,multiply(X_111,X_110))
    | multiply(least_upper_bound(X_111,inverse(X_110)),X_110) = least_upper_bound(identity,multiply(X_111,X_110)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_111,inverse(X_110)),X_110),least_upper_bound(identity,multiply(X_111,X_110))) ),[0],$fot(least_upper_bound(multiply(X_111,X_110),identity))]]) ).

cnf(refute_0_91,plain,
    ( multiply(least_upper_bound(X_111,inverse(X_110)),X_110) != least_upper_bound(multiply(X_111,X_110),identity)
    | multiply(least_upper_bound(X_111,inverse(X_110)),X_110) = least_upper_bound(identity,multiply(X_111,X_110)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_111,X_110),identity),least_upper_bound(identity,multiply(X_111,X_110))) )],[refute_0_89,refute_0_90]) ).

cnf(refute_0_92,plain,
    multiply(least_upper_bound(X_111,inverse(X_110)),X_110) = least_upper_bound(identity,multiply(X_111,X_110)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,inverse(X_110)),X_110),least_upper_bound(multiply(X_111,X_110),identity)) )],[refute_0_74,refute_0_91]) ).

cnf(refute_0_93,plain,
    multiply(least_upper_bound(X_17,inverse(X_60)),X_60) = least_upper_bound(identity,multiply(X_17,X_60)),
    inference(subst,[],[refute_0_92:[bind(X_110,$fot(X_60)),bind(X_111,$fot(X_17))]]) ).

cnf(refute_0_94,plain,
    ( X_60 != multiply(inverse(least_upper_bound(inverse(X_60),X_17)),multiply(least_upper_bound(X_17,inverse(X_60)),X_60))
    | multiply(least_upper_bound(X_17,inverse(X_60)),X_60) != least_upper_bound(identity,multiply(X_17,X_60))
    | X_60 = multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))) ),
    introduced(tautology,[equality,[$cnf( $equal(X_60,multiply(inverse(least_upper_bound(inverse(X_60),X_17)),multiply(least_upper_bound(X_17,inverse(X_60)),X_60))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_17,X_60)))]]) ).

cnf(refute_0_95,plain,
    ( X_60 != multiply(inverse(least_upper_bound(inverse(X_60),X_17)),multiply(least_upper_bound(X_17,inverse(X_60)),X_60))
    | X_60 = multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_17,inverse(X_60)),X_60),least_upper_bound(identity,multiply(X_17,X_60))) )],[refute_0_93,refute_0_94]) ).

cnf(refute_0_96,plain,
    X_60 = multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))),
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(least_upper_bound(inverse(X_60),X_17)),multiply(least_upper_bound(X_17,inverse(X_60)),X_60))) )],[refute_0_69,refute_0_95]) ).

cnf(refute_0_97,plain,
    inverse(least_upper_bound(inverse(X_89),Y)) = greatest_lower_bound(inverse(inverse(X_89)),inverse(Y)),
    inference(subst,[],[p12x_4:[bind(X,$fot(inverse(X_89)))]]) ).

cnf(refute_0_98,plain,
    inverse(inverse(X_89)) = X_89,
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(X_89))]]) ).

cnf(refute_0_99,plain,
    ( inverse(inverse(X_89)) != X_89
    | inverse(least_upper_bound(inverse(X_89),Y)) != greatest_lower_bound(inverse(inverse(X_89)),inverse(Y))
    | inverse(least_upper_bound(inverse(X_89),Y)) = greatest_lower_bound(X_89,inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(X_89),Y)),greatest_lower_bound(inverse(inverse(X_89)),inverse(Y))) ),[1,0],$fot(X_89)]]) ).

cnf(refute_0_100,plain,
    ( inverse(least_upper_bound(inverse(X_89),Y)) != greatest_lower_bound(inverse(inverse(X_89)),inverse(Y))
    | inverse(least_upper_bound(inverse(X_89),Y)) = greatest_lower_bound(X_89,inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_89)),X_89) )],[refute_0_98,refute_0_99]) ).

cnf(refute_0_101,plain,
    inverse(least_upper_bound(inverse(X_89),Y)) = greatest_lower_bound(X_89,inverse(Y)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_89),Y)),greatest_lower_bound(inverse(inverse(X_89)),inverse(Y))) )],[refute_0_97,refute_0_100]) ).

cnf(refute_0_102,plain,
    inverse(least_upper_bound(inverse(X_60),X_17)) = greatest_lower_bound(X_60,inverse(X_17)),
    inference(subst,[],[refute_0_101:[bind(Y,$fot(X_17)),bind(X_89,$fot(X_60))]]) ).

cnf(refute_0_103,plain,
    multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))) = multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))),
    introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))))]]) ).

cnf(refute_0_104,plain,
    ( multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))) != multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60)))
    | inverse(least_upper_bound(inverse(X_60),X_17)) != greatest_lower_bound(X_60,inverse(X_17))
    | multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))) = multiply(greatest_lower_bound(X_60,inverse(X_17)),least_upper_bound(identity,multiply(X_17,X_60))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))),multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60)))) ),[1,0],$fot(greatest_lower_bound(X_60,inverse(X_17)))]]) ).

cnf(refute_0_105,plain,
    ( inverse(least_upper_bound(inverse(X_60),X_17)) != greatest_lower_bound(X_60,inverse(X_17))
    | multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))) = multiply(greatest_lower_bound(X_60,inverse(X_17)),least_upper_bound(identity,multiply(X_17,X_60))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))),multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60)))) )],[refute_0_103,refute_0_104]) ).

cnf(refute_0_106,plain,
    multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))) = multiply(greatest_lower_bound(X_60,inverse(X_17)),least_upper_bound(identity,multiply(X_17,X_60))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(X_60),X_17)),greatest_lower_bound(X_60,inverse(X_17))) )],[refute_0_102,refute_0_105]) ).

cnf(refute_0_107,plain,
    ( X_60 != multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60)))
    | multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))) != multiply(greatest_lower_bound(X_60,inverse(X_17)),least_upper_bound(identity,multiply(X_17,X_60)))
    | X_60 = multiply(greatest_lower_bound(X_60,inverse(X_17)),least_upper_bound(identity,multiply(X_17,X_60))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_60,multiply(greatest_lower_bound(X_60,inverse(X_17)),least_upper_bound(identity,multiply(X_17,X_60)))) ),[0],$fot(multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))))]]) ).

cnf(refute_0_108,plain,
    ( X_60 != multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60)))
    | X_60 = multiply(greatest_lower_bound(X_60,inverse(X_17)),least_upper_bound(identity,multiply(X_17,X_60))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60))),multiply(greatest_lower_bound(X_60,inverse(X_17)),least_upper_bound(identity,multiply(X_17,X_60)))) )],[refute_0_106,refute_0_107]) ).

cnf(refute_0_109,plain,
    X_60 = multiply(greatest_lower_bound(X_60,inverse(X_17)),least_upper_bound(identity,multiply(X_17,X_60))),
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(least_upper_bound(inverse(X_60),X_17)),least_upper_bound(identity,multiply(X_17,X_60)))) )],[refute_0_96,refute_0_108]) ).

cnf(refute_0_110,plain,
    inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) = multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))))),
    inference(subst,[],[refute_0_109:[bind(X_17,$fot(least_upper_bound(a,c))),bind(X_60,$fot(inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_111,plain,
    least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) = X_8,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).

cnf(refute_0_112,plain,
    greatest_lower_bound(X_9,X_8) = greatest_lower_bound(X_8,X_9),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).

cnf(refute_0_113,plain,
    ( greatest_lower_bound(X_9,X_8) != greatest_lower_bound(X_8,X_9)
    | greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_9,X_8))),bind(Y0,$fot(greatest_lower_bound(X_8,X_9)))]]) ).

cnf(refute_0_114,plain,
    greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,X_8),greatest_lower_bound(X_8,X_9)) )],[refute_0_112,refute_0_113]) ).

cnf(refute_0_115,plain,
    ( greatest_lower_bound(X_8,X_9) != greatest_lower_bound(X_9,X_8)
    | least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
    | least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) ),[0,1],$fot(greatest_lower_bound(X_9,X_8))]]) ).

cnf(refute_0_116,plain,
    ( least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
    | least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,X_9),greatest_lower_bound(X_9,X_8)) )],[refute_0_114,refute_0_115]) ).

cnf(refute_0_117,plain,
    least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8,
    inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) )],[refute_0_111,refute_0_116]) ).

cnf(refute_0_118,plain,
    least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))) = multiply(c,inverse(greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_117:[bind(X_8,$fot(multiply(c,inverse(greatest_lower_bound(a,c))))),bind(X_9,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_119,plain,
    multiply(X_107,greatest_lower_bound(X_108,identity)) = greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,identity)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_107)),bind(Y,$fot(X_108)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_120,plain,
    X_107 = multiply(X_107,identity),
    inference(subst,[],[refute_0_29:[bind(X_62,$fot(X_107))]]) ).

cnf(refute_0_121,plain,
    ( X_107 != multiply(X_107,identity)
    | multiply(X_107,identity) = X_107 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_107)),bind(Y0,$fot(multiply(X_107,identity)))]]) ).

cnf(refute_0_122,plain,
    multiply(X_107,identity) = X_107,
    inference(resolve,[$cnf( $equal(X_107,multiply(X_107,identity)) )],[refute_0_120,refute_0_121]) ).

cnf(refute_0_123,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,identity)) != greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,identity))
    | multiply(X_107,identity) != X_107
    | multiply(X_107,greatest_lower_bound(X_108,identity)) = greatest_lower_bound(multiply(X_107,X_108),X_107) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,identity)),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,identity))) ),[1,1],$fot(X_107)]]) ).

cnf(refute_0_124,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,identity)) != greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,identity))
    | multiply(X_107,greatest_lower_bound(X_108,identity)) = greatest_lower_bound(multiply(X_107,X_108),X_107) ),
    inference(resolve,[$cnf( $equal(multiply(X_107,identity),X_107) )],[refute_0_122,refute_0_123]) ).

cnf(refute_0_125,plain,
    multiply(X_107,greatest_lower_bound(X_108,identity)) = greatest_lower_bound(multiply(X_107,X_108),X_107),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,identity)),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,identity))) )],[refute_0_119,refute_0_124]) ).

cnf(refute_0_126,plain,
    greatest_lower_bound(X_25,X_24) = multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24))),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(inverse(greatest_lower_bound(X_24,X_25)))),bind(X_60,$fot(greatest_lower_bound(X_25,X_24)))]]) ).

cnf(refute_0_127,plain,
    multiply(inverse(greatest_lower_bound(X_25,X_24)),greatest_lower_bound(X_25,X_24)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(greatest_lower_bound(X_25,X_24)))]]) ).

cnf(refute_0_128,plain,
    least_upper_bound(inverse(X_13),inverse(X_12)) = least_upper_bound(inverse(X_12),inverse(X_13)),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(inverse(X_13))),bind(Y,$fot(inverse(X_12)))]]) ).

cnf(refute_0_129,plain,
    inverse(greatest_lower_bound(X_12,X_13)) = least_upper_bound(inverse(X_12),inverse(X_13)),
    inference(subst,[],[p12x_3:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).

cnf(refute_0_130,plain,
    ( inverse(greatest_lower_bound(X_12,X_13)) != least_upper_bound(inverse(X_12),inverse(X_13))
    | least_upper_bound(inverse(X_12),inverse(X_13)) = inverse(greatest_lower_bound(X_12,X_13)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(X_12,X_13)))),bind(Y0,$fot(least_upper_bound(inverse(X_12),inverse(X_13))))]]) ).

cnf(refute_0_131,plain,
    least_upper_bound(inverse(X_12),inverse(X_13)) = inverse(greatest_lower_bound(X_12,X_13)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_12,X_13)),least_upper_bound(inverse(X_12),inverse(X_13))) )],[refute_0_129,refute_0_130]) ).

cnf(refute_0_132,plain,
    ( least_upper_bound(inverse(X_12),inverse(X_13)) != inverse(greatest_lower_bound(X_12,X_13))
    | least_upper_bound(inverse(X_13),inverse(X_12)) != least_upper_bound(inverse(X_12),inverse(X_13))
    | least_upper_bound(inverse(X_13),inverse(X_12)) = inverse(greatest_lower_bound(X_12,X_13)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X_13),inverse(X_12)),least_upper_bound(inverse(X_12),inverse(X_13))) ),[1],$fot(inverse(greatest_lower_bound(X_12,X_13)))]]) ).

cnf(refute_0_133,plain,
    ( least_upper_bound(inverse(X_13),inverse(X_12)) != least_upper_bound(inverse(X_12),inverse(X_13))
    | least_upper_bound(inverse(X_13),inverse(X_12)) = inverse(greatest_lower_bound(X_12,X_13)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_12),inverse(X_13)),inverse(greatest_lower_bound(X_12,X_13))) )],[refute_0_131,refute_0_132]) ).

cnf(refute_0_134,plain,
    least_upper_bound(inverse(X_13),inverse(X_12)) = inverse(greatest_lower_bound(X_12,X_13)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_13),inverse(X_12)),least_upper_bound(inverse(X_12),inverse(X_13))) )],[refute_0_128,refute_0_133]) ).

cnf(refute_0_135,plain,
    ( inverse(greatest_lower_bound(X,Y)) != least_upper_bound(inverse(X),inverse(Y))
    | least_upper_bound(inverse(X),inverse(Y)) = inverse(greatest_lower_bound(X,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(X,Y)))),bind(Y0,$fot(least_upper_bound(inverse(X),inverse(Y))))]]) ).

cnf(refute_0_136,plain,
    least_upper_bound(inverse(X),inverse(Y)) = inverse(greatest_lower_bound(X,Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),least_upper_bound(inverse(X),inverse(Y))) )],[p12x_3,refute_0_135]) ).

cnf(refute_0_137,plain,
    least_upper_bound(inverse(X_13),inverse(X_12)) = inverse(greatest_lower_bound(X_13,X_12)),
    inference(subst,[],[refute_0_136:[bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).

cnf(refute_0_138,plain,
    ( least_upper_bound(inverse(X_13),inverse(X_12)) != inverse(greatest_lower_bound(X_12,X_13))
    | least_upper_bound(inverse(X_13),inverse(X_12)) != inverse(greatest_lower_bound(X_13,X_12))
    | inverse(greatest_lower_bound(X_13,X_12)) = inverse(greatest_lower_bound(X_12,X_13)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X_13),inverse(X_12)),inverse(greatest_lower_bound(X_12,X_13))) ),[0],$fot(inverse(greatest_lower_bound(X_13,X_12)))]]) ).

cnf(refute_0_139,plain,
    ( least_upper_bound(inverse(X_13),inverse(X_12)) != inverse(greatest_lower_bound(X_12,X_13))
    | inverse(greatest_lower_bound(X_13,X_12)) = inverse(greatest_lower_bound(X_12,X_13)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_13),inverse(X_12)),inverse(greatest_lower_bound(X_13,X_12))) )],[refute_0_137,refute_0_138]) ).

cnf(refute_0_140,plain,
    inverse(greatest_lower_bound(X_13,X_12)) = inverse(greatest_lower_bound(X_12,X_13)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_13),inverse(X_12)),inverse(greatest_lower_bound(X_12,X_13))) )],[refute_0_134,refute_0_139]) ).

cnf(refute_0_141,plain,
    inverse(greatest_lower_bound(X_25,X_24)) = inverse(greatest_lower_bound(X_24,X_25)),
    inference(subst,[],[refute_0_140:[bind(X_12,$fot(X_24)),bind(X_13,$fot(X_25))]]) ).

cnf(refute_0_142,plain,
    ( multiply(inverse(greatest_lower_bound(X_25,X_24)),greatest_lower_bound(X_25,X_24)) != identity
    | inverse(greatest_lower_bound(X_25,X_24)) != inverse(greatest_lower_bound(X_24,X_25))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_25,X_24)),greatest_lower_bound(X_25,X_24)),identity) ),[0,0],$fot(inverse(greatest_lower_bound(X_24,X_25)))]]) ).

cnf(refute_0_143,plain,
    ( multiply(inverse(greatest_lower_bound(X_25,X_24)),greatest_lower_bound(X_25,X_24)) != identity
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)) = identity ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_25,X_24)),inverse(greatest_lower_bound(X_24,X_25))) )],[refute_0_141,refute_0_142]) ).

cnf(refute_0_144,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_25,X_24)),greatest_lower_bound(X_25,X_24)),identity) )],[refute_0_127,refute_0_143]) ).

cnf(refute_0_145,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)) != identity
    | greatest_lower_bound(X_25,X_24) != multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)))
    | greatest_lower_bound(X_25,X_24) = multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_25,X_24),multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_146,plain,
    ( greatest_lower_bound(X_25,X_24) != multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)))
    | greatest_lower_bound(X_25,X_24) = multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),identity) )],[refute_0_144,refute_0_145]) ).

cnf(refute_0_147,plain,
    greatest_lower_bound(X_25,X_24) = multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_25,X_24),multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)))) )],[refute_0_126,refute_0_146]) ).

cnf(refute_0_148,plain,
    multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),identity) = multiply(greatest_lower_bound(X_24,X_25),identity),
    inference(subst,[],[refute_0_25:[bind(X_61,$fot(greatest_lower_bound(X_24,X_25))),bind(X_62,$fot(identity))]]) ).

cnf(refute_0_149,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),identity) != multiply(greatest_lower_bound(X_24,X_25),identity)
    | greatest_lower_bound(X_25,X_24) != multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),identity)
    | greatest_lower_bound(X_25,X_24) = multiply(greatest_lower_bound(X_24,X_25),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_25,X_24),multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),identity)) ),[1],$fot(multiply(greatest_lower_bound(X_24,X_25),identity))]]) ).

cnf(refute_0_150,plain,
    ( greatest_lower_bound(X_25,X_24) != multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),identity)
    | greatest_lower_bound(X_25,X_24) = multiply(greatest_lower_bound(X_24,X_25),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),identity),multiply(greatest_lower_bound(X_24,X_25),identity)) )],[refute_0_148,refute_0_149]) ).

cnf(refute_0_151,plain,
    greatest_lower_bound(X_25,X_24) = multiply(greatest_lower_bound(X_24,X_25),identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_25,X_24),multiply(inverse(inverse(greatest_lower_bound(X_24,X_25))),identity)) )],[refute_0_147,refute_0_150]) ).

cnf(refute_0_152,plain,
    multiply(greatest_lower_bound(X_24,X_25),identity) = greatest_lower_bound(X_24,X_25),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(greatest_lower_bound(X_24,X_25)))]]) ).

cnf(refute_0_153,plain,
    ( multiply(greatest_lower_bound(X_24,X_25),identity) != greatest_lower_bound(X_24,X_25)
    | greatest_lower_bound(X_25,X_24) != multiply(greatest_lower_bound(X_24,X_25),identity)
    | greatest_lower_bound(X_25,X_24) = greatest_lower_bound(X_24,X_25) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_25,X_24),multiply(greatest_lower_bound(X_24,X_25),identity)) ),[1],$fot(greatest_lower_bound(X_24,X_25))]]) ).

cnf(refute_0_154,plain,
    ( greatest_lower_bound(X_25,X_24) != multiply(greatest_lower_bound(X_24,X_25),identity)
    | greatest_lower_bound(X_25,X_24) = greatest_lower_bound(X_24,X_25) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_24,X_25),identity),greatest_lower_bound(X_24,X_25)) )],[refute_0_152,refute_0_153]) ).

cnf(refute_0_155,plain,
    greatest_lower_bound(X_25,X_24) = greatest_lower_bound(X_24,X_25),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_25,X_24),multiply(greatest_lower_bound(X_24,X_25),identity)) )],[refute_0_151,refute_0_154]) ).

cnf(refute_0_156,plain,
    ( greatest_lower_bound(X_25,X_24) != greatest_lower_bound(X_24,X_25)
    | greatest_lower_bound(X_24,X_25) = greatest_lower_bound(X_25,X_24) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_25,X_24))),bind(Y0,$fot(greatest_lower_bound(X_24,X_25)))]]) ).

cnf(refute_0_157,plain,
    greatest_lower_bound(X_24,X_25) = greatest_lower_bound(X_25,X_24),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_25,X_24),greatest_lower_bound(X_24,X_25)) )],[refute_0_155,refute_0_156]) ).

cnf(refute_0_158,plain,
    greatest_lower_bound(multiply(X_107,X_108),X_107) = greatest_lower_bound(X_107,multiply(X_107,X_108)),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(multiply(X_107,X_108))),bind(X_25,$fot(X_107))]]) ).

cnf(refute_0_159,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,identity)) != greatest_lower_bound(multiply(X_107,X_108),X_107)
    | greatest_lower_bound(multiply(X_107,X_108),X_107) != greatest_lower_bound(X_107,multiply(X_107,X_108))
    | multiply(X_107,greatest_lower_bound(X_108,identity)) = greatest_lower_bound(X_107,multiply(X_107,X_108)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_107,greatest_lower_bound(X_108,identity)),greatest_lower_bound(X_107,multiply(X_107,X_108))) ),[0],$fot(greatest_lower_bound(multiply(X_107,X_108),X_107))]]) ).

cnf(refute_0_160,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,identity)) != greatest_lower_bound(multiply(X_107,X_108),X_107)
    | multiply(X_107,greatest_lower_bound(X_108,identity)) = greatest_lower_bound(X_107,multiply(X_107,X_108)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),X_107),greatest_lower_bound(X_107,multiply(X_107,X_108))) )],[refute_0_158,refute_0_159]) ).

cnf(refute_0_161,plain,
    multiply(X_107,greatest_lower_bound(X_108,identity)) = greatest_lower_bound(X_107,multiply(X_107,X_108)),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,identity)),greatest_lower_bound(multiply(X_107,X_108),X_107)) )],[refute_0_125,refute_0_160]) ).

cnf(refute_0_162,plain,
    multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) = greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,c),inverse(b))),
    inference(subst,[],[refute_0_161:[bind(X_107,$fot(least_upper_bound(a,c))),bind(X_108,$fot(inverse(b)))]]) ).

cnf(refute_0_163,plain,
    multiply(least_upper_bound(inverse(X_110),X_112),X_110) = least_upper_bound(multiply(inverse(X_110),X_110),multiply(X_112,X_110)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_110)),bind(Y,$fot(inverse(X_110))),bind(Z,$fot(X_112))]]) ).

cnf(refute_0_164,plain,
    ( multiply(inverse(X_110),X_110) != identity
    | multiply(least_upper_bound(inverse(X_110),X_112),X_110) != least_upper_bound(multiply(inverse(X_110),X_110),multiply(X_112,X_110))
    | multiply(least_upper_bound(inverse(X_110),X_112),X_110) = least_upper_bound(identity,multiply(X_112,X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_110),X_112),X_110),least_upper_bound(multiply(inverse(X_110),X_110),multiply(X_112,X_110))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_165,plain,
    ( multiply(least_upper_bound(inverse(X_110),X_112),X_110) != least_upper_bound(multiply(inverse(X_110),X_110),multiply(X_112,X_110))
    | multiply(least_upper_bound(inverse(X_110),X_112),X_110) = least_upper_bound(identity,multiply(X_112,X_110)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_110),X_110),identity) )],[refute_0_71,refute_0_164]) ).

cnf(refute_0_166,plain,
    multiply(least_upper_bound(inverse(X_110),X_112),X_110) = least_upper_bound(identity,multiply(X_112,X_110)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_110),X_112),X_110),least_upper_bound(multiply(inverse(X_110),X_110),multiply(X_112,X_110))) )],[refute_0_163,refute_0_165]) ).

cnf(refute_0_167,plain,
    multiply(least_upper_bound(inverse(inverse(X_87)),X_116),inverse(X_87)) = least_upper_bound(identity,multiply(X_116,inverse(X_87))),
    inference(subst,[],[refute_0_166:[bind(X_110,$fot(inverse(X_87))),bind(X_112,$fot(X_116))]]) ).

cnf(refute_0_168,plain,
    ( multiply(least_upper_bound(inverse(inverse(X_87)),X_116),inverse(X_87)) != least_upper_bound(identity,multiply(X_116,inverse(X_87)))
    | inverse(inverse(X_87)) != X_87
    | multiply(least_upper_bound(X_87,X_116),inverse(X_87)) = least_upper_bound(identity,multiply(X_116,inverse(X_87))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(X_87)),X_116),inverse(X_87)),least_upper_bound(identity,multiply(X_116,inverse(X_87)))) ),[0,0,0],$fot(X_87)]]) ).

cnf(refute_0_169,plain,
    ( multiply(least_upper_bound(inverse(inverse(X_87)),X_116),inverse(X_87)) != least_upper_bound(identity,multiply(X_116,inverse(X_87)))
    | multiply(least_upper_bound(X_87,X_116),inverse(X_87)) = least_upper_bound(identity,multiply(X_116,inverse(X_87))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_87)),X_87) )],[refute_0_42,refute_0_168]) ).

cnf(refute_0_170,plain,
    multiply(least_upper_bound(X_87,X_116),inverse(X_87)) = least_upper_bound(identity,multiply(X_116,inverse(X_87))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(X_87)),X_116),inverse(X_87)),least_upper_bound(identity,multiply(X_116,inverse(X_87)))) )],[refute_0_167,refute_0_169]) ).

cnf(refute_0_171,plain,
    multiply(least_upper_bound(b,c),inverse(b)) = least_upper_bound(identity,multiply(c,inverse(b))),
    inference(subst,[],[refute_0_170:[bind(X_116,$fot(c)),bind(X_87,$fot(b))]]) ).

cnf(refute_0_172,plain,
    ( least_upper_bound(a,c) != least_upper_bound(b,c)
    | least_upper_bound(b,c) = least_upper_bound(a,c) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(a,c))),bind(Y0,$fot(least_upper_bound(b,c)))]]) ).

cnf(refute_0_173,plain,
    least_upper_bound(b,c) = least_upper_bound(a,c),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,c),least_upper_bound(b,c)) )],[p12x_2,refute_0_172]) ).

cnf(refute_0_174,plain,
    ( multiply(least_upper_bound(b,c),inverse(b)) != least_upper_bound(identity,multiply(c,inverse(b)))
    | least_upper_bound(b,c) != least_upper_bound(a,c)
    | multiply(least_upper_bound(a,c),inverse(b)) = least_upper_bound(identity,multiply(c,inverse(b))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,c),inverse(b)),least_upper_bound(identity,multiply(c,inverse(b)))) ),[0,0],$fot(least_upper_bound(a,c))]]) ).

cnf(refute_0_175,plain,
    ( multiply(least_upper_bound(b,c),inverse(b)) != least_upper_bound(identity,multiply(c,inverse(b)))
    | multiply(least_upper_bound(a,c),inverse(b)) = least_upper_bound(identity,multiply(c,inverse(b))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,c),least_upper_bound(a,c)) )],[refute_0_173,refute_0_174]) ).

cnf(refute_0_176,plain,
    multiply(least_upper_bound(a,c),inverse(b)) = least_upper_bound(identity,multiply(c,inverse(b))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,c),inverse(b)),least_upper_bound(identity,multiply(c,inverse(b)))) )],[refute_0_171,refute_0_175]) ).

cnf(refute_0_177,plain,
    ( greatest_lower_bound(a,c) != greatest_lower_bound(b,c)
    | greatest_lower_bound(b,c) = greatest_lower_bound(a,c) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(a,c))),bind(Y0,$fot(greatest_lower_bound(b,c)))]]) ).

cnf(refute_0_178,plain,
    greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,c),greatest_lower_bound(b,c)) )],[p12x_1,refute_0_177]) ).

cnf(refute_0_179,plain,
    inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(b,c)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(b,c)))]]) ).

cnf(refute_0_180,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | inverse(greatest_lower_bound(b,c)) != inverse(greatest_lower_bound(b,c))
    | inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,c)),inverse(greatest_lower_bound(b,c))) ),[1,0],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_181,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,c)),inverse(greatest_lower_bound(b,c))) )],[refute_0_179,refute_0_180]) ).

cnf(refute_0_182,plain,
    inverse(greatest_lower_bound(b,c)) = inverse(greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_178,refute_0_181]) ).

cnf(refute_0_183,plain,
    multiply(c,inverse(greatest_lower_bound(b,c))) = multiply(c,inverse(greatest_lower_bound(b,c))),
    introduced(tautology,[refl,[$fot(multiply(c,inverse(greatest_lower_bound(b,c))))]]) ).

cnf(refute_0_184,plain,
    ( multiply(c,inverse(greatest_lower_bound(b,c))) != multiply(c,inverse(greatest_lower_bound(b,c)))
    | inverse(greatest_lower_bound(b,c)) != inverse(greatest_lower_bound(a,c))
    | multiply(c,inverse(greatest_lower_bound(b,c))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(b,c))),multiply(c,inverse(greatest_lower_bound(b,c)))) ),[1,1],$fot(inverse(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_185,plain,
    ( inverse(greatest_lower_bound(b,c)) != inverse(greatest_lower_bound(a,c))
    | multiply(c,inverse(greatest_lower_bound(b,c))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(b,c))),multiply(c,inverse(greatest_lower_bound(b,c)))) )],[refute_0_183,refute_0_184]) ).

cnf(refute_0_186,plain,
    multiply(c,inverse(greatest_lower_bound(b,c))) = multiply(c,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,c)),inverse(greatest_lower_bound(a,c))) )],[refute_0_182,refute_0_185]) ).

cnf(refute_0_187,plain,
    multiply(X_93,least_upper_bound(inverse(X_93),X_95)) = least_upper_bound(multiply(X_93,inverse(X_93)),multiply(X_93,X_95)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_93)),bind(Y,$fot(inverse(X_93))),bind(Z,$fot(X_95))]]) ).

cnf(refute_0_188,plain,
    multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),least_upper_bound(inverse(X),inverse(Y))) = identity,
    inference(subst,[],[refute_0_62:[bind(X_16,$fot(inverse(Y))),bind(X_17,$fot(inverse(X)))]]) ).

cnf(refute_0_189,plain,
    ( multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),least_upper_bound(inverse(X),inverse(Y))) != identity
    | least_upper_bound(inverse(X),inverse(Y)) != inverse(greatest_lower_bound(X,Y))
    | multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),least_upper_bound(inverse(X),inverse(Y))),identity) ),[0,1],$fot(inverse(greatest_lower_bound(X,Y)))]]) ).

cnf(refute_0_190,plain,
    ( multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),least_upper_bound(inverse(X),inverse(Y))) != identity
    | multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(Y)),inverse(greatest_lower_bound(X,Y))) )],[refute_0_136,refute_0_189]) ).

cnf(refute_0_191,plain,
    multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),least_upper_bound(inverse(X),inverse(Y))),identity) )],[refute_0_188,refute_0_190]) ).

cnf(refute_0_192,plain,
    least_upper_bound(inverse(Y),inverse(X)) = inverse(greatest_lower_bound(Y,X)),
    inference(subst,[],[refute_0_136:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).

cnf(refute_0_193,plain,
    inverse(least_upper_bound(inverse(Y),inverse(X))) = inverse(least_upper_bound(inverse(Y),inverse(X))),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(Y),inverse(X))))]]) ).

cnf(refute_0_194,plain,
    ( inverse(least_upper_bound(inverse(Y),inverse(X))) != inverse(least_upper_bound(inverse(Y),inverse(X)))
    | least_upper_bound(inverse(Y),inverse(X)) != inverse(greatest_lower_bound(Y,X))
    | inverse(least_upper_bound(inverse(Y),inverse(X))) = inverse(inverse(greatest_lower_bound(Y,X))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(inverse(Y),inverse(X)))) ),[1,0],$fot(inverse(greatest_lower_bound(Y,X)))]]) ).

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

cnf(refute_0_196,plain,
    inverse(least_upper_bound(inverse(Y),inverse(X))) = inverse(inverse(greatest_lower_bound(Y,X))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(Y),inverse(X)),inverse(greatest_lower_bound(Y,X))) )],[refute_0_192,refute_0_195]) ).

cnf(refute_0_197,plain,
    multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))) = multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))),
    introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))))]]) ).

cnf(refute_0_198,plain,
    ( multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))) != multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y)))
    | inverse(least_upper_bound(inverse(Y),inverse(X))) != inverse(inverse(greatest_lower_bound(Y,X)))
    | multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))) = multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))),multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y)))) ),[1,0],$fot(inverse(inverse(greatest_lower_bound(Y,X))))]]) ).

cnf(refute_0_199,plain,
    ( inverse(least_upper_bound(inverse(Y),inverse(X))) != inverse(inverse(greatest_lower_bound(Y,X)))
    | multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))) = multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))),multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y)))) )],[refute_0_197,refute_0_198]) ).

cnf(refute_0_200,plain,
    multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))) = multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(inverse(greatest_lower_bound(Y,X)))) )],[refute_0_196,refute_0_199]) ).

cnf(refute_0_201,plain,
    ( multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))) != multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y)))
    | multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))) != identity
    | multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))),identity) ),[0],$fot(multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))))]]) ).

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

cnf(refute_0_203,plain,
    multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(X,Y))),identity) )],[refute_0_191,refute_0_202]) ).

cnf(refute_0_204,plain,
    multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))) = multiply(greatest_lower_bound(Y,X),inverse(greatest_lower_bound(X,Y))),
    inference(subst,[],[refute_0_25:[bind(X_61,$fot(greatest_lower_bound(Y,X))),bind(X_62,$fot(inverse(greatest_lower_bound(X,Y))))]]) ).

cnf(refute_0_205,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))) != multiply(greatest_lower_bound(Y,X),inverse(greatest_lower_bound(X,Y)))
    | multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))) != identity
    | multiply(greatest_lower_bound(Y,X),inverse(greatest_lower_bound(X,Y))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))),identity) ),[0],$fot(multiply(greatest_lower_bound(Y,X),inverse(greatest_lower_bound(X,Y))))]]) ).

cnf(refute_0_206,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))) != identity
    | multiply(greatest_lower_bound(Y,X),inverse(greatest_lower_bound(X,Y))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))),multiply(greatest_lower_bound(Y,X),inverse(greatest_lower_bound(X,Y)))) )],[refute_0_204,refute_0_205]) ).

cnf(refute_0_207,plain,
    multiply(greatest_lower_bound(Y,X),inverse(greatest_lower_bound(X,Y))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))),identity) )],[refute_0_203,refute_0_206]) ).

cnf(refute_0_208,plain,
    multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)))) = identity,
    inference(subst,[],[refute_0_207:[bind(X,$fot(X_66)),bind(Y,$fot(least_upper_bound(X_11,X_66)))]]) ).

cnf(refute_0_209,plain,
    greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) = X_10,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).

cnf(refute_0_210,plain,
    least_upper_bound(X_11,X_10) = least_upper_bound(X_10,X_11),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).

cnf(refute_0_211,plain,
    ( least_upper_bound(X_11,X_10) != least_upper_bound(X_10,X_11)
    | least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_11,X_10))),bind(Y0,$fot(least_upper_bound(X_10,X_11)))]]) ).

cnf(refute_0_212,plain,
    least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,X_10),least_upper_bound(X_10,X_11)) )],[refute_0_210,refute_0_211]) ).

cnf(refute_0_213,plain,
    ( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
    | least_upper_bound(X_10,X_11) != least_upper_bound(X_11,X_10)
    | greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) ),[0,1],$fot(least_upper_bound(X_11,X_10))]]) ).

cnf(refute_0_214,plain,
    ( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
    | greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_10,X_11),least_upper_bound(X_11,X_10)) )],[refute_0_212,refute_0_213]) ).

cnf(refute_0_215,plain,
    greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) )],[refute_0_209,refute_0_214]) ).

cnf(refute_0_216,plain,
    greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)) = X_66,
    inference(subst,[],[refute_0_215:[bind(X_10,$fot(X_66))]]) ).

cnf(refute_0_217,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)))) != identity
    | greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)) != X_66
    | multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)))),identity) ),[0,1,0],$fot(X_66)]]) ).

cnf(refute_0_218,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)))) != identity
    | multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)),X_66) )],[refute_0_216,refute_0_217]) ).

cnf(refute_0_219,plain,
    multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)) = identity,
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)))),identity) )],[refute_0_208,refute_0_218]) ).

cnf(refute_0_220,plain,
    greatest_lower_bound(least_upper_bound(X_11,X_66),X_66) = greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(least_upper_bound(X_11,X_66))),bind(X_25,$fot(X_66))]]) ).

cnf(refute_0_221,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_222,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_18,refute_0_221]) ).

cnf(refute_0_223,plain,
    ( greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)) != X_66
    | greatest_lower_bound(least_upper_bound(X_11,X_66),X_66) != greatest_lower_bound(X_66,least_upper_bound(X_11,X_66))
    | greatest_lower_bound(least_upper_bound(X_11,X_66),X_66) = X_66 ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66))),bind(Y0,$fot(greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)))),bind(Z0,$fot(X_66))]]) ).

cnf(refute_0_224,plain,
    ( greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)) != X_66
    | greatest_lower_bound(least_upper_bound(X_11,X_66),X_66) = X_66 ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),greatest_lower_bound(X_66,least_upper_bound(X_11,X_66))) )],[refute_0_220,refute_0_223]) ).

cnf(refute_0_225,plain,
    greatest_lower_bound(least_upper_bound(X_11,X_66),X_66) = X_66,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_66,least_upper_bound(X_11,X_66)),X_66) )],[refute_0_216,refute_0_224]) ).

cnf(refute_0_226,plain,
    multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)) = multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)))]]) ).

cnf(refute_0_227,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)) != multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66))
    | greatest_lower_bound(least_upper_bound(X_11,X_66),X_66) != X_66
    | multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)) = multiply(X_66,inverse(X_66)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)),multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66))) ),[1,0],$fot(X_66)]]) ).

cnf(refute_0_228,plain,
    ( greatest_lower_bound(least_upper_bound(X_11,X_66),X_66) != X_66
    | multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)) = multiply(X_66,inverse(X_66)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)),multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66))) )],[refute_0_226,refute_0_227]) ).

cnf(refute_0_229,plain,
    multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)) = multiply(X_66,inverse(X_66)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),X_66) )],[refute_0_225,refute_0_228]) ).

cnf(refute_0_230,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)) != multiply(X_66,inverse(X_66))
    | multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)) != identity
    | multiply(X_66,inverse(X_66)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)),identity) ),[0],$fot(multiply(X_66,inverse(X_66)))]]) ).

cnf(refute_0_231,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)) != identity
    | multiply(X_66,inverse(X_66)) = identity ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)),multiply(X_66,inverse(X_66))) )],[refute_0_229,refute_0_230]) ).

cnf(refute_0_232,plain,
    multiply(X_66,inverse(X_66)) = identity,
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(X_11,X_66),X_66),inverse(X_66)),identity) )],[refute_0_219,refute_0_231]) ).

cnf(refute_0_233,plain,
    multiply(X_93,inverse(X_93)) = identity,
    inference(subst,[],[refute_0_232:[bind(X_66,$fot(X_93))]]) ).

cnf(refute_0_234,plain,
    ( multiply(X_93,inverse(X_93)) != identity
    | multiply(X_93,least_upper_bound(inverse(X_93),X_95)) != least_upper_bound(multiply(X_93,inverse(X_93)),multiply(X_93,X_95))
    | multiply(X_93,least_upper_bound(inverse(X_93),X_95)) = least_upper_bound(identity,multiply(X_93,X_95)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(X_93),X_95)),least_upper_bound(multiply(X_93,inverse(X_93)),multiply(X_93,X_95))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_235,plain,
    ( multiply(X_93,least_upper_bound(inverse(X_93),X_95)) != least_upper_bound(multiply(X_93,inverse(X_93)),multiply(X_93,X_95))
    | multiply(X_93,least_upper_bound(inverse(X_93),X_95)) = least_upper_bound(identity,multiply(X_93,X_95)) ),
    inference(resolve,[$cnf( $equal(multiply(X_93,inverse(X_93)),identity) )],[refute_0_233,refute_0_234]) ).

cnf(refute_0_236,plain,
    multiply(X_93,least_upper_bound(inverse(X_93),X_95)) = least_upper_bound(identity,multiply(X_93,X_95)),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(X_93),X_95)),least_upper_bound(multiply(X_93,inverse(X_93)),multiply(X_93,X_95))) )],[refute_0_187,refute_0_235]) ).

cnf(refute_0_237,plain,
    multiply(X_99,least_upper_bound(inverse(X_99),inverse(Y))) = least_upper_bound(identity,multiply(X_99,inverse(Y))),
    inference(subst,[],[refute_0_236:[bind(X_93,$fot(X_99)),bind(X_95,$fot(inverse(Y)))]]) ).

cnf(refute_0_238,plain,
    inverse(greatest_lower_bound(X_99,Y)) = least_upper_bound(inverse(X_99),inverse(Y)),
    inference(subst,[],[p12x_3:[bind(X,$fot(X_99))]]) ).

cnf(refute_0_239,plain,
    ( inverse(greatest_lower_bound(X_99,Y)) != least_upper_bound(inverse(X_99),inverse(Y))
    | least_upper_bound(inverse(X_99),inverse(Y)) = inverse(greatest_lower_bound(X_99,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(X_99,Y)))),bind(Y0,$fot(least_upper_bound(inverse(X_99),inverse(Y))))]]) ).

cnf(refute_0_240,plain,
    least_upper_bound(inverse(X_99),inverse(Y)) = inverse(greatest_lower_bound(X_99,Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_99,Y)),least_upper_bound(inverse(X_99),inverse(Y))) )],[refute_0_238,refute_0_239]) ).

cnf(refute_0_241,plain,
    ( multiply(X_99,least_upper_bound(inverse(X_99),inverse(Y))) != least_upper_bound(identity,multiply(X_99,inverse(Y)))
    | least_upper_bound(inverse(X_99),inverse(Y)) != inverse(greatest_lower_bound(X_99,Y))
    | multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) = least_upper_bound(identity,multiply(X_99,inverse(Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_99,least_upper_bound(inverse(X_99),inverse(Y))),least_upper_bound(identity,multiply(X_99,inverse(Y)))) ),[0,1],$fot(inverse(greatest_lower_bound(X_99,Y)))]]) ).

cnf(refute_0_242,plain,
    ( multiply(X_99,least_upper_bound(inverse(X_99),inverse(Y))) != least_upper_bound(identity,multiply(X_99,inverse(Y)))
    | multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) = least_upper_bound(identity,multiply(X_99,inverse(Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_99),inverse(Y)),inverse(greatest_lower_bound(X_99,Y))) )],[refute_0_240,refute_0_241]) ).

cnf(refute_0_243,plain,
    multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) = least_upper_bound(identity,multiply(X_99,inverse(Y))),
    inference(resolve,[$cnf( $equal(multiply(X_99,least_upper_bound(inverse(X_99),inverse(Y))),least_upper_bound(identity,multiply(X_99,inverse(Y)))) )],[refute_0_237,refute_0_242]) ).

cnf(refute_0_244,plain,
    multiply(X_93,least_upper_bound(X_94,inverse(X_93))) = least_upper_bound(multiply(X_93,X_94),multiply(X_93,inverse(X_93))),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_93)),bind(Y,$fot(X_94)),bind(Z,$fot(inverse(X_93)))]]) ).

cnf(refute_0_245,plain,
    ( multiply(X_93,inverse(X_93)) != identity
    | multiply(X_93,least_upper_bound(X_94,inverse(X_93))) != least_upper_bound(multiply(X_93,X_94),multiply(X_93,inverse(X_93)))
    | multiply(X_93,least_upper_bound(X_94,inverse(X_93))) = least_upper_bound(multiply(X_93,X_94),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_93,least_upper_bound(X_94,inverse(X_93))),least_upper_bound(multiply(X_93,X_94),multiply(X_93,inverse(X_93)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_246,plain,
    ( multiply(X_93,least_upper_bound(X_94,inverse(X_93))) != least_upper_bound(multiply(X_93,X_94),multiply(X_93,inverse(X_93)))
    | multiply(X_93,least_upper_bound(X_94,inverse(X_93))) = least_upper_bound(multiply(X_93,X_94),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_93,inverse(X_93)),identity) )],[refute_0_233,refute_0_245]) ).

cnf(refute_0_247,plain,
    multiply(X_93,least_upper_bound(X_94,inverse(X_93))) = least_upper_bound(multiply(X_93,X_94),identity),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(X_94,inverse(X_93))),least_upper_bound(multiply(X_93,X_94),multiply(X_93,inverse(X_93)))) )],[refute_0_244,refute_0_246]) ).

cnf(refute_0_248,plain,
    least_upper_bound(multiply(X_93,X_94),identity) = least_upper_bound(identity,multiply(X_93,X_94)),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(multiply(X_93,X_94))),bind(X_17,$fot(identity))]]) ).

cnf(refute_0_249,plain,
    ( multiply(X_93,least_upper_bound(X_94,inverse(X_93))) != least_upper_bound(multiply(X_93,X_94),identity)
    | least_upper_bound(multiply(X_93,X_94),identity) != least_upper_bound(identity,multiply(X_93,X_94))
    | multiply(X_93,least_upper_bound(X_94,inverse(X_93))) = least_upper_bound(identity,multiply(X_93,X_94)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_93,least_upper_bound(X_94,inverse(X_93))),least_upper_bound(identity,multiply(X_93,X_94))) ),[0],$fot(least_upper_bound(multiply(X_93,X_94),identity))]]) ).

cnf(refute_0_250,plain,
    ( multiply(X_93,least_upper_bound(X_94,inverse(X_93))) != least_upper_bound(multiply(X_93,X_94),identity)
    | multiply(X_93,least_upper_bound(X_94,inverse(X_93))) = least_upper_bound(identity,multiply(X_93,X_94)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_93,X_94),identity),least_upper_bound(identity,multiply(X_93,X_94))) )],[refute_0_248,refute_0_249]) ).

cnf(refute_0_251,plain,
    multiply(X_93,least_upper_bound(X_94,inverse(X_93))) = least_upper_bound(identity,multiply(X_93,X_94)),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(X_94,inverse(X_93))),least_upper_bound(multiply(X_93,X_94),identity)) )],[refute_0_247,refute_0_250]) ).

cnf(refute_0_252,plain,
    multiply(X_96,least_upper_bound(inverse(X),inverse(X_96))) = least_upper_bound(identity,multiply(X_96,inverse(X))),
    inference(subst,[],[refute_0_251:[bind(X_93,$fot(X_96)),bind(X_94,$fot(inverse(X)))]]) ).

cnf(refute_0_253,plain,
    inverse(greatest_lower_bound(X,X_96)) = least_upper_bound(inverse(X),inverse(X_96)),
    inference(subst,[],[p12x_3:[bind(Y,$fot(X_96))]]) ).

cnf(refute_0_254,plain,
    ( inverse(greatest_lower_bound(X,X_96)) != least_upper_bound(inverse(X),inverse(X_96))
    | least_upper_bound(inverse(X),inverse(X_96)) = inverse(greatest_lower_bound(X,X_96)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(X,X_96)))),bind(Y0,$fot(least_upper_bound(inverse(X),inverse(X_96))))]]) ).

cnf(refute_0_255,plain,
    least_upper_bound(inverse(X),inverse(X_96)) = inverse(greatest_lower_bound(X,X_96)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,X_96)),least_upper_bound(inverse(X),inverse(X_96))) )],[refute_0_253,refute_0_254]) ).

cnf(refute_0_256,plain,
    ( multiply(X_96,least_upper_bound(inverse(X),inverse(X_96))) != least_upper_bound(identity,multiply(X_96,inverse(X)))
    | least_upper_bound(inverse(X),inverse(X_96)) != inverse(greatest_lower_bound(X,X_96))
    | multiply(X_96,inverse(greatest_lower_bound(X,X_96))) = least_upper_bound(identity,multiply(X_96,inverse(X))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_96,least_upper_bound(inverse(X),inverse(X_96))),least_upper_bound(identity,multiply(X_96,inverse(X)))) ),[0,1],$fot(inverse(greatest_lower_bound(X,X_96)))]]) ).

cnf(refute_0_257,plain,
    ( multiply(X_96,least_upper_bound(inverse(X),inverse(X_96))) != least_upper_bound(identity,multiply(X_96,inverse(X)))
    | multiply(X_96,inverse(greatest_lower_bound(X,X_96))) = least_upper_bound(identity,multiply(X_96,inverse(X))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(X_96)),inverse(greatest_lower_bound(X,X_96))) )],[refute_0_255,refute_0_256]) ).

cnf(refute_0_258,plain,
    multiply(X_96,inverse(greatest_lower_bound(X,X_96))) = least_upper_bound(identity,multiply(X_96,inverse(X))),
    inference(resolve,[$cnf( $equal(multiply(X_96,least_upper_bound(inverse(X),inverse(X_96))),least_upper_bound(identity,multiply(X_96,inverse(X)))) )],[refute_0_252,refute_0_257]) ).

cnf(refute_0_259,plain,
    multiply(X_99,inverse(greatest_lower_bound(Y,X_99))) = least_upper_bound(identity,multiply(X_99,inverse(Y))),
    inference(subst,[],[refute_0_258:[bind(X,$fot(Y)),bind(X_96,$fot(X_99))]]) ).

cnf(refute_0_260,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(Y,X_99))) != least_upper_bound(identity,multiply(X_99,inverse(Y)))
    | least_upper_bound(identity,multiply(X_99,inverse(Y))) = multiply(X_99,inverse(greatest_lower_bound(Y,X_99))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_99,inverse(greatest_lower_bound(Y,X_99))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_99,inverse(Y)))))]]) ).

cnf(refute_0_261,plain,
    least_upper_bound(identity,multiply(X_99,inverse(Y))) = multiply(X_99,inverse(greatest_lower_bound(Y,X_99))),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(Y,X_99))),least_upper_bound(identity,multiply(X_99,inverse(Y)))) )],[refute_0_259,refute_0_260]) ).

cnf(refute_0_262,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) != least_upper_bound(identity,multiply(X_99,inverse(Y)))
    | least_upper_bound(identity,multiply(X_99,inverse(Y))) != multiply(X_99,inverse(greatest_lower_bound(Y,X_99)))
    | multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) = multiply(X_99,inverse(greatest_lower_bound(Y,X_99))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,Y))),multiply(X_99,inverse(greatest_lower_bound(Y,X_99)))) ),[0],$fot(least_upper_bound(identity,multiply(X_99,inverse(Y))))]]) ).

cnf(refute_0_263,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) != least_upper_bound(identity,multiply(X_99,inverse(Y)))
    | multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) = multiply(X_99,inverse(greatest_lower_bound(Y,X_99))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_99,inverse(Y))),multiply(X_99,inverse(greatest_lower_bound(Y,X_99)))) )],[refute_0_261,refute_0_262]) ).

cnf(refute_0_264,plain,
    multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) = multiply(X_99,inverse(greatest_lower_bound(Y,X_99))),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,Y))),least_upper_bound(identity,multiply(X_99,inverse(Y)))) )],[refute_0_243,refute_0_263]) ).

cnf(refute_0_265,plain,
    multiply(c,inverse(greatest_lower_bound(c,b))) = multiply(c,inverse(greatest_lower_bound(b,c))),
    inference(subst,[],[refute_0_264:[bind(Y,$fot(b)),bind(X_99,$fot(c))]]) ).

cnf(refute_0_266,plain,
    multiply(least_upper_bound(Y,X_99),inverse(Y)) = least_upper_bound(identity,multiply(X_99,inverse(Y))),
    inference(subst,[],[refute_0_170:[bind(X_116,$fot(X_99)),bind(X_87,$fot(Y))]]) ).

cnf(refute_0_267,plain,
    ( multiply(least_upper_bound(Y,X_99),inverse(Y)) != least_upper_bound(identity,multiply(X_99,inverse(Y)))
    | least_upper_bound(identity,multiply(X_99,inverse(Y))) = multiply(least_upper_bound(Y,X_99),inverse(Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(Y,X_99),inverse(Y)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_99,inverse(Y)))))]]) ).

cnf(refute_0_268,plain,
    least_upper_bound(identity,multiply(X_99,inverse(Y))) = multiply(least_upper_bound(Y,X_99),inverse(Y)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,X_99),inverse(Y)),least_upper_bound(identity,multiply(X_99,inverse(Y)))) )],[refute_0_266,refute_0_267]) ).

cnf(refute_0_269,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) != least_upper_bound(identity,multiply(X_99,inverse(Y)))
    | least_upper_bound(identity,multiply(X_99,inverse(Y))) != multiply(least_upper_bound(Y,X_99),inverse(Y))
    | multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) = multiply(least_upper_bound(Y,X_99),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,Y))),multiply(least_upper_bound(Y,X_99),inverse(Y))) ),[0],$fot(least_upper_bound(identity,multiply(X_99,inverse(Y))))]]) ).

cnf(refute_0_270,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) != least_upper_bound(identity,multiply(X_99,inverse(Y)))
    | multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) = multiply(least_upper_bound(Y,X_99),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_99,inverse(Y))),multiply(least_upper_bound(Y,X_99),inverse(Y))) )],[refute_0_268,refute_0_269]) ).

cnf(refute_0_271,plain,
    multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) = multiply(least_upper_bound(Y,X_99),inverse(Y)),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,Y))),least_upper_bound(identity,multiply(X_99,inverse(Y)))) )],[refute_0_243,refute_0_270]) ).

cnf(refute_0_272,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) != multiply(least_upper_bound(Y,X_99),inverse(Y))
    | multiply(least_upper_bound(Y,X_99),inverse(Y)) = multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_99,inverse(greatest_lower_bound(X_99,Y))))),bind(Y0,$fot(multiply(least_upper_bound(Y,X_99),inverse(Y))))]]) ).

cnf(refute_0_273,plain,
    multiply(least_upper_bound(Y,X_99),inverse(Y)) = multiply(X_99,inverse(greatest_lower_bound(X_99,Y))),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,Y))),multiply(least_upper_bound(Y,X_99),inverse(Y))) )],[refute_0_271,refute_0_272]) ).

cnf(refute_0_274,plain,
    multiply(least_upper_bound(b,c),inverse(b)) = multiply(c,inverse(greatest_lower_bound(c,b))),
    inference(subst,[],[refute_0_273:[bind(Y,$fot(b)),bind(X_99,$fot(c))]]) ).

cnf(refute_0_275,plain,
    ( multiply(c,inverse(greatest_lower_bound(c,b))) != multiply(c,inverse(greatest_lower_bound(b,c)))
    | multiply(least_upper_bound(b,c),inverse(b)) != multiply(c,inverse(greatest_lower_bound(c,b)))
    | multiply(least_upper_bound(b,c),inverse(b)) = multiply(c,inverse(greatest_lower_bound(b,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(b,c),inverse(b)))),bind(Y0,$fot(multiply(c,inverse(greatest_lower_bound(c,b))))),bind(Z0,$fot(multiply(c,inverse(greatest_lower_bound(b,c)))))]]) ).

cnf(refute_0_276,plain,
    ( multiply(c,inverse(greatest_lower_bound(c,b))) != multiply(c,inverse(greatest_lower_bound(b,c)))
    | multiply(least_upper_bound(b,c),inverse(b)) = multiply(c,inverse(greatest_lower_bound(b,c))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,c),inverse(b)),multiply(c,inverse(greatest_lower_bound(c,b)))) )],[refute_0_274,refute_0_275]) ).

cnf(refute_0_277,plain,
    multiply(least_upper_bound(b,c),inverse(b)) = multiply(c,inverse(greatest_lower_bound(b,c))),
    inference(resolve,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(c,b))),multiply(c,inverse(greatest_lower_bound(b,c)))) )],[refute_0_265,refute_0_276]) ).

cnf(refute_0_278,plain,
    X_60 = multiply(inverse(inverse(least_upper_bound(identity,X_60))),multiply(inverse(least_upper_bound(identity,X_60)),X_60)),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(inverse(least_upper_bound(identity,X_60))))]]) ).

cnf(refute_0_279,plain,
    multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121) = greatest_lower_bound(multiply(X_122,X_121),multiply(inverse(X_121),X_121)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_121)),bind(Y,$fot(X_122)),bind(Z,$fot(inverse(X_121)))]]) ).

cnf(refute_0_280,plain,
    multiply(inverse(X_121),X_121) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_121))]]) ).

cnf(refute_0_281,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121) != greatest_lower_bound(multiply(X_122,X_121),multiply(inverse(X_121),X_121))
    | multiply(inverse(X_121),X_121) != identity
    | multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121) = greatest_lower_bound(multiply(X_122,X_121),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(inverse(X_121),X_121))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_282,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121) != greatest_lower_bound(multiply(X_122,X_121),multiply(inverse(X_121),X_121))
    | multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121) = greatest_lower_bound(multiply(X_122,X_121),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_121),X_121),identity) )],[refute_0_280,refute_0_281]) ).

cnf(refute_0_283,plain,
    multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121) = greatest_lower_bound(multiply(X_122,X_121),identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(inverse(X_121),X_121))) )],[refute_0_279,refute_0_282]) ).

cnf(refute_0_284,plain,
    greatest_lower_bound(multiply(X_122,X_121),identity) = greatest_lower_bound(identity,multiply(X_122,X_121)),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(multiply(X_122,X_121))),bind(X_25,$fot(identity))]]) ).

cnf(refute_0_285,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121) != greatest_lower_bound(multiply(X_122,X_121),identity)
    | greatest_lower_bound(multiply(X_122,X_121),identity) != greatest_lower_bound(identity,multiply(X_122,X_121))
    | multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121) = greatest_lower_bound(identity,multiply(X_122,X_121)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121),greatest_lower_bound(identity,multiply(X_122,X_121))) ),[0],$fot(greatest_lower_bound(multiply(X_122,X_121),identity))]]) ).

cnf(refute_0_286,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121) != greatest_lower_bound(multiply(X_122,X_121),identity)
    | multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121) = greatest_lower_bound(identity,multiply(X_122,X_121)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),identity),greatest_lower_bound(identity,multiply(X_122,X_121))) )],[refute_0_284,refute_0_285]) ).

cnf(refute_0_287,plain,
    multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121) = greatest_lower_bound(identity,multiply(X_122,X_121)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(X_121)),X_121),greatest_lower_bound(multiply(X_122,X_121),identity)) )],[refute_0_283,refute_0_286]) ).

cnf(refute_0_288,plain,
    multiply(greatest_lower_bound(identity,inverse(X_124)),X_124) = greatest_lower_bound(identity,multiply(identity,X_124)),
    inference(subst,[],[refute_0_287:[bind(X_121,$fot(X_124)),bind(X_122,$fot(identity))]]) ).

cnf(refute_0_289,plain,
    inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(inverse(identity),inverse(Y)),
    inference(subst,[],[p12x_4:[bind(X,$fot(identity))]]) ).

cnf(refute_0_290,plain,
    multiply(inverse(identity),identity) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(identity))]]) ).

cnf(refute_0_291,plain,
    inverse(identity) = multiply(inverse(identity),identity),
    inference(subst,[],[refute_0_29:[bind(X_62,$fot(inverse(identity)))]]) ).

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

cnf(refute_0_293,plain,
    multiply(inverse(identity),identity) = inverse(identity),
    inference(resolve,[$cnf( $equal(inverse(identity),multiply(inverse(identity),identity)) )],[refute_0_291,refute_0_292]) ).

cnf(refute_0_294,plain,
    ( multiply(inverse(identity),identity) != identity
    | multiply(inverse(identity),identity) != inverse(identity)
    | inverse(identity) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),identity),identity) ),[0],$fot(inverse(identity))]]) ).

cnf(refute_0_295,plain,
    ( multiply(inverse(identity),identity) != identity
    | inverse(identity) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_293,refute_0_294]) ).

cnf(refute_0_296,plain,
    inverse(identity) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),identity) )],[refute_0_290,refute_0_295]) ).

cnf(refute_0_297,plain,
    ( inverse(identity) != identity
    | inverse(least_upper_bound(identity,Y)) != greatest_lower_bound(inverse(identity),inverse(Y))
    | inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(inverse(identity),inverse(Y))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_298,plain,
    ( inverse(least_upper_bound(identity,Y)) != greatest_lower_bound(inverse(identity),inverse(Y))
    | inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_297]) ).

cnf(refute_0_299,plain,
    inverse(least_upper_bound(identity,Y)) = greatest_lower_bound(identity,inverse(Y)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(inverse(identity),inverse(Y))) )],[refute_0_289,refute_0_298]) ).

cnf(refute_0_300,plain,
    inverse(least_upper_bound(identity,X_124)) = greatest_lower_bound(identity,inverse(X_124)),
    inference(subst,[],[refute_0_299:[bind(Y,$fot(X_124))]]) ).

cnf(refute_0_301,plain,
    ( inverse(least_upper_bound(identity,X_124)) != greatest_lower_bound(identity,inverse(X_124))
    | greatest_lower_bound(identity,inverse(X_124)) = inverse(least_upper_bound(identity,X_124)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(least_upper_bound(identity,X_124)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_124))))]]) ).

cnf(refute_0_302,plain,
    greatest_lower_bound(identity,inverse(X_124)) = inverse(least_upper_bound(identity,X_124)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_124)),greatest_lower_bound(identity,inverse(X_124))) )],[refute_0_300,refute_0_301]) ).

cnf(refute_0_303,plain,
    ( multiply(greatest_lower_bound(identity,inverse(X_124)),X_124) != greatest_lower_bound(identity,multiply(identity,X_124))
    | greatest_lower_bound(identity,inverse(X_124)) != inverse(least_upper_bound(identity,X_124))
    | multiply(inverse(least_upper_bound(identity,X_124)),X_124) = greatest_lower_bound(identity,multiply(identity,X_124)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_124)),X_124),greatest_lower_bound(identity,multiply(identity,X_124))) ),[0,0],$fot(inverse(least_upper_bound(identity,X_124)))]]) ).

cnf(refute_0_304,plain,
    ( multiply(greatest_lower_bound(identity,inverse(X_124)),X_124) != greatest_lower_bound(identity,multiply(identity,X_124))
    | multiply(inverse(least_upper_bound(identity,X_124)),X_124) = greatest_lower_bound(identity,multiply(identity,X_124)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_124)),inverse(least_upper_bound(identity,X_124))) )],[refute_0_302,refute_0_303]) ).

cnf(refute_0_305,plain,
    multiply(inverse(least_upper_bound(identity,X_124)),X_124) = greatest_lower_bound(identity,multiply(identity,X_124)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_124)),X_124),greatest_lower_bound(identity,multiply(identity,X_124))) )],[refute_0_288,refute_0_304]) ).

cnf(refute_0_306,plain,
    multiply(identity,greatest_lower_bound(X_124,identity)) = greatest_lower_bound(X_124,identity),
    inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_124,identity)))]]) ).

cnf(refute_0_307,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,identity)) != greatest_lower_bound(X_107,multiply(X_107,X_108))
    | greatest_lower_bound(X_107,multiply(X_107,X_108)) = multiply(X_107,greatest_lower_bound(X_108,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_107,greatest_lower_bound(X_108,identity)))),bind(Y0,$fot(greatest_lower_bound(X_107,multiply(X_107,X_108))))]]) ).

cnf(refute_0_308,plain,
    greatest_lower_bound(X_107,multiply(X_107,X_108)) = multiply(X_107,greatest_lower_bound(X_108,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,identity)),greatest_lower_bound(X_107,multiply(X_107,X_108))) )],[refute_0_161,refute_0_307]) ).

cnf(refute_0_309,plain,
    greatest_lower_bound(identity,multiply(identity,X_124)) = multiply(identity,greatest_lower_bound(X_124,identity)),
    inference(subst,[],[refute_0_308:[bind(X_107,$fot(identity)),bind(X_108,$fot(X_124))]]) ).

cnf(refute_0_310,plain,
    ( multiply(identity,greatest_lower_bound(X_124,identity)) != greatest_lower_bound(X_124,identity)
    | greatest_lower_bound(identity,multiply(identity,X_124)) != multiply(identity,greatest_lower_bound(X_124,identity))
    | greatest_lower_bound(identity,multiply(identity,X_124)) = greatest_lower_bound(X_124,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,X_124)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(X_124,identity)))),bind(Z0,$fot(greatest_lower_bound(X_124,identity)))]]) ).

cnf(refute_0_311,plain,
    ( multiply(identity,greatest_lower_bound(X_124,identity)) != greatest_lower_bound(X_124,identity)
    | greatest_lower_bound(identity,multiply(identity,X_124)) = greatest_lower_bound(X_124,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_124)),multiply(identity,greatest_lower_bound(X_124,identity))) )],[refute_0_309,refute_0_310]) ).

cnf(refute_0_312,plain,
    greatest_lower_bound(identity,multiply(identity,X_124)) = greatest_lower_bound(X_124,identity),
    inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_124,identity)),greatest_lower_bound(X_124,identity)) )],[refute_0_306,refute_0_311]) ).

cnf(refute_0_313,plain,
    ( multiply(inverse(least_upper_bound(identity,X_124)),X_124) != greatest_lower_bound(identity,multiply(identity,X_124))
    | greatest_lower_bound(identity,multiply(identity,X_124)) != greatest_lower_bound(X_124,identity)
    | multiply(inverse(least_upper_bound(identity,X_124)),X_124) = greatest_lower_bound(X_124,identity) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(least_upper_bound(identity,X_124)),X_124),greatest_lower_bound(X_124,identity)) ),[0],$fot(greatest_lower_bound(identity,multiply(identity,X_124)))]]) ).

cnf(refute_0_314,plain,
    ( multiply(inverse(least_upper_bound(identity,X_124)),X_124) != greatest_lower_bound(identity,multiply(identity,X_124))
    | multiply(inverse(least_upper_bound(identity,X_124)),X_124) = greatest_lower_bound(X_124,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_124)),greatest_lower_bound(X_124,identity)) )],[refute_0_312,refute_0_313]) ).

cnf(refute_0_315,plain,
    multiply(inverse(least_upper_bound(identity,X_124)),X_124) = greatest_lower_bound(X_124,identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_124)),X_124),greatest_lower_bound(identity,multiply(identity,X_124))) )],[refute_0_305,refute_0_314]) ).

cnf(refute_0_316,plain,
    multiply(inverse(least_upper_bound(identity,X_60)),X_60) = greatest_lower_bound(X_60,identity),
    inference(subst,[],[refute_0_315:[bind(X_124,$fot(X_60))]]) ).

cnf(refute_0_317,plain,
    ( X_60 != multiply(inverse(inverse(least_upper_bound(identity,X_60))),multiply(inverse(least_upper_bound(identity,X_60)),X_60))
    | multiply(inverse(least_upper_bound(identity,X_60)),X_60) != greatest_lower_bound(X_60,identity)
    | X_60 = multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(X_60,multiply(inverse(inverse(least_upper_bound(identity,X_60))),multiply(inverse(least_upper_bound(identity,X_60)),X_60))) ),[1,1],$fot(greatest_lower_bound(X_60,identity))]]) ).

cnf(refute_0_318,plain,
    ( X_60 != multiply(inverse(inverse(least_upper_bound(identity,X_60))),multiply(inverse(least_upper_bound(identity,X_60)),X_60))
    | X_60 = multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_60)),X_60),greatest_lower_bound(X_60,identity)) )],[refute_0_316,refute_0_317]) ).

cnf(refute_0_319,plain,
    X_60 = multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)),
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(inverse(least_upper_bound(identity,X_60))),multiply(inverse(least_upper_bound(identity,X_60)),X_60))) )],[refute_0_278,refute_0_318]) ).

cnf(refute_0_320,plain,
    inverse(inverse(least_upper_bound(identity,X_60))) = least_upper_bound(identity,X_60),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(least_upper_bound(identity,X_60)))]]) ).

cnf(refute_0_321,plain,
    multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)) = multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)),
    introduced(tautology,[refl,[$fot(multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)))]]) ).

cnf(refute_0_322,plain,
    ( multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)) != multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity))
    | inverse(inverse(least_upper_bound(identity,X_60))) != least_upper_bound(identity,X_60)
    | multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)) = multiply(least_upper_bound(identity,X_60),greatest_lower_bound(X_60,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)),multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity))) ),[1,0],$fot(least_upper_bound(identity,X_60))]]) ).

cnf(refute_0_323,plain,
    ( inverse(inverse(least_upper_bound(identity,X_60))) != least_upper_bound(identity,X_60)
    | multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)) = multiply(least_upper_bound(identity,X_60),greatest_lower_bound(X_60,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)),multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity))) )],[refute_0_321,refute_0_322]) ).

cnf(refute_0_324,plain,
    multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)) = multiply(least_upper_bound(identity,X_60),greatest_lower_bound(X_60,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,X_60))),least_upper_bound(identity,X_60)) )],[refute_0_320,refute_0_323]) ).

cnf(refute_0_325,plain,
    ( X_60 != multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity))
    | multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)) != multiply(least_upper_bound(identity,X_60),greatest_lower_bound(X_60,identity))
    | X_60 = multiply(least_upper_bound(identity,X_60),greatest_lower_bound(X_60,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_60,multiply(least_upper_bound(identity,X_60),greatest_lower_bound(X_60,identity))) ),[0],$fot(multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)))]]) ).

cnf(refute_0_326,plain,
    ( X_60 != multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity))
    | X_60 = multiply(least_upper_bound(identity,X_60),greatest_lower_bound(X_60,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity)),multiply(least_upper_bound(identity,X_60),greatest_lower_bound(X_60,identity))) )],[refute_0_324,refute_0_325]) ).

cnf(refute_0_327,plain,
    X_60 = multiply(least_upper_bound(identity,X_60),greatest_lower_bound(X_60,identity)),
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(inverse(least_upper_bound(identity,X_60))),greatest_lower_bound(X_60,identity))) )],[refute_0_319,refute_0_326]) ).

cnf(refute_0_328,plain,
    X_129 = multiply(least_upper_bound(identity,X_129),greatest_lower_bound(X_129,identity)),
    inference(subst,[],[refute_0_327:[bind(X_60,$fot(X_129))]]) ).

cnf(refute_0_329,plain,
    greatest_lower_bound(identity,X_129) = greatest_lower_bound(X_129,identity),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_129))]]) ).

cnf(refute_0_330,plain,
    ( greatest_lower_bound(identity,X_129) != greatest_lower_bound(X_129,identity)
    | greatest_lower_bound(X_129,identity) = greatest_lower_bound(identity,X_129) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(identity,X_129))),bind(Y0,$fot(greatest_lower_bound(X_129,identity)))]]) ).

cnf(refute_0_331,plain,
    greatest_lower_bound(X_129,identity) = greatest_lower_bound(identity,X_129),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_129),greatest_lower_bound(X_129,identity)) )],[refute_0_329,refute_0_330]) ).

cnf(refute_0_332,plain,
    ( X_129 != multiply(least_upper_bound(identity,X_129),greatest_lower_bound(X_129,identity))
    | greatest_lower_bound(X_129,identity) != greatest_lower_bound(identity,X_129)
    | X_129 = multiply(least_upper_bound(identity,X_129),greatest_lower_bound(identity,X_129)) ),
    introduced(tautology,[equality,[$cnf( $equal(X_129,multiply(least_upper_bound(identity,X_129),greatest_lower_bound(X_129,identity))) ),[1,1],$fot(greatest_lower_bound(identity,X_129))]]) ).

cnf(refute_0_333,plain,
    ( X_129 != multiply(least_upper_bound(identity,X_129),greatest_lower_bound(X_129,identity))
    | X_129 = multiply(least_upper_bound(identity,X_129),greatest_lower_bound(identity,X_129)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_129,identity),greatest_lower_bound(identity,X_129)) )],[refute_0_331,refute_0_332]) ).

cnf(refute_0_334,plain,
    X_129 = multiply(least_upper_bound(identity,X_129),greatest_lower_bound(identity,X_129)),
    inference(resolve,[$cnf( $equal(X_129,multiply(least_upper_bound(identity,X_129),greatest_lower_bound(X_129,identity))) )],[refute_0_328,refute_0_333]) ).

cnf(refute_0_335,plain,
    multiply(least_upper_bound(X_132,Y),inverse(X_132)) = multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))),
    inference(subst,[],[refute_0_334:[bind(X_129,$fot(multiply(least_upper_bound(X_132,Y),inverse(X_132))))]]) ).

cnf(refute_0_336,plain,
    multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) = greatest_lower_bound(multiply(X_122,inverse(X_122)),multiply(X_123,inverse(X_122))),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_122))),bind(Y,$fot(X_122)),bind(Z,$fot(X_123))]]) ).

cnf(refute_0_337,plain,
    multiply(X_122,inverse(X_122)) = identity,
    inference(subst,[],[refute_0_232:[bind(X_66,$fot(X_122))]]) ).

cnf(refute_0_338,plain,
    ( multiply(X_122,inverse(X_122)) != identity
    | multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) != greatest_lower_bound(multiply(X_122,inverse(X_122)),multiply(X_123,inverse(X_122)))
    | multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) = greatest_lower_bound(identity,multiply(X_123,inverse(X_122))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)),greatest_lower_bound(multiply(X_122,inverse(X_122)),multiply(X_123,inverse(X_122)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_339,plain,
    ( multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) != greatest_lower_bound(multiply(X_122,inverse(X_122)),multiply(X_123,inverse(X_122)))
    | multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) = greatest_lower_bound(identity,multiply(X_123,inverse(X_122))) ),
    inference(resolve,[$cnf( $equal(multiply(X_122,inverse(X_122)),identity) )],[refute_0_337,refute_0_338]) ).

cnf(refute_0_340,plain,
    multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) = greatest_lower_bound(identity,multiply(X_123,inverse(X_122))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)),greatest_lower_bound(multiply(X_122,inverse(X_122)),multiply(X_123,inverse(X_122)))) )],[refute_0_336,refute_0_339]) ).

cnf(refute_0_341,plain,
    multiply(greatest_lower_bound(X_132,least_upper_bound(X_132,Y)),inverse(X_132)) = greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),
    inference(subst,[],[refute_0_340:[bind(X_122,$fot(X_132)),bind(X_123,$fot(least_upper_bound(X_132,Y)))]]) ).

cnf(refute_0_342,plain,
    greatest_lower_bound(X_132,least_upper_bound(X_132,Y)) = X_132,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_132))]]) ).

cnf(refute_0_343,plain,
    ( multiply(greatest_lower_bound(X_132,least_upper_bound(X_132,Y)),inverse(X_132)) != greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))
    | greatest_lower_bound(X_132,least_upper_bound(X_132,Y)) != X_132
    | multiply(X_132,inverse(X_132)) = greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_132,least_upper_bound(X_132,Y)),inverse(X_132)),greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))) ),[0,0],$fot(X_132)]]) ).

cnf(refute_0_344,plain,
    ( multiply(greatest_lower_bound(X_132,least_upper_bound(X_132,Y)),inverse(X_132)) != greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))
    | multiply(X_132,inverse(X_132)) = greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_132,least_upper_bound(X_132,Y)),X_132) )],[refute_0_342,refute_0_343]) ).

cnf(refute_0_345,plain,
    multiply(X_132,inverse(X_132)) = greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,least_upper_bound(X_132,Y)),inverse(X_132)),greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))) )],[refute_0_341,refute_0_344]) ).

cnf(refute_0_346,plain,
    multiply(X_132,inverse(X_132)) = identity,
    inference(subst,[],[refute_0_232:[bind(X_66,$fot(X_132))]]) ).

cnf(refute_0_347,plain,
    ( multiply(X_132,inverse(X_132)) != greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))
    | multiply(X_132,inverse(X_132)) != identity
    | identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_132,inverse(X_132)),greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))) ),[0],$fot(identity)]]) ).

cnf(refute_0_348,plain,
    ( multiply(X_132,inverse(X_132)) != greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))
    | identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))) ),
    inference(resolve,[$cnf( $equal(multiply(X_132,inverse(X_132)),identity) )],[refute_0_346,refute_0_347]) ).

cnf(refute_0_349,plain,
    identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),
    inference(resolve,[$cnf( $equal(multiply(X_132,inverse(X_132)),greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))) )],[refute_0_345,refute_0_348]) ).

cnf(refute_0_350,plain,
    ( identity != greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))))]]) ).

cnf(refute_0_351,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))) = identity,
    inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))) )],[refute_0_349,refute_0_350]) ).

cnf(refute_0_352,plain,
    ( multiply(least_upper_bound(X_132,Y),inverse(X_132)) != multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))) != identity
    | multiply(least_upper_bound(X_132,Y),inverse(X_132)) = multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_132,Y),inverse(X_132)),multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_353,plain,
    ( multiply(least_upper_bound(X_132,Y),inverse(X_132)) != multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))))
    | multiply(least_upper_bound(X_132,Y),inverse(X_132)) = multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity) )],[refute_0_351,refute_0_352]) ).

cnf(refute_0_354,plain,
    multiply(least_upper_bound(X_132,Y),inverse(X_132)) = multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_132,Y),inverse(X_132)),multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),greatest_lower_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))))) )],[refute_0_335,refute_0_353]) ).

cnf(refute_0_355,plain,
    multiply(least_upper_bound(X_111,X_112),inverse(X_112)) = least_upper_bound(multiply(X_111,inverse(X_112)),multiply(X_112,inverse(X_112))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_112))),bind(Y,$fot(X_111)),bind(Z,$fot(X_112))]]) ).

cnf(refute_0_356,plain,
    multiply(X_112,inverse(X_112)) = identity,
    inference(subst,[],[refute_0_232:[bind(X_66,$fot(X_112))]]) ).

cnf(refute_0_357,plain,
    ( multiply(X_112,inverse(X_112)) != identity
    | multiply(least_upper_bound(X_111,X_112),inverse(X_112)) != least_upper_bound(multiply(X_111,inverse(X_112)),multiply(X_112,inverse(X_112)))
    | multiply(least_upper_bound(X_111,X_112),inverse(X_112)) = least_upper_bound(multiply(X_111,inverse(X_112)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),least_upper_bound(multiply(X_111,inverse(X_112)),multiply(X_112,inverse(X_112)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_358,plain,
    ( multiply(least_upper_bound(X_111,X_112),inverse(X_112)) != least_upper_bound(multiply(X_111,inverse(X_112)),multiply(X_112,inverse(X_112)))
    | multiply(least_upper_bound(X_111,X_112),inverse(X_112)) = least_upper_bound(multiply(X_111,inverse(X_112)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_112,inverse(X_112)),identity) )],[refute_0_356,refute_0_357]) ).

cnf(refute_0_359,plain,
    multiply(least_upper_bound(X_111,X_112),inverse(X_112)) = least_upper_bound(multiply(X_111,inverse(X_112)),identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),least_upper_bound(multiply(X_111,inverse(X_112)),multiply(X_112,inverse(X_112)))) )],[refute_0_355,refute_0_358]) ).

cnf(refute_0_360,plain,
    least_upper_bound(multiply(X_111,inverse(X_112)),identity) = least_upper_bound(identity,multiply(X_111,inverse(X_112))),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(multiply(X_111,inverse(X_112)))),bind(X_17,$fot(identity))]]) ).

cnf(refute_0_361,plain,
    ( multiply(least_upper_bound(X_111,X_112),inverse(X_112)) != least_upper_bound(multiply(X_111,inverse(X_112)),identity)
    | least_upper_bound(multiply(X_111,inverse(X_112)),identity) != least_upper_bound(identity,multiply(X_111,inverse(X_112)))
    | multiply(least_upper_bound(X_111,X_112),inverse(X_112)) = least_upper_bound(identity,multiply(X_111,inverse(X_112))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),least_upper_bound(identity,multiply(X_111,inverse(X_112)))) ),[0],$fot(least_upper_bound(multiply(X_111,inverse(X_112)),identity))]]) ).

cnf(refute_0_362,plain,
    ( multiply(least_upper_bound(X_111,X_112),inverse(X_112)) != least_upper_bound(multiply(X_111,inverse(X_112)),identity)
    | multiply(least_upper_bound(X_111,X_112),inverse(X_112)) = least_upper_bound(identity,multiply(X_111,inverse(X_112))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_111,inverse(X_112)),identity),least_upper_bound(identity,multiply(X_111,inverse(X_112)))) )],[refute_0_360,refute_0_361]) ).

cnf(refute_0_363,plain,
    multiply(least_upper_bound(X_111,X_112),inverse(X_112)) = least_upper_bound(identity,multiply(X_111,inverse(X_112))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),least_upper_bound(multiply(X_111,inverse(X_112)),identity)) )],[refute_0_359,refute_0_362]) ).

cnf(refute_0_364,plain,
    multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) = least_upper_bound(identity,multiply(least_upper_bound(inverse(inverse(X_119)),X_112),inverse(X_119))),
    inference(subst,[],[refute_0_363:[bind(X_111,$fot(least_upper_bound(inverse(inverse(X_119)),X_112))),bind(X_112,$fot(X_119))]]) ).

cnf(refute_0_365,plain,
    multiply(least_upper_bound(inverse(inverse(X_119)),X_112),inverse(X_119)) = least_upper_bound(identity,multiply(X_112,inverse(X_119))),
    inference(subst,[],[refute_0_166:[bind(X_110,$fot(inverse(X_119)))]]) ).

cnf(refute_0_366,plain,
    ( multiply(least_upper_bound(inverse(inverse(X_119)),X_112),inverse(X_119)) != least_upper_bound(identity,multiply(X_112,inverse(X_119)))
    | multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) != least_upper_bound(identity,multiply(least_upper_bound(inverse(inverse(X_119)),X_112),inverse(X_119)))
    | multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)),least_upper_bound(identity,multiply(least_upper_bound(inverse(inverse(X_119)),X_112),inverse(X_119)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_112,inverse(X_119))))]]) ).

cnf(refute_0_367,plain,
    ( multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) != least_upper_bound(identity,multiply(least_upper_bound(inverse(inverse(X_119)),X_112),inverse(X_119)))
    | multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(inverse(X_119)),X_112),inverse(X_119)),least_upper_bound(identity,multiply(X_112,inverse(X_119)))) )],[refute_0_365,refute_0_366]) ).

cnf(refute_0_368,plain,
    multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)),least_upper_bound(identity,multiply(least_upper_bound(inverse(inverse(X_119)),X_112),inverse(X_119)))) )],[refute_0_364,refute_0_367]) ).

cnf(refute_0_369,plain,
    multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) = least_upper_bound(multiply(least_upper_bound(X_114,inverse(X)),X),multiply(Z,X)),
    inference(subst,[],[monotony_lub2:[bind(Y,$fot(least_upper_bound(X_114,inverse(X))))]]) ).

cnf(refute_0_370,plain,
    multiply(least_upper_bound(X_114,inverse(X)),X) = least_upper_bound(identity,multiply(X_114,X)),
    inference(subst,[],[refute_0_92:[bind(X_110,$fot(X)),bind(X_111,$fot(X_114))]]) ).

cnf(refute_0_371,plain,
    ( multiply(least_upper_bound(X_114,inverse(X)),X) != least_upper_bound(identity,multiply(X_114,X))
    | multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) != least_upper_bound(multiply(least_upper_bound(X_114,inverse(X)),X),multiply(Z,X))
    | multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X),least_upper_bound(multiply(least_upper_bound(X_114,inverse(X)),X),multiply(Z,X))) ),[1,0],$fot(least_upper_bound(identity,multiply(X_114,X)))]]) ).

cnf(refute_0_372,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) != least_upper_bound(multiply(least_upper_bound(X_114,inverse(X)),X),multiply(Z,X))
    | multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_114,inverse(X)),X),least_upper_bound(identity,multiply(X_114,X))) )],[refute_0_370,refute_0_371]) ).

cnf(refute_0_373,plain,
    multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) = least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X),least_upper_bound(multiply(least_upper_bound(X_114,inverse(X)),X),multiply(Z,X))) )],[refute_0_369,refute_0_372]) ).

cnf(refute_0_374,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_375,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_374]) ).

cnf(refute_0_376,plain,
    least_upper_bound(least_upper_bound(X_114,inverse(X)),Z) = least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(X_114)),bind(Y,$fot(inverse(X)))]]) ).

cnf(refute_0_377,plain,
    multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) = multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X))]]) ).

cnf(refute_0_378,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) != multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X)
    | least_upper_bound(least_upper_bound(X_114,inverse(X)),Z) != least_upper_bound(X_114,least_upper_bound(inverse(X),Z))
    | multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) = multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X),multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X)) ),[1,0],$fot(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)))]]) ).

cnf(refute_0_379,plain,
    ( least_upper_bound(least_upper_bound(X_114,inverse(X)),Z) != least_upper_bound(X_114,least_upper_bound(inverse(X),Z))
    | multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) = multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X),multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X)) )],[refute_0_377,refute_0_378]) ).

cnf(refute_0_380,plain,
    multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) = multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),least_upper_bound(X_114,least_upper_bound(inverse(X),Z))) )],[refute_0_376,refute_0_379]) ).

cnf(refute_0_381,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) != multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X)
    | multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X))
    | multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X),least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X))) ),[0],$fot(multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X))]]) ).

cnf(refute_0_382,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X))
    | multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X),multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X)) )],[refute_0_380,refute_0_381]) ).

cnf(refute_0_383,plain,
    ( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
    | least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).

cnf(refute_0_384,plain,
    least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_383]) ).

cnf(refute_0_385,plain,
    least_upper_bound(multiply(X_114,X),multiply(Z,X)) = multiply(least_upper_bound(X_114,Z),X),
    inference(subst,[],[refute_0_384:[bind(Y,$fot(X_114))]]) ).

cnf(refute_0_386,plain,
    least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))) = least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))))]]) ).

cnf(refute_0_387,plain,
    ( least_upper_bound(multiply(X_114,X),multiply(Z,X)) != multiply(least_upper_bound(X_114,Z),X)
    | least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))) != least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X)))
    | least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))),least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X)))) ),[1,1],$fot(multiply(least_upper_bound(X_114,Z),X))]]) ).

cnf(refute_0_388,plain,
    ( least_upper_bound(multiply(X_114,X),multiply(Z,X)) != multiply(least_upper_bound(X_114,Z),X)
    | least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))),least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X)))) )],[refute_0_386,refute_0_387]) ).

cnf(refute_0_389,plain,
    least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))) = least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_114,X),multiply(Z,X)),multiply(least_upper_bound(X_114,Z),X)) )],[refute_0_385,refute_0_388]) ).

cnf(refute_0_390,plain,
    least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)) = least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))),
    inference(subst,[],[refute_0_375:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_114,X))),bind(Z,$fot(multiply(Z,X)))]]) ).

cnf(refute_0_391,plain,
    ( least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))) != least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X))
    | least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)) != least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X)))
    | least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X))))]]) ).

cnf(refute_0_392,plain,
    ( least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))) != least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X))
    | least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)),least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X)))) )],[refute_0_390,refute_0_391]) ).

cnf(refute_0_393,plain,
    least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)) = least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_114,X),multiply(Z,X))),least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X))) )],[refute_0_389,refute_0_392]) ).

cnf(refute_0_394,plain,
    ( multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X))
    | least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)) != least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X))
    | multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X),least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)))]]) ).

cnf(refute_0_395,plain,
    ( multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X))
    | multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X)),least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X))) )],[refute_0_393,refute_0_394]) ).

cnf(refute_0_396,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X) != least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X))
    | multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X),least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X))) )],[refute_0_382,refute_0_395]) ).

cnf(refute_0_397,plain,
    multiply(least_upper_bound(X_114,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(X_114,Z),X)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_114,inverse(X)),Z),X),least_upper_bound(least_upper_bound(identity,multiply(X_114,X)),multiply(Z,X))) )],[refute_0_373,refute_0_396]) ).

cnf(refute_0_398,plain,
    multiply(least_upper_bound(X_119,least_upper_bound(inverse(inverse(X_119)),X_112)),inverse(X_119)) = least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))),
    inference(subst,[],[refute_0_397:[bind(X,$fot(inverse(X_119))),bind(Z,$fot(X_112)),bind(X_114,$fot(X_119))]]) ).

cnf(refute_0_399,plain,
    least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) = least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(multiply(X_112,X_110))),bind(Y,$fot(multiply(X_111,X_110)))]]) ).

cnf(refute_0_400,plain,
    multiply(least_upper_bound(X_111,X_112),X_110) = least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_110)),bind(Y,$fot(X_111)),bind(Z,$fot(X_112))]]) ).

cnf(refute_0_401,plain,
    ( multiply(least_upper_bound(X_111,X_112),X_110) != least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110))
    | least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)) = multiply(least_upper_bound(X_111,X_112),X_110) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_111,X_112),X_110))),bind(Y0,$fot(least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110))))]]) ).

cnf(refute_0_402,plain,
    least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)) = multiply(least_upper_bound(X_111,X_112),X_110),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,X_112),X_110),least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110))) )],[refute_0_400,refute_0_401]) ).

cnf(refute_0_403,plain,
    ( least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)) != multiply(least_upper_bound(X_111,X_112),X_110)
    | least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) != least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110))
    | least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) = multiply(least_upper_bound(X_111,X_112),X_110) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)),least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110))) ),[1],$fot(multiply(least_upper_bound(X_111,X_112),X_110))]]) ).

cnf(refute_0_404,plain,
    ( least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) != least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110))
    | least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) = multiply(least_upper_bound(X_111,X_112),X_110) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)),multiply(least_upper_bound(X_111,X_112),X_110)) )],[refute_0_402,refute_0_403]) ).

cnf(refute_0_405,plain,
    least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) = multiply(least_upper_bound(X_111,X_112),X_110),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)),least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110))) )],[refute_0_399,refute_0_404]) ).

cnf(refute_0_406,plain,
    least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) = multiply(least_upper_bound(X_112,X_111),X_110),
    inference(subst,[],[refute_0_384:[bind(X,$fot(X_110)),bind(Y,$fot(X_112)),bind(Z,$fot(X_111))]]) ).

cnf(refute_0_407,plain,
    ( least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) != multiply(least_upper_bound(X_111,X_112),X_110)
    | least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) != multiply(least_upper_bound(X_112,X_111),X_110)
    | multiply(least_upper_bound(X_112,X_111),X_110) = multiply(least_upper_bound(X_111,X_112),X_110) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(least_upper_bound(X_111,X_112),X_110)) ),[0],$fot(multiply(least_upper_bound(X_112,X_111),X_110))]]) ).

cnf(refute_0_408,plain,
    ( least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) != multiply(least_upper_bound(X_111,X_112),X_110)
    | multiply(least_upper_bound(X_112,X_111),X_110) = multiply(least_upper_bound(X_111,X_112),X_110) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(least_upper_bound(X_112,X_111),X_110)) )],[refute_0_406,refute_0_407]) ).

cnf(refute_0_409,plain,
    multiply(least_upper_bound(X_112,X_111),X_110) = multiply(least_upper_bound(X_111,X_112),X_110),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(least_upper_bound(X_111,X_112),X_110)) )],[refute_0_405,refute_0_408]) ).

cnf(refute_0_410,plain,
    ( multiply(least_upper_bound(X_112,X_111),X_110) != multiply(least_upper_bound(X_111,X_112),X_110)
    | multiply(least_upper_bound(X_111,X_112),X_110) = multiply(least_upper_bound(X_112,X_111),X_110) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_112,X_111),X_110))),bind(Y0,$fot(multiply(least_upper_bound(X_111,X_112),X_110)))]]) ).

cnf(refute_0_411,plain,
    multiply(least_upper_bound(X_111,X_112),X_110) = multiply(least_upper_bound(X_112,X_111),X_110),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_112,X_111),X_110),multiply(least_upper_bound(X_111,X_112),X_110)) )],[refute_0_409,refute_0_410]) ).

cnf(refute_0_412,plain,
    multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) = multiply(least_upper_bound(X_119,least_upper_bound(inverse(inverse(X_119)),X_112)),inverse(X_119)),
    inference(subst,[],[refute_0_411:[bind(X_110,$fot(inverse(X_119))),bind(X_111,$fot(least_upper_bound(inverse(inverse(X_119)),X_112))),bind(X_112,$fot(X_119))]]) ).

cnf(refute_0_413,plain,
    ( multiply(least_upper_bound(X_119,least_upper_bound(inverse(inverse(X_119)),X_112)),inverse(X_119)) != least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119)))
    | multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) != multiply(least_upper_bound(X_119,least_upper_bound(inverse(inverse(X_119)),X_112)),inverse(X_119))
    | multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) = least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)))),bind(Y0,$fot(multiply(least_upper_bound(X_119,least_upper_bound(inverse(inverse(X_119)),X_112)),inverse(X_119)))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119)))))]]) ).

cnf(refute_0_414,plain,
    ( multiply(least_upper_bound(X_119,least_upper_bound(inverse(inverse(X_119)),X_112)),inverse(X_119)) != least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119)))
    | multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) = least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)),multiply(least_upper_bound(X_119,least_upper_bound(inverse(inverse(X_119)),X_112)),inverse(X_119))) )],[refute_0_412,refute_0_413]) ).

cnf(refute_0_415,plain,
    multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) = least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_119,least_upper_bound(inverse(inverse(X_119)),X_112)),inverse(X_119)),least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119)))) )],[refute_0_398,refute_0_414]) ).

cnf(refute_0_416,plain,
    ( multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) != least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119)))
    | multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119))))
    | least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119))))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))))]]) ).

cnf(refute_0_417,plain,
    ( multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119))))
    | least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)),least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119)))) )],[refute_0_415,refute_0_416]) ).

cnf(refute_0_418,plain,
    least_upper_bound(least_upper_bound(X_21,Y),greatest_lower_bound(X_21,least_upper_bound(X_21,Y))) = least_upper_bound(X_21,Y),
    inference(subst,[],[refute_0_117:[bind(X_8,$fot(least_upper_bound(X_21,Y))),bind(X_9,$fot(X_21))]]) ).

cnf(refute_0_419,plain,
    greatest_lower_bound(X_21,least_upper_bound(X_21,Y)) = X_21,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_21))]]) ).

cnf(refute_0_420,plain,
    ( greatest_lower_bound(X_21,least_upper_bound(X_21,Y)) != X_21
    | least_upper_bound(least_upper_bound(X_21,Y),greatest_lower_bound(X_21,least_upper_bound(X_21,Y))) != least_upper_bound(X_21,Y)
    | least_upper_bound(least_upper_bound(X_21,Y),X_21) = least_upper_bound(X_21,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),greatest_lower_bound(X_21,least_upper_bound(X_21,Y))),least_upper_bound(X_21,Y)) ),[0,1],$fot(X_21)]]) ).

cnf(refute_0_421,plain,
    ( least_upper_bound(least_upper_bound(X_21,Y),greatest_lower_bound(X_21,least_upper_bound(X_21,Y))) != least_upper_bound(X_21,Y)
    | least_upper_bound(least_upper_bound(X_21,Y),X_21) = least_upper_bound(X_21,Y) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_21,least_upper_bound(X_21,Y)),X_21) )],[refute_0_419,refute_0_420]) ).

cnf(refute_0_422,plain,
    least_upper_bound(least_upper_bound(X_21,Y),X_21) = least_upper_bound(X_21,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),greatest_lower_bound(X_21,least_upper_bound(X_21,Y))),least_upper_bound(X_21,Y)) )],[refute_0_418,refute_0_421]) ).

cnf(refute_0_423,plain,
    least_upper_bound(least_upper_bound(X_21,Y),X_21) = least_upper_bound(X_21,least_upper_bound(Y,X_21)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(X_21)),bind(Z,$fot(X_21))]]) ).

cnf(refute_0_424,plain,
    ( least_upper_bound(least_upper_bound(X_21,Y),X_21) != least_upper_bound(X_21,Y)
    | least_upper_bound(least_upper_bound(X_21,Y),X_21) != least_upper_bound(X_21,least_upper_bound(Y,X_21))
    | least_upper_bound(X_21,least_upper_bound(Y,X_21)) = least_upper_bound(X_21,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),X_21),least_upper_bound(X_21,Y)) ),[0],$fot(least_upper_bound(X_21,least_upper_bound(Y,X_21)))]]) ).

cnf(refute_0_425,plain,
    ( least_upper_bound(least_upper_bound(X_21,Y),X_21) != least_upper_bound(X_21,Y)
    | least_upper_bound(X_21,least_upper_bound(Y,X_21)) = least_upper_bound(X_21,Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),X_21),least_upper_bound(X_21,least_upper_bound(Y,X_21))) )],[refute_0_423,refute_0_424]) ).

cnf(refute_0_426,plain,
    least_upper_bound(X_21,least_upper_bound(Y,X_21)) = least_upper_bound(X_21,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_21,Y),X_21),least_upper_bound(X_21,Y)) )],[refute_0_422,refute_0_425]) ).

cnf(refute_0_427,plain,
    least_upper_bound(X_31,least_upper_bound(X_30,X_31)) = least_upper_bound(X_31,X_30),
    inference(subst,[],[refute_0_426:[bind(Y,$fot(X_30)),bind(X_21,$fot(X_31))]]) ).

cnf(refute_0_428,plain,
    least_upper_bound(X_31,X_30) = least_upper_bound(X_30,X_31),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_31)),bind(Y,$fot(X_30))]]) ).

cnf(refute_0_429,plain,
    ( least_upper_bound(X_31,X_30) != least_upper_bound(X_30,X_31)
    | least_upper_bound(X_30,X_31) = least_upper_bound(X_31,X_30) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_31,X_30))),bind(Y0,$fot(least_upper_bound(X_30,X_31)))]]) ).

cnf(refute_0_430,plain,
    least_upper_bound(X_30,X_31) = least_upper_bound(X_31,X_30),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,X_30),least_upper_bound(X_30,X_31)) )],[refute_0_428,refute_0_429]) ).

cnf(refute_0_431,plain,
    ( least_upper_bound(X_30,X_31) != least_upper_bound(X_31,X_30)
    | least_upper_bound(X_31,least_upper_bound(X_30,X_31)) != least_upper_bound(X_31,X_30)
    | least_upper_bound(X_31,least_upper_bound(X_31,X_30)) = least_upper_bound(X_31,X_30) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_30,X_31)),least_upper_bound(X_31,X_30)) ),[0,1],$fot(least_upper_bound(X_31,X_30))]]) ).

cnf(refute_0_432,plain,
    ( least_upper_bound(X_31,least_upper_bound(X_30,X_31)) != least_upper_bound(X_31,X_30)
    | least_upper_bound(X_31,least_upper_bound(X_31,X_30)) = least_upper_bound(X_31,X_30) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_30,X_31),least_upper_bound(X_31,X_30)) )],[refute_0_430,refute_0_431]) ).

cnf(refute_0_433,plain,
    least_upper_bound(X_31,least_upper_bound(X_31,X_30)) = least_upper_bound(X_31,X_30),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_30,X_31)),least_upper_bound(X_31,X_30)) )],[refute_0_427,refute_0_432]) ).

cnf(refute_0_434,plain,
    least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119)))) = least_upper_bound(identity,multiply(X_112,inverse(X_119))),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(multiply(X_112,inverse(X_119)))),bind(X_31,$fot(identity))]]) ).

cnf(refute_0_435,plain,
    ( least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119))))
    | least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119)))) != least_upper_bound(identity,multiply(X_112,inverse(X_119)))
    | least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))) = least_upper_bound(identity,multiply(X_112,inverse(X_119))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))),least_upper_bound(identity,multiply(X_112,inverse(X_119)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119)))))]]) ).

cnf(refute_0_436,plain,
    ( least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119))))
    | least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))) = least_upper_bound(identity,multiply(X_112,inverse(X_119))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119)))),least_upper_bound(identity,multiply(X_112,inverse(X_119)))) )],[refute_0_434,refute_0_435]) ).

cnf(refute_0_437,plain,
    ( multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119))))
    | least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))) = least_upper_bound(identity,multiply(X_112,inverse(X_119))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119))))) )],[refute_0_417,refute_0_436]) ).

cnf(refute_0_438,plain,
    least_upper_bound(identity,multiply(least_upper_bound(X_119,X_112),inverse(X_119))) = least_upper_bound(identity,multiply(X_112,inverse(X_119))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(inverse(inverse(X_119)),X_112),X_119),inverse(X_119)),least_upper_bound(identity,least_upper_bound(identity,multiply(X_112,inverse(X_119))))) )],[refute_0_368,refute_0_437]) ).

cnf(refute_0_439,plain,
    least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))) = least_upper_bound(identity,multiply(Y,inverse(X_132))),
    inference(subst,[],[refute_0_438:[bind(X_112,$fot(Y)),bind(X_119,$fot(X_132))]]) ).

cnf(refute_0_440,plain,
    multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity) = least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))))]]) ).

cnf(refute_0_441,plain,
    ( multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity) != least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))
    | least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))) != least_upper_bound(identity,multiply(Y,inverse(X_132)))
    | multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity) = least_upper_bound(identity,multiply(Y,inverse(X_132))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))))),bind(Z0,$fot(least_upper_bound(identity,multiply(Y,inverse(X_132)))))]]) ).

cnf(refute_0_442,plain,
    ( least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))) != least_upper_bound(identity,multiply(Y,inverse(X_132)))
    | multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity) = least_upper_bound(identity,multiply(Y,inverse(X_132))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity),least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132)))) )],[refute_0_440,refute_0_441]) ).

cnf(refute_0_443,plain,
    multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity) = least_upper_bound(identity,multiply(Y,inverse(X_132))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),least_upper_bound(identity,multiply(Y,inverse(X_132)))) )],[refute_0_439,refute_0_442]) ).

cnf(refute_0_444,plain,
    ( multiply(least_upper_bound(X_132,Y),inverse(X_132)) != multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity)
    | multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity) != least_upper_bound(identity,multiply(Y,inverse(X_132)))
    | multiply(least_upper_bound(X_132,Y),inverse(X_132)) = least_upper_bound(identity,multiply(Y,inverse(X_132))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_132,Y),inverse(X_132)),least_upper_bound(identity,multiply(Y,inverse(X_132)))) ),[0],$fot(multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity))]]) ).

cnf(refute_0_445,plain,
    ( multiply(least_upper_bound(X_132,Y),inverse(X_132)) != multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity)
    | multiply(least_upper_bound(X_132,Y),inverse(X_132)) = least_upper_bound(identity,multiply(Y,inverse(X_132))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity),least_upper_bound(identity,multiply(Y,inverse(X_132)))) )],[refute_0_443,refute_0_444]) ).

cnf(refute_0_446,plain,
    multiply(least_upper_bound(X_132,Y),inverse(X_132)) = least_upper_bound(identity,multiply(Y,inverse(X_132))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_132,Y),inverse(X_132)),multiply(least_upper_bound(identity,multiply(least_upper_bound(X_132,Y),inverse(X_132))),identity)) )],[refute_0_354,refute_0_445]) ).

cnf(refute_0_447,plain,
    ( multiply(least_upper_bound(X_132,Y),inverse(X_132)) != least_upper_bound(identity,multiply(Y,inverse(X_132)))
    | least_upper_bound(identity,multiply(Y,inverse(X_132))) = multiply(least_upper_bound(X_132,Y),inverse(X_132)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_132,Y),inverse(X_132)))),bind(Y0,$fot(least_upper_bound(identity,multiply(Y,inverse(X_132)))))]]) ).

cnf(refute_0_448,plain,
    least_upper_bound(identity,multiply(Y,inverse(X_132))) = multiply(least_upper_bound(X_132,Y),inverse(X_132)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_132,Y),inverse(X_132)),least_upper_bound(identity,multiply(Y,inverse(X_132)))) )],[refute_0_446,refute_0_447]) ).

cnf(refute_0_449,plain,
    least_upper_bound(identity,multiply(c,inverse(b))) = multiply(least_upper_bound(b,c),inverse(b)),
    inference(subst,[],[refute_0_448:[bind(Y,$fot(c)),bind(X_132,$fot(b))]]) ).

cnf(refute_0_450,plain,
    ( multiply(least_upper_bound(b,c),inverse(b)) != multiply(c,inverse(greatest_lower_bound(b,c)))
    | least_upper_bound(identity,multiply(c,inverse(b))) != multiply(least_upper_bound(b,c),inverse(b))
    | least_upper_bound(identity,multiply(c,inverse(b))) = multiply(c,inverse(greatest_lower_bound(b,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(c,inverse(b))))),bind(Y0,$fot(multiply(least_upper_bound(b,c),inverse(b)))),bind(Z0,$fot(multiply(c,inverse(greatest_lower_bound(b,c)))))]]) ).

cnf(refute_0_451,plain,
    ( multiply(least_upper_bound(b,c),inverse(b)) != multiply(c,inverse(greatest_lower_bound(b,c)))
    | least_upper_bound(identity,multiply(c,inverse(b))) = multiply(c,inverse(greatest_lower_bound(b,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(c,inverse(b))),multiply(least_upper_bound(b,c),inverse(b))) )],[refute_0_449,refute_0_450]) ).

cnf(refute_0_452,plain,
    least_upper_bound(identity,multiply(c,inverse(b))) = multiply(c,inverse(greatest_lower_bound(b,c))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,c),inverse(b)),multiply(c,inverse(greatest_lower_bound(b,c)))) )],[refute_0_277,refute_0_451]) ).

cnf(refute_0_453,plain,
    ( multiply(c,inverse(greatest_lower_bound(b,c))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(identity,multiply(c,inverse(b))) != multiply(c,inverse(greatest_lower_bound(b,c)))
    | least_upper_bound(identity,multiply(c,inverse(b))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(c,inverse(b))))),bind(Y0,$fot(multiply(c,inverse(greatest_lower_bound(b,c))))),bind(Z0,$fot(multiply(c,inverse(greatest_lower_bound(a,c)))))]]) ).

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

cnf(refute_0_455,plain,
    least_upper_bound(identity,multiply(c,inverse(b))) = multiply(c,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(b,c))),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_186,refute_0_454]) ).

cnf(refute_0_456,plain,
    ( multiply(least_upper_bound(a,c),inverse(b)) != least_upper_bound(identity,multiply(c,inverse(b)))
    | least_upper_bound(identity,multiply(c,inverse(b))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | multiply(least_upper_bound(a,c),inverse(b)) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(a,c),inverse(b)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),[0],$fot(least_upper_bound(identity,multiply(c,inverse(b))))]]) ).

cnf(refute_0_457,plain,
    ( multiply(least_upper_bound(a,c),inverse(b)) != least_upper_bound(identity,multiply(c,inverse(b)))
    | multiply(least_upper_bound(a,c),inverse(b)) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(c,inverse(b))),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_455,refute_0_456]) ).

cnf(refute_0_458,plain,
    multiply(least_upper_bound(a,c),inverse(b)) = multiply(c,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(b)),least_upper_bound(identity,multiply(c,inverse(b)))) )],[refute_0_176,refute_0_457]) ).

cnf(refute_0_459,plain,
    ( multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,c),inverse(b)))
    | multiply(least_upper_bound(a,c),inverse(b)) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) = greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,c),inverse(b)))) ),[1,1],$fot(multiply(c,inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_460,plain,
    ( multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) != greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,c),inverse(b)))
    | multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) = greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(b)),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_458,refute_0_459]) ).

cnf(refute_0_461,plain,
    multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) = greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)),greatest_lower_bound(least_upper_bound(a,c),multiply(least_upper_bound(a,c),inverse(b)))) )],[refute_0_162,refute_0_460]) ).

cnf(refute_0_462,plain,
    multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122))),inverse(X_122)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))),
    inference(subst,[],[refute_0_340:[bind(X_123,$fot(inverse(greatest_lower_bound(identity,X_122))))]]) ).

cnf(refute_0_463,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_11,X_36),X_38)) = greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_11,X_36)),X_38),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(least_upper_bound(X_11,X_36))),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_464,plain,
    greatest_lower_bound(X_36,least_upper_bound(X_11,X_36)) = X_36,
    inference(subst,[],[refute_0_215:[bind(X_10,$fot(X_36))]]) ).

cnf(refute_0_465,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_11,X_36),X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_11,X_36)),X_38)
    | greatest_lower_bound(X_36,least_upper_bound(X_11,X_36)) != X_36
    | greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_11,X_36),X_38)) = greatest_lower_bound(X_36,X_38) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_11,X_36),X_38)),greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_11,X_36)),X_38)) ),[1,0],$fot(X_36)]]) ).

cnf(refute_0_466,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_11,X_36),X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_11,X_36)),X_38)
    | greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_11,X_36),X_38)) = greatest_lower_bound(X_36,X_38) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,least_upper_bound(X_11,X_36)),X_36) )],[refute_0_464,refute_0_465]) ).

cnf(refute_0_467,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_11,X_36),X_38)) = greatest_lower_bound(X_36,X_38),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_11,X_36),X_38)),greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_11,X_36)),X_38)) )],[refute_0_463,refute_0_466]) ).

cnf(refute_0_468,plain,
    greatest_lower_bound(X_204,greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(identity,X_204)))) = greatest_lower_bound(X_204,inverse(greatest_lower_bound(identity,X_204))),
    inference(subst,[],[refute_0_467:[bind(X_11,$fot(identity)),bind(X_36,$fot(X_204)),bind(X_38,$fot(inverse(greatest_lower_bound(identity,X_204))))]]) ).

cnf(refute_0_469,plain,
    multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))) = identity,
    inference(subst,[],[refute_0_62:[bind(X_16,$fot(inverse(least_upper_bound(identity,X_166)))),bind(X_17,$fot(greatest_lower_bound(identity,X_166)))]]) ).

cnf(refute_0_470,plain,
    multiply(X_93,least_upper_bound(X_94,identity)) = least_upper_bound(multiply(X_93,X_94),multiply(X_93,identity)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_93)),bind(Y,$fot(X_94)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_471,plain,
    X_93 = multiply(X_93,identity),
    inference(subst,[],[refute_0_29:[bind(X_62,$fot(X_93))]]) ).

cnf(refute_0_472,plain,
    ( X_93 != multiply(X_93,identity)
    | multiply(X_93,identity) = X_93 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_93)),bind(Y0,$fot(multiply(X_93,identity)))]]) ).

cnf(refute_0_473,plain,
    multiply(X_93,identity) = X_93,
    inference(resolve,[$cnf( $equal(X_93,multiply(X_93,identity)) )],[refute_0_471,refute_0_472]) ).

cnf(refute_0_474,plain,
    ( multiply(X_93,identity) != X_93
    | multiply(X_93,least_upper_bound(X_94,identity)) != least_upper_bound(multiply(X_93,X_94),multiply(X_93,identity))
    | multiply(X_93,least_upper_bound(X_94,identity)) = least_upper_bound(multiply(X_93,X_94),X_93) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_93,least_upper_bound(X_94,identity)),least_upper_bound(multiply(X_93,X_94),multiply(X_93,identity))) ),[1,1],$fot(X_93)]]) ).

cnf(refute_0_475,plain,
    ( multiply(X_93,least_upper_bound(X_94,identity)) != least_upper_bound(multiply(X_93,X_94),multiply(X_93,identity))
    | multiply(X_93,least_upper_bound(X_94,identity)) = least_upper_bound(multiply(X_93,X_94),X_93) ),
    inference(resolve,[$cnf( $equal(multiply(X_93,identity),X_93) )],[refute_0_473,refute_0_474]) ).

cnf(refute_0_476,plain,
    multiply(X_93,least_upper_bound(X_94,identity)) = least_upper_bound(multiply(X_93,X_94),X_93),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(X_94,identity)),least_upper_bound(multiply(X_93,X_94),multiply(X_93,identity))) )],[refute_0_470,refute_0_475]) ).

cnf(refute_0_477,plain,
    least_upper_bound(multiply(X_93,X_94),X_93) = least_upper_bound(X_93,multiply(X_93,X_94)),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(multiply(X_93,X_94))),bind(X_17,$fot(X_93))]]) ).

cnf(refute_0_478,plain,
    ( multiply(X_93,least_upper_bound(X_94,identity)) != least_upper_bound(multiply(X_93,X_94),X_93)
    | least_upper_bound(multiply(X_93,X_94),X_93) != least_upper_bound(X_93,multiply(X_93,X_94))
    | multiply(X_93,least_upper_bound(X_94,identity)) = least_upper_bound(X_93,multiply(X_93,X_94)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_93,least_upper_bound(X_94,identity)),least_upper_bound(X_93,multiply(X_93,X_94))) ),[0],$fot(least_upper_bound(multiply(X_93,X_94),X_93))]]) ).

cnf(refute_0_479,plain,
    ( multiply(X_93,least_upper_bound(X_94,identity)) != least_upper_bound(multiply(X_93,X_94),X_93)
    | multiply(X_93,least_upper_bound(X_94,identity)) = least_upper_bound(X_93,multiply(X_93,X_94)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_93,X_94),X_93),least_upper_bound(X_93,multiply(X_93,X_94))) )],[refute_0_477,refute_0_478]) ).

cnf(refute_0_480,plain,
    multiply(X_93,least_upper_bound(X_94,identity)) = least_upper_bound(X_93,multiply(X_93,X_94)),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(X_94,identity)),least_upper_bound(multiply(X_93,X_94),X_93)) )],[refute_0_476,refute_0_479]) ).

cnf(refute_0_481,plain,
    multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) = least_upper_bound(greatest_lower_bound(identity,Y),multiply(greatest_lower_bound(identity,Y),inverse(Y))),
    inference(subst,[],[refute_0_480:[bind(X_93,$fot(greatest_lower_bound(identity,Y))),bind(X_94,$fot(inverse(Y)))]]) ).

cnf(refute_0_482,plain,
    multiply(inverse(least_upper_bound(identity,inverse(Y))),inverse(Y)) = greatest_lower_bound(inverse(Y),identity),
    inference(subst,[],[refute_0_315:[bind(X_124,$fot(inverse(Y)))]]) ).

cnf(refute_0_483,plain,
    inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(inverse(identity),inverse(Y)),
    inference(subst,[],[p12x_3:[bind(X,$fot(identity))]]) ).

cnf(refute_0_484,plain,
    ( inverse(greatest_lower_bound(identity,Y)) != least_upper_bound(inverse(identity),inverse(Y))
    | inverse(identity) != identity
    | inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(inverse(identity),inverse(Y))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_485,plain,
    ( inverse(greatest_lower_bound(identity,Y)) != least_upper_bound(inverse(identity),inverse(Y))
    | inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_484]) ).

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

cnf(refute_0_487,plain,
    ( inverse(greatest_lower_bound(identity,Y)) != least_upper_bound(identity,inverse(Y))
    | least_upper_bound(identity,inverse(Y)) = inverse(greatest_lower_bound(identity,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(identity,Y)))),bind(Y0,$fot(least_upper_bound(identity,inverse(Y))))]]) ).

cnf(refute_0_488,plain,
    least_upper_bound(identity,inverse(Y)) = inverse(greatest_lower_bound(identity,Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,inverse(Y))) )],[refute_0_486,refute_0_487]) ).

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

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

cnf(refute_0_491,plain,
    multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)) = greatest_lower_bound(inverse(Y),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(Y))),inverse(Y)),greatest_lower_bound(inverse(Y),identity)) )],[refute_0_482,refute_0_490]) ).

cnf(refute_0_492,plain,
    inverse(inverse(greatest_lower_bound(identity,Y))) = greatest_lower_bound(identity,Y),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(identity,Y)))]]) ).

cnf(refute_0_493,plain,
    multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)) = multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)),
    introduced(tautology,[refl,[$fot(multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)))]]) ).

cnf(refute_0_494,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)) != multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y))
    | inverse(inverse(greatest_lower_bound(identity,Y))) != greatest_lower_bound(identity,Y)
    | multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)) = multiply(greatest_lower_bound(identity,Y),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)),multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y))) ),[1,0],$fot(greatest_lower_bound(identity,Y))]]) ).

cnf(refute_0_495,plain,
    ( inverse(inverse(greatest_lower_bound(identity,Y))) != greatest_lower_bound(identity,Y)
    | multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)) = multiply(greatest_lower_bound(identity,Y),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)),multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y))) )],[refute_0_493,refute_0_494]) ).

cnf(refute_0_496,plain,
    multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)) = multiply(greatest_lower_bound(identity,Y),inverse(Y)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,Y))),greatest_lower_bound(identity,Y)) )],[refute_0_492,refute_0_495]) ).

cnf(refute_0_497,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)) != multiply(greatest_lower_bound(identity,Y),inverse(Y))
    | multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)) != greatest_lower_bound(inverse(Y),identity)
    | multiply(greatest_lower_bound(identity,Y),inverse(Y)) = greatest_lower_bound(inverse(Y),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)),greatest_lower_bound(inverse(Y),identity)) ),[0],$fot(multiply(greatest_lower_bound(identity,Y),inverse(Y)))]]) ).

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

cnf(refute_0_499,plain,
    ( inverse(least_upper_bound(identity,Y)) != greatest_lower_bound(identity,inverse(Y))
    | greatest_lower_bound(identity,inverse(Y)) = inverse(least_upper_bound(identity,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(least_upper_bound(identity,Y)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(Y))))]]) ).

cnf(refute_0_500,plain,
    greatest_lower_bound(identity,inverse(Y)) = inverse(least_upper_bound(identity,Y)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,Y)),greatest_lower_bound(identity,inverse(Y))) )],[refute_0_299,refute_0_499]) ).

cnf(refute_0_501,plain,
    greatest_lower_bound(inverse(Y),identity) = greatest_lower_bound(identity,inverse(Y)),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(inverse(Y))),bind(X_25,$fot(identity))]]) ).

cnf(refute_0_502,plain,
    ( greatest_lower_bound(identity,inverse(Y)) != inverse(least_upper_bound(identity,Y))
    | greatest_lower_bound(inverse(Y),identity) != greatest_lower_bound(identity,inverse(Y))
    | greatest_lower_bound(inverse(Y),identity) = inverse(least_upper_bound(identity,Y)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(inverse(Y),identity))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(Y)))),bind(Z0,$fot(inverse(least_upper_bound(identity,Y))))]]) ).

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

cnf(refute_0_504,plain,
    greatest_lower_bound(inverse(Y),identity) = inverse(least_upper_bound(identity,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(Y)),inverse(least_upper_bound(identity,Y))) )],[refute_0_500,refute_0_503]) ).

cnf(refute_0_505,plain,
    ( multiply(greatest_lower_bound(identity,Y),inverse(Y)) != greatest_lower_bound(inverse(Y),identity)
    | greatest_lower_bound(inverse(Y),identity) != inverse(least_upper_bound(identity,Y))
    | multiply(greatest_lower_bound(identity,Y),inverse(Y)) = inverse(least_upper_bound(identity,Y)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,Y),inverse(Y)),inverse(least_upper_bound(identity,Y))) ),[0],$fot(greatest_lower_bound(inverse(Y),identity))]]) ).

cnf(refute_0_506,plain,
    ( multiply(greatest_lower_bound(identity,Y),inverse(Y)) != greatest_lower_bound(inverse(Y),identity)
    | multiply(greatest_lower_bound(identity,Y),inverse(Y)) = inverse(least_upper_bound(identity,Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(Y),identity),inverse(least_upper_bound(identity,Y))) )],[refute_0_504,refute_0_505]) ).

cnf(refute_0_507,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)) != greatest_lower_bound(inverse(Y),identity)
    | multiply(greatest_lower_bound(identity,Y),inverse(Y)) = inverse(least_upper_bound(identity,Y)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),inverse(Y)),greatest_lower_bound(inverse(Y),identity)) )],[refute_0_498,refute_0_506]) ).

cnf(refute_0_508,plain,
    multiply(greatest_lower_bound(identity,Y),inverse(Y)) = inverse(least_upper_bound(identity,Y)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,Y))),inverse(Y)),greatest_lower_bound(inverse(Y),identity)) )],[refute_0_491,refute_0_507]) ).

cnf(refute_0_509,plain,
    ( multiply(greatest_lower_bound(identity,Y),inverse(Y)) != inverse(least_upper_bound(identity,Y))
    | multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) != least_upper_bound(greatest_lower_bound(identity,Y),multiply(greatest_lower_bound(identity,Y),inverse(Y)))
    | multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) = least_upper_bound(greatest_lower_bound(identity,Y),inverse(least_upper_bound(identity,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)),least_upper_bound(greatest_lower_bound(identity,Y),multiply(greatest_lower_bound(identity,Y),inverse(Y)))) ),[1,1],$fot(inverse(least_upper_bound(identity,Y)))]]) ).

cnf(refute_0_510,plain,
    ( multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) != least_upper_bound(greatest_lower_bound(identity,Y),multiply(greatest_lower_bound(identity,Y),inverse(Y)))
    | multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) = least_upper_bound(greatest_lower_bound(identity,Y),inverse(least_upper_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),inverse(Y)),inverse(least_upper_bound(identity,Y))) )],[refute_0_508,refute_0_509]) ).

cnf(refute_0_511,plain,
    multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) = least_upper_bound(greatest_lower_bound(identity,Y),inverse(least_upper_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)),least_upper_bound(greatest_lower_bound(identity,Y),multiply(greatest_lower_bound(identity,Y),inverse(Y)))) )],[refute_0_481,refute_0_510]) ).

cnf(refute_0_512,plain,
    multiply(greatest_lower_bound(identity,Y),inverse(greatest_lower_bound(identity,Y))) = identity,
    inference(subst,[],[refute_0_232:[bind(X_66,$fot(greatest_lower_bound(identity,Y)))]]) ).

cnf(refute_0_513,plain,
    multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))) = multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))))]]) ).

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

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

cnf(refute_0_516,plain,
    multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))) = multiply(greatest_lower_bound(identity,Y),inverse(greatest_lower_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(Y)),inverse(greatest_lower_bound(identity,Y))) )],[refute_0_488,refute_0_515]) ).

cnf(refute_0_517,plain,
    ( multiply(greatest_lower_bound(identity,Y),inverse(greatest_lower_bound(identity,Y))) != identity
    | multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))) != multiply(greatest_lower_bound(identity,Y),inverse(greatest_lower_bound(identity,Y)))
    | multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,Y),inverse(greatest_lower_bound(identity,Y))))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_518,plain,
    ( multiply(greatest_lower_bound(identity,Y),inverse(greatest_lower_bound(identity,Y))) != identity
    | multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))),multiply(greatest_lower_bound(identity,Y),inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_516,refute_0_517]) ).

cnf(refute_0_519,plain,
    multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))) = identity,
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),inverse(greatest_lower_bound(identity,Y))),identity) )],[refute_0_512,refute_0_518]) ).

cnf(refute_0_520,plain,
    least_upper_bound(X_31,least_upper_bound(X_31,multiply(X_31,X_165))) = least_upper_bound(X_31,multiply(X_31,X_165)),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(multiply(X_31,X_165)))]]) ).

cnf(refute_0_521,plain,
    multiply(X_31,least_upper_bound(X_165,identity)) = least_upper_bound(X_31,multiply(X_31,X_165)),
    inference(subst,[],[refute_0_480:[bind(X_93,$fot(X_31)),bind(X_94,$fot(X_165))]]) ).

cnf(refute_0_522,plain,
    ( multiply(X_31,least_upper_bound(X_165,identity)) != least_upper_bound(X_31,multiply(X_31,X_165))
    | least_upper_bound(X_31,multiply(X_31,X_165)) = multiply(X_31,least_upper_bound(X_165,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_31,least_upper_bound(X_165,identity)))),bind(Y0,$fot(least_upper_bound(X_31,multiply(X_31,X_165))))]]) ).

cnf(refute_0_523,plain,
    least_upper_bound(X_31,multiply(X_31,X_165)) = multiply(X_31,least_upper_bound(X_165,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_31,least_upper_bound(X_165,identity)),least_upper_bound(X_31,multiply(X_31,X_165))) )],[refute_0_521,refute_0_522]) ).

cnf(refute_0_524,plain,
    ( least_upper_bound(X_31,multiply(X_31,X_165)) != multiply(X_31,least_upper_bound(X_165,identity))
    | least_upper_bound(X_31,least_upper_bound(X_31,multiply(X_31,X_165))) != least_upper_bound(X_31,multiply(X_31,X_165))
    | least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) = least_upper_bound(X_31,multiply(X_31,X_165)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_31,multiply(X_31,X_165))),least_upper_bound(X_31,multiply(X_31,X_165))) ),[0,1],$fot(multiply(X_31,least_upper_bound(X_165,identity)))]]) ).

cnf(refute_0_525,plain,
    ( least_upper_bound(X_31,least_upper_bound(X_31,multiply(X_31,X_165))) != least_upper_bound(X_31,multiply(X_31,X_165))
    | least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) = least_upper_bound(X_31,multiply(X_31,X_165)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(X_31,X_165)),multiply(X_31,least_upper_bound(X_165,identity))) )],[refute_0_523,refute_0_524]) ).

cnf(refute_0_526,plain,
    least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) = least_upper_bound(X_31,multiply(X_31,X_165)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_31,multiply(X_31,X_165))),least_upper_bound(X_31,multiply(X_31,X_165))) )],[refute_0_520,refute_0_525]) ).

cnf(refute_0_527,plain,
    least_upper_bound(identity,least_upper_bound(X_165,identity)) = least_upper_bound(identity,X_165),
    inference(subst,[],[refute_0_426:[bind(Y,$fot(X_165)),bind(X_21,$fot(identity))]]) ).

cnf(refute_0_528,plain,
    multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))) = multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))),
    introduced(tautology,[refl,[$fot(multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))))]]) ).

cnf(refute_0_529,plain,
    ( multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))) != multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity)))
    | least_upper_bound(identity,least_upper_bound(X_165,identity)) != least_upper_bound(identity,X_165)
    | multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))) = multiply(X_31,least_upper_bound(identity,X_165)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))),multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_165))]]) ).

cnf(refute_0_530,plain,
    ( least_upper_bound(identity,least_upper_bound(X_165,identity)) != least_upper_bound(identity,X_165)
    | multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))) = multiply(X_31,least_upper_bound(identity,X_165)) ),
    inference(resolve,[$cnf( $equal(multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))),multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity)))) )],[refute_0_528,refute_0_529]) ).

cnf(refute_0_531,plain,
    multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))) = multiply(X_31,least_upper_bound(identity,X_165)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_165,identity)),least_upper_bound(identity,X_165)) )],[refute_0_527,refute_0_530]) ).

cnf(refute_0_532,plain,
    least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)) = least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(multiply(X_93,X_95))),bind(Y,$fot(multiply(X_93,X_94)))]]) ).

cnf(refute_0_533,plain,
    multiply(X_93,least_upper_bound(X_94,X_95)) = least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_93)),bind(Y,$fot(X_94)),bind(Z,$fot(X_95))]]) ).

cnf(refute_0_534,plain,
    ( multiply(X_93,least_upper_bound(X_94,X_95)) != least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95))
    | least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)) = multiply(X_93,least_upper_bound(X_94,X_95)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_93,least_upper_bound(X_94,X_95)))),bind(Y0,$fot(least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95))))]]) ).

cnf(refute_0_535,plain,
    least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)) = multiply(X_93,least_upper_bound(X_94,X_95)),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(X_94,X_95)),least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95))) )],[refute_0_533,refute_0_534]) ).

cnf(refute_0_536,plain,
    ( least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)) != multiply(X_93,least_upper_bound(X_94,X_95))
    | least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)) != least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95))
    | least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)) = multiply(X_93,least_upper_bound(X_94,X_95)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)),least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95))) ),[1],$fot(multiply(X_93,least_upper_bound(X_94,X_95)))]]) ).

cnf(refute_0_537,plain,
    ( least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)) != least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95))
    | least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)) = multiply(X_93,least_upper_bound(X_94,X_95)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)),multiply(X_93,least_upper_bound(X_94,X_95))) )],[refute_0_535,refute_0_536]) ).

cnf(refute_0_538,plain,
    least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)) = multiply(X_93,least_upper_bound(X_94,X_95)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)),least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95))) )],[refute_0_532,refute_0_537]) ).

cnf(refute_0_539,plain,
    ( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
    | least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).

cnf(refute_0_540,plain,
    least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_539]) ).

cnf(refute_0_541,plain,
    least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)) = multiply(X_93,least_upper_bound(X_95,X_94)),
    inference(subst,[],[refute_0_540:[bind(X,$fot(X_93)),bind(Y,$fot(X_95)),bind(Z,$fot(X_94))]]) ).

cnf(refute_0_542,plain,
    ( least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)) != multiply(X_93,least_upper_bound(X_94,X_95))
    | least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)) != multiply(X_93,least_upper_bound(X_95,X_94))
    | multiply(X_93,least_upper_bound(X_95,X_94)) = multiply(X_93,least_upper_bound(X_94,X_95)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)),multiply(X_93,least_upper_bound(X_94,X_95))) ),[0],$fot(multiply(X_93,least_upper_bound(X_95,X_94)))]]) ).

cnf(refute_0_543,plain,
    ( least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)) != multiply(X_93,least_upper_bound(X_94,X_95))
    | multiply(X_93,least_upper_bound(X_95,X_94)) = multiply(X_93,least_upper_bound(X_94,X_95)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)),multiply(X_93,least_upper_bound(X_95,X_94))) )],[refute_0_541,refute_0_542]) ).

cnf(refute_0_544,plain,
    multiply(X_93,least_upper_bound(X_95,X_94)) = multiply(X_93,least_upper_bound(X_94,X_95)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_93,X_95),multiply(X_93,X_94)),multiply(X_93,least_upper_bound(X_94,X_95))) )],[refute_0_538,refute_0_543]) ).

cnf(refute_0_545,plain,
    ( multiply(X_93,least_upper_bound(X_95,X_94)) != multiply(X_93,least_upper_bound(X_94,X_95))
    | multiply(X_93,least_upper_bound(X_94,X_95)) = multiply(X_93,least_upper_bound(X_95,X_94)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_93,least_upper_bound(X_95,X_94)))),bind(Y0,$fot(multiply(X_93,least_upper_bound(X_94,X_95))))]]) ).

cnf(refute_0_546,plain,
    multiply(X_93,least_upper_bound(X_94,X_95)) = multiply(X_93,least_upper_bound(X_95,X_94)),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(X_95,X_94)),multiply(X_93,least_upper_bound(X_94,X_95))) )],[refute_0_544,refute_0_545]) ).

cnf(refute_0_547,plain,
    multiply(X_31,least_upper_bound(least_upper_bound(X_165,identity),identity)) = multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))),
    inference(subst,[],[refute_0_546:[bind(X_93,$fot(X_31)),bind(X_94,$fot(least_upper_bound(X_165,identity))),bind(X_95,$fot(identity))]]) ).

cnf(refute_0_548,plain,
    ( multiply(X_93,least_upper_bound(X_94,identity)) != least_upper_bound(X_93,multiply(X_93,X_94))
    | least_upper_bound(X_93,multiply(X_93,X_94)) = multiply(X_93,least_upper_bound(X_94,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_93,least_upper_bound(X_94,identity)))),bind(Y0,$fot(least_upper_bound(X_93,multiply(X_93,X_94))))]]) ).

cnf(refute_0_549,plain,
    least_upper_bound(X_93,multiply(X_93,X_94)) = multiply(X_93,least_upper_bound(X_94,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(X_94,identity)),least_upper_bound(X_93,multiply(X_93,X_94))) )],[refute_0_480,refute_0_548]) ).

cnf(refute_0_550,plain,
    least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) = multiply(X_31,least_upper_bound(least_upper_bound(X_165,identity),identity)),
    inference(subst,[],[refute_0_549:[bind(X_93,$fot(X_31)),bind(X_94,$fot(least_upper_bound(X_165,identity)))]]) ).

cnf(refute_0_551,plain,
    ( multiply(X_31,least_upper_bound(least_upper_bound(X_165,identity),identity)) != multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity)))
    | least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) != multiply(X_31,least_upper_bound(least_upper_bound(X_165,identity),identity))
    | least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) = multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))))),bind(Y0,$fot(multiply(X_31,least_upper_bound(least_upper_bound(X_165,identity),identity)))),bind(Z0,$fot(multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity)))))]]) ).

cnf(refute_0_552,plain,
    ( multiply(X_31,least_upper_bound(least_upper_bound(X_165,identity),identity)) != multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity)))
    | least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) = multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))),multiply(X_31,least_upper_bound(least_upper_bound(X_165,identity),identity))) )],[refute_0_550,refute_0_551]) ).

cnf(refute_0_553,plain,
    least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) = multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))),
    inference(resolve,[$cnf( $equal(multiply(X_31,least_upper_bound(least_upper_bound(X_165,identity),identity)),multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity)))) )],[refute_0_547,refute_0_552]) ).

cnf(refute_0_554,plain,
    ( multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))) != multiply(X_31,least_upper_bound(identity,X_165))
    | least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) != multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity)))
    | least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) = multiply(X_31,least_upper_bound(identity,X_165)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))))),bind(Y0,$fot(multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))))),bind(Z0,$fot(multiply(X_31,least_upper_bound(identity,X_165))))]]) ).

cnf(refute_0_555,plain,
    ( multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))) != multiply(X_31,least_upper_bound(identity,X_165))
    | least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) = multiply(X_31,least_upper_bound(identity,X_165)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))),multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity)))) )],[refute_0_553,refute_0_554]) ).

cnf(refute_0_556,plain,
    least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) = multiply(X_31,least_upper_bound(identity,X_165)),
    inference(resolve,[$cnf( $equal(multiply(X_31,least_upper_bound(identity,least_upper_bound(X_165,identity))),multiply(X_31,least_upper_bound(identity,X_165))) )],[refute_0_531,refute_0_555]) ).

cnf(refute_0_557,plain,
    ( least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) != multiply(X_31,least_upper_bound(identity,X_165))
    | least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) != least_upper_bound(X_31,multiply(X_31,X_165))
    | multiply(X_31,least_upper_bound(identity,X_165)) = least_upper_bound(X_31,multiply(X_31,X_165)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))),least_upper_bound(X_31,multiply(X_31,X_165))) ),[0],$fot(multiply(X_31,least_upper_bound(identity,X_165)))]]) ).

cnf(refute_0_558,plain,
    ( least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) != least_upper_bound(X_31,multiply(X_31,X_165))
    | multiply(X_31,least_upper_bound(identity,X_165)) = least_upper_bound(X_31,multiply(X_31,X_165)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))),multiply(X_31,least_upper_bound(identity,X_165))) )],[refute_0_556,refute_0_557]) ).

cnf(refute_0_559,plain,
    ( multiply(X_31,least_upper_bound(identity,X_165)) != least_upper_bound(X_31,multiply(X_31,X_165))
    | least_upper_bound(X_31,multiply(X_31,X_165)) != multiply(X_31,least_upper_bound(X_165,identity))
    | multiply(X_31,least_upper_bound(identity,X_165)) = multiply(X_31,least_upper_bound(X_165,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_31,least_upper_bound(identity,X_165)),multiply(X_31,least_upper_bound(X_165,identity))) ),[0],$fot(least_upper_bound(X_31,multiply(X_31,X_165)))]]) ).

cnf(refute_0_560,plain,
    ( multiply(X_31,least_upper_bound(identity,X_165)) != least_upper_bound(X_31,multiply(X_31,X_165))
    | multiply(X_31,least_upper_bound(identity,X_165)) = multiply(X_31,least_upper_bound(X_165,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(X_31,X_165)),multiply(X_31,least_upper_bound(X_165,identity))) )],[refute_0_523,refute_0_559]) ).

cnf(refute_0_561,plain,
    ( least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))) != least_upper_bound(X_31,multiply(X_31,X_165))
    | multiply(X_31,least_upper_bound(identity,X_165)) = multiply(X_31,least_upper_bound(X_165,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(X_31,least_upper_bound(identity,X_165)),least_upper_bound(X_31,multiply(X_31,X_165))) )],[refute_0_558,refute_0_560]) ).

cnf(refute_0_562,plain,
    multiply(X_31,least_upper_bound(identity,X_165)) = multiply(X_31,least_upper_bound(X_165,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(X_31,least_upper_bound(X_165,identity))),least_upper_bound(X_31,multiply(X_31,X_165))) )],[refute_0_526,refute_0_561]) ).

cnf(refute_0_563,plain,
    ( multiply(X_31,least_upper_bound(identity,X_165)) != multiply(X_31,least_upper_bound(X_165,identity))
    | multiply(X_31,least_upper_bound(X_165,identity)) = multiply(X_31,least_upper_bound(identity,X_165)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_31,least_upper_bound(identity,X_165)))),bind(Y0,$fot(multiply(X_31,least_upper_bound(X_165,identity))))]]) ).

cnf(refute_0_564,plain,
    multiply(X_31,least_upper_bound(X_165,identity)) = multiply(X_31,least_upper_bound(identity,X_165)),
    inference(resolve,[$cnf( $equal(multiply(X_31,least_upper_bound(identity,X_165)),multiply(X_31,least_upper_bound(X_165,identity))) )],[refute_0_562,refute_0_563]) ).

cnf(refute_0_565,plain,
    multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) = multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))),
    inference(subst,[],[refute_0_564:[bind(X_165,$fot(inverse(Y))),bind(X_31,$fot(greatest_lower_bound(identity,Y)))]]) ).

cnf(refute_0_566,plain,
    ( multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))) != identity
    | multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) != multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))
    | multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_567,plain,
    ( multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))) != identity
    | multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) = identity ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)),multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) )],[refute_0_565,refute_0_566]) ).

cnf(refute_0_568,plain,
    multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) = identity,
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))),identity) )],[refute_0_519,refute_0_567]) ).

cnf(refute_0_569,plain,
    ( multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) != identity
    | multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) != least_upper_bound(greatest_lower_bound(identity,Y),inverse(least_upper_bound(identity,Y)))
    | identity = least_upper_bound(greatest_lower_bound(identity,Y),inverse(least_upper_bound(identity,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)),least_upper_bound(greatest_lower_bound(identity,Y),inverse(least_upper_bound(identity,Y)))) ),[0],$fot(identity)]]) ).

cnf(refute_0_570,plain,
    ( multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)) != least_upper_bound(greatest_lower_bound(identity,Y),inverse(least_upper_bound(identity,Y)))
    | identity = least_upper_bound(greatest_lower_bound(identity,Y),inverse(least_upper_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)),identity) )],[refute_0_568,refute_0_569]) ).

cnf(refute_0_571,plain,
    identity = least_upper_bound(greatest_lower_bound(identity,Y),inverse(least_upper_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),least_upper_bound(inverse(Y),identity)),least_upper_bound(greatest_lower_bound(identity,Y),inverse(least_upper_bound(identity,Y)))) )],[refute_0_511,refute_0_570]) ).

cnf(refute_0_572,plain,
    identity = least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166))),
    inference(subst,[],[refute_0_571:[bind(Y,$fot(X_166))]]) ).

cnf(refute_0_573,plain,
    ( identity != least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))
    | least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))))]]) ).

cnf(refute_0_574,plain,
    least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166))) = identity,
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))) )],[refute_0_572,refute_0_573]) ).

cnf(refute_0_575,plain,
    ( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))) != identity
    | least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166))) != identity
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_576,plain,
    ( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))) != identity
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166))),identity) )],[refute_0_574,refute_0_575]) ).

cnf(refute_0_577,plain,
    multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity) )],[refute_0_469,refute_0_576]) ).

cnf(refute_0_578,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(identity,X_166)),least_upper_bound(identity,X_166)) = greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(inverse(greatest_lower_bound(identity,X_166)))),bind(X_25,$fot(least_upper_bound(identity,X_166)))]]) ).

cnf(refute_0_579,plain,
    inverse(least_upper_bound(X,inverse(X_89))) = greatest_lower_bound(inverse(X),inverse(inverse(X_89))),
    inference(subst,[],[p12x_4:[bind(Y,$fot(inverse(X_89)))]]) ).

cnf(refute_0_580,plain,
    ( inverse(inverse(X_89)) != X_89
    | inverse(least_upper_bound(X,inverse(X_89))) != greatest_lower_bound(inverse(X),inverse(inverse(X_89)))
    | inverse(least_upper_bound(X,inverse(X_89))) = greatest_lower_bound(inverse(X),X_89) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X,inverse(X_89))),greatest_lower_bound(inverse(X),inverse(inverse(X_89)))) ),[1,1],$fot(X_89)]]) ).

cnf(refute_0_581,plain,
    ( inverse(least_upper_bound(X,inverse(X_89))) != greatest_lower_bound(inverse(X),inverse(inverse(X_89)))
    | inverse(least_upper_bound(X,inverse(X_89))) = greatest_lower_bound(inverse(X),X_89) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_89)),X_89) )],[refute_0_98,refute_0_580]) ).

cnf(refute_0_582,plain,
    inverse(least_upper_bound(X,inverse(X_89))) = greatest_lower_bound(inverse(X),X_89),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X,inverse(X_89))),greatest_lower_bound(inverse(X),inverse(inverse(X_89)))) )],[refute_0_579,refute_0_581]) ).

cnf(refute_0_583,plain,
    inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_166)),least_upper_bound(identity,X_166)),
    inference(subst,[],[refute_0_582:[bind(X,$fot(greatest_lower_bound(identity,X_166))),bind(X_89,$fot(least_upper_bound(identity,X_166)))]]) ).

cnf(refute_0_584,plain,
    ( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_166)),least_upper_bound(identity,X_166)) != greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))
    | inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_166)),least_upper_bound(identity,X_166))
    | inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))) = greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_166)),least_upper_bound(identity,X_166)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))))]]) ).

cnf(refute_0_585,plain,
    ( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_166)),least_upper_bound(identity,X_166)) != greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))
    | inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))) = greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_166)),least_upper_bound(identity,X_166))) )],[refute_0_583,refute_0_584]) ).

cnf(refute_0_586,plain,
    inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))) = greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_166)),least_upper_bound(identity,X_166)),greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))) )],[refute_0_578,refute_0_585]) ).

cnf(refute_0_587,plain,
    multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity) = inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166))))))]]) ).

cnf(refute_0_588,plain,
    ( multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity) != inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166))))
    | inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))) != greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))
    | multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity) = greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity))),bind(Y0,$fot(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))))]]) ).

cnf(refute_0_589,plain,
    ( inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))) != greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))
    | multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity) = greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity),inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166))))) )],[refute_0_587,refute_0_588]) ).

cnf(refute_0_590,plain,
    multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity) = greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))) )],[refute_0_586,refute_0_589]) ).

cnf(refute_0_591,plain,
    multiply(inverse(least_upper_bound(Y,X)),X_88) = multiply(inverse(inverse(inverse(least_upper_bound(Y,X)))),X_88),
    inference(subst,[],[refute_0_23:[bind(X_61,$fot(inverse(least_upper_bound(Y,X)))),bind(X_62,$fot(X_88))]]) ).

cnf(refute_0_592,plain,
    inverse(greatest_lower_bound(inverse(X),inverse(Y))) = inverse(greatest_lower_bound(inverse(Y),inverse(X))),
    inference(subst,[],[refute_0_140:[bind(X_12,$fot(inverse(Y))),bind(X_13,$fot(inverse(X)))]]) ).

cnf(refute_0_593,plain,
    ( greatest_lower_bound(inverse(X),inverse(Y)) != inverse(least_upper_bound(X,Y))
    | inverse(greatest_lower_bound(inverse(X),inverse(Y))) != inverse(greatest_lower_bound(inverse(Y),inverse(X)))
    | inverse(inverse(least_upper_bound(X,Y))) = inverse(greatest_lower_bound(inverse(Y),inverse(X))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X),inverse(Y))),inverse(greatest_lower_bound(inverse(Y),inverse(X)))) ),[0,0],$fot(inverse(least_upper_bound(X,Y)))]]) ).

cnf(refute_0_594,plain,
    ( inverse(greatest_lower_bound(inverse(X),inverse(Y))) != inverse(greatest_lower_bound(inverse(Y),inverse(X)))
    | inverse(inverse(least_upper_bound(X,Y))) = inverse(greatest_lower_bound(inverse(Y),inverse(X))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X),inverse(Y)),inverse(least_upper_bound(X,Y))) )],[refute_0_54,refute_0_593]) ).

cnf(refute_0_595,plain,
    inverse(inverse(least_upper_bound(X,Y))) = inverse(greatest_lower_bound(inverse(Y),inverse(X))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X),inverse(Y))),inverse(greatest_lower_bound(inverse(Y),inverse(X)))) )],[refute_0_592,refute_0_594]) ).

cnf(refute_0_596,plain,
    greatest_lower_bound(inverse(Y),inverse(X)) = inverse(least_upper_bound(Y,X)),
    inference(subst,[],[refute_0_54:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).

cnf(refute_0_597,plain,
    inverse(greatest_lower_bound(inverse(Y),inverse(X))) = inverse(greatest_lower_bound(inverse(Y),inverse(X))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(inverse(Y),inverse(X))))]]) ).

cnf(refute_0_598,plain,
    ( greatest_lower_bound(inverse(Y),inverse(X)) != inverse(least_upper_bound(Y,X))
    | inverse(greatest_lower_bound(inverse(Y),inverse(X))) != inverse(greatest_lower_bound(inverse(Y),inverse(X)))
    | inverse(greatest_lower_bound(inverse(Y),inverse(X))) = inverse(inverse(least_upper_bound(Y,X))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(inverse(Y),inverse(X)))) ),[1,0],$fot(inverse(least_upper_bound(Y,X)))]]) ).

cnf(refute_0_599,plain,
    ( greatest_lower_bound(inverse(Y),inverse(X)) != inverse(least_upper_bound(Y,X))
    | inverse(greatest_lower_bound(inverse(Y),inverse(X))) = inverse(inverse(least_upper_bound(Y,X))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(greatest_lower_bound(inverse(Y),inverse(X)))) )],[refute_0_597,refute_0_598]) ).

cnf(refute_0_600,plain,
    inverse(greatest_lower_bound(inverse(Y),inverse(X))) = inverse(inverse(least_upper_bound(Y,X))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(Y),inverse(X)),inverse(least_upper_bound(Y,X))) )],[refute_0_596,refute_0_599]) ).

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

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

cnf(refute_0_603,plain,
    inverse(inverse(least_upper_bound(X,Y))) = inverse(inverse(least_upper_bound(Y,X))),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X,Y))),inverse(greatest_lower_bound(inverse(Y),inverse(X)))) )],[refute_0_595,refute_0_602]) ).

cnf(refute_0_604,plain,
    ( inverse(inverse(least_upper_bound(X,Y))) != inverse(inverse(least_upper_bound(Y,X)))
    | inverse(inverse(least_upper_bound(Y,X))) = inverse(inverse(least_upper_bound(X,Y))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(inverse(least_upper_bound(X,Y))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(Y,X)))))]]) ).

cnf(refute_0_605,plain,
    inverse(inverse(least_upper_bound(Y,X))) = inverse(inverse(least_upper_bound(X,Y))),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X,Y))),inverse(inverse(least_upper_bound(Y,X)))) )],[refute_0_603,refute_0_604]) ).

cnf(refute_0_606,plain,
    ( multiply(inverse(least_upper_bound(Y,X)),X_88) != multiply(inverse(inverse(inverse(least_upper_bound(Y,X)))),X_88)
    | inverse(inverse(least_upper_bound(Y,X))) != inverse(inverse(least_upper_bound(X,Y)))
    | multiply(inverse(least_upper_bound(Y,X)),X_88) = multiply(inverse(inverse(inverse(least_upper_bound(X,Y)))),X_88) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X)),X_88),multiply(inverse(inverse(inverse(least_upper_bound(Y,X)))),X_88)) ),[1,0,0],$fot(inverse(inverse(least_upper_bound(X,Y))))]]) ).

cnf(refute_0_607,plain,
    ( multiply(inverse(least_upper_bound(Y,X)),X_88) != multiply(inverse(inverse(inverse(least_upper_bound(Y,X)))),X_88)
    | multiply(inverse(least_upper_bound(Y,X)),X_88) = multiply(inverse(inverse(inverse(least_upper_bound(X,Y)))),X_88) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(Y,X))),inverse(inverse(least_upper_bound(X,Y)))) )],[refute_0_605,refute_0_606]) ).

cnf(refute_0_608,plain,
    multiply(inverse(least_upper_bound(Y,X)),X_88) = multiply(inverse(inverse(inverse(least_upper_bound(X,Y)))),X_88),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X)),X_88),multiply(inverse(inverse(inverse(least_upper_bound(Y,X)))),X_88)) )],[refute_0_591,refute_0_607]) ).

cnf(refute_0_609,plain,
    multiply(inverse(inverse(inverse(least_upper_bound(X,Y)))),X_88) = multiply(inverse(least_upper_bound(X,Y)),X_88),
    inference(subst,[],[refute_0_25:[bind(X_61,$fot(inverse(least_upper_bound(X,Y)))),bind(X_62,$fot(X_88))]]) ).

cnf(refute_0_610,plain,
    ( multiply(inverse(inverse(inverse(least_upper_bound(X,Y)))),X_88) != multiply(inverse(least_upper_bound(X,Y)),X_88)
    | multiply(inverse(least_upper_bound(Y,X)),X_88) != multiply(inverse(inverse(inverse(least_upper_bound(X,Y)))),X_88)
    | multiply(inverse(least_upper_bound(Y,X)),X_88) = multiply(inverse(least_upper_bound(X,Y)),X_88) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X)),X_88),multiply(inverse(inverse(inverse(least_upper_bound(X,Y)))),X_88)) ),[1],$fot(multiply(inverse(least_upper_bound(X,Y)),X_88))]]) ).

cnf(refute_0_611,plain,
    ( multiply(inverse(least_upper_bound(Y,X)),X_88) != multiply(inverse(inverse(inverse(least_upper_bound(X,Y)))),X_88)
    | multiply(inverse(least_upper_bound(Y,X)),X_88) = multiply(inverse(least_upper_bound(X,Y)),X_88) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(inverse(least_upper_bound(X,Y)))),X_88),multiply(inverse(least_upper_bound(X,Y)),X_88)) )],[refute_0_609,refute_0_610]) ).

cnf(refute_0_612,plain,
    multiply(inverse(least_upper_bound(Y,X)),X_88) = multiply(inverse(least_upper_bound(X,Y)),X_88),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X)),X_88),multiply(inverse(inverse(inverse(least_upper_bound(X,Y)))),X_88)) )],[refute_0_608,refute_0_611]) ).

cnf(refute_0_613,plain,
    ( multiply(inverse(least_upper_bound(Y,X)),X_88) != multiply(inverse(least_upper_bound(X,Y)),X_88)
    | multiply(inverse(least_upper_bound(X,Y)),X_88) = multiply(inverse(least_upper_bound(Y,X)),X_88) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(inverse(least_upper_bound(Y,X)),X_88))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X,Y)),X_88)))]]) ).

cnf(refute_0_614,plain,
    multiply(inverse(least_upper_bound(X,Y)),X_88) = multiply(inverse(least_upper_bound(Y,X)),X_88),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(Y,X)),X_88),multiply(inverse(least_upper_bound(X,Y)),X_88)) )],[refute_0_612,refute_0_613]) ).

cnf(refute_0_615,plain,
    multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity) = multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity),
    inference(subst,[],[refute_0_614:[bind(X,$fot(inverse(least_upper_bound(identity,X_166)))),bind(Y,$fot(greatest_lower_bound(identity,X_166))),bind(X_88,$fot(identity))]]) ).

cnf(refute_0_616,plain,
    ( multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity) != greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity) != multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity)
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity) = greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity))),bind(Y0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))))]]) ).

cnf(refute_0_617,plain,
    ( multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity) != greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity) = greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity),multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity)) )],[refute_0_615,refute_0_616]) ).

cnf(refute_0_618,plain,
    multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity) = greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(identity,X_166),inverse(least_upper_bound(identity,X_166)))),identity),greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))) )],[refute_0_590,refute_0_617]) ).

cnf(refute_0_619,plain,
    ( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity) != greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity) != identity
    | greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity),identity) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))))]]) ).

cnf(refute_0_620,plain,
    ( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity) != identity
    | greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity),greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166)))) )],[refute_0_618,refute_0_619]) ).

cnf(refute_0_621,plain,
    greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_166)),greatest_lower_bound(identity,X_166))),identity),identity) )],[refute_0_577,refute_0_620]) ).

cnf(refute_0_622,plain,
    greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(identity,X_204))) = identity,
    inference(subst,[],[refute_0_621:[bind(X_166,$fot(X_204))]]) ).

cnf(refute_0_623,plain,
    ( greatest_lower_bound(X_204,greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(identity,X_204)))) != greatest_lower_bound(X_204,inverse(greatest_lower_bound(identity,X_204)))
    | greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(identity,X_204))) != identity
    | greatest_lower_bound(X_204,identity) = greatest_lower_bound(X_204,inverse(greatest_lower_bound(identity,X_204))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_204,greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(identity,X_204)))),greatest_lower_bound(X_204,inverse(greatest_lower_bound(identity,X_204)))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_624,plain,
    ( greatest_lower_bound(X_204,greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(identity,X_204)))) != greatest_lower_bound(X_204,inverse(greatest_lower_bound(identity,X_204)))
    | greatest_lower_bound(X_204,identity) = greatest_lower_bound(X_204,inverse(greatest_lower_bound(identity,X_204))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(identity,X_204))),identity) )],[refute_0_622,refute_0_623]) ).

cnf(refute_0_625,plain,
    greatest_lower_bound(X_204,identity) = greatest_lower_bound(X_204,inverse(greatest_lower_bound(identity,X_204))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_204,greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(identity,X_204)))),greatest_lower_bound(X_204,inverse(greatest_lower_bound(identity,X_204)))) )],[refute_0_468,refute_0_624]) ).

cnf(refute_0_626,plain,
    greatest_lower_bound(X_122,identity) = greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122))),
    inference(subst,[],[refute_0_625:[bind(X_204,$fot(X_122))]]) ).

cnf(refute_0_627,plain,
    ( greatest_lower_bound(X_122,identity) != greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122)))
    | greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122))) = greatest_lower_bound(X_122,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_122,identity))),bind(Y0,$fot(greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122)))))]]) ).

cnf(refute_0_628,plain,
    greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122))) = greatest_lower_bound(X_122,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122)))) )],[refute_0_626,refute_0_627]) ).

cnf(refute_0_629,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122))),inverse(X_122)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))
    | greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122))) != greatest_lower_bound(X_122,identity)
    | multiply(greatest_lower_bound(X_122,identity),inverse(X_122)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122))),inverse(X_122)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))) ),[0,0],$fot(greatest_lower_bound(X_122,identity))]]) ).

cnf(refute_0_630,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122))),inverse(X_122)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))
    | multiply(greatest_lower_bound(X_122,identity),inverse(X_122)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122))),greatest_lower_bound(X_122,identity)) )],[refute_0_628,refute_0_629]) ).

cnf(refute_0_631,plain,
    multiply(greatest_lower_bound(X_122,identity),inverse(X_122)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(identity,X_122))),inverse(X_122)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))) )],[refute_0_462,refute_0_630]) ).

cnf(refute_0_632,plain,
    multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) = greatest_lower_bound(identity,multiply(identity,inverse(X_132))),
    inference(subst,[],[refute_0_340:[bind(X_122,$fot(X_132)),bind(X_123,$fot(identity))]]) ).

cnf(refute_0_633,plain,
    multiply(identity,inverse(X_132)) = inverse(X_132),
    inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_132)))]]) ).

cnf(refute_0_634,plain,
    ( multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) != greatest_lower_bound(identity,multiply(identity,inverse(X_132)))
    | multiply(identity,inverse(X_132)) != inverse(X_132)
    | multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) = greatest_lower_bound(identity,inverse(X_132)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),inverse(X_132)),greatest_lower_bound(identity,multiply(identity,inverse(X_132)))) ),[1,1],$fot(inverse(X_132))]]) ).

cnf(refute_0_635,plain,
    ( multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) != greatest_lower_bound(identity,multiply(identity,inverse(X_132)))
    | multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) = greatest_lower_bound(identity,inverse(X_132)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_132)),inverse(X_132)) )],[refute_0_633,refute_0_634]) ).

cnf(refute_0_636,plain,
    multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) = greatest_lower_bound(identity,inverse(X_132)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),inverse(X_132)),greatest_lower_bound(identity,multiply(identity,inverse(X_132)))) )],[refute_0_632,refute_0_635]) ).

cnf(refute_0_637,plain,
    greatest_lower_bound(identity,inverse(X_132)) = inverse(least_upper_bound(identity,X_132)),
    inference(subst,[],[refute_0_500:[bind(Y,$fot(X_132))]]) ).

cnf(refute_0_638,plain,
    ( multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) != greatest_lower_bound(identity,inverse(X_132))
    | greatest_lower_bound(identity,inverse(X_132)) != inverse(least_upper_bound(identity,X_132))
    | multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) = inverse(least_upper_bound(identity,X_132)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_132,identity),inverse(X_132)),inverse(least_upper_bound(identity,X_132))) ),[0],$fot(greatest_lower_bound(identity,inverse(X_132)))]]) ).

cnf(refute_0_639,plain,
    ( multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) != greatest_lower_bound(identity,inverse(X_132))
    | multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) = inverse(least_upper_bound(identity,X_132)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_132)),inverse(least_upper_bound(identity,X_132))) )],[refute_0_637,refute_0_638]) ).

cnf(refute_0_640,plain,
    multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) = inverse(least_upper_bound(identity,X_132)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),inverse(X_132)),greatest_lower_bound(identity,inverse(X_132))) )],[refute_0_636,refute_0_639]) ).

cnf(refute_0_641,plain,
    multiply(greatest_lower_bound(X_122,identity),inverse(X_122)) = inverse(least_upper_bound(identity,X_122)),
    inference(subst,[],[refute_0_640:[bind(X_132,$fot(X_122))]]) ).

cnf(refute_0_642,plain,
    ( multiply(greatest_lower_bound(X_122,identity),inverse(X_122)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))
    | multiply(greatest_lower_bound(X_122,identity),inverse(X_122)) != inverse(least_upper_bound(identity,X_122))
    | inverse(least_upper_bound(identity,X_122)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),inverse(X_122)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))) ),[0],$fot(inverse(least_upper_bound(identity,X_122)))]]) ).

cnf(refute_0_643,plain,
    ( multiply(greatest_lower_bound(X_122,identity),inverse(X_122)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))
    | inverse(least_upper_bound(identity,X_122)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),inverse(X_122)),inverse(least_upper_bound(identity,X_122))) )],[refute_0_641,refute_0_642]) ).

cnf(refute_0_644,plain,
    greatest_lower_bound(identity,inverse(multiply(X_122,greatest_lower_bound(identity,X_122)))) = inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))),
    inference(subst,[],[refute_0_500:[bind(Y,$fot(multiply(X_122,greatest_lower_bound(identity,X_122))))]]) ).

cnf(refute_0_645,plain,
    inverse(multiply(X_198,X_59)) = multiply(inverse(X_59),multiply(X_59,inverse(multiply(X_198,X_59)))),
    inference(subst,[],[refute_0_8:[bind(X_60,$fot(inverse(multiply(X_198,X_59))))]]) ).

cnf(refute_0_646,plain,
    multiply(X_138,inverse(multiply(X_59,X_138))) = multiply(inverse(X_59),multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138))))),
    inference(subst,[],[refute_0_8:[bind(X_60,$fot(multiply(X_138,inverse(multiply(X_59,X_138)))))]]) ).

cnf(refute_0_647,plain,
    multiply(multiply(X,Y),inverse(multiply(X,Y))) = multiply(X,multiply(Y,inverse(multiply(X,Y)))),
    inference(subst,[],[associativity:[bind(Z,$fot(inverse(multiply(X,Y))))]]) ).

cnf(refute_0_648,plain,
    multiply(multiply(X,Y),inverse(multiply(X,Y))) = identity,
    inference(subst,[],[refute_0_232:[bind(X_66,$fot(multiply(X,Y)))]]) ).

cnf(refute_0_649,plain,
    ( multiply(multiply(X,Y),inverse(multiply(X,Y))) != multiply(X,multiply(Y,inverse(multiply(X,Y))))
    | multiply(multiply(X,Y),inverse(multiply(X,Y))) != identity
    | identity = multiply(X,multiply(Y,inverse(multiply(X,Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),multiply(X,multiply(Y,inverse(multiply(X,Y))))) ),[0],$fot(identity)]]) ).

cnf(refute_0_650,plain,
    ( multiply(multiply(X,Y),inverse(multiply(X,Y))) != multiply(X,multiply(Y,inverse(multiply(X,Y))))
    | identity = multiply(X,multiply(Y,inverse(multiply(X,Y)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),identity) )],[refute_0_648,refute_0_649]) ).

cnf(refute_0_651,plain,
    identity = multiply(X,multiply(Y,inverse(multiply(X,Y)))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(multiply(X,Y))),multiply(X,multiply(Y,inverse(multiply(X,Y))))) )],[refute_0_647,refute_0_650]) ).

cnf(refute_0_652,plain,
    identity = multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138)))),
    inference(subst,[],[refute_0_651:[bind(X,$fot(X_59)),bind(Y,$fot(X_138))]]) ).

cnf(refute_0_653,plain,
    ( identity != multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138))))
    | multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138)))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138))))))]]) ).

cnf(refute_0_654,plain,
    multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138)))) = identity,
    inference(resolve,[$cnf( $equal(identity,multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138))))) )],[refute_0_652,refute_0_653]) ).

cnf(refute_0_655,plain,
    ( multiply(X_138,inverse(multiply(X_59,X_138))) != multiply(inverse(X_59),multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138)))))
    | multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138)))) != identity
    | multiply(X_138,inverse(multiply(X_59,X_138))) = multiply(inverse(X_59),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_138,inverse(multiply(X_59,X_138))),multiply(inverse(X_59),multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138)))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_656,plain,
    ( multiply(X_138,inverse(multiply(X_59,X_138))) != multiply(inverse(X_59),multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138)))))
    | multiply(X_138,inverse(multiply(X_59,X_138))) = multiply(inverse(X_59),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138)))),identity) )],[refute_0_654,refute_0_655]) ).

cnf(refute_0_657,plain,
    multiply(X_138,inverse(multiply(X_59,X_138))) = multiply(inverse(X_59),identity),
    inference(resolve,[$cnf( $equal(multiply(X_138,inverse(multiply(X_59,X_138))),multiply(inverse(X_59),multiply(X_59,multiply(X_138,inverse(multiply(X_59,X_138)))))) )],[refute_0_646,refute_0_656]) ).

cnf(refute_0_658,plain,
    multiply(inverse(X_59),identity) = inverse(X_59),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(inverse(X_59)))]]) ).

cnf(refute_0_659,plain,
    ( multiply(X_138,inverse(multiply(X_59,X_138))) != multiply(inverse(X_59),identity)
    | multiply(inverse(X_59),identity) != inverse(X_59)
    | multiply(X_138,inverse(multiply(X_59,X_138))) = inverse(X_59) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_138,inverse(multiply(X_59,X_138))),inverse(X_59)) ),[0],$fot(multiply(inverse(X_59),identity))]]) ).

cnf(refute_0_660,plain,
    ( multiply(X_138,inverse(multiply(X_59,X_138))) != multiply(inverse(X_59),identity)
    | multiply(X_138,inverse(multiply(X_59,X_138))) = inverse(X_59) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_59),identity),inverse(X_59)) )],[refute_0_658,refute_0_659]) ).

cnf(refute_0_661,plain,
    multiply(X_138,inverse(multiply(X_59,X_138))) = inverse(X_59),
    inference(resolve,[$cnf( $equal(multiply(X_138,inverse(multiply(X_59,X_138))),multiply(inverse(X_59),identity)) )],[refute_0_657,refute_0_660]) ).

cnf(refute_0_662,plain,
    multiply(X_59,inverse(multiply(X_198,X_59))) = inverse(X_198),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(X_59)),bind(X_59,$fot(X_198))]]) ).

cnf(refute_0_663,plain,
    ( multiply(X_59,inverse(multiply(X_198,X_59))) != inverse(X_198)
    | inverse(multiply(X_198,X_59)) != multiply(inverse(X_59),multiply(X_59,inverse(multiply(X_198,X_59))))
    | inverse(multiply(X_198,X_59)) = multiply(inverse(X_59),inverse(X_198)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_198,X_59)),multiply(inverse(X_59),multiply(X_59,inverse(multiply(X_198,X_59))))) ),[1,1],$fot(inverse(X_198))]]) ).

cnf(refute_0_664,plain,
    ( inverse(multiply(X_198,X_59)) != multiply(inverse(X_59),multiply(X_59,inverse(multiply(X_198,X_59))))
    | inverse(multiply(X_198,X_59)) = multiply(inverse(X_59),inverse(X_198)) ),
    inference(resolve,[$cnf( $equal(multiply(X_59,inverse(multiply(X_198,X_59))),inverse(X_198)) )],[refute_0_662,refute_0_663]) ).

cnf(refute_0_665,plain,
    inverse(multiply(X_198,X_59)) = multiply(inverse(X_59),inverse(X_198)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_198,X_59)),multiply(inverse(X_59),multiply(X_59,inverse(multiply(X_198,X_59))))) )],[refute_0_645,refute_0_664]) ).

cnf(refute_0_666,plain,
    ( inverse(multiply(X_198,X_59)) != multiply(inverse(X_59),inverse(X_198))
    | multiply(inverse(X_59),inverse(X_198)) = inverse(multiply(X_198,X_59)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(multiply(X_198,X_59)))),bind(Y0,$fot(multiply(inverse(X_59),inverse(X_198))))]]) ).

cnf(refute_0_667,plain,
    multiply(inverse(X_59),inverse(X_198)) = inverse(multiply(X_198,X_59)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_198,X_59)),multiply(inverse(X_59),inverse(X_198))) )],[refute_0_665,refute_0_666]) ).

cnf(refute_0_668,plain,
    multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)) = inverse(multiply(X_122,greatest_lower_bound(identity,X_122))),
    inference(subst,[],[refute_0_667:[bind(X_198,$fot(X_122)),bind(X_59,$fot(greatest_lower_bound(identity,X_122)))]]) ).

cnf(refute_0_669,plain,
    greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))))]]) ).

cnf(refute_0_670,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)) != inverse(multiply(X_122,greatest_lower_bound(identity,X_122)))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) = greatest_lower_bound(identity,inverse(multiply(X_122,greatest_lower_bound(identity,X_122)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))) ),[1,1],$fot(inverse(multiply(X_122,greatest_lower_bound(identity,X_122))))]]) ).

cnf(refute_0_671,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)) != inverse(multiply(X_122,greatest_lower_bound(identity,X_122)))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) = greatest_lower_bound(identity,inverse(multiply(X_122,greatest_lower_bound(identity,X_122)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))) )],[refute_0_669,refute_0_670]) ).

cnf(refute_0_672,plain,
    greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) = greatest_lower_bound(identity,inverse(multiply(X_122,greatest_lower_bound(identity,X_122)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)),inverse(multiply(X_122,greatest_lower_bound(identity,X_122)))) )],[refute_0_668,refute_0_671]) ).

cnf(refute_0_673,plain,
    ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) != greatest_lower_bound(identity,inverse(multiply(X_122,greatest_lower_bound(identity,X_122))))
    | greatest_lower_bound(identity,inverse(multiply(X_122,greatest_lower_bound(identity,X_122)))) != inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) = inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(multiply(X_122,greatest_lower_bound(identity,X_122)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))))]]) ).

cnf(refute_0_674,plain,
    ( greatest_lower_bound(identity,inverse(multiply(X_122,greatest_lower_bound(identity,X_122)))) != inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) = inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))),greatest_lower_bound(identity,inverse(multiply(X_122,greatest_lower_bound(identity,X_122))))) )],[refute_0_672,refute_0_673]) ).

cnf(refute_0_675,plain,
    greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) = inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(X_122,greatest_lower_bound(identity,X_122)))),inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))) )],[refute_0_644,refute_0_674]) ).

cnf(refute_0_676,plain,
    ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))) != inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))
    | inverse(least_upper_bound(identity,X_122)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))
    | inverse(least_upper_bound(identity,X_122)) = inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_122)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))) ),[1],$fot(inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))))]]) ).

cnf(refute_0_677,plain,
    ( inverse(least_upper_bound(identity,X_122)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))
    | inverse(least_upper_bound(identity,X_122)) = inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122))),inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))) )],[refute_0_675,refute_0_676]) ).

cnf(refute_0_678,plain,
    ( multiply(greatest_lower_bound(X_122,identity),inverse(X_122)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))
    | inverse(least_upper_bound(identity,X_122)) = inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_122)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))) )],[refute_0_643,refute_0_677]) ).

cnf(refute_0_679,plain,
    inverse(least_upper_bound(identity,X_122)) = inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),inverse(X_122)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,X_122)),inverse(X_122)))) )],[refute_0_631,refute_0_678]) ).

cnf(refute_0_680,plain,
    multiply(X_93,least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93))))) = least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))),
    inference(subst,[],[refute_0_236:[bind(X_95,$fot(inverse(least_upper_bound(identity,inverse(X_93)))))]]) ).

cnf(refute_0_681,plain,
    least_upper_bound(X_43,least_upper_bound(greatest_lower_bound(X_43,Y),X_45)) = least_upper_bound(least_upper_bound(X_43,greatest_lower_bound(X_43,Y)),X_45),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_43)),bind(Y,$fot(greatest_lower_bound(X_43,Y))),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_682,plain,
    least_upper_bound(X_43,greatest_lower_bound(X_43,Y)) = X_43,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_43))]]) ).

cnf(refute_0_683,plain,
    ( least_upper_bound(X_43,greatest_lower_bound(X_43,Y)) != X_43
    | least_upper_bound(X_43,least_upper_bound(greatest_lower_bound(X_43,Y),X_45)) != least_upper_bound(least_upper_bound(X_43,greatest_lower_bound(X_43,Y)),X_45)
    | least_upper_bound(X_43,least_upper_bound(greatest_lower_bound(X_43,Y),X_45)) = least_upper_bound(X_43,X_45) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(greatest_lower_bound(X_43,Y),X_45)),least_upper_bound(least_upper_bound(X_43,greatest_lower_bound(X_43,Y)),X_45)) ),[1,0],$fot(X_43)]]) ).

cnf(refute_0_684,plain,
    ( least_upper_bound(X_43,least_upper_bound(greatest_lower_bound(X_43,Y),X_45)) != least_upper_bound(least_upper_bound(X_43,greatest_lower_bound(X_43,Y)),X_45)
    | least_upper_bound(X_43,least_upper_bound(greatest_lower_bound(X_43,Y),X_45)) = least_upper_bound(X_43,X_45) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,greatest_lower_bound(X_43,Y)),X_43) )],[refute_0_682,refute_0_683]) ).

cnf(refute_0_685,plain,
    least_upper_bound(X_43,least_upper_bound(greatest_lower_bound(X_43,Y),X_45)) = least_upper_bound(X_43,X_45),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(greatest_lower_bound(X_43,Y),X_45)),least_upper_bound(least_upper_bound(X_43,greatest_lower_bound(X_43,Y)),X_45)) )],[refute_0_681,refute_0_684]) ).

cnf(refute_0_686,plain,
    least_upper_bound(X_210,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210)))) = least_upper_bound(X_210,inverse(least_upper_bound(identity,X_210))),
    inference(subst,[],[refute_0_685:[bind(Y,$fot(identity)),bind(X_43,$fot(X_210)),bind(X_45,$fot(inverse(least_upper_bound(identity,X_210))))]]) ).

cnf(refute_0_687,plain,
    multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) = least_upper_bound(greatest_lower_bound(X_132,identity),multiply(greatest_lower_bound(X_132,identity),inverse(X_132))),
    inference(subst,[],[refute_0_480:[bind(X_93,$fot(greatest_lower_bound(X_132,identity))),bind(X_94,$fot(inverse(X_132)))]]) ).

cnf(refute_0_688,plain,
    ( multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) != inverse(least_upper_bound(identity,X_132))
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) != least_upper_bound(greatest_lower_bound(X_132,identity),multiply(greatest_lower_bound(X_132,identity),inverse(X_132)))
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) = least_upper_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)),least_upper_bound(greatest_lower_bound(X_132,identity),multiply(greatest_lower_bound(X_132,identity),inverse(X_132)))) ),[1,1],$fot(inverse(least_upper_bound(identity,X_132)))]]) ).

cnf(refute_0_689,plain,
    ( multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) != least_upper_bound(greatest_lower_bound(X_132,identity),multiply(greatest_lower_bound(X_132,identity),inverse(X_132)))
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) = least_upper_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),inverse(X_132)),inverse(least_upper_bound(identity,X_132))) )],[refute_0_640,refute_0_688]) ).

cnf(refute_0_690,plain,
    multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) = least_upper_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)),least_upper_bound(greatest_lower_bound(X_132,identity),multiply(greatest_lower_bound(X_132,identity),inverse(X_132)))) )],[refute_0_687,refute_0_689]) ).

cnf(refute_0_691,plain,
    multiply(greatest_lower_bound(X_132,identity),inverse(greatest_lower_bound(identity,X_132))) = identity,
    inference(subst,[],[refute_0_207:[bind(X,$fot(identity)),bind(Y,$fot(X_132))]]) ).

cnf(refute_0_692,plain,
    least_upper_bound(identity,inverse(X_132)) = inverse(greatest_lower_bound(identity,X_132)),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(X_132))]]) ).

cnf(refute_0_693,plain,
    multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))) = multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))))]]) ).

cnf(refute_0_694,plain,
    ( multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))) != multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132)))
    | least_upper_bound(identity,inverse(X_132)) != inverse(greatest_lower_bound(identity,X_132))
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))) = multiply(greatest_lower_bound(X_132,identity),inverse(greatest_lower_bound(identity,X_132))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))),multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132)))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,X_132)))]]) ).

cnf(refute_0_695,plain,
    ( least_upper_bound(identity,inverse(X_132)) != inverse(greatest_lower_bound(identity,X_132))
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))) = multiply(greatest_lower_bound(X_132,identity),inverse(greatest_lower_bound(identity,X_132))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))),multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132)))) )],[refute_0_693,refute_0_694]) ).

cnf(refute_0_696,plain,
    multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))) = multiply(greatest_lower_bound(X_132,identity),inverse(greatest_lower_bound(identity,X_132))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_132)),inverse(greatest_lower_bound(identity,X_132))) )],[refute_0_692,refute_0_695]) ).

cnf(refute_0_697,plain,
    ( multiply(greatest_lower_bound(X_132,identity),inverse(greatest_lower_bound(identity,X_132))) != identity
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))) != multiply(greatest_lower_bound(X_132,identity),inverse(greatest_lower_bound(identity,X_132)))
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_132,identity),inverse(greatest_lower_bound(identity,X_132))))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_698,plain,
    ( multiply(greatest_lower_bound(X_132,identity),inverse(greatest_lower_bound(identity,X_132))) != identity
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))),multiply(greatest_lower_bound(X_132,identity),inverse(greatest_lower_bound(identity,X_132)))) )],[refute_0_696,refute_0_697]) ).

cnf(refute_0_699,plain,
    multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))) = identity,
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),inverse(greatest_lower_bound(identity,X_132))),identity) )],[refute_0_691,refute_0_698]) ).

cnf(refute_0_700,plain,
    multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) = multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))),
    inference(subst,[],[refute_0_564:[bind(X_165,$fot(inverse(X_132))),bind(X_31,$fot(greatest_lower_bound(X_132,identity)))]]) ).

cnf(refute_0_701,plain,
    ( multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))) != identity
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) != multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132)))
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_702,plain,
    ( multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))) != identity
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) = identity ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)),multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132)))) )],[refute_0_700,refute_0_701]) ).

cnf(refute_0_703,plain,
    multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) = identity,
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(identity,inverse(X_132))),identity) )],[refute_0_699,refute_0_702]) ).

cnf(refute_0_704,plain,
    ( multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) != identity
    | multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) != least_upper_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))
    | identity = least_upper_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)),least_upper_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))) ),[0],$fot(identity)]]) ).

cnf(refute_0_705,plain,
    ( multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)) != least_upper_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))
    | identity = least_upper_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)),identity) )],[refute_0_703,refute_0_704]) ).

cnf(refute_0_706,plain,
    identity = least_upper_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),least_upper_bound(inverse(X_132),identity)),least_upper_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))) )],[refute_0_690,refute_0_705]) ).

cnf(refute_0_707,plain,
    identity = least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210))),
    inference(subst,[],[refute_0_706:[bind(X_132,$fot(X_210))]]) ).

cnf(refute_0_708,plain,
    ( identity != least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210)))
    | least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210)))))]]) ).

cnf(refute_0_709,plain,
    least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210))) = identity,
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210)))) )],[refute_0_707,refute_0_708]) ).

cnf(refute_0_710,plain,
    ( least_upper_bound(X_210,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210)))) != least_upper_bound(X_210,inverse(least_upper_bound(identity,X_210)))
    | least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210))) != identity
    | least_upper_bound(X_210,identity) = least_upper_bound(X_210,inverse(least_upper_bound(identity,X_210))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_210,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210)))),least_upper_bound(X_210,inverse(least_upper_bound(identity,X_210)))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_711,plain,
    ( least_upper_bound(X_210,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210)))) != least_upper_bound(X_210,inverse(least_upper_bound(identity,X_210)))
    | least_upper_bound(X_210,identity) = least_upper_bound(X_210,inverse(least_upper_bound(identity,X_210))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210))),identity) )],[refute_0_709,refute_0_710]) ).

cnf(refute_0_712,plain,
    least_upper_bound(X_210,identity) = least_upper_bound(X_210,inverse(least_upper_bound(identity,X_210))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_210,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(identity,X_210)))),least_upper_bound(X_210,inverse(least_upper_bound(identity,X_210)))) )],[refute_0_686,refute_0_711]) ).

cnf(refute_0_713,plain,
    least_upper_bound(inverse(X_93),identity) = least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93)))),
    inference(subst,[],[refute_0_712:[bind(X_210,$fot(inverse(X_93)))]]) ).

cnf(refute_0_714,plain,
    ( least_upper_bound(inverse(X_93),identity) != least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93))))
    | least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93)))) = least_upper_bound(inverse(X_93),identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(inverse(X_93),identity))),bind(Y0,$fot(least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93))))))]]) ).

cnf(refute_0_715,plain,
    least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93)))) = least_upper_bound(inverse(X_93),identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_93),identity),least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93))))) )],[refute_0_713,refute_0_714]) ).

cnf(refute_0_716,plain,
    ( multiply(X_93,least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93))))) != least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))
    | least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93)))) != least_upper_bound(inverse(X_93),identity)
    | multiply(X_93,least_upper_bound(inverse(X_93),identity)) = least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93))))),least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))) ),[0,1],$fot(least_upper_bound(inverse(X_93),identity))]]) ).

cnf(refute_0_717,plain,
    ( multiply(X_93,least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93))))) != least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))
    | multiply(X_93,least_upper_bound(inverse(X_93),identity)) = least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93)))),least_upper_bound(inverse(X_93),identity)) )],[refute_0_715,refute_0_716]) ).

cnf(refute_0_718,plain,
    multiply(X_93,least_upper_bound(inverse(X_93),identity)) = least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(X_93),inverse(least_upper_bound(identity,inverse(X_93))))),least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))) )],[refute_0_680,refute_0_717]) ).

cnf(refute_0_719,plain,
    multiply(least_upper_bound(X_93,identity),identity) = least_upper_bound(X_93,identity),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(least_upper_bound(X_93,identity)))]]) ).

cnf(refute_0_720,plain,
    multiply(least_upper_bound(X_111,identity),X_110) = least_upper_bound(multiply(X_111,X_110),multiply(identity,X_110)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_110)),bind(Y,$fot(X_111)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_721,plain,
    multiply(identity,X_110) = X_110,
    inference(subst,[],[left_identity:[bind(X,$fot(X_110))]]) ).

cnf(refute_0_722,plain,
    ( multiply(identity,X_110) != X_110
    | multiply(least_upper_bound(X_111,identity),X_110) != least_upper_bound(multiply(X_111,X_110),multiply(identity,X_110))
    | multiply(least_upper_bound(X_111,identity),X_110) = least_upper_bound(multiply(X_111,X_110),X_110) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_111,identity),X_110),least_upper_bound(multiply(X_111,X_110),multiply(identity,X_110))) ),[1,1],$fot(X_110)]]) ).

cnf(refute_0_723,plain,
    ( multiply(least_upper_bound(X_111,identity),X_110) != least_upper_bound(multiply(X_111,X_110),multiply(identity,X_110))
    | multiply(least_upper_bound(X_111,identity),X_110) = least_upper_bound(multiply(X_111,X_110),X_110) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_110),X_110) )],[refute_0_721,refute_0_722]) ).

cnf(refute_0_724,plain,
    multiply(least_upper_bound(X_111,identity),X_110) = least_upper_bound(multiply(X_111,X_110),X_110),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,identity),X_110),least_upper_bound(multiply(X_111,X_110),multiply(identity,X_110))) )],[refute_0_720,refute_0_723]) ).

cnf(refute_0_725,plain,
    least_upper_bound(multiply(X_111,X_110),X_110) = least_upper_bound(X_110,multiply(X_111,X_110)),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(multiply(X_111,X_110))),bind(X_17,$fot(X_110))]]) ).

cnf(refute_0_726,plain,
    ( multiply(least_upper_bound(X_111,identity),X_110) != least_upper_bound(multiply(X_111,X_110),X_110)
    | least_upper_bound(multiply(X_111,X_110),X_110) != least_upper_bound(X_110,multiply(X_111,X_110))
    | multiply(least_upper_bound(X_111,identity),X_110) = least_upper_bound(X_110,multiply(X_111,X_110)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_111,identity),X_110),least_upper_bound(X_110,multiply(X_111,X_110))) ),[0],$fot(least_upper_bound(multiply(X_111,X_110),X_110))]]) ).

cnf(refute_0_727,plain,
    ( multiply(least_upper_bound(X_111,identity),X_110) != least_upper_bound(multiply(X_111,X_110),X_110)
    | multiply(least_upper_bound(X_111,identity),X_110) = least_upper_bound(X_110,multiply(X_111,X_110)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_111,X_110),X_110),least_upper_bound(X_110,multiply(X_111,X_110))) )],[refute_0_725,refute_0_726]) ).

cnf(refute_0_728,plain,
    multiply(least_upper_bound(X_111,identity),X_110) = least_upper_bound(X_110,multiply(X_111,X_110)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,identity),X_110),least_upper_bound(multiply(X_111,X_110),X_110)) )],[refute_0_724,refute_0_727]) ).

cnf(refute_0_729,plain,
    ( multiply(least_upper_bound(X_111,identity),X_110) != least_upper_bound(X_110,multiply(X_111,X_110))
    | least_upper_bound(X_110,multiply(X_111,X_110)) = multiply(least_upper_bound(X_111,identity),X_110) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_111,identity),X_110))),bind(Y0,$fot(least_upper_bound(X_110,multiply(X_111,X_110))))]]) ).

cnf(refute_0_730,plain,
    least_upper_bound(X_110,multiply(X_111,X_110)) = multiply(least_upper_bound(X_111,identity),X_110),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,identity),X_110),least_upper_bound(X_110,multiply(X_111,X_110))) )],[refute_0_728,refute_0_729]) ).

cnf(refute_0_731,plain,
    least_upper_bound(identity,multiply(X_93,identity)) = multiply(least_upper_bound(X_93,identity),identity),
    inference(subst,[],[refute_0_730:[bind(X_110,$fot(identity)),bind(X_111,$fot(X_93))]]) ).

cnf(refute_0_732,plain,
    ( multiply(least_upper_bound(X_93,identity),identity) != least_upper_bound(X_93,identity)
    | least_upper_bound(identity,multiply(X_93,identity)) != multiply(least_upper_bound(X_93,identity),identity)
    | least_upper_bound(identity,multiply(X_93,identity)) = least_upper_bound(X_93,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(X_93,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_93,identity),identity))),bind(Z0,$fot(least_upper_bound(X_93,identity)))]]) ).

cnf(refute_0_733,plain,
    ( multiply(least_upper_bound(X_93,identity),identity) != least_upper_bound(X_93,identity)
    | least_upper_bound(identity,multiply(X_93,identity)) = least_upper_bound(X_93,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_93,identity)),multiply(least_upper_bound(X_93,identity),identity)) )],[refute_0_731,refute_0_732]) ).

cnf(refute_0_734,plain,
    least_upper_bound(identity,multiply(X_93,identity)) = least_upper_bound(X_93,identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_93,identity),identity),least_upper_bound(X_93,identity)) )],[refute_0_719,refute_0_733]) ).

cnf(refute_0_735,plain,
    multiply(X_93,least_upper_bound(identity,inverse(X_93))) = least_upper_bound(identity,multiply(X_93,identity)),
    inference(subst,[],[refute_0_251:[bind(X_94,$fot(identity))]]) ).

cnf(refute_0_736,plain,
    ( multiply(X_93,least_upper_bound(identity,inverse(X_93))) != least_upper_bound(identity,multiply(X_93,identity))
    | least_upper_bound(identity,multiply(X_93,identity)) != least_upper_bound(X_93,identity)
    | multiply(X_93,least_upper_bound(identity,inverse(X_93))) = least_upper_bound(X_93,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(X_93,least_upper_bound(identity,inverse(X_93))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_93,identity)))),bind(Z0,$fot(least_upper_bound(X_93,identity)))]]) ).

cnf(refute_0_737,plain,
    ( least_upper_bound(identity,multiply(X_93,identity)) != least_upper_bound(X_93,identity)
    | multiply(X_93,least_upper_bound(identity,inverse(X_93))) = least_upper_bound(X_93,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(identity,inverse(X_93))),least_upper_bound(identity,multiply(X_93,identity))) )],[refute_0_735,refute_0_736]) ).

cnf(refute_0_738,plain,
    multiply(X_93,least_upper_bound(identity,inverse(X_93))) = least_upper_bound(X_93,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_93,identity)),least_upper_bound(X_93,identity)) )],[refute_0_734,refute_0_737]) ).

cnf(refute_0_739,plain,
    multiply(X_93,least_upper_bound(inverse(X_93),identity)) = multiply(X_93,least_upper_bound(identity,inverse(X_93))),
    inference(subst,[],[refute_0_564:[bind(X_165,$fot(inverse(X_93))),bind(X_31,$fot(X_93))]]) ).

cnf(refute_0_740,plain,
    ( multiply(X_93,least_upper_bound(identity,inverse(X_93))) != least_upper_bound(X_93,identity)
    | multiply(X_93,least_upper_bound(inverse(X_93),identity)) != multiply(X_93,least_upper_bound(identity,inverse(X_93)))
    | multiply(X_93,least_upper_bound(inverse(X_93),identity)) = least_upper_bound(X_93,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(X_93,least_upper_bound(inverse(X_93),identity)))),bind(Y0,$fot(multiply(X_93,least_upper_bound(identity,inverse(X_93))))),bind(Z0,$fot(least_upper_bound(X_93,identity)))]]) ).

cnf(refute_0_741,plain,
    ( multiply(X_93,least_upper_bound(identity,inverse(X_93))) != least_upper_bound(X_93,identity)
    | multiply(X_93,least_upper_bound(inverse(X_93),identity)) = least_upper_bound(X_93,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(X_93),identity)),multiply(X_93,least_upper_bound(identity,inverse(X_93)))) )],[refute_0_739,refute_0_740]) ).

cnf(refute_0_742,plain,
    multiply(X_93,least_upper_bound(inverse(X_93),identity)) = least_upper_bound(X_93,identity),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(identity,inverse(X_93))),least_upper_bound(X_93,identity)) )],[refute_0_738,refute_0_741]) ).

cnf(refute_0_743,plain,
    ( multiply(X_93,least_upper_bound(inverse(X_93),identity)) != least_upper_bound(X_93,identity)
    | multiply(X_93,least_upper_bound(inverse(X_93),identity)) != least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))
    | least_upper_bound(X_93,identity) = least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(X_93),identity)),least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))) ),[0],$fot(least_upper_bound(X_93,identity))]]) ).

cnf(refute_0_744,plain,
    ( multiply(X_93,least_upper_bound(inverse(X_93),identity)) != least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))
    | least_upper_bound(X_93,identity) = least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) ),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(X_93),identity)),least_upper_bound(X_93,identity)) )],[refute_0_742,refute_0_743]) ).

cnf(refute_0_745,plain,
    greatest_lower_bound(inverse(identity),X_93) = greatest_lower_bound(inverse(identity),X_93),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(identity),X_93))]]) ).

cnf(refute_0_746,plain,
    ( greatest_lower_bound(inverse(identity),X_93) != greatest_lower_bound(inverse(identity),X_93)
    | inverse(identity) != identity
    | greatest_lower_bound(inverse(identity),X_93) = greatest_lower_bound(identity,X_93) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(identity),X_93),greatest_lower_bound(inverse(identity),X_93)) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_747,plain,
    ( inverse(identity) != identity
    | greatest_lower_bound(inverse(identity),X_93) = greatest_lower_bound(identity,X_93) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(identity),X_93),greatest_lower_bound(inverse(identity),X_93)) )],[refute_0_745,refute_0_746]) ).

cnf(refute_0_748,plain,
    greatest_lower_bound(inverse(identity),X_93) = greatest_lower_bound(identity,X_93),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_747]) ).

cnf(refute_0_749,plain,
    inverse(least_upper_bound(identity,inverse(X_93))) = greatest_lower_bound(inverse(identity),X_93),
    inference(subst,[],[refute_0_582:[bind(X,$fot(identity)),bind(X_89,$fot(X_93))]]) ).

cnf(refute_0_750,plain,
    ( greatest_lower_bound(inverse(identity),X_93) != greatest_lower_bound(identity,X_93)
    | inverse(least_upper_bound(identity,inverse(X_93))) != greatest_lower_bound(inverse(identity),X_93)
    | inverse(least_upper_bound(identity,inverse(X_93))) = greatest_lower_bound(identity,X_93) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_93))))),bind(Y0,$fot(greatest_lower_bound(inverse(identity),X_93))),bind(Z0,$fot(greatest_lower_bound(identity,X_93)))]]) ).

cnf(refute_0_751,plain,
    ( greatest_lower_bound(inverse(identity),X_93) != greatest_lower_bound(identity,X_93)
    | inverse(least_upper_bound(identity,inverse(X_93))) = greatest_lower_bound(identity,X_93) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_93))),greatest_lower_bound(inverse(identity),X_93)) )],[refute_0_749,refute_0_750]) ).

cnf(refute_0_752,plain,
    inverse(least_upper_bound(identity,inverse(X_93))) = greatest_lower_bound(identity,X_93),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(identity),X_93),greatest_lower_bound(identity,X_93)) )],[refute_0_748,refute_0_751]) ).

cnf(refute_0_753,plain,
    multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))) = multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))),
    introduced(tautology,[refl,[$fot(multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))]]) ).

cnf(refute_0_754,plain,
    ( multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))) != multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))
    | inverse(least_upper_bound(identity,inverse(X_93))) != greatest_lower_bound(identity,X_93)
    | multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))) = multiply(X_93,greatest_lower_bound(identity,X_93)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))),multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) ),[1,1],$fot(greatest_lower_bound(identity,X_93))]]) ).

cnf(refute_0_755,plain,
    ( inverse(least_upper_bound(identity,inverse(X_93))) != greatest_lower_bound(identity,X_93)
    | multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))) = multiply(X_93,greatest_lower_bound(identity,X_93)) ),
    inference(resolve,[$cnf( $equal(multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))),multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) )],[refute_0_753,refute_0_754]) ).

cnf(refute_0_756,plain,
    multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))) = multiply(X_93,greatest_lower_bound(identity,X_93)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_93))),greatest_lower_bound(identity,X_93)) )],[refute_0_752,refute_0_755]) ).

cnf(refute_0_757,plain,
    least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) = least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))))]]) ).

cnf(refute_0_758,plain,
    ( multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))) != multiply(X_93,greatest_lower_bound(identity,X_93))
    | least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) != least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))
    | least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) = least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))),least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))) ),[1,1],$fot(multiply(X_93,greatest_lower_bound(identity,X_93)))]]) ).

cnf(refute_0_759,plain,
    ( multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))) != multiply(X_93,greatest_lower_bound(identity,X_93))
    | least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) = least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))),least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))) )],[refute_0_757,refute_0_758]) ).

cnf(refute_0_760,plain,
    least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) = least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93))),
    inference(resolve,[$cnf( $equal(multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))),multiply(X_93,greatest_lower_bound(identity,X_93))) )],[refute_0_756,refute_0_759]) ).

cnf(refute_0_761,plain,
    ( least_upper_bound(X_93,identity) != least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))
    | least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))) != least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93)))
    | least_upper_bound(X_93,identity) = least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_93,identity),least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93)))) ),[0],$fot(least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))))]]) ).

cnf(refute_0_762,plain,
    ( least_upper_bound(X_93,identity) != least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))
    | least_upper_bound(X_93,identity) = least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93))))),least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93)))) )],[refute_0_760,refute_0_761]) ).

cnf(refute_0_763,plain,
    ( multiply(X_93,least_upper_bound(inverse(X_93),identity)) != least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))
    | least_upper_bound(X_93,identity) = least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_93,identity),least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))) )],[refute_0_744,refute_0_762]) ).

cnf(refute_0_764,plain,
    least_upper_bound(X_93,identity) = least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93))),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(X_93),identity)),least_upper_bound(identity,multiply(X_93,inverse(least_upper_bound(identity,inverse(X_93)))))) )],[refute_0_718,refute_0_763]) ).

cnf(refute_0_765,plain,
    ( least_upper_bound(X_93,identity) != least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93)))
    | least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93))) = least_upper_bound(X_93,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_93,identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93)))))]]) ).

cnf(refute_0_766,plain,
    least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93))) = least_upper_bound(X_93,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_93,identity),least_upper_bound(identity,multiply(X_93,greatest_lower_bound(identity,X_93)))) )],[refute_0_764,refute_0_765]) ).

cnf(refute_0_767,plain,
    least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))) = least_upper_bound(X_122,identity),
    inference(subst,[],[refute_0_766:[bind(X_93,$fot(X_122))]]) ).

cnf(refute_0_768,plain,
    inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))) = inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))))]]) ).

cnf(refute_0_769,plain,
    ( inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))) != inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))
    | least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))) != least_upper_bound(X_122,identity)
    | inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))) = inverse(least_upper_bound(X_122,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))),inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))) ),[1,0],$fot(least_upper_bound(X_122,identity))]]) ).

cnf(refute_0_770,plain,
    ( least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))) != least_upper_bound(X_122,identity)
    | inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))) = inverse(least_upper_bound(X_122,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))),inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))) )],[refute_0_768,refute_0_769]) ).

cnf(refute_0_771,plain,
    inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))) = inverse(least_upper_bound(X_122,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))),least_upper_bound(X_122,identity)) )],[refute_0_767,refute_0_770]) ).

cnf(refute_0_772,plain,
    ( inverse(least_upper_bound(identity,X_122)) != inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))
    | inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))) != inverse(least_upper_bound(X_122,identity))
    | inverse(least_upper_bound(identity,X_122)) = inverse(least_upper_bound(X_122,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(least_upper_bound(identity,X_122)),inverse(least_upper_bound(X_122,identity))) ),[0],$fot(inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))))]]) ).

cnf(refute_0_773,plain,
    ( inverse(least_upper_bound(identity,X_122)) != inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))
    | inverse(least_upper_bound(identity,X_122)) = inverse(least_upper_bound(X_122,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122)))),inverse(least_upper_bound(X_122,identity))) )],[refute_0_771,refute_0_772]) ).

cnf(refute_0_774,plain,
    inverse(least_upper_bound(identity,X_122)) = inverse(least_upper_bound(X_122,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_122)),inverse(least_upper_bound(identity,multiply(X_122,greatest_lower_bound(identity,X_122))))) )],[refute_0_679,refute_0_773]) ).

cnf(refute_0_775,plain,
    inverse(least_upper_bound(identity,b)) = inverse(least_upper_bound(b,identity)),
    inference(subst,[],[refute_0_774:[bind(X_122,$fot(b))]]) ).

cnf(refute_0_776,plain,
    greatest_lower_bound(identity,inverse(b)) = inverse(least_upper_bound(identity,b)),
    inference(subst,[],[refute_0_500:[bind(Y,$fot(b))]]) ).

cnf(refute_0_777,plain,
    ( greatest_lower_bound(identity,inverse(b)) != inverse(least_upper_bound(identity,b))
    | inverse(least_upper_bound(identity,b)) != inverse(least_upper_bound(b,identity))
    | greatest_lower_bound(identity,inverse(b)) = inverse(least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,inverse(b)))),bind(Y0,$fot(inverse(least_upper_bound(identity,b)))),bind(Z0,$fot(inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_778,plain,
    ( inverse(least_upper_bound(identity,b)) != inverse(least_upper_bound(b,identity))
    | greatest_lower_bound(identity,inverse(b)) = inverse(least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(b)),inverse(least_upper_bound(identity,b))) )],[refute_0_776,refute_0_777]) ).

cnf(refute_0_779,plain,
    greatest_lower_bound(identity,inverse(b)) = inverse(least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,b)),inverse(least_upper_bound(b,identity))) )],[refute_0_775,refute_0_778]) ).

cnf(refute_0_780,plain,
    multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))) = multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))))]]) ).

cnf(refute_0_781,plain,
    ( multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))) != multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b)))
    | greatest_lower_bound(identity,inverse(b)) != inverse(least_upper_bound(b,identity))
    | multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))),multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b)))) ),[1,1],$fot(inverse(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_782,plain,
    ( greatest_lower_bound(identity,inverse(b)) != inverse(least_upper_bound(b,identity))
    | multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))),multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b)))) )],[refute_0_780,refute_0_781]) ).

cnf(refute_0_783,plain,
    multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(b)),inverse(least_upper_bound(b,identity))) )],[refute_0_779,refute_0_782]) ).

cnf(refute_0_784,plain,
    greatest_lower_bound(greatest_lower_bound(X_23,Y),least_upper_bound(X_23,greatest_lower_bound(X_23,Y))) = greatest_lower_bound(X_23,Y),
    inference(subst,[],[refute_0_215:[bind(X_10,$fot(greatest_lower_bound(X_23,Y))),bind(X_11,$fot(X_23))]]) ).

cnf(refute_0_785,plain,
    least_upper_bound(X_23,greatest_lower_bound(X_23,Y)) = X_23,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_23))]]) ).

cnf(refute_0_786,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_23,Y),least_upper_bound(X_23,greatest_lower_bound(X_23,Y))) != greatest_lower_bound(X_23,Y)
    | least_upper_bound(X_23,greatest_lower_bound(X_23,Y)) != X_23
    | greatest_lower_bound(greatest_lower_bound(X_23,Y),X_23) = greatest_lower_bound(X_23,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_23,Y),least_upper_bound(X_23,greatest_lower_bound(X_23,Y))),greatest_lower_bound(X_23,Y)) ),[0,1],$fot(X_23)]]) ).

cnf(refute_0_787,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_23,Y),least_upper_bound(X_23,greatest_lower_bound(X_23,Y))) != greatest_lower_bound(X_23,Y)
    | greatest_lower_bound(greatest_lower_bound(X_23,Y),X_23) = greatest_lower_bound(X_23,Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_23,greatest_lower_bound(X_23,Y)),X_23) )],[refute_0_785,refute_0_786]) ).

cnf(refute_0_788,plain,
    greatest_lower_bound(greatest_lower_bound(X_23,Y),X_23) = greatest_lower_bound(X_23,Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_23,Y),least_upper_bound(X_23,greatest_lower_bound(X_23,Y))),greatest_lower_bound(X_23,Y)) )],[refute_0_784,refute_0_787]) ).

cnf(refute_0_789,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_790,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_789]) ).

cnf(refute_0_791,plain,
    greatest_lower_bound(greatest_lower_bound(X_23,Y),X_23) = greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_23)),bind(Z,$fot(X_23))]]) ).

cnf(refute_0_792,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_23,Y),X_23) != greatest_lower_bound(X_23,Y)
    | greatest_lower_bound(greatest_lower_bound(X_23,Y),X_23) != greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23))
    | greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23)) = greatest_lower_bound(X_23,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_23,Y),X_23),greatest_lower_bound(X_23,Y)) ),[0],$fot(greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23)))]]) ).

cnf(refute_0_793,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_23,Y),X_23) != greatest_lower_bound(X_23,Y)
    | greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23)) = greatest_lower_bound(X_23,Y) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_23,Y),X_23),greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23))) )],[refute_0_791,refute_0_792]) ).

cnf(refute_0_794,plain,
    greatest_lower_bound(X_23,greatest_lower_bound(Y,X_23)) = greatest_lower_bound(X_23,Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_23,Y),X_23),greatest_lower_bound(X_23,Y)) )],[refute_0_788,refute_0_793]) ).

cnf(refute_0_795,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_32,X_33)) = greatest_lower_bound(X_33,X_32),
    inference(subst,[],[refute_0_794:[bind(Y,$fot(X_32)),bind(X_23,$fot(X_33))]]) ).

cnf(refute_0_796,plain,
    greatest_lower_bound(X_33,X_32) = greatest_lower_bound(X_32,X_33),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_33)),bind(Y,$fot(X_32))]]) ).

cnf(refute_0_797,plain,
    ( greatest_lower_bound(X_33,X_32) != greatest_lower_bound(X_32,X_33)
    | greatest_lower_bound(X_32,X_33) = greatest_lower_bound(X_33,X_32) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_33,X_32))),bind(Y0,$fot(greatest_lower_bound(X_32,X_33)))]]) ).

cnf(refute_0_798,plain,
    greatest_lower_bound(X_32,X_33) = greatest_lower_bound(X_33,X_32),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,X_32),greatest_lower_bound(X_32,X_33)) )],[refute_0_796,refute_0_797]) ).

cnf(refute_0_799,plain,
    ( greatest_lower_bound(X_32,X_33) != greatest_lower_bound(X_33,X_32)
    | greatest_lower_bound(X_33,greatest_lower_bound(X_32,X_33)) != greatest_lower_bound(X_33,X_32)
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,X_32)) = greatest_lower_bound(X_33,X_32) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_32,X_33)),greatest_lower_bound(X_33,X_32)) ),[0,1],$fot(greatest_lower_bound(X_33,X_32))]]) ).

cnf(refute_0_800,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_32,X_33)) != greatest_lower_bound(X_33,X_32)
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,X_32)) = greatest_lower_bound(X_33,X_32) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_32,X_33),greatest_lower_bound(X_33,X_32)) )],[refute_0_798,refute_0_799]) ).

cnf(refute_0_801,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_33,X_32)) = greatest_lower_bound(X_33,X_32),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_32,X_33)),greatest_lower_bound(X_33,X_32)) )],[refute_0_795,refute_0_800]) ).

cnf(refute_0_802,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) = greatest_lower_bound(X_33,multiply(X_33,X_232)),
    inference(subst,[],[refute_0_801:[bind(X_32,$fot(multiply(X_33,X_232)))]]) ).

cnf(refute_0_803,plain,
    multiply(X_33,greatest_lower_bound(X_232,identity)) = greatest_lower_bound(X_33,multiply(X_33,X_232)),
    inference(subst,[],[refute_0_161:[bind(X_107,$fot(X_33)),bind(X_108,$fot(X_232))]]) ).

cnf(refute_0_804,plain,
    ( multiply(X_33,greatest_lower_bound(X_232,identity)) != greatest_lower_bound(X_33,multiply(X_33,X_232))
    | greatest_lower_bound(X_33,multiply(X_33,X_232)) = multiply(X_33,greatest_lower_bound(X_232,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_33,greatest_lower_bound(X_232,identity)))),bind(Y0,$fot(greatest_lower_bound(X_33,multiply(X_33,X_232))))]]) ).

cnf(refute_0_805,plain,
    greatest_lower_bound(X_33,multiply(X_33,X_232)) = multiply(X_33,greatest_lower_bound(X_232,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_33,greatest_lower_bound(X_232,identity)),greatest_lower_bound(X_33,multiply(X_33,X_232))) )],[refute_0_803,refute_0_804]) ).

cnf(refute_0_806,plain,
    ( greatest_lower_bound(X_33,multiply(X_33,X_232)) != multiply(X_33,greatest_lower_bound(X_232,identity))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) != greatest_lower_bound(X_33,multiply(X_33,X_232))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) = multiply(X_33,greatest_lower_bound(X_232,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))),greatest_lower_bound(X_33,multiply(X_33,X_232))) ),[1],$fot(multiply(X_33,greatest_lower_bound(X_232,identity)))]]) ).

cnf(refute_0_807,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) != greatest_lower_bound(X_33,multiply(X_33,X_232))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) = multiply(X_33,greatest_lower_bound(X_232,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,multiply(X_33,X_232)),multiply(X_33,greatest_lower_bound(X_232,identity))) )],[refute_0_805,refute_0_806]) ).

cnf(refute_0_808,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) = multiply(X_33,greatest_lower_bound(X_232,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))),greatest_lower_bound(X_33,multiply(X_33,X_232))) )],[refute_0_802,refute_0_807]) ).

cnf(refute_0_809,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)) = greatest_lower_bound(identity,X_232),
    inference(subst,[],[refute_0_794:[bind(Y,$fot(X_232)),bind(X_23,$fot(identity))]]) ).

cnf(refute_0_810,plain,
    multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))) = multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))),
    introduced(tautology,[refl,[$fot(multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))))]]) ).

cnf(refute_0_811,plain,
    ( multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))) != multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))
    | greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)) != greatest_lower_bound(identity,X_232)
    | multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))) = multiply(X_33,greatest_lower_bound(identity,X_232)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))),multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,X_232))]]) ).

cnf(refute_0_812,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)) != greatest_lower_bound(identity,X_232)
    | multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))) = multiply(X_33,greatest_lower_bound(identity,X_232)) ),
    inference(resolve,[$cnf( $equal(multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))),multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))) )],[refute_0_810,refute_0_811]) ).

cnf(refute_0_813,plain,
    multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))) = multiply(X_33,greatest_lower_bound(identity,X_232)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)),greatest_lower_bound(identity,X_232)) )],[refute_0_809,refute_0_812]) ).

cnf(refute_0_814,plain,
    greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109)),
    inference(subst,[],[refute_0_801:[bind(X_32,$fot(multiply(X_107,X_109))),bind(X_33,$fot(multiply(X_107,X_108)))]]) ).

cnf(refute_0_815,plain,
    multiply(X_107,greatest_lower_bound(X_108,X_109)) = greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_107)),bind(Y,$fot(X_108)),bind(Z,$fot(X_109))]]) ).

cnf(refute_0_816,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,X_109)) != greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))
    | greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109)) = multiply(X_107,greatest_lower_bound(X_108,X_109)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_107,greatest_lower_bound(X_108,X_109)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))))]]) ).

cnf(refute_0_817,plain,
    greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109)) = multiply(X_107,greatest_lower_bound(X_108,X_109)),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,X_109)),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) )],[refute_0_815,refute_0_816]) ).

cnf(refute_0_818,plain,
    ( greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109)) != multiply(X_107,greatest_lower_bound(X_108,X_109))
    | greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) != greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))
    | greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = multiply(X_107,greatest_lower_bound(X_108,X_109)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) ),[1],$fot(multiply(X_107,greatest_lower_bound(X_108,X_109)))]]) ).

cnf(refute_0_819,plain,
    ( greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) != greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))
    | greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = multiply(X_107,greatest_lower_bound(X_108,X_109)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109)),multiply(X_107,greatest_lower_bound(X_108,X_109))) )],[refute_0_817,refute_0_818]) ).

cnf(refute_0_820,plain,
    greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = multiply(X_107,greatest_lower_bound(X_108,X_109)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) )],[refute_0_814,refute_0_819]) ).

cnf(refute_0_821,plain,
    greatest_lower_bound(X_108,X_108) = X_108,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_108))]]) ).

cnf(refute_0_822,plain,
    greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)) = greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)))]]) ).

cnf(refute_0_823,plain,
    ( greatest_lower_bound(X_108,X_108) != X_108
    | greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)) != greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))
    | greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)) = greatest_lower_bound(X_109,X_108) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)),greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))) ),[1,1],$fot(X_108)]]) ).

cnf(refute_0_824,plain,
    ( greatest_lower_bound(X_108,X_108) != X_108
    | greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)) = greatest_lower_bound(X_109,X_108) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)),greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))) )],[refute_0_822,refute_0_823]) ).

cnf(refute_0_825,plain,
    greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)) = greatest_lower_bound(X_109,X_108),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_108,X_108),X_108) )],[refute_0_821,refute_0_824]) ).

cnf(refute_0_826,plain,
    multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))) = multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))),
    introduced(tautology,[refl,[$fot(multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))))]]) ).

cnf(refute_0_827,plain,
    ( multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))) != multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)))
    | greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)) != greatest_lower_bound(X_109,X_108)
    | multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))) = multiply(X_107,greatest_lower_bound(X_109,X_108)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))),multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)))) ),[1,1],$fot(greatest_lower_bound(X_109,X_108))]]) ).

cnf(refute_0_828,plain,
    ( greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)) != greatest_lower_bound(X_109,X_108)
    | multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))) = multiply(X_107,greatest_lower_bound(X_109,X_108)) ),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))),multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)))) )],[refute_0_826,refute_0_827]) ).

cnf(refute_0_829,plain,
    multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))) = multiply(X_107,greatest_lower_bound(X_109,X_108)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)),greatest_lower_bound(X_109,X_108)) )],[refute_0_825,refute_0_828]) ).

cnf(refute_0_830,plain,
    ( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
    | greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).

cnf(refute_0_831,plain,
    greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_830]) ).

cnf(refute_0_832,plain,
    greatest_lower_bound(multiply(X_107,X_109),multiply(X_107,greatest_lower_bound(X_108,X_108))) = multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))),
    inference(subst,[],[refute_0_831:[bind(X,$fot(X_107)),bind(Y,$fot(X_109)),bind(Z,$fot(greatest_lower_bound(X_108,X_108)))]]) ).

cnf(refute_0_833,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X),
    inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_36,X_37)))]]) ).

cnf(refute_0_834,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X))]]) ).

cnf(refute_0_835,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),X) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)))]]) ).

cnf(refute_0_836,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),X) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)) )],[refute_0_834,refute_0_835]) ).

cnf(refute_0_837,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),X) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))
    | greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X))]]) ).

cnf(refute_0_838,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)
    | greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))) )],[refute_0_836,refute_0_837]) ).

cnf(refute_0_839,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)) )],[refute_0_833,refute_0_838]) ).

cnf(refute_0_840,plain,
    greatest_lower_bound(X,greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X)),
    inference(subst,[],[refute_0_839:[bind(X_36,$fot(multiply(X_107,X_108))),bind(X_37,$fot(multiply(X_107,X_109)))]]) ).

cnf(refute_0_841,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) != greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X))
    | greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109)) != multiply(X_107,greatest_lower_bound(X_108,X_109))
    | greatest_lower_bound(X,multiply(X_107,greatest_lower_bound(X_108,X_109))) = greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))),greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X))) ),[0,1],$fot(multiply(X_107,greatest_lower_bound(X_108,X_109)))]]) ).

cnf(refute_0_842,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) != greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X))
    | greatest_lower_bound(X,multiply(X_107,greatest_lower_bound(X_108,X_109))) = greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109)),multiply(X_107,greatest_lower_bound(X_108,X_109))) )],[refute_0_817,refute_0_841]) ).

cnf(refute_0_843,plain,
    greatest_lower_bound(X,multiply(X_107,greatest_lower_bound(X_108,X_109))) = greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))),greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X))) )],[refute_0_840,refute_0_842]) ).

cnf(refute_0_844,plain,
    ( greatest_lower_bound(X,multiply(X_107,greatest_lower_bound(X_108,X_109))) != greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X))
    | greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X)) = greatest_lower_bound(X,multiply(X_107,greatest_lower_bound(X_108,X_109))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,multiply(X_107,greatest_lower_bound(X_108,X_109))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X))))]]) ).

cnf(refute_0_845,plain,
    greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X)) = greatest_lower_bound(X,multiply(X_107,greatest_lower_bound(X_108,X_109))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,multiply(X_107,greatest_lower_bound(X_108,X_109))),greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_109),X))) )],[refute_0_843,refute_0_844]) ).

cnf(refute_0_846,plain,
    greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = greatest_lower_bound(multiply(X_107,X_109),multiply(X_107,greatest_lower_bound(X_108,X_108))),
    inference(subst,[],[refute_0_845:[bind(X,$fot(multiply(X_107,X_109))),bind(X_109,$fot(X_108))]]) ).

cnf(refute_0_847,plain,
    ( greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) != greatest_lower_bound(multiply(X_107,X_109),multiply(X_107,greatest_lower_bound(X_108,X_108)))
    | greatest_lower_bound(multiply(X_107,X_109),multiply(X_107,greatest_lower_bound(X_108,X_108))) != multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)))
    | greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_107,X_109),multiply(X_107,greatest_lower_bound(X_108,X_108))))),bind(Z0,$fot(multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)))))]]) ).

cnf(refute_0_848,plain,
    ( greatest_lower_bound(multiply(X_107,X_109),multiply(X_107,greatest_lower_bound(X_108,X_108))) != multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)))
    | greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))),greatest_lower_bound(multiply(X_107,X_109),multiply(X_107,greatest_lower_bound(X_108,X_108)))) )],[refute_0_846,refute_0_847]) ).

cnf(refute_0_849,plain,
    greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_109),multiply(X_107,greatest_lower_bound(X_108,X_108))),multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)))) )],[refute_0_832,refute_0_848]) ).

cnf(refute_0_850,plain,
    ( multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))) != multiply(X_107,greatest_lower_bound(X_109,X_108))
    | greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) != multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)))
    | greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = multiply(X_107,greatest_lower_bound(X_109,X_108)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))))),bind(Y0,$fot(multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))))),bind(Z0,$fot(multiply(X_107,greatest_lower_bound(X_109,X_108))))]]) ).

cnf(refute_0_851,plain,
    ( multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))) != multiply(X_107,greatest_lower_bound(X_109,X_108))
    | greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = multiply(X_107,greatest_lower_bound(X_109,X_108)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))),multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108)))) )],[refute_0_849,refute_0_850]) ).

cnf(refute_0_852,plain,
    greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) = multiply(X_107,greatest_lower_bound(X_109,X_108)),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_109,greatest_lower_bound(X_108,X_108))),multiply(X_107,greatest_lower_bound(X_109,X_108))) )],[refute_0_829,refute_0_851]) ).

cnf(refute_0_853,plain,
    ( greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) != multiply(X_107,greatest_lower_bound(X_108,X_109))
    | greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) != multiply(X_107,greatest_lower_bound(X_109,X_108))
    | multiply(X_107,greatest_lower_bound(X_109,X_108)) = multiply(X_107,greatest_lower_bound(X_108,X_109)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))),multiply(X_107,greatest_lower_bound(X_108,X_109))) ),[0],$fot(multiply(X_107,greatest_lower_bound(X_109,X_108)))]]) ).

cnf(refute_0_854,plain,
    ( greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))) != multiply(X_107,greatest_lower_bound(X_108,X_109))
    | multiply(X_107,greatest_lower_bound(X_109,X_108)) = multiply(X_107,greatest_lower_bound(X_108,X_109)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))),multiply(X_107,greatest_lower_bound(X_109,X_108))) )],[refute_0_852,refute_0_853]) ).

cnf(refute_0_855,plain,
    multiply(X_107,greatest_lower_bound(X_109,X_108)) = multiply(X_107,greatest_lower_bound(X_108,X_109)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,X_109))),multiply(X_107,greatest_lower_bound(X_108,X_109))) )],[refute_0_820,refute_0_854]) ).

cnf(refute_0_856,plain,
    ( multiply(X_107,greatest_lower_bound(X_109,X_108)) != multiply(X_107,greatest_lower_bound(X_108,X_109))
    | multiply(X_107,greatest_lower_bound(X_108,X_109)) = multiply(X_107,greatest_lower_bound(X_109,X_108)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_107,greatest_lower_bound(X_109,X_108)))),bind(Y0,$fot(multiply(X_107,greatest_lower_bound(X_108,X_109))))]]) ).

cnf(refute_0_857,plain,
    multiply(X_107,greatest_lower_bound(X_108,X_109)) = multiply(X_107,greatest_lower_bound(X_109,X_108)),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_109,X_108)),multiply(X_107,greatest_lower_bound(X_108,X_109))) )],[refute_0_855,refute_0_856]) ).

cnf(refute_0_858,plain,
    multiply(X_33,greatest_lower_bound(greatest_lower_bound(X_232,identity),identity)) = multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))),
    inference(subst,[],[refute_0_857:[bind(X_107,$fot(X_33)),bind(X_108,$fot(greatest_lower_bound(X_232,identity))),bind(X_109,$fot(identity))]]) ).

cnf(refute_0_859,plain,
    greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))) = multiply(X_33,greatest_lower_bound(greatest_lower_bound(X_232,identity),identity)),
    inference(subst,[],[refute_0_308:[bind(X_107,$fot(X_33)),bind(X_108,$fot(greatest_lower_bound(X_232,identity)))]]) ).

cnf(refute_0_860,plain,
    ( multiply(X_33,greatest_lower_bound(greatest_lower_bound(X_232,identity),identity)) != multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))
    | greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))) != multiply(X_33,greatest_lower_bound(greatest_lower_bound(X_232,identity),identity))
    | greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))) = multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))))),bind(Y0,$fot(multiply(X_33,greatest_lower_bound(greatest_lower_bound(X_232,identity),identity)))),bind(Z0,$fot(multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))))]]) ).

cnf(refute_0_861,plain,
    ( multiply(X_33,greatest_lower_bound(greatest_lower_bound(X_232,identity),identity)) != multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))
    | greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))) = multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))),multiply(X_33,greatest_lower_bound(greatest_lower_bound(X_232,identity),identity))) )],[refute_0_859,refute_0_860]) ).

cnf(refute_0_862,plain,
    greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))) = multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))),
    inference(resolve,[$cnf( $equal(multiply(X_33,greatest_lower_bound(greatest_lower_bound(X_232,identity),identity)),multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))) )],[refute_0_858,refute_0_861]) ).

cnf(refute_0_863,plain,
    greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,multiply(X_37,X_232))),
    inference(subst,[],[refute_0_839:[bind(X,$fot(multiply(X_37,X_232)))]]) ).

cnf(refute_0_864,plain,
    multiply(X_37,greatest_lower_bound(X_232,identity)) = greatest_lower_bound(X_37,multiply(X_37,X_232)),
    inference(subst,[],[refute_0_161:[bind(X_107,$fot(X_37)),bind(X_108,$fot(X_232))]]) ).

cnf(refute_0_865,plain,
    ( multiply(X_37,greatest_lower_bound(X_232,identity)) != greatest_lower_bound(X_37,multiply(X_37,X_232))
    | greatest_lower_bound(X_37,multiply(X_37,X_232)) = multiply(X_37,greatest_lower_bound(X_232,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_37,greatest_lower_bound(X_232,identity)))),bind(Y0,$fot(greatest_lower_bound(X_37,multiply(X_37,X_232))))]]) ).

cnf(refute_0_866,plain,
    greatest_lower_bound(X_37,multiply(X_37,X_232)) = multiply(X_37,greatest_lower_bound(X_232,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_37,greatest_lower_bound(X_232,identity)),greatest_lower_bound(X_37,multiply(X_37,X_232))) )],[refute_0_864,refute_0_865]) ).

cnf(refute_0_867,plain,
    ( greatest_lower_bound(X_37,multiply(X_37,X_232)) != multiply(X_37,greatest_lower_bound(X_232,identity))
    | greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,multiply(X_37,X_232)))
    | greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,multiply(X_37,greatest_lower_bound(X_232,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,greatest_lower_bound(X_37,multiply(X_37,X_232)))) ),[1,1],$fot(multiply(X_37,greatest_lower_bound(X_232,identity)))]]) ).

cnf(refute_0_868,plain,
    ( greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,multiply(X_37,X_232)))
    | greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,multiply(X_37,greatest_lower_bound(X_232,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,multiply(X_37,X_232)),multiply(X_37,greatest_lower_bound(X_232,identity))) )],[refute_0_866,refute_0_867]) ).

cnf(refute_0_869,plain,
    greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,multiply(X_37,greatest_lower_bound(X_232,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,greatest_lower_bound(X_37,multiply(X_37,X_232)))) )],[refute_0_863,refute_0_868]) ).

cnf(refute_0_870,plain,
    greatest_lower_bound(X_75,greatest_lower_bound(X_76,greatest_lower_bound(Y,X_76))) = greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)),
    inference(subst,[],[refute_0_839:[bind(X,$fot(X_75)),bind(X_36,$fot(X_76)),bind(X_37,$fot(greatest_lower_bound(Y,X_76)))]]) ).

cnf(refute_0_871,plain,
    greatest_lower_bound(X_76,greatest_lower_bound(Y,X_76)) = greatest_lower_bound(X_76,Y),
    inference(subst,[],[refute_0_794:[bind(X_23,$fot(X_76))]]) ).

cnf(refute_0_872,plain,
    ( greatest_lower_bound(X_75,greatest_lower_bound(X_76,greatest_lower_bound(Y,X_76))) != greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75))
    | greatest_lower_bound(X_76,greatest_lower_bound(Y,X_76)) != greatest_lower_bound(X_76,Y)
    | greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)) = greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_75,greatest_lower_bound(X_76,greatest_lower_bound(Y,X_76))),greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75))) ),[0,1],$fot(greatest_lower_bound(X_76,Y))]]) ).

cnf(refute_0_873,plain,
    ( greatest_lower_bound(X_75,greatest_lower_bound(X_76,greatest_lower_bound(Y,X_76))) != greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75))
    | greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)) = greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_76,greatest_lower_bound(Y,X_76)),greatest_lower_bound(X_76,Y)) )],[refute_0_871,refute_0_872]) ).

cnf(refute_0_874,plain,
    greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)) = greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_75,greatest_lower_bound(X_76,greatest_lower_bound(Y,X_76))),greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75))) )],[refute_0_870,refute_0_873]) ).

cnf(refute_0_875,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(greatest_lower_bound(Y,X_37)))]]) ).

cnf(refute_0_876,plain,
    greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37)) = greatest_lower_bound(X_37,Y),
    inference(subst,[],[refute_0_794:[bind(X_23,$fot(X_37))]]) ).

cnf(refute_0_877,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))
    | greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37)) != greatest_lower_bound(X_37,Y)
    | greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))),greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))) ),[0,1],$fot(greatest_lower_bound(X_37,Y))]]) ).

cnf(refute_0_878,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))
    | greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)) )],[refute_0_876,refute_0_877]) ).

cnf(refute_0_879,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))),greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))) )],[refute_0_875,refute_0_878]) ).

cnf(refute_0_880,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_881,plain,
    greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) = greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)))]]) ).

cnf(refute_0_882,plain,
    ( greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) != greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y))
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))
    | greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y))) ),[1,1],$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))]]) ).

cnf(refute_0_883,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))
    | greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y))) )],[refute_0_881,refute_0_882]) ).

cnf(refute_0_884,plain,
    greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y),greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) )],[refute_0_880,refute_0_883]) ).

cnf(refute_0_885,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))
    | greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) = greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)))),bind(Y0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))))]]) ).

cnf(refute_0_886,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) = greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))) )],[refute_0_839,refute_0_885]) ).

cnf(refute_0_887,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),
    inference(subst,[],[refute_0_886:[bind(X,$fot(X_37)),bind(X_36,$fot(greatest_lower_bound(X_36,X_37))),bind(X_37,$fot(Y))]]) ).

cnf(refute_0_888,plain,
    ( greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) != greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y))
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)))),bind(Y0,$fot(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)))),bind(Z0,$fot(greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))))]]) ).

cnf(refute_0_889,plain,
    ( greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y))) )],[refute_0_887,refute_0_888]) ).

cnf(refute_0_890,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))) )],[refute_0_884,refute_0_889]) ).

cnf(refute_0_891,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))
    | greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)))]]) ).

cnf(refute_0_892,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))
    | greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))) )],[refute_0_890,refute_0_891]) ).

cnf(refute_0_893,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))) )],[refute_0_879,refute_0_892]) ).

cnf(refute_0_894,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))
    | greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))),bind(Y0,$fot(greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))))]]) ).

cnf(refute_0_895,plain,
    greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))) )],[refute_0_893,refute_0_894]) ).

cnf(refute_0_896,plain,
    greatest_lower_bound(X_76,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))) = greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)),
    inference(subst,[],[refute_0_895:[bind(Y,$fot(X_75)),bind(X_36,$fot(Y)),bind(X_37,$fot(X_76))]]) ).

cnf(refute_0_897,plain,
    greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75) = greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(Y)),bind(Y,$fot(X_76)),bind(Z,$fot(X_75))]]) ).

cnf(refute_0_898,plain,
    greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) = greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)))]]) ).

cnf(refute_0_899,plain,
    ( greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) != greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75))
    | greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75) != greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))
    | greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) = greatest_lower_bound(X_76,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)),greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)))]]) ).

cnf(refute_0_900,plain,
    ( greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75) != greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))
    | greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) = greatest_lower_bound(X_76,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)),greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75))) )],[refute_0_898,refute_0_899]) ).

cnf(refute_0_901,plain,
    greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) = greatest_lower_bound(X_76,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75),greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))) )],[refute_0_897,refute_0_900]) ).

cnf(refute_0_902,plain,
    ( greatest_lower_bound(X_76,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))) != greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))
    | greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) != greatest_lower_bound(X_76,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)))
    | greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) = greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)))),bind(Y0,$fot(greatest_lower_bound(X_76,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))))]]) ).

cnf(refute_0_903,plain,
    ( greatest_lower_bound(X_76,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))) != greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))
    | greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) = greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)),greatest_lower_bound(X_76,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)))) )],[refute_0_901,refute_0_902]) ).

cnf(refute_0_904,plain,
    greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) = greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_76,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))),greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))) )],[refute_0_896,refute_0_903]) ).

cnf(refute_0_905,plain,
    ( greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)) != greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75))
    | greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)) != greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))
    | greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))) ),[0],$fot(greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)))]]) ).

cnf(refute_0_906,plain,
    ( greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)) != greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75))
    | greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75)),greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))) )],[refute_0_904,refute_0_905]) ).

cnf(refute_0_907,plain,
    greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)),greatest_lower_bound(X_76,greatest_lower_bound(greatest_lower_bound(Y,X_76),X_75))) )],[refute_0_874,refute_0_906]) ).

cnf(refute_0_908,plain,
    ( greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)) != greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))
    | greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)) = greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))))]]) ).

cnf(refute_0_909,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75)) = greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_75,greatest_lower_bound(X_76,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_76,X_75))) )],[refute_0_907,refute_0_908]) ).

cnf(refute_0_910,plain,
    greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_37,X_232))),
    inference(subst,[],[refute_0_909:[bind(Y,$fot(multiply(X_37,X_232))),bind(X_75,$fot(X_37)),bind(X_76,$fot(X_36))]]) ).

cnf(refute_0_911,plain,
    ( greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,multiply(X_37,greatest_lower_bound(X_232,identity)))
    | greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_37,X_232)))
    | greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_37,X_232))) = greatest_lower_bound(X_36,multiply(X_37,greatest_lower_bound(X_232,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,multiply(X_37,greatest_lower_bound(X_232,identity)))) ),[0],$fot(greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_37,X_232))))]]) ).

cnf(refute_0_912,plain,
    ( greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,multiply(X_37,greatest_lower_bound(X_232,identity)))
    | greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_37,X_232))) = greatest_lower_bound(X_36,multiply(X_37,greatest_lower_bound(X_232,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_37,X_232)))) )],[refute_0_910,refute_0_911]) ).

cnf(refute_0_913,plain,
    greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_37,X_232))) = greatest_lower_bound(X_36,multiply(X_37,greatest_lower_bound(X_232,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_37,X_232),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,multiply(X_37,greatest_lower_bound(X_232,identity)))) )],[refute_0_869,refute_0_912]) ).

cnf(refute_0_914,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) = greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))),
    inference(subst,[],[refute_0_913:[bind(X_36,$fot(X_33)),bind(X_37,$fot(X_33))]]) ).

cnf(refute_0_915,plain,
    ( greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))) != multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) != greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity)))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) = multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))))),bind(Y0,$fot(greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))))),bind(Z0,$fot(multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))))]]) ).

cnf(refute_0_916,plain,
    ( greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))) != multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) = multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))),greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity)))) )],[refute_0_914,refute_0_915]) ).

cnf(refute_0_917,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) = multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,multiply(X_33,greatest_lower_bound(X_232,identity))),multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))) )],[refute_0_862,refute_0_916]) ).

cnf(refute_0_918,plain,
    ( multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))) != multiply(X_33,greatest_lower_bound(identity,X_232))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) != multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) = multiply(X_33,greatest_lower_bound(identity,X_232)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))))),bind(Y0,$fot(multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))))),bind(Z0,$fot(multiply(X_33,greatest_lower_bound(identity,X_232))))]]) ).

cnf(refute_0_919,plain,
    ( multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))) != multiply(X_33,greatest_lower_bound(identity,X_232))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) = multiply(X_33,greatest_lower_bound(identity,X_232)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))),multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity)))) )],[refute_0_917,refute_0_918]) ).

cnf(refute_0_920,plain,
    greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) = multiply(X_33,greatest_lower_bound(identity,X_232)),
    inference(resolve,[$cnf( $equal(multiply(X_33,greatest_lower_bound(identity,greatest_lower_bound(X_232,identity))),multiply(X_33,greatest_lower_bound(identity,X_232))) )],[refute_0_813,refute_0_919]) ).

cnf(refute_0_921,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) != multiply(X_33,greatest_lower_bound(X_232,identity))
    | greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) != multiply(X_33,greatest_lower_bound(identity,X_232))
    | multiply(X_33,greatest_lower_bound(identity,X_232)) = multiply(X_33,greatest_lower_bound(X_232,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))),multiply(X_33,greatest_lower_bound(X_232,identity))) ),[0],$fot(multiply(X_33,greatest_lower_bound(identity,X_232)))]]) ).

cnf(refute_0_922,plain,
    ( greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))) != multiply(X_33,greatest_lower_bound(X_232,identity))
    | multiply(X_33,greatest_lower_bound(identity,X_232)) = multiply(X_33,greatest_lower_bound(X_232,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))),multiply(X_33,greatest_lower_bound(identity,X_232))) )],[refute_0_920,refute_0_921]) ).

cnf(refute_0_923,plain,
    multiply(X_33,greatest_lower_bound(identity,X_232)) = multiply(X_33,greatest_lower_bound(X_232,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_33,greatest_lower_bound(X_33,multiply(X_33,X_232))),multiply(X_33,greatest_lower_bound(X_232,identity))) )],[refute_0_808,refute_0_922]) ).

cnf(refute_0_924,plain,
    ( multiply(X_33,greatest_lower_bound(identity,X_232)) != multiply(X_33,greatest_lower_bound(X_232,identity))
    | multiply(X_33,greatest_lower_bound(X_232,identity)) = multiply(X_33,greatest_lower_bound(identity,X_232)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_33,greatest_lower_bound(identity,X_232)))),bind(Y0,$fot(multiply(X_33,greatest_lower_bound(X_232,identity))))]]) ).

cnf(refute_0_925,plain,
    multiply(X_33,greatest_lower_bound(X_232,identity)) = multiply(X_33,greatest_lower_bound(identity,X_232)),
    inference(resolve,[$cnf( $equal(multiply(X_33,greatest_lower_bound(identity,X_232)),multiply(X_33,greatest_lower_bound(X_232,identity))) )],[refute_0_923,refute_0_924]) ).

cnf(refute_0_926,plain,
    multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) = multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))),
    inference(subst,[],[refute_0_925:[bind(X_232,$fot(inverse(b))),bind(X_33,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_927,plain,
    ( multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))) != multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))
    | multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) != multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b)))
    | multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)))),bind(Y0,$fot(multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))))),bind(Z0,$fot(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_928,plain,
    ( multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))) != multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))
    | multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)),multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b)))) )],[refute_0_926,refute_0_927]) ).

cnf(refute_0_929,plain,
    multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),greatest_lower_bound(identity,inverse(b))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) )],[refute_0_783,refute_0_928]) ).

cnf(refute_0_930,plain,
    ( multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) != multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))
    | multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) != greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))
    | multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) = greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)),greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))) ),[0],$fot(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_931,plain,
    ( multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)) != greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))
    | multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) = greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) )],[refute_0_929,refute_0_930]) ).

cnf(refute_0_932,plain,
    multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) = greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),greatest_lower_bound(inverse(b),identity)),greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_461,refute_0_931]) ).

cnf(refute_0_933,plain,
    ( multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) != greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))
    | greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_934,plain,
    greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))),greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_932,refute_0_933]) ).

cnf(refute_0_935,plain,
    ( greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c)))) != multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))
    | least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))),multiply(c,inverse(greatest_lower_bound(a,c)))) ),[0,1],$fot(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_936,plain,
    ( least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c)))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) )],[refute_0_934,refute_0_935]) ).

cnf(refute_0_937,plain,
    least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(c,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),greatest_lower_bound(least_upper_bound(a,c),multiply(c,inverse(greatest_lower_bound(a,c))))),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_118,refute_0_936]) ).

cnf(refute_0_938,plain,
    least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))) = inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_136:[bind(X,$fot(a)),bind(Y,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_939,plain,
    multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_940,plain,
    ( multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))))
    | least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))) != inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))
    | multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))))) ),[1,1],$fot(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_941,plain,
    ( least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))) != inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))
    | multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))))) )],[refute_0_939,refute_0_940]) ).

cnf(refute_0_942,plain,
    multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) )],[refute_0_938,refute_0_941]) ).

cnf(refute_0_943,plain,
    multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) = least_upper_bound(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(least_upper_bound(X_278,X_277))),bind(Y,$fot(inverse(X_278)))]]) ).

cnf(refute_0_944,plain,
    multiply(least_upper_bound(X_278,X_277),inverse(X_278)) = least_upper_bound(identity,multiply(X_277,inverse(X_278))),
    inference(subst,[],[refute_0_170:[bind(X_116,$fot(X_277)),bind(X_87,$fot(X_278))]]) ).

cnf(refute_0_945,plain,
    ( multiply(least_upper_bound(X_278,X_277),inverse(X_278)) != least_upper_bound(identity,multiply(X_277,inverse(X_278)))
    | multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) != least_upper_bound(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z))
    | multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X_277,inverse(X_278))),multiply(least_upper_bound(X_278,X_277),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)),least_upper_bound(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z))) ),[1,0],$fot(least_upper_bound(identity,multiply(X_277,inverse(X_278))))]]) ).

cnf(refute_0_946,plain,
    ( multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) != least_upper_bound(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z))
    | multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X_277,inverse(X_278))),multiply(least_upper_bound(X_278,X_277),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))) )],[refute_0_944,refute_0_945]) ).

cnf(refute_0_947,plain,
    multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X_277,inverse(X_278))),multiply(least_upper_bound(X_278,X_277),Z)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)),least_upper_bound(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z))) )],[refute_0_943,refute_0_946]) ).

cnf(refute_0_948,plain,
    least_upper_bound(least_upper_bound(identity,multiply(X_277,inverse(X_278))),multiply(least_upper_bound(X_278,X_277),Z)) = least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z))),
    inference(subst,[],[refute_0_375:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_277,inverse(X_278)))),bind(Z,$fot(multiply(least_upper_bound(X_278,X_277),Z)))]]) ).

cnf(refute_0_949,plain,
    ( multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X_277,inverse(X_278))),multiply(least_upper_bound(X_278,X_277),Z))
    | least_upper_bound(least_upper_bound(identity,multiply(X_277,inverse(X_278))),multiply(least_upper_bound(X_278,X_277),Z)) != least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z)))
    | multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) = least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)),least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z)))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,multiply(X_277,inverse(X_278))),multiply(least_upper_bound(X_278,X_277),Z)))]]) ).

cnf(refute_0_950,plain,
    ( multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X_277,inverse(X_278))),multiply(least_upper_bound(X_278,X_277),Z))
    | multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) = least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,multiply(X_277,inverse(X_278))),multiply(least_upper_bound(X_278,X_277),Z)),least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z)))) )],[refute_0_948,refute_0_949]) ).

cnf(refute_0_951,plain,
    multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) = least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)),least_upper_bound(least_upper_bound(identity,multiply(X_277,inverse(X_278))),multiply(least_upper_bound(X_278,X_277),Z))) )],[refute_0_947,refute_0_950]) ).

cnf(refute_0_952,plain,
    ( multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) != least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z)))
    | least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z))) = multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z)))))]]) ).

cnf(refute_0_953,plain,
    least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z))) = multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),least_upper_bound(inverse(X_278),Z)),least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),Z)))) )],[refute_0_951,refute_0_952]) ).

cnf(refute_0_954,plain,
    least_upper_bound(identity,least_upper_bound(multiply(c,inverse(a)),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) = multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_953:[bind(Z,$fot(inverse(least_upper_bound(b,identity)))),bind(X_277,$fot(c)),bind(X_278,$fot(a))]]) ).

cnf(refute_0_955,plain,
    least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)) = least_upper_bound(least_upper_bound(identity,multiply(X_235,inverse(X_234))),Z),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_235,inverse(X_234))))]]) ).

cnf(refute_0_956,plain,
    multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))) = least_upper_bound(identity,multiply(X_235,inverse(X_234))),
    inference(subst,[],[refute_0_258:[bind(X,$fot(X_234)),bind(X_96,$fot(X_235))]]) ).

cnf(refute_0_957,plain,
    ( multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))) != least_upper_bound(identity,multiply(X_235,inverse(X_234)))
    | least_upper_bound(identity,multiply(X_235,inverse(X_234))) = multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_235,inverse(X_234)))))]]) ).

cnf(refute_0_958,plain,
    least_upper_bound(identity,multiply(X_235,inverse(X_234))) = multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))),
    inference(resolve,[$cnf( $equal(multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))),least_upper_bound(identity,multiply(X_235,inverse(X_234)))) )],[refute_0_956,refute_0_957]) ).

cnf(refute_0_959,plain,
    ( least_upper_bound(identity,multiply(X_235,inverse(X_234))) != multiply(X_235,inverse(greatest_lower_bound(X_234,X_235)))
    | least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X_235,inverse(X_234))),Z)
    | least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)) = least_upper_bound(multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X_235,inverse(X_234))),Z)) ),[1,0],$fot(multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))))]]) ).

cnf(refute_0_960,plain,
    ( least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)) != least_upper_bound(least_upper_bound(identity,multiply(X_235,inverse(X_234))),Z)
    | least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)) = least_upper_bound(multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))),Z) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_235,inverse(X_234))),multiply(X_235,inverse(greatest_lower_bound(X_234,X_235)))) )],[refute_0_958,refute_0_959]) ).

cnf(refute_0_961,plain,
    least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)) = least_upper_bound(multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))),Z),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)),least_upper_bound(least_upper_bound(identity,multiply(X_235,inverse(X_234))),Z)) )],[refute_0_955,refute_0_960]) ).

cnf(refute_0_962,plain,
    ( least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)) != least_upper_bound(multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))),Z)
    | least_upper_bound(multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))),Z) = least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)))),bind(Y0,$fot(least_upper_bound(multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))),Z)))]]) ).

cnf(refute_0_963,plain,
    least_upper_bound(multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))),Z) = least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_235,inverse(X_234)),Z)),least_upper_bound(multiply(X_235,inverse(greatest_lower_bound(X_234,X_235))),Z)) )],[refute_0_961,refute_0_962]) ).

cnf(refute_0_964,plain,
    least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = least_upper_bound(identity,least_upper_bound(multiply(c,inverse(a)),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),
    inference(subst,[],[refute_0_963:[bind(Z,$fot(multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),bind(X_234,$fot(a)),bind(X_235,$fot(c))]]) ).

cnf(refute_0_965,plain,
    ( least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != least_upper_bound(identity,least_upper_bound(multiply(c,inverse(a)),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))
    | least_upper_bound(identity,least_upper_bound(multiply(c,inverse(a)),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))))
    | least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(c,inverse(a)),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))))),bind(Z0,$fot(multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_966,plain,
    ( least_upper_bound(identity,least_upper_bound(multiply(c,inverse(a)),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))) != multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))))
    | least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),least_upper_bound(identity,least_upper_bound(multiply(c,inverse(a)),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))) )],[refute_0_964,refute_0_965]) ).

cnf(refute_0_967,plain,
    least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(c,inverse(a)),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity))))),multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))))) )],[refute_0_954,refute_0_966]) ).

cnf(refute_0_968,plain,
    ( multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))
    | least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))))
    | least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))))),bind(Y0,$fot(multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))))),bind(Z0,$fot(multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_969,plain,
    ( multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))
    | least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity))))) )],[refute_0_967,refute_0_968]) ).

cnf(refute_0_970,plain,
    least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),least_upper_bound(inverse(a),inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_942,refute_0_969]) ).

cnf(refute_0_971,plain,
    ( least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))
    | multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(a,c)))) ),[0],$fot(multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_972,plain,
    ( least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_970,refute_0_971]) ).

cnf(refute_0_973,plain,
    multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) = multiply(c,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(c,inverse(greatest_lower_bound(a,c))),multiply(least_upper_bound(a,c),inverse(least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_937,refute_0_972]) ).

cnf(refute_0_974,plain,
    ( multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) != multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))))
    | inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) = multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))))) ),[1,1,1],$fot(multiply(c,inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_975,plain,
    ( inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) != multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))))
    | inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) = multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_973,refute_0_974]) ).

cnf(refute_0_976,plain,
    inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) = multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))))) )],[refute_0_110,refute_0_975]) ).

cnf(refute_0_977,plain,
    inverse(b) = multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b)))),
    inference(subst,[],[refute_0_109:[bind(X_17,$fot(least_upper_bound(a,c))),bind(X_60,$fot(inverse(b)))]]) ).

cnf(refute_0_978,plain,
    ( multiply(least_upper_bound(a,c),inverse(b)) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | inverse(b) != multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b))))
    | inverse(b) = multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b))))) ),[1,1,1],$fot(multiply(c,inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_979,plain,
    ( inverse(b) != multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b))))
    | inverse(b) = multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(b)),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_458,refute_0_978]) ).

cnf(refute_0_980,plain,
    inverse(b) = multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(inverse(b),multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b))))) )],[refute_0_977,refute_0_979]) ).

cnf(refute_0_981,plain,
    greatest_lower_bound(c,c) = c,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(c))]]) ).

cnf(refute_0_982,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,c)) = greatest_lower_bound(a,greatest_lower_bound(c,c)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(c,c)))]]) ).

cnf(refute_0_983,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,c)) != greatest_lower_bound(a,greatest_lower_bound(c,c))
    | greatest_lower_bound(c,c) != c
    | greatest_lower_bound(a,greatest_lower_bound(c,c)) = greatest_lower_bound(a,c) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,c)),greatest_lower_bound(a,greatest_lower_bound(c,c))) ),[1,1],$fot(c)]]) ).

cnf(refute_0_984,plain,
    ( greatest_lower_bound(c,c) != c
    | greatest_lower_bound(a,greatest_lower_bound(c,c)) = greatest_lower_bound(a,c) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,c)),greatest_lower_bound(a,greatest_lower_bound(c,c))) )],[refute_0_982,refute_0_983]) ).

cnf(refute_0_985,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,c)) = greatest_lower_bound(a,c),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,c),c) )],[refute_0_981,refute_0_984]) ).

cnf(refute_0_986,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))))]]) ).

cnf(refute_0_987,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,c)) != greatest_lower_bound(a,c)
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))) != inverse(greatest_lower_bound(a,greatest_lower_bound(c,c)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))) = inverse(greatest_lower_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))),inverse(greatest_lower_bound(a,greatest_lower_bound(c,c)))) ),[1,0],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_988,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,c)) != greatest_lower_bound(a,c)
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))) = inverse(greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))),inverse(greatest_lower_bound(a,greatest_lower_bound(c,c)))) )],[refute_0_986,refute_0_987]) ).

cnf(refute_0_989,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))) = inverse(greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,c)),greatest_lower_bound(a,c)) )],[refute_0_985,refute_0_988]) ).

cnf(refute_0_990,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) = least_upper_bound(inverse(greatest_lower_bound(X_25,X_24)),inverse(Y)),
    inference(subst,[],[p12x_3:[bind(X,$fot(greatest_lower_bound(X_25,X_24)))]]) ).

cnf(refute_0_991,plain,
    ( inverse(greatest_lower_bound(X_25,X_24)) != inverse(greatest_lower_bound(X_24,X_25))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) != least_upper_bound(inverse(greatest_lower_bound(X_25,X_24)),inverse(Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) = least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)),least_upper_bound(inverse(greatest_lower_bound(X_25,X_24)),inverse(Y))) ),[1,0],$fot(inverse(greatest_lower_bound(X_24,X_25)))]]) ).

cnf(refute_0_992,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) != least_upper_bound(inverse(greatest_lower_bound(X_25,X_24)),inverse(Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) = least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_25,X_24)),inverse(greatest_lower_bound(X_24,X_25))) )],[refute_0_141,refute_0_991]) ).

cnf(refute_0_993,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) = least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)),least_upper_bound(inverse(greatest_lower_bound(X_25,X_24)),inverse(Y))) )],[refute_0_990,refute_0_992]) ).

cnf(refute_0_994,plain,
    greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y) = greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_25)),bind(Y,$fot(X_24)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_995,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) = inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)))]]) ).

cnf(refute_0_996,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y) != greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) != inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) = inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)),inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y))) ),[1,0],$fot(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y)))]]) ).

cnf(refute_0_997,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y) != greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) = inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)),inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y))) )],[refute_0_995,refute_0_996]) ).

cnf(refute_0_998,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) = inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y),greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) )],[refute_0_994,refute_0_997]) ).

cnf(refute_0_999,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) != inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y)))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) != least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)),least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y))) ),[0],$fot(inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))))]]) ).

cnf(refute_0_1000,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) != least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)),inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y)))) )],[refute_0_998,refute_0_999]) ).

cnf(refute_0_1001,plain,
    greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y) = greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_1002,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)) = inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)))]]) ).

cnf(refute_0_1003,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y) != greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)) != inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)),inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y))) ),[1,0],$fot(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))]]) ).

cnf(refute_0_1004,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y) != greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)),inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y))) )],[refute_0_1002,refute_0_1003]) ).

cnf(refute_0_1005,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y),greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) )],[refute_0_1001,refute_0_1004]) ).

cnf(refute_0_1006,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)) = inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)),
    inference(subst,[],[refute_0_136:[bind(X,$fot(greatest_lower_bound(X_24,X_25)))]]) ).

cnf(refute_0_1007,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))
    | least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)) != inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y))
    | least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)))),bind(Y0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)))),bind(Z0,$fot(inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))))]]) ).

cnf(refute_0_1008,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))
    | least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)),inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y))) )],[refute_0_1006,refute_0_1007]) ).

cnf(refute_0_1009,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),Y)),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))) )],[refute_0_1005,refute_0_1008]) ).

cnf(refute_0_1010,plain,
    ( inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) != least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y))
    | least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)))]]) ).

cnf(refute_0_1011,plain,
    ( inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) != least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y)),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))) )],[refute_0_1009,refute_0_1010]) ).

cnf(refute_0_1012,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)) != least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))),least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y))) )],[refute_0_1000,refute_0_1011]) ).

cnf(refute_0_1013,plain,
    inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_25,X_24),Y)),least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(Y))) )],[refute_0_993,refute_0_1012]) ).

cnf(refute_0_1014,plain,
    inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))) = inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178))),
    inference(subst,[],[refute_0_1013:[bind(Y,$fot(X_178)),bind(X_24,$fot(X_179)),bind(X_25,$fot(X_180))]]) ).

cnf(refute_0_1015,plain,
    greatest_lower_bound(X_178,X_179) = greatest_lower_bound(X_179,X_178),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_178)),bind(Y,$fot(X_179))]]) ).

cnf(refute_0_1016,plain,
    ( greatest_lower_bound(X_178,X_179) != greatest_lower_bound(X_179,X_178)
    | greatest_lower_bound(X_179,X_178) = greatest_lower_bound(X_178,X_179) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_178,X_179))),bind(Y0,$fot(greatest_lower_bound(X_179,X_178)))]]) ).

cnf(refute_0_1017,plain,
    greatest_lower_bound(X_179,X_178) = greatest_lower_bound(X_178,X_179),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_178,X_179),greatest_lower_bound(X_179,X_178)) )],[refute_0_1015,refute_0_1016]) ).

cnf(refute_0_1018,plain,
    ( greatest_lower_bound(X_179,X_178) != greatest_lower_bound(X_178,X_179)
    | inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))) != inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))
    | inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_178,X_179))) = inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))),inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))) ),[0,0,1],$fot(greatest_lower_bound(X_178,X_179))]]) ).

cnf(refute_0_1019,plain,
    ( inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))) != inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))
    | inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_178,X_179))) = inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_179,X_178),greatest_lower_bound(X_178,X_179)) )],[refute_0_1017,refute_0_1018]) ).

cnf(refute_0_1020,plain,
    inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_178,X_179))) = inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))),inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))) )],[refute_0_1014,refute_0_1019]) ).

cnf(refute_0_1021,plain,
    ( inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_178,X_179))) != inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))
    | inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178))) = inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_178,X_179))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_178,X_179))))),bind(Y0,$fot(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))))]]) ).

cnf(refute_0_1022,plain,
    inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178))) = inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_178,X_179))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_178,X_179))),inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))) )],[refute_0_1020,refute_0_1021]) ).

cnf(refute_0_1023,plain,
    inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))),
    inference(subst,[],[refute_0_1022:[bind(X_178,$fot(c)),bind(X_179,$fot(c)),bind(X_180,$fot(a))]]) ).

cnf(refute_0_1024,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))) != inverse(greatest_lower_bound(a,c))
    | inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(a,greatest_lower_bound(c,c)))
    | inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,c)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))))),bind(Y0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))))),bind(Z0,$fot(inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1025,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))) != inverse(greatest_lower_bound(a,c))
    | inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))),inverse(greatest_lower_bound(a,greatest_lower_bound(c,c)))) )],[refute_0_1023,refute_0_1024]) ).

cnf(refute_0_1026,plain,
    inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,c))),inverse(greatest_lower_bound(a,c))) )],[refute_0_989,refute_0_1025]) ).

cnf(refute_0_1027,plain,
    multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))) = multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))),
    introduced(tautology,[refl,[$fot(multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_1028,plain,
    ( multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))) != multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))))
    | inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(a,c))
    | multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))),multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))))) ),[1,1],$fot(inverse(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_1029,plain,
    ( inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(a,c))
    | multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))),multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))))) )],[refute_0_1027,refute_0_1028]) ).

cnf(refute_0_1030,plain,
    multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))) = multiply(c,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))),inverse(greatest_lower_bound(a,c))) )],[refute_0_1026,refute_0_1029]) ).

cnf(refute_0_1031,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) != multiply(X_99,inverse(greatest_lower_bound(Y,X_99)))
    | multiply(X_99,inverse(greatest_lower_bound(Y,X_99))) = multiply(X_99,inverse(greatest_lower_bound(X_99,Y))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_99,inverse(greatest_lower_bound(X_99,Y))))),bind(Y0,$fot(multiply(X_99,inverse(greatest_lower_bound(Y,X_99)))))]]) ).

cnf(refute_0_1032,plain,
    multiply(X_99,inverse(greatest_lower_bound(Y,X_99))) = multiply(X_99,inverse(greatest_lower_bound(X_99,Y))),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,Y))),multiply(X_99,inverse(greatest_lower_bound(Y,X_99)))) )],[refute_0_264,refute_0_1031]) ).

cnf(refute_0_1033,plain,
    multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))) = multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_1032:[bind(Y,$fot(greatest_lower_bound(a,c))),bind(X_99,$fot(c))]]) ).

cnf(refute_0_1034,plain,
    ( multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))) != multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))))
    | multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))),bind(Y0,$fot(multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))))),bind(Z0,$fot(multiply(c,inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_1035,plain,
    ( multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))) = multiply(c,inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))),multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c))))) )],[refute_0_1033,refute_0_1034]) ).

cnf(refute_0_1036,plain,
    multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))) = multiply(c,inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(c,greatest_lower_bound(a,c)))),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_1030,refute_0_1035]) ).

cnf(refute_0_1037,plain,
    multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),
    introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))))]]) ).

cnf(refute_0_1038,plain,
    ( multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))
    | multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) ),[1,1],$fot(multiply(c,inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_1039,plain,
    ( multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) )],[refute_0_1037,refute_0_1038]) ).

cnf(refute_0_1040,plain,
    multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_1036,refute_0_1039]) ).

cnf(refute_0_1041,plain,
    least_upper_bound(a,least_upper_bound(a,c)) = least_upper_bound(a,c),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(c)),bind(X_31,$fot(a))]]) ).

cnf(refute_0_1042,plain,
    least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(a,least_upper_bound(b,c)),
    introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(b,c)))]]) ).

cnf(refute_0_1043,plain,
    ( least_upper_bound(a,least_upper_bound(b,c)) != least_upper_bound(a,least_upper_bound(b,c))
    | least_upper_bound(b,c) != least_upper_bound(a,c)
    | least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(a,least_upper_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,c)),least_upper_bound(a,least_upper_bound(b,c))) ),[1,1],$fot(least_upper_bound(a,c))]]) ).

cnf(refute_0_1044,plain,
    ( least_upper_bound(b,c) != least_upper_bound(a,c)
    | least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(a,least_upper_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,c)),least_upper_bound(a,least_upper_bound(b,c))) )],[refute_0_1042,refute_0_1043]) ).

cnf(refute_0_1045,plain,
    least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(a,least_upper_bound(a,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,c),least_upper_bound(a,c)) )],[refute_0_173,refute_0_1044]) ).

cnf(refute_0_1046,plain,
    ( least_upper_bound(a,least_upper_bound(a,c)) != least_upper_bound(a,c)
    | least_upper_bound(a,least_upper_bound(b,c)) != least_upper_bound(a,least_upper_bound(a,c))
    | least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(a,c) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(b,c)))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(a,c)))),bind(Z0,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_1047,plain,
    ( least_upper_bound(a,least_upper_bound(a,c)) != least_upper_bound(a,c)
    | least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(a,c) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,c)),least_upper_bound(a,least_upper_bound(a,c))) )],[refute_0_1045,refute_0_1046]) ).

cnf(refute_0_1048,plain,
    least_upper_bound(a,least_upper_bound(b,c)) = least_upper_bound(a,c),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(a,c)),least_upper_bound(a,c)) )],[refute_0_1041,refute_0_1047]) ).

cnf(refute_0_1049,plain,
    inverse(least_upper_bound(a,least_upper_bound(b,c))) = inverse(least_upper_bound(a,least_upper_bound(b,c))),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(a,least_upper_bound(b,c))))]]) ).

cnf(refute_0_1050,plain,
    ( inverse(least_upper_bound(a,least_upper_bound(b,c))) != inverse(least_upper_bound(a,least_upper_bound(b,c)))
    | least_upper_bound(a,least_upper_bound(b,c)) != least_upper_bound(a,c)
    | inverse(least_upper_bound(a,least_upper_bound(b,c))) = inverse(least_upper_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(b,c))),inverse(least_upper_bound(a,least_upper_bound(b,c)))) ),[1,0],$fot(least_upper_bound(a,c))]]) ).

cnf(refute_0_1051,plain,
    ( least_upper_bound(a,least_upper_bound(b,c)) != least_upper_bound(a,c)
    | inverse(least_upper_bound(a,least_upper_bound(b,c))) = inverse(least_upper_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(b,c))),inverse(least_upper_bound(a,least_upper_bound(b,c)))) )],[refute_0_1049,refute_0_1050]) ).

cnf(refute_0_1052,plain,
    inverse(least_upper_bound(a,least_upper_bound(b,c))) = inverse(least_upper_bound(a,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,c)),least_upper_bound(a,c)) )],[refute_0_1048,refute_0_1051]) ).

cnf(refute_0_1053,plain,
    inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) = inverse(least_upper_bound(X_14,least_upper_bound(X_83,X_84))),
    inference(subst,[],[refute_0_58:[bind(X_15,$fot(least_upper_bound(X_83,X_84)))]]) ).

cnf(refute_0_1054,plain,
    least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) = least_upper_bound(least_upper_bound(X_43,least_upper_bound(Y,X_43)),X_45),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_43)),bind(Y,$fot(least_upper_bound(Y,X_43))),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_1055,plain,
    least_upper_bound(X_43,least_upper_bound(Y,X_43)) = least_upper_bound(X_43,Y),
    inference(subst,[],[refute_0_426:[bind(X_21,$fot(X_43))]]) ).

cnf(refute_0_1056,plain,
    ( least_upper_bound(X_43,least_upper_bound(Y,X_43)) != least_upper_bound(X_43,Y)
    | least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) != least_upper_bound(least_upper_bound(X_43,least_upper_bound(Y,X_43)),X_45)
    | least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) = least_upper_bound(least_upper_bound(X_43,Y),X_45) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)),least_upper_bound(least_upper_bound(X_43,least_upper_bound(Y,X_43)),X_45)) ),[1,0],$fot(least_upper_bound(X_43,Y))]]) ).

cnf(refute_0_1057,plain,
    ( least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) != least_upper_bound(least_upper_bound(X_43,least_upper_bound(Y,X_43)),X_45)
    | least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) = least_upper_bound(least_upper_bound(X_43,Y),X_45) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(Y,X_43)),least_upper_bound(X_43,Y)) )],[refute_0_1055,refute_0_1056]) ).

cnf(refute_0_1058,plain,
    least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) = least_upper_bound(least_upper_bound(X_43,Y),X_45),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)),least_upper_bound(least_upper_bound(X_43,least_upper_bound(Y,X_43)),X_45)) )],[refute_0_1054,refute_0_1057]) ).

cnf(refute_0_1059,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,least_upper_bound(Y,X_44))) = least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(least_upper_bound(Y,X_44)))]]) ).

cnf(refute_0_1060,plain,
    least_upper_bound(X_44,least_upper_bound(Y,X_44)) = least_upper_bound(X_44,Y),
    inference(subst,[],[refute_0_426:[bind(X_21,$fot(X_44))]]) ).

cnf(refute_0_1061,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,least_upper_bound(Y,X_44))) != least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44))
    | least_upper_bound(X_44,least_upper_bound(Y,X_44)) != least_upper_bound(X_44,Y)
    | least_upper_bound(X_43,least_upper_bound(X_44,Y)) = least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,least_upper_bound(Y,X_44))),least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44))) ),[0,1],$fot(least_upper_bound(X_44,Y))]]) ).

cnf(refute_0_1062,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,least_upper_bound(Y,X_44))) != least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44))
    | least_upper_bound(X_43,least_upper_bound(X_44,Y)) = least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(Y,X_44)),least_upper_bound(X_44,Y)) )],[refute_0_1060,refute_0_1061]) ).

cnf(refute_0_1063,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,Y)) = least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,least_upper_bound(Y,X_44))),least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44))) )],[refute_0_1059,refute_0_1062]) ).

cnf(refute_0_1064,plain,
    least_upper_bound(least_upper_bound(X_43,X_44),Y) = least_upper_bound(X_43,least_upper_bound(X_44,Y)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_1065,plain,
    least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)) = least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)))]]) ).

cnf(refute_0_1066,plain,
    ( least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)) != least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y))
    | least_upper_bound(least_upper_bound(X_43,X_44),Y) != least_upper_bound(X_43,least_upper_bound(X_44,Y))
    | least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)) = least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)),least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y))) ),[1,1],$fot(least_upper_bound(X_43,least_upper_bound(X_44,Y)))]]) ).

cnf(refute_0_1067,plain,
    ( least_upper_bound(least_upper_bound(X_43,X_44),Y) != least_upper_bound(X_43,least_upper_bound(X_44,Y))
    | least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)) = least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)),least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y))) )],[refute_0_1065,refute_0_1066]) ).

cnf(refute_0_1068,plain,
    least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)) = least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_43,X_44),Y),least_upper_bound(X_43,least_upper_bound(X_44,Y))) )],[refute_0_1064,refute_0_1067]) ).

cnf(refute_0_1069,plain,
    least_upper_bound(X,least_upper_bound(X_43,X_44)) = least_upper_bound(least_upper_bound(X_43,X_44),X),
    inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_43,X_44)))]]) ).

cnf(refute_0_1070,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,X)) = least_upper_bound(least_upper_bound(X_43,X_44),X),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(X))]]) ).

cnf(refute_0_1071,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,X)) != least_upper_bound(least_upper_bound(X_43,X_44),X)
    | least_upper_bound(least_upper_bound(X_43,X_44),X) = least_upper_bound(X_43,least_upper_bound(X_44,X)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_43,least_upper_bound(X_44,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_43,X_44),X)))]]) ).

cnf(refute_0_1072,plain,
    least_upper_bound(least_upper_bound(X_43,X_44),X) = least_upper_bound(X_43,least_upper_bound(X_44,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,X)),least_upper_bound(least_upper_bound(X_43,X_44),X)) )],[refute_0_1070,refute_0_1071]) ).

cnf(refute_0_1073,plain,
    ( least_upper_bound(X,least_upper_bound(X_43,X_44)) != least_upper_bound(least_upper_bound(X_43,X_44),X)
    | least_upper_bound(least_upper_bound(X_43,X_44),X) != least_upper_bound(X_43,least_upper_bound(X_44,X))
    | least_upper_bound(X,least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_43,X_44)),least_upper_bound(X_43,least_upper_bound(X_44,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_43,X_44),X))]]) ).

cnf(refute_0_1074,plain,
    ( least_upper_bound(X,least_upper_bound(X_43,X_44)) != least_upper_bound(least_upper_bound(X_43,X_44),X)
    | least_upper_bound(X,least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_43,X_44),X),least_upper_bound(X_43,least_upper_bound(X_44,X))) )],[refute_0_1072,refute_0_1073]) ).

cnf(refute_0_1075,plain,
    least_upper_bound(X,least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_43,X_44)),least_upper_bound(least_upper_bound(X_43,X_44),X)) )],[refute_0_1069,refute_0_1074]) ).

cnf(refute_0_1076,plain,
    ( least_upper_bound(X,least_upper_bound(X_43,X_44)) != least_upper_bound(X_43,least_upper_bound(X_44,X))
    | least_upper_bound(X_43,least_upper_bound(X_44,X)) = least_upper_bound(X,least_upper_bound(X_43,X_44)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_43,X_44)))),bind(Y0,$fot(least_upper_bound(X_43,least_upper_bound(X_44,X))))]]) ).

cnf(refute_0_1077,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,X)) = least_upper_bound(X,least_upper_bound(X_43,X_44)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_43,X_44)),least_upper_bound(X_43,least_upper_bound(X_44,X))) )],[refute_0_1075,refute_0_1076]) ).

cnf(refute_0_1078,plain,
    least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)) = least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)),
    inference(subst,[],[refute_0_1077:[bind(X,$fot(X_44)),bind(X_43,$fot(least_upper_bound(X_43,X_44))),bind(X_44,$fot(Y))]]) ).

cnf(refute_0_1079,plain,
    ( least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)) != least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y)))
    | least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)) != least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y))
    | least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)) = least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)))),bind(Y0,$fot(least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)))),bind(Z0,$fot(least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y)))))]]) ).

cnf(refute_0_1080,plain,
    ( least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)) != least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y)))
    | least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)) = least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)),least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y))) )],[refute_0_1078,refute_0_1079]) ).

cnf(refute_0_1081,plain,
    least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)) = least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(least_upper_bound(X_43,X_44),Y)),least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y)))) )],[refute_0_1068,refute_0_1080]) ).

cnf(refute_0_1082,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,Y)) != least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44))
    | least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)) != least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y)))
    | least_upper_bound(X_43,least_upper_bound(X_44,Y)) = least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_43,least_upper_bound(X_44,Y)),least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)))]]) ).

cnf(refute_0_1083,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,Y)) != least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44))
    | least_upper_bound(X_43,least_upper_bound(X_44,Y)) = least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44)),least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y)))) )],[refute_0_1081,refute_0_1082]) ).

cnf(refute_0_1084,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,Y)) = least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,Y)),least_upper_bound(least_upper_bound(X_43,X_44),least_upper_bound(Y,X_44))) )],[refute_0_1063,refute_0_1083]) ).

cnf(refute_0_1085,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,Y)) != least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y)))
    | least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y))) = least_upper_bound(X_43,least_upper_bound(X_44,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_43,least_upper_bound(X_44,Y)))),bind(Y0,$fot(least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y)))))]]) ).

cnf(refute_0_1086,plain,
    least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y))) = least_upper_bound(X_43,least_upper_bound(X_44,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,Y)),least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_44,Y)))) )],[refute_0_1084,refute_0_1085]) ).

cnf(refute_0_1087,plain,
    least_upper_bound(X_43,least_upper_bound(Y,least_upper_bound(X_43,X_45))) = least_upper_bound(Y,least_upper_bound(X_43,X_45)),
    inference(subst,[],[refute_0_1086:[bind(Y,$fot(X_45)),bind(X_43,$fot(Y)),bind(X_44,$fot(X_43))]]) ).

cnf(refute_0_1088,plain,
    least_upper_bound(least_upper_bound(Y,X_43),X_45) = least_upper_bound(Y,least_upper_bound(X_43,X_45)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(Y)),bind(Y,$fot(X_43)),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_1089,plain,
    least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) = least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)))]]) ).

cnf(refute_0_1090,plain,
    ( least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) != least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45))
    | least_upper_bound(least_upper_bound(Y,X_43),X_45) != least_upper_bound(Y,least_upper_bound(X_43,X_45))
    | least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) = least_upper_bound(X_43,least_upper_bound(Y,least_upper_bound(X_43,X_45))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)),least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_43,X_45)))]]) ).

cnf(refute_0_1091,plain,
    ( least_upper_bound(least_upper_bound(Y,X_43),X_45) != least_upper_bound(Y,least_upper_bound(X_43,X_45))
    | least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) = least_upper_bound(X_43,least_upper_bound(Y,least_upper_bound(X_43,X_45))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)),least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45))) )],[refute_0_1089,refute_0_1090]) ).

cnf(refute_0_1092,plain,
    least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) = least_upper_bound(X_43,least_upper_bound(Y,least_upper_bound(X_43,X_45))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_43),X_45),least_upper_bound(Y,least_upper_bound(X_43,X_45))) )],[refute_0_1088,refute_0_1091]) ).

cnf(refute_0_1093,plain,
    ( least_upper_bound(X_43,least_upper_bound(Y,least_upper_bound(X_43,X_45))) != least_upper_bound(Y,least_upper_bound(X_43,X_45))
    | least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) != least_upper_bound(X_43,least_upper_bound(Y,least_upper_bound(X_43,X_45)))
    | least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) = least_upper_bound(Y,least_upper_bound(X_43,X_45)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)))),bind(Y0,$fot(least_upper_bound(X_43,least_upper_bound(Y,least_upper_bound(X_43,X_45))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_43,X_45))))]]) ).

cnf(refute_0_1094,plain,
    ( least_upper_bound(X_43,least_upper_bound(Y,least_upper_bound(X_43,X_45))) != least_upper_bound(Y,least_upper_bound(X_43,X_45))
    | least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) = least_upper_bound(Y,least_upper_bound(X_43,X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)),least_upper_bound(X_43,least_upper_bound(Y,least_upper_bound(X_43,X_45)))) )],[refute_0_1092,refute_0_1093]) ).

cnf(refute_0_1095,plain,
    least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) = least_upper_bound(Y,least_upper_bound(X_43,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(Y,least_upper_bound(X_43,X_45))),least_upper_bound(Y,least_upper_bound(X_43,X_45))) )],[refute_0_1087,refute_0_1094]) ).

cnf(refute_0_1096,plain,
    ( least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) != least_upper_bound(Y,least_upper_bound(X_43,X_45))
    | least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) != least_upper_bound(least_upper_bound(X_43,Y),X_45)
    | least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(least_upper_bound(X_43,Y),X_45) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)),least_upper_bound(least_upper_bound(X_43,Y),X_45)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_43,X_45)))]]) ).

cnf(refute_0_1097,plain,
    ( least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) != least_upper_bound(least_upper_bound(X_43,Y),X_45)
    | least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(least_upper_bound(X_43,Y),X_45) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)),least_upper_bound(Y,least_upper_bound(X_43,X_45))) )],[refute_0_1095,refute_0_1096]) ).

cnf(refute_0_1098,plain,
    least_upper_bound(least_upper_bound(X_43,Y),X_45) = least_upper_bound(X_43,least_upper_bound(Y,X_45)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(X_43)),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_1099,plain,
    ( least_upper_bound(Y,least_upper_bound(X_43,X_45)) != least_upper_bound(least_upper_bound(X_43,Y),X_45)
    | least_upper_bound(least_upper_bound(X_43,Y),X_45) != least_upper_bound(X_43,least_upper_bound(Y,X_45))
    | least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(X_43,least_upper_bound(Y,X_45)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_43,X_45)),least_upper_bound(X_43,least_upper_bound(Y,X_45))) ),[0],$fot(least_upper_bound(least_upper_bound(X_43,Y),X_45))]]) ).

cnf(refute_0_1100,plain,
    ( least_upper_bound(Y,least_upper_bound(X_43,X_45)) != least_upper_bound(least_upper_bound(X_43,Y),X_45)
    | least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(X_43,least_upper_bound(Y,X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_43,Y),X_45),least_upper_bound(X_43,least_upper_bound(Y,X_45))) )],[refute_0_1098,refute_0_1099]) ).

cnf(refute_0_1101,plain,
    ( least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)) != least_upper_bound(least_upper_bound(X_43,Y),X_45)
    | least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(X_43,least_upper_bound(Y,X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_43,X_45)),least_upper_bound(least_upper_bound(X_43,Y),X_45)) )],[refute_0_1097,refute_0_1100]) ).

cnf(refute_0_1102,plain,
    least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(X_43,least_upper_bound(Y,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(Y,X_43),X_45)),least_upper_bound(least_upper_bound(X_43,Y),X_45)) )],[refute_0_1058,refute_0_1101]) ).

cnf(refute_0_1103,plain,
    least_upper_bound(X_14,least_upper_bound(X_83,X_84)) = least_upper_bound(X_83,least_upper_bound(X_14,X_84)),
    inference(subst,[],[refute_0_1102:[bind(Y,$fot(X_14)),bind(X_43,$fot(X_83)),bind(X_45,$fot(X_84))]]) ).

cnf(refute_0_1104,plain,
    ( inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) != inverse(least_upper_bound(X_14,least_upper_bound(X_83,X_84)))
    | least_upper_bound(X_14,least_upper_bound(X_83,X_84)) != least_upper_bound(X_83,least_upper_bound(X_14,X_84))
    | inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) = inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)),inverse(least_upper_bound(X_14,least_upper_bound(X_83,X_84)))) ),[1,0],$fot(least_upper_bound(X_83,least_upper_bound(X_14,X_84)))]]) ).

cnf(refute_0_1105,plain,
    ( inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) != inverse(least_upper_bound(X_14,least_upper_bound(X_83,X_84)))
    | inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) = inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_14,least_upper_bound(X_83,X_84)),least_upper_bound(X_83,least_upper_bound(X_14,X_84))) )],[refute_0_1103,refute_0_1104]) ).

cnf(refute_0_1106,plain,
    inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) = inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)),inverse(least_upper_bound(X_14,least_upper_bound(X_83,X_84)))) )],[refute_0_1053,refute_0_1105]) ).

cnf(refute_0_1107,plain,
    least_upper_bound(least_upper_bound(X_83,X_84),X_14) = least_upper_bound(X_83,least_upper_bound(X_84,X_14)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(X_83)),bind(Y,$fot(X_84)),bind(Z,$fot(X_14))]]) ).

cnf(refute_0_1108,plain,
    inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) = inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)))]]) ).

cnf(refute_0_1109,plain,
    ( inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) != inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14))
    | least_upper_bound(least_upper_bound(X_83,X_84),X_14) != least_upper_bound(X_83,least_upper_bound(X_84,X_14))
    | inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) = inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)),inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14))) ),[1,0],$fot(least_upper_bound(X_83,least_upper_bound(X_84,X_14)))]]) ).

cnf(refute_0_1110,plain,
    ( least_upper_bound(least_upper_bound(X_83,X_84),X_14) != least_upper_bound(X_83,least_upper_bound(X_84,X_14))
    | inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) = inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)),inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14))) )],[refute_0_1108,refute_0_1109]) ).

cnf(refute_0_1111,plain,
    inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) = inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_83,X_84),X_14),least_upper_bound(X_83,least_upper_bound(X_84,X_14))) )],[refute_0_1107,refute_0_1110]) ).

cnf(refute_0_1112,plain,
    ( inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) != inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84)))
    | inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) != inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14)))
    | inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))) = inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)),inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84)))) ),[0],$fot(inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))))]]) ).

cnf(refute_0_1113,plain,
    ( inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)) != inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84)))
    | inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))) = inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)),inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14)))) )],[refute_0_1111,refute_0_1112]) ).

cnf(refute_0_1114,plain,
    inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))) = inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_84),X_14)),inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84)))) )],[refute_0_1106,refute_0_1113]) ).

cnf(refute_0_1115,plain,
    ( inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))) != inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84)))
    | inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84))) = inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))))),bind(Y0,$fot(inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84)))))]]) ).

cnf(refute_0_1116,plain,
    inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84))) = inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_83,least_upper_bound(X_84,X_14))),inverse(least_upper_bound(X_83,least_upper_bound(X_14,X_84)))) )],[refute_0_1114,refute_0_1115]) ).

cnf(refute_0_1117,plain,
    inverse(least_upper_bound(a,least_upper_bound(c,b))) = inverse(least_upper_bound(a,least_upper_bound(b,c))),
    inference(subst,[],[refute_0_1116:[bind(X_14,$fot(c)),bind(X_83,$fot(a)),bind(X_84,$fot(b))]]) ).

cnf(refute_0_1118,plain,
    inverse(least_upper_bound(least_upper_bound(c,X_85),a)) = inverse(least_upper_bound(a,least_upper_bound(c,X_85))),
    inference(subst,[],[refute_0_58:[bind(X_14,$fot(a)),bind(X_15,$fot(least_upper_bound(c,X_85)))]]) ).

cnf(refute_0_1119,plain,
    least_upper_bound(b,least_upper_bound(c,X_45)) = least_upper_bound(least_upper_bound(b,c),X_45),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(b)),bind(Y,$fot(c)),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_1120,plain,
    ( least_upper_bound(b,c) != least_upper_bound(a,c)
    | least_upper_bound(b,least_upper_bound(c,X_45)) != least_upper_bound(least_upper_bound(b,c),X_45)
    | least_upper_bound(b,least_upper_bound(c,X_45)) = least_upper_bound(least_upper_bound(a,c),X_45) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_45)),least_upper_bound(least_upper_bound(b,c),X_45)) ),[1,0],$fot(least_upper_bound(a,c))]]) ).

cnf(refute_0_1121,plain,
    ( least_upper_bound(b,least_upper_bound(c,X_45)) != least_upper_bound(least_upper_bound(b,c),X_45)
    | least_upper_bound(b,least_upper_bound(c,X_45)) = least_upper_bound(least_upper_bound(a,c),X_45) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,c),least_upper_bound(a,c)) )],[refute_0_173,refute_0_1120]) ).

cnf(refute_0_1122,plain,
    least_upper_bound(b,least_upper_bound(c,X_45)) = least_upper_bound(least_upper_bound(a,c),X_45),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_45)),least_upper_bound(least_upper_bound(b,c),X_45)) )],[refute_0_1119,refute_0_1121]) ).

cnf(refute_0_1123,plain,
    least_upper_bound(least_upper_bound(a,c),X_45) = least_upper_bound(a,least_upper_bound(c,X_45)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_1124,plain,
    ( least_upper_bound(b,least_upper_bound(c,X_45)) != least_upper_bound(least_upper_bound(a,c),X_45)
    | least_upper_bound(least_upper_bound(a,c),X_45) != least_upper_bound(a,least_upper_bound(c,X_45))
    | least_upper_bound(b,least_upper_bound(c,X_45)) = least_upper_bound(a,least_upper_bound(c,X_45)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(b,least_upper_bound(c,X_45)),least_upper_bound(a,least_upper_bound(c,X_45))) ),[0],$fot(least_upper_bound(least_upper_bound(a,c),X_45))]]) ).

cnf(refute_0_1125,plain,
    ( least_upper_bound(b,least_upper_bound(c,X_45)) != least_upper_bound(least_upper_bound(a,c),X_45)
    | least_upper_bound(b,least_upper_bound(c,X_45)) = least_upper_bound(a,least_upper_bound(c,X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,c),X_45),least_upper_bound(a,least_upper_bound(c,X_45))) )],[refute_0_1123,refute_0_1124]) ).

cnf(refute_0_1126,plain,
    least_upper_bound(b,least_upper_bound(c,X_45)) = least_upper_bound(a,least_upper_bound(c,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_45)),least_upper_bound(least_upper_bound(a,c),X_45)) )],[refute_0_1122,refute_0_1125]) ).

cnf(refute_0_1127,plain,
    least_upper_bound(b,least_upper_bound(c,X_79)) = least_upper_bound(a,least_upper_bound(c,X_79)),
    inference(subst,[],[refute_0_1126:[bind(X_45,$fot(X_79))]]) ).

cnf(refute_0_1128,plain,
    least_upper_bound(X_79,c) = least_upper_bound(c,X_79),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_79)),bind(Y,$fot(c))]]) ).

cnf(refute_0_1129,plain,
    ( least_upper_bound(X_79,c) != least_upper_bound(c,X_79)
    | least_upper_bound(c,X_79) = least_upper_bound(X_79,c) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_79,c))),bind(Y0,$fot(least_upper_bound(c,X_79)))]]) ).

cnf(refute_0_1130,plain,
    least_upper_bound(c,X_79) = least_upper_bound(X_79,c),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_79,c),least_upper_bound(c,X_79)) )],[refute_0_1128,refute_0_1129]) ).

cnf(refute_0_1131,plain,
    ( least_upper_bound(b,least_upper_bound(c,X_79)) != least_upper_bound(a,least_upper_bound(c,X_79))
    | least_upper_bound(c,X_79) != least_upper_bound(X_79,c)
    | least_upper_bound(b,least_upper_bound(c,X_79)) = least_upper_bound(a,least_upper_bound(X_79,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_79)),least_upper_bound(a,least_upper_bound(c,X_79))) ),[1,1],$fot(least_upper_bound(X_79,c))]]) ).

cnf(refute_0_1132,plain,
    ( least_upper_bound(b,least_upper_bound(c,X_79)) != least_upper_bound(a,least_upper_bound(c,X_79))
    | least_upper_bound(b,least_upper_bound(c,X_79)) = least_upper_bound(a,least_upper_bound(X_79,c)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(c,X_79),least_upper_bound(X_79,c)) )],[refute_0_1130,refute_0_1131]) ).

cnf(refute_0_1133,plain,
    least_upper_bound(b,least_upper_bound(c,X_79)) = least_upper_bound(a,least_upper_bound(X_79,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_79)),least_upper_bound(a,least_upper_bound(c,X_79))) )],[refute_0_1127,refute_0_1132]) ).

cnf(refute_0_1134,plain,
    ( least_upper_bound(b,least_upper_bound(c,X_79)) != least_upper_bound(a,least_upper_bound(X_79,c))
    | least_upper_bound(b,least_upper_bound(c,X_79)) != least_upper_bound(a,least_upper_bound(c,X_79))
    | least_upper_bound(a,least_upper_bound(c,X_79)) = least_upper_bound(a,least_upper_bound(X_79,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_79)),least_upper_bound(a,least_upper_bound(X_79,c))) ),[0],$fot(least_upper_bound(a,least_upper_bound(c,X_79)))]]) ).

cnf(refute_0_1135,plain,
    ( least_upper_bound(b,least_upper_bound(c,X_79)) != least_upper_bound(a,least_upper_bound(X_79,c))
    | least_upper_bound(a,least_upper_bound(c,X_79)) = least_upper_bound(a,least_upper_bound(X_79,c)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_79)),least_upper_bound(a,least_upper_bound(c,X_79))) )],[refute_0_1127,refute_0_1134]) ).

cnf(refute_0_1136,plain,
    least_upper_bound(a,least_upper_bound(c,X_79)) = least_upper_bound(a,least_upper_bound(X_79,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(c,X_79)),least_upper_bound(a,least_upper_bound(X_79,c))) )],[refute_0_1133,refute_0_1135]) ).

cnf(refute_0_1137,plain,
    least_upper_bound(a,least_upper_bound(X_79,c)) = least_upper_bound(X_79,least_upper_bound(a,c)),
    inference(subst,[],[refute_0_1102:[bind(Y,$fot(a)),bind(X_43,$fot(X_79)),bind(X_45,$fot(c))]]) ).

cnf(refute_0_1138,plain,
    ( least_upper_bound(a,least_upper_bound(X_79,c)) != least_upper_bound(X_79,least_upper_bound(a,c))
    | least_upper_bound(a,least_upper_bound(c,X_79)) != least_upper_bound(a,least_upper_bound(X_79,c))
    | least_upper_bound(a,least_upper_bound(c,X_79)) = least_upper_bound(X_79,least_upper_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,X_79)),least_upper_bound(a,least_upper_bound(X_79,c))) ),[1],$fot(least_upper_bound(X_79,least_upper_bound(a,c)))]]) ).

cnf(refute_0_1139,plain,
    ( least_upper_bound(a,least_upper_bound(c,X_79)) != least_upper_bound(a,least_upper_bound(X_79,c))
    | least_upper_bound(a,least_upper_bound(c,X_79)) = least_upper_bound(X_79,least_upper_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_79,c)),least_upper_bound(X_79,least_upper_bound(a,c))) )],[refute_0_1137,refute_0_1138]) ).

cnf(refute_0_1140,plain,
    least_upper_bound(a,least_upper_bound(c,X_79)) = least_upper_bound(X_79,least_upper_bound(a,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,X_79)),least_upper_bound(a,least_upper_bound(X_79,c))) )],[refute_0_1136,refute_0_1139]) ).

cnf(refute_0_1141,plain,
    least_upper_bound(a,least_upper_bound(c,X_85)) = least_upper_bound(X_85,least_upper_bound(a,c)),
    inference(subst,[],[refute_0_1140:[bind(X_79,$fot(X_85))]]) ).

cnf(refute_0_1142,plain,
    ( inverse(least_upper_bound(least_upper_bound(c,X_85),a)) != inverse(least_upper_bound(a,least_upper_bound(c,X_85)))
    | least_upper_bound(a,least_upper_bound(c,X_85)) != least_upper_bound(X_85,least_upper_bound(a,c))
    | inverse(least_upper_bound(least_upper_bound(c,X_85),a)) = inverse(least_upper_bound(X_85,least_upper_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(c,X_85),a)),inverse(least_upper_bound(a,least_upper_bound(c,X_85)))) ),[1,0],$fot(least_upper_bound(X_85,least_upper_bound(a,c)))]]) ).

cnf(refute_0_1143,plain,
    ( inverse(least_upper_bound(least_upper_bound(c,X_85),a)) != inverse(least_upper_bound(a,least_upper_bound(c,X_85)))
    | inverse(least_upper_bound(least_upper_bound(c,X_85),a)) = inverse(least_upper_bound(X_85,least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,X_85)),least_upper_bound(X_85,least_upper_bound(a,c))) )],[refute_0_1141,refute_0_1142]) ).

cnf(refute_0_1144,plain,
    inverse(least_upper_bound(least_upper_bound(c,X_85),a)) = inverse(least_upper_bound(X_85,least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(c,X_85),a)),inverse(least_upper_bound(a,least_upper_bound(c,X_85)))) )],[refute_0_1118,refute_0_1143]) ).

cnf(refute_0_1145,plain,
    ( inverse(least_upper_bound(least_upper_bound(c,X_85),a)) != inverse(least_upper_bound(X_85,least_upper_bound(a,c)))
    | inverse(least_upper_bound(least_upper_bound(c,X_85),a)) != inverse(least_upper_bound(a,least_upper_bound(c,X_85)))
    | inverse(least_upper_bound(a,least_upper_bound(c,X_85))) = inverse(least_upper_bound(X_85,least_upper_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(c,X_85),a)),inverse(least_upper_bound(X_85,least_upper_bound(a,c)))) ),[0],$fot(inverse(least_upper_bound(a,least_upper_bound(c,X_85))))]]) ).

cnf(refute_0_1146,plain,
    ( inverse(least_upper_bound(least_upper_bound(c,X_85),a)) != inverse(least_upper_bound(X_85,least_upper_bound(a,c)))
    | inverse(least_upper_bound(a,least_upper_bound(c,X_85))) = inverse(least_upper_bound(X_85,least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(c,X_85),a)),inverse(least_upper_bound(a,least_upper_bound(c,X_85)))) )],[refute_0_1118,refute_0_1145]) ).

cnf(refute_0_1147,plain,
    inverse(least_upper_bound(a,least_upper_bound(c,X_85))) = inverse(least_upper_bound(X_85,least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(c,X_85),a)),inverse(least_upper_bound(X_85,least_upper_bound(a,c)))) )],[refute_0_1144,refute_0_1146]) ).

cnf(refute_0_1148,plain,
    ( inverse(least_upper_bound(a,least_upper_bound(c,X_85))) != inverse(least_upper_bound(X_85,least_upper_bound(a,c)))
    | inverse(least_upper_bound(X_85,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,X_85))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(least_upper_bound(a,least_upper_bound(c,X_85))))),bind(Y0,$fot(inverse(least_upper_bound(X_85,least_upper_bound(a,c)))))]]) ).

cnf(refute_0_1149,plain,
    inverse(least_upper_bound(X_85,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,X_85))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(c,X_85))),inverse(least_upper_bound(X_85,least_upper_bound(a,c)))) )],[refute_0_1147,refute_0_1148]) ).

cnf(refute_0_1150,plain,
    inverse(least_upper_bound(b,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(c,b))),
    inference(subst,[],[refute_0_1149:[bind(X_85,$fot(b))]]) ).

cnf(refute_0_1151,plain,
    ( inverse(least_upper_bound(a,least_upper_bound(c,b))) != inverse(least_upper_bound(a,least_upper_bound(b,c)))
    | inverse(least_upper_bound(b,least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(c,b)))
    | inverse(least_upper_bound(b,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(b,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(b,least_upper_bound(a,c))))),bind(Y0,$fot(inverse(least_upper_bound(a,least_upper_bound(c,b))))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(b,c)))))]]) ).

cnf(refute_0_1152,plain,
    ( inverse(least_upper_bound(a,least_upper_bound(c,b))) != inverse(least_upper_bound(a,least_upper_bound(b,c)))
    | inverse(least_upper_bound(b,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(b,c))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(b,least_upper_bound(a,c))),inverse(least_upper_bound(a,least_upper_bound(c,b)))) )],[refute_0_1150,refute_0_1151]) ).

cnf(refute_0_1153,plain,
    inverse(least_upper_bound(b,least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(b,c))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(c,b))),inverse(least_upper_bound(a,least_upper_bound(b,c)))) )],[refute_0_1117,refute_0_1152]) ).

cnf(refute_0_1154,plain,
    greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(b,least_upper_bound(a,c))),
    inference(subst,[],[refute_0_54:[bind(X,$fot(b)),bind(Y,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_1155,plain,
    ( greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))) != inverse(least_upper_bound(b,least_upper_bound(a,c)))
    | inverse(least_upper_bound(b,least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(b,c)))
    | greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(b,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))))),bind(Y0,$fot(inverse(least_upper_bound(b,least_upper_bound(a,c))))),bind(Z0,$fot(inverse(least_upper_bound(a,least_upper_bound(b,c)))))]]) ).

cnf(refute_0_1156,plain,
    ( inverse(least_upper_bound(b,least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(b,c)))
    | greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(b,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),inverse(least_upper_bound(b,least_upper_bound(a,c)))) )],[refute_0_1154,refute_0_1155]) ).

cnf(refute_0_1157,plain,
    greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(a,least_upper_bound(b,c))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(b,least_upper_bound(a,c))),inverse(least_upper_bound(a,least_upper_bound(b,c)))) )],[refute_0_1153,refute_0_1156]) ).

cnf(refute_0_1158,plain,
    ( greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))) != inverse(least_upper_bound(a,least_upper_bound(b,c)))
    | inverse(least_upper_bound(a,least_upper_bound(b,c))) != inverse(least_upper_bound(a,c))
    | greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(a,c)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))))),bind(Y0,$fot(inverse(least_upper_bound(a,least_upper_bound(b,c))))),bind(Z0,$fot(inverse(least_upper_bound(a,c))))]]) ).

cnf(refute_0_1159,plain,
    ( inverse(least_upper_bound(a,least_upper_bound(b,c))) != inverse(least_upper_bound(a,c))
    | greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),inverse(least_upper_bound(a,least_upper_bound(b,c)))) )],[refute_0_1157,refute_0_1158]) ).

cnf(refute_0_1160,plain,
    greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(a,c)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,least_upper_bound(b,c))),inverse(least_upper_bound(a,c))) )],[refute_0_1052,refute_0_1159]) ).

cnf(refute_0_1161,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))))]]) ).

cnf(refute_0_1162,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))
    | greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))) != inverse(least_upper_bound(a,c))
    | multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) ),[1,0],$fot(inverse(least_upper_bound(a,c)))]]) ).

cnf(refute_0_1163,plain,
    ( greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))) != inverse(least_upper_bound(a,c))
    | multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) )],[refute_0_1161,refute_0_1162]) ).

cnf(refute_0_1164,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),inverse(least_upper_bound(a,c))) )],[refute_0_1160,refute_0_1163]) ).

cnf(refute_0_1165,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))
    | multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
    | multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1166,plain,
    ( multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
    | multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) )],[refute_0_1164,refute_0_1165]) ).

cnf(refute_0_1167,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1040,refute_0_1166]) ).

cnf(refute_0_1168,plain,
    multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))) = multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y)))),
    inference(subst,[],[associativity:[bind(Z,$fot(inverse(greatest_lower_bound(X_234,Y))))]]) ).

cnf(refute_0_1169,plain,
    multiply(Y,inverse(greatest_lower_bound(X_234,Y))) = least_upper_bound(identity,multiply(Y,inverse(X_234))),
    inference(subst,[],[refute_0_258:[bind(X,$fot(X_234)),bind(X_96,$fot(Y))]]) ).

cnf(refute_0_1170,plain,
    ( multiply(Y,inverse(greatest_lower_bound(X_234,Y))) != least_upper_bound(identity,multiply(Y,inverse(X_234)))
    | multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))) != multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y))))
    | multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))) = multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))),multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y))))) ),[1,1],$fot(least_upper_bound(identity,multiply(Y,inverse(X_234))))]]) ).

cnf(refute_0_1171,plain,
    ( multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))) != multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y))))
    | multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))) = multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234)))) ),
    inference(resolve,[$cnf( $equal(multiply(Y,inverse(greatest_lower_bound(X_234,Y))),least_upper_bound(identity,multiply(Y,inverse(X_234)))) )],[refute_0_1169,refute_0_1170]) ).

cnf(refute_0_1172,plain,
    multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))) = multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234)))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))),multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y))))) )],[refute_0_1168,refute_0_1171]) ).

cnf(refute_0_1173,plain,
    ( multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))) != multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y))))
    | multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))) != multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234))))
    | multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y)))) = multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))),multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234))))) ),[0],$fot(multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y)))))]]) ).

cnf(refute_0_1174,plain,
    ( multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))) != multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234))))
    | multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y)))) = multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))),multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y))))) )],[refute_0_1168,refute_0_1173]) ).

cnf(refute_0_1175,plain,
    multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y)))) = multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234)))),
    inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),inverse(greatest_lower_bound(X_234,Y))),multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234))))) )],[refute_0_1172,refute_0_1174]) ).

cnf(refute_0_1176,plain,
    ( multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y)))) != multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234))))
    | multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234)))) = multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y)))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y)))))),bind(Y0,$fot(multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234))))))]]) ).

cnf(refute_0_1177,plain,
    multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234)))) = multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y)))),
    inference(resolve,[$cnf( $equal(multiply(X,multiply(Y,inverse(greatest_lower_bound(X_234,Y)))),multiply(X,least_upper_bound(identity,multiply(Y,inverse(X_234))))) )],[refute_0_1175,refute_0_1176]) ).

cnf(refute_0_1178,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),
    inference(subst,[],[refute_0_1177:[bind(X,$fot(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))))),bind(Y,$fot(c)),bind(X_234,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_1179,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
    | multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) != multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))
    | multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1180,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
    | multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))),multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) )],[refute_0_1178,refute_0_1179]) ).

cnf(refute_0_1181,plain,
    multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1167,refute_0_1180]) ).

cnf(refute_0_1182,plain,
    ( multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
    | inverse(b) != multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))))
    | inverse(b) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(b),multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))))) ),[1],$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_1183,plain,
    ( inverse(b) != multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))))
    | inverse(b) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1181,refute_0_1182]) ).

cnf(refute_0_1184,plain,
    inverse(b) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(inverse(b),multiply(greatest_lower_bound(inverse(b),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_980,refute_0_1183]) ).

cnf(refute_0_1185,plain,
    ( inverse(b) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
    | multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) = inverse(b) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(b))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1186,plain,
    multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) = inverse(b),
    inference(resolve,[$cnf( $equal(inverse(b),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1184,refute_0_1185]) ).

cnf(refute_0_1187,plain,
    least_upper_bound(c,a) = least_upper_bound(a,c),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(c)),bind(X_17,$fot(a))]]) ).

cnf(refute_0_1188,plain,
    least_upper_bound(X_82,least_upper_bound(X_83,greatest_lower_bound(X_83,Y))) = least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y))),
    inference(subst,[],[refute_0_1102:[bind(Y,$fot(X_82)),bind(X_43,$fot(X_83)),bind(X_45,$fot(greatest_lower_bound(X_83,Y)))]]) ).

cnf(refute_0_1189,plain,
    least_upper_bound(X_83,greatest_lower_bound(X_83,Y)) = X_83,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_83))]]) ).

cnf(refute_0_1190,plain,
    ( least_upper_bound(X_82,least_upper_bound(X_83,greatest_lower_bound(X_83,Y))) != least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y)))
    | least_upper_bound(X_83,greatest_lower_bound(X_83,Y)) != X_83
    | least_upper_bound(X_82,X_83) = least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_82,least_upper_bound(X_83,greatest_lower_bound(X_83,Y))),least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y)))) ),[0,1],$fot(X_83)]]) ).

cnf(refute_0_1191,plain,
    ( least_upper_bound(X_82,least_upper_bound(X_83,greatest_lower_bound(X_83,Y))) != least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y)))
    | least_upper_bound(X_82,X_83) = least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_83,greatest_lower_bound(X_83,Y)),X_83) )],[refute_0_1189,refute_0_1190]) ).

cnf(refute_0_1192,plain,
    least_upper_bound(X_82,X_83) = least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_82,least_upper_bound(X_83,greatest_lower_bound(X_83,Y))),least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y)))) )],[refute_0_1188,refute_0_1191]) ).

cnf(refute_0_1193,plain,
    ( least_upper_bound(X_82,X_83) != least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y)))
    | least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y))) = least_upper_bound(X_82,X_83) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_82,X_83))),bind(Y0,$fot(least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y)))))]]) ).

cnf(refute_0_1194,plain,
    least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y))) = least_upper_bound(X_82,X_83),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_82,X_83),least_upper_bound(X_83,least_upper_bound(X_82,greatest_lower_bound(X_83,Y)))) )],[refute_0_1192,refute_0_1193]) ).

cnf(refute_0_1195,plain,
    least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))) = least_upper_bound(c,a),
    inference(subst,[],[refute_0_1194:[bind(Y,$fot(least_upper_bound(b,identity))),bind(X_82,$fot(c)),bind(X_83,$fot(a))]]) ).

cnf(refute_0_1196,plain,
    ( least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))) != least_upper_bound(c,a)
    | least_upper_bound(c,a) != least_upper_bound(a,c)
    | least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))) = least_upper_bound(a,c) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))))),bind(Y0,$fot(least_upper_bound(c,a))),bind(Z0,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_1197,plain,
    ( least_upper_bound(c,a) != least_upper_bound(a,c)
    | least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))) = least_upper_bound(a,c) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))),least_upper_bound(c,a)) )],[refute_0_1195,refute_0_1196]) ).

cnf(refute_0_1198,plain,
    least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))) = least_upper_bound(a,c),
    inference(resolve,[$cnf( $equal(least_upper_bound(c,a),least_upper_bound(a,c)) )],[refute_0_1187,refute_0_1197]) ).

cnf(refute_0_1199,plain,
    least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))) = least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_375:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(greatest_lower_bound(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_1200,plain,
    ( least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))) != least_upper_bound(a,c)
    | least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))) != least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))) = least_upper_bound(a,c) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))))),bind(Z0,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_1201,plain,
    ( least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))) != least_upper_bound(a,c)
    | least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))) = least_upper_bound(a,c) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))),least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_1199,refute_0_1200]) ).

cnf(refute_0_1202,plain,
    least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))) = least_upper_bound(a,c),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,greatest_lower_bound(a,least_upper_bound(b,identity)))),least_upper_bound(a,c)) )],[refute_0_1198,refute_0_1201]) ).

cnf(refute_0_1203,plain,
    inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_1204,plain,
    ( inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))))
    | least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))) != least_upper_bound(a,c)
    | inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))))) ),[1,0],$fot(least_upper_bound(a,c))]]) ).

cnf(refute_0_1205,plain,
    ( least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))) != least_upper_bound(a,c)
    | inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_1203,refute_0_1204]) ).

cnf(refute_0_1206,plain,
    inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(a,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))),least_upper_bound(a,c)) )],[refute_0_1202,refute_0_1205]) ).

cnf(refute_0_1207,plain,
    greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_54:[bind(X,$fot(least_upper_bound(a,c))),bind(Y,$fot(greatest_lower_bound(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_1208,plain,
    ( greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))))
    | inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(a,c))
    | greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(a,c)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))))),bind(Y0,$fot(inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))))),bind(Z0,$fot(inverse(least_upper_bound(a,c))))]]) ).

cnf(refute_0_1209,plain,
    ( inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(a,c))
    | greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_1207,refute_0_1208]) ).

cnf(refute_0_1210,plain,
    greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(a,c)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(a,c),greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(least_upper_bound(a,c))) )],[refute_0_1206,refute_0_1209]) ).

cnf(refute_0_1211,plain,
    multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))))]]) ).

cnf(refute_0_1212,plain,
    ( multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))
    | greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(a,c))
    | multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) ),[1,0],$fot(inverse(least_upper_bound(a,c)))]]) ).

cnf(refute_0_1213,plain,
    ( greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(a,c))
    | multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) )],[refute_0_1211,refute_0_1212]) ).

cnf(refute_0_1214,plain,
    multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(least_upper_bound(a,c))) )],[refute_0_1210,refute_0_1213]) ).

cnf(refute_0_1215,plain,
    ( multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))
    | multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
    | multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))))),bind(Z0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_1216,plain,
    ( multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
    | multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) )],[refute_0_1214,refute_0_1215]) ).

cnf(refute_0_1217,plain,
    multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1040,refute_0_1216]) ).

cnf(refute_0_1218,plain,
    ( multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))
    | multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) != inverse(b)
    | multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = inverse(b) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))))),bind(Z0,$fot(inverse(b)))]]) ).

cnf(refute_0_1219,plain,
    ( multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))) != inverse(b)
    | multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = inverse(b) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_1217,refute_0_1218]) ).

cnf(refute_0_1220,plain,
    multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = inverse(b),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),multiply(c,inverse(greatest_lower_bound(a,c)))),inverse(b)) )],[refute_0_1186,refute_0_1219]) ).

cnf(refute_0_1221,plain,
    greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121)),
    inference(subst,[],[refute_0_801:[bind(X_32,$fot(multiply(X_123,X_121))),bind(X_33,$fot(multiply(X_122,X_121)))]]) ).

cnf(refute_0_1222,plain,
    multiply(greatest_lower_bound(X_122,X_123),X_121) = greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_121)),bind(Y,$fot(X_122)),bind(Z,$fot(X_123))]]) ).

cnf(refute_0_1223,plain,
    ( multiply(greatest_lower_bound(X_122,X_123),X_121) != greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))
    | greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121)) = multiply(greatest_lower_bound(X_122,X_123),X_121) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(X_122,X_123),X_121))),bind(Y0,$fot(greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))))]]) ).

cnf(refute_0_1224,plain,
    greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121)) = multiply(greatest_lower_bound(X_122,X_123),X_121),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,X_123),X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) )],[refute_0_1222,refute_0_1223]) ).

cnf(refute_0_1225,plain,
    ( greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121)) != multiply(greatest_lower_bound(X_122,X_123),X_121)
    | greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) != greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))
    | greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = multiply(greatest_lower_bound(X_122,X_123),X_121) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) ),[1],$fot(multiply(greatest_lower_bound(X_122,X_123),X_121))]]) ).

cnf(refute_0_1226,plain,
    ( greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) != greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))
    | greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = multiply(greatest_lower_bound(X_122,X_123),X_121) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121)),multiply(greatest_lower_bound(X_122,X_123),X_121)) )],[refute_0_1224,refute_0_1225]) ).

cnf(refute_0_1227,plain,
    greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = multiply(greatest_lower_bound(X_122,X_123),X_121),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) )],[refute_0_1221,refute_0_1226]) ).

cnf(refute_0_1228,plain,
    greatest_lower_bound(X_122,X_122) = X_122,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_122))]]) ).

cnf(refute_0_1229,plain,
    greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)) = greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)))]]) ).

cnf(refute_0_1230,plain,
    ( greatest_lower_bound(X_122,X_122) != X_122
    | greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)) != greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122))
    | greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)) = greatest_lower_bound(X_123,X_122) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122))) ),[1,1],$fot(X_122)]]) ).

cnf(refute_0_1231,plain,
    ( greatest_lower_bound(X_122,X_122) != X_122
    | greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)) = greatest_lower_bound(X_123,X_122) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122))) )],[refute_0_1229,refute_0_1230]) ).

cnf(refute_0_1232,plain,
    greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)) = greatest_lower_bound(X_123,X_122),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_122,X_122),X_122) )],[refute_0_1228,refute_0_1231]) ).

cnf(refute_0_1233,plain,
    multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121) = multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121))]]) ).

cnf(refute_0_1234,plain,
    ( multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121) != multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121)
    | greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)) != greatest_lower_bound(X_123,X_122)
    | multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121) = multiply(greatest_lower_bound(X_123,X_122),X_121) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121),multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121)) ),[1,0],$fot(greatest_lower_bound(X_123,X_122))]]) ).

cnf(refute_0_1235,plain,
    ( greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)) != greatest_lower_bound(X_123,X_122)
    | multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121) = multiply(greatest_lower_bound(X_123,X_122),X_121) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121),multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121)) )],[refute_0_1233,refute_0_1234]) ).

cnf(refute_0_1236,plain,
    multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121) = multiply(greatest_lower_bound(X_123,X_122),X_121),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),greatest_lower_bound(X_123,X_122)) )],[refute_0_1232,refute_0_1235]) ).

cnf(refute_0_1237,plain,
    ( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
    | greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).

cnf(refute_0_1238,plain,
    greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_1237]) ).

cnf(refute_0_1239,plain,
    greatest_lower_bound(multiply(X_123,X_121),multiply(greatest_lower_bound(X_122,X_122),X_121)) = multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121),
    inference(subst,[],[refute_0_1238:[bind(X,$fot(X_121)),bind(Y,$fot(X_123)),bind(Z,$fot(greatest_lower_bound(X_122,X_122)))]]) ).

cnf(refute_0_1240,plain,
    greatest_lower_bound(X,greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X)),
    inference(subst,[],[refute_0_839:[bind(X_36,$fot(multiply(X_122,X_121))),bind(X_37,$fot(multiply(X_123,X_121)))]]) ).

cnf(refute_0_1241,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) != greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X))
    | greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121)) != multiply(greatest_lower_bound(X_122,X_123),X_121)
    | greatest_lower_bound(X,multiply(greatest_lower_bound(X_122,X_123),X_121)) = greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))),greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X))) ),[0,1],$fot(multiply(greatest_lower_bound(X_122,X_123),X_121))]]) ).

cnf(refute_0_1242,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) != greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X))
    | greatest_lower_bound(X,multiply(greatest_lower_bound(X_122,X_123),X_121)) = greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121)),multiply(greatest_lower_bound(X_122,X_123),X_121)) )],[refute_0_1224,refute_0_1241]) ).

cnf(refute_0_1243,plain,
    greatest_lower_bound(X,multiply(greatest_lower_bound(X_122,X_123),X_121)) = greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))),greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X))) )],[refute_0_1240,refute_0_1242]) ).

cnf(refute_0_1244,plain,
    ( greatest_lower_bound(X,multiply(greatest_lower_bound(X_122,X_123),X_121)) != greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X))
    | greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_122,X_123),X_121)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,multiply(greatest_lower_bound(X_122,X_123),X_121)))),bind(Y0,$fot(greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X))))]]) ).

cnf(refute_0_1245,plain,
    greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X)) = greatest_lower_bound(X,multiply(greatest_lower_bound(X_122,X_123),X_121)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,multiply(greatest_lower_bound(X_122,X_123),X_121)),greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_123,X_121),X))) )],[refute_0_1243,refute_0_1244]) ).

cnf(refute_0_1246,plain,
    greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = greatest_lower_bound(multiply(X_123,X_121),multiply(greatest_lower_bound(X_122,X_122),X_121)),
    inference(subst,[],[refute_0_1245:[bind(X,$fot(multiply(X_123,X_121))),bind(X_123,$fot(X_122))]]) ).

cnf(refute_0_1247,plain,
    ( greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) != greatest_lower_bound(multiply(X_123,X_121),multiply(greatest_lower_bound(X_122,X_122),X_121))
    | greatest_lower_bound(multiply(X_123,X_121),multiply(greatest_lower_bound(X_122,X_122),X_121)) != multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121)
    | greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_123,X_121),multiply(greatest_lower_bound(X_122,X_122),X_121)))),bind(Z0,$fot(multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121)))]]) ).

cnf(refute_0_1248,plain,
    ( greatest_lower_bound(multiply(X_123,X_121),multiply(greatest_lower_bound(X_122,X_122),X_121)) != multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121)
    | greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))),greatest_lower_bound(multiply(X_123,X_121),multiply(greatest_lower_bound(X_122,X_122),X_121))) )],[refute_0_1246,refute_0_1247]) ).

cnf(refute_0_1249,plain,
    greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_123,X_121),multiply(greatest_lower_bound(X_122,X_122),X_121)),multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121)) )],[refute_0_1239,refute_0_1248]) ).

cnf(refute_0_1250,plain,
    ( multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121) != multiply(greatest_lower_bound(X_123,X_122),X_121)
    | greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) != multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121)
    | greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = multiply(greatest_lower_bound(X_123,X_122),X_121) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121))),bind(Z0,$fot(multiply(greatest_lower_bound(X_123,X_122),X_121)))]]) ).

cnf(refute_0_1251,plain,
    ( multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121) != multiply(greatest_lower_bound(X_123,X_122),X_121)
    | greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = multiply(greatest_lower_bound(X_123,X_122),X_121) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))),multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121)) )],[refute_0_1249,refute_0_1250]) ).

cnf(refute_0_1252,plain,
    greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) = multiply(greatest_lower_bound(X_123,X_122),X_121),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_123,greatest_lower_bound(X_122,X_122)),X_121),multiply(greatest_lower_bound(X_123,X_122),X_121)) )],[refute_0_1236,refute_0_1251]) ).

cnf(refute_0_1253,plain,
    ( greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) != multiply(greatest_lower_bound(X_122,X_123),X_121)
    | greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) != multiply(greatest_lower_bound(X_123,X_122),X_121)
    | multiply(greatest_lower_bound(X_123,X_122),X_121) = multiply(greatest_lower_bound(X_122,X_123),X_121) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))),multiply(greatest_lower_bound(X_122,X_123),X_121)) ),[0],$fot(multiply(greatest_lower_bound(X_123,X_122),X_121))]]) ).

cnf(refute_0_1254,plain,
    ( greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))) != multiply(greatest_lower_bound(X_122,X_123),X_121)
    | multiply(greatest_lower_bound(X_123,X_122),X_121) = multiply(greatest_lower_bound(X_122,X_123),X_121) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))),multiply(greatest_lower_bound(X_123,X_122),X_121)) )],[refute_0_1252,refute_0_1253]) ).

cnf(refute_0_1255,plain,
    multiply(greatest_lower_bound(X_123,X_122),X_121) = multiply(greatest_lower_bound(X_122,X_123),X_121),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(X_123,X_121))),multiply(greatest_lower_bound(X_122,X_123),X_121)) )],[refute_0_1227,refute_0_1254]) ).

cnf(refute_0_1256,plain,
    ( multiply(greatest_lower_bound(X_123,X_122),X_121) != multiply(greatest_lower_bound(X_122,X_123),X_121)
    | multiply(greatest_lower_bound(X_122,X_123),X_121) = multiply(greatest_lower_bound(X_123,X_122),X_121) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(X_123,X_122),X_121))),bind(Y0,$fot(multiply(greatest_lower_bound(X_122,X_123),X_121)))]]) ).

cnf(refute_0_1257,plain,
    multiply(greatest_lower_bound(X_122,X_123),X_121) = multiply(greatest_lower_bound(X_123,X_122),X_121),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_123,X_122),X_121),multiply(greatest_lower_bound(X_122,X_123),X_121)) )],[refute_0_1255,refute_0_1256]) ).

cnf(refute_0_1258,plain,
    multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) = multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),
    inference(subst,[],[refute_0_1257:[bind(X_121,$fot(multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))),bind(X_122,$fot(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))),bind(X_123,$fot(inverse(least_upper_bound(a,c))))]]) ).

cnf(refute_0_1259,plain,
    multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),
    inference(subst,[],[refute_0_1177:[bind(X,$fot(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))))),bind(Y,$fot(c)),bind(X_234,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_1260,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))
    | multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) != multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))
    | multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))))),bind(Z0,$fot(multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))))]]) ).

cnf(refute_0_1261,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))
    | multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))),multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) )],[refute_0_1259,refute_0_1260]) ).

cnf(refute_0_1262,plain,
    multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) = multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) )],[refute_0_1258,refute_0_1261]) ).

cnf(refute_0_1263,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) != multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))
    | multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != inverse(b)
    | multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) = inverse(b) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))))),bind(Z0,$fot(inverse(b)))]]) ).

cnf(refute_0_1264,plain,
    ( multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))) != inverse(b)
    | multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) = inverse(b) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))),multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c))))) )],[refute_0_1262,refute_0_1263]) ).

cnf(refute_0_1265,plain,
    multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) = inverse(b),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(least_upper_bound(a,c)),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(c,inverse(greatest_lower_bound(greatest_lower_bound(a,c),c)))),inverse(b)) )],[refute_0_1220,refute_0_1264]) ).

cnf(refute_0_1266,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))) != inverse(b)
    | inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) != multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))))
    | inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) = inverse(b) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))))) ),[1],$fot(inverse(b))]]) ).

cnf(refute_0_1267,plain,
    ( inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) != multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))))
    | inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) = inverse(b) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c))))),inverse(b)) )],[refute_0_1265,refute_0_1266]) ).

cnf(refute_0_1268,plain,
    inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) = inverse(b),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(least_upper_bound(a,c))),least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_976,refute_0_1267]) ).

cnf(refute_0_1269,plain,
    ( inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) != inverse(b)
    | inverse(inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) != greatest_lower_bound(a,least_upper_bound(b,identity))
    | inverse(inverse(b)) = greatest_lower_bound(a,least_upper_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),greatest_lower_bound(a,least_upper_bound(b,identity))) ),[0,0],$fot(inverse(b))]]) ).

cnf(refute_0_1270,plain,
    ( inverse(inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) != greatest_lower_bound(a,least_upper_bound(b,identity))
    | inverse(inverse(b)) = greatest_lower_bound(a,least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) )],[refute_0_1268,refute_0_1269]) ).

cnf(refute_0_1271,plain,
    inverse(inverse(b)) = greatest_lower_bound(a,least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),greatest_lower_bound(a,least_upper_bound(b,identity))) )],[refute_0_43,refute_0_1270]) ).

cnf(refute_0_1272,plain,
    inverse(inverse(b)) = b,
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(b))]]) ).

cnf(refute_0_1273,plain,
    ( inverse(inverse(b)) != b
    | inverse(inverse(b)) != greatest_lower_bound(a,least_upper_bound(b,identity))
    | b = greatest_lower_bound(a,least_upper_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(b)),greatest_lower_bound(a,least_upper_bound(b,identity))) ),[0],$fot(b)]]) ).

cnf(refute_0_1274,plain,
    ( inverse(inverse(b)) != greatest_lower_bound(a,least_upper_bound(b,identity))
    | b = greatest_lower_bound(a,least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),b) )],[refute_0_1272,refute_0_1273]) ).

cnf(refute_0_1275,plain,
    b = greatest_lower_bound(a,least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),greatest_lower_bound(a,least_upper_bound(b,identity))) )],[refute_0_1271,refute_0_1274]) ).

cnf(refute_0_1276,plain,
    greatest_lower_bound(a,least_upper_bound(a,identity)) = a,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(a)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_1277,plain,
    multiply(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))),
    inference(subst,[],[refute_0_363:[bind(X_111,$fot(b)),bind(X_112,$fot(inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_1278,plain,
    least_upper_bound(least_upper_bound(b,inverse(a)),greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) = least_upper_bound(b,inverse(a)),
    inference(subst,[],[refute_0_117:[bind(X_8,$fot(least_upper_bound(b,inverse(a)))),bind(X_9,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_1279,plain,
    greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) = multiply(inverse(a),multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(a)),bind(X_60,$fot(greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))))]]) ).

cnf(refute_0_1280,plain,
    multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity))),
    inference(subst,[],[refute_0_161:[bind(X_107,$fot(least_upper_bound(identity,multiply(a,b)))),bind(X_108,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_1281,plain,
    multiply(a,least_upper_bound(b,identity)) = multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_334:[bind(X_129,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_1282,plain,
    multiply(X_107,greatest_lower_bound(inverse(X_107),X_109)) = greatest_lower_bound(multiply(X_107,inverse(X_107)),multiply(X_107,X_109)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_107)),bind(Y,$fot(inverse(X_107))),bind(Z,$fot(X_109))]]) ).

cnf(refute_0_1283,plain,
    multiply(X_107,inverse(X_107)) = identity,
    inference(subst,[],[refute_0_232:[bind(X_66,$fot(X_107))]]) ).

cnf(refute_0_1284,plain,
    ( multiply(X_107,greatest_lower_bound(inverse(X_107),X_109)) != greatest_lower_bound(multiply(X_107,inverse(X_107)),multiply(X_107,X_109))
    | multiply(X_107,inverse(X_107)) != identity
    | multiply(X_107,greatest_lower_bound(inverse(X_107),X_109)) = greatest_lower_bound(identity,multiply(X_107,X_109)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_107,greatest_lower_bound(inverse(X_107),X_109)),greatest_lower_bound(multiply(X_107,inverse(X_107)),multiply(X_107,X_109))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1285,plain,
    ( multiply(X_107,greatest_lower_bound(inverse(X_107),X_109)) != greatest_lower_bound(multiply(X_107,inverse(X_107)),multiply(X_107,X_109))
    | multiply(X_107,greatest_lower_bound(inverse(X_107),X_109)) = greatest_lower_bound(identity,multiply(X_107,X_109)) ),
    inference(resolve,[$cnf( $equal(multiply(X_107,inverse(X_107)),identity) )],[refute_0_1283,refute_0_1284]) ).

cnf(refute_0_1286,plain,
    multiply(X_107,greatest_lower_bound(inverse(X_107),X_109)) = greatest_lower_bound(identity,multiply(X_107,X_109)),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(inverse(X_107),X_109)),greatest_lower_bound(multiply(X_107,inverse(X_107)),multiply(X_107,X_109))) )],[refute_0_1282,refute_0_1285]) ).

cnf(refute_0_1287,plain,
    multiply(a,greatest_lower_bound(inverse(a),least_upper_bound(b,identity))) = greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_1286:[bind(X_107,$fot(a)),bind(X_109,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_1288,plain,
    inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) = inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_58:[bind(X_14,$fot(a)),bind(X_15,$fot(inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_1289,plain,
    least_upper_bound(a,least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))) = least_upper_bound(a,inverse(least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_685:[bind(Y,$fot(identity)),bind(X_43,$fot(a)),bind(X_45,$fot(inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_1290,plain,
    multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) = least_upper_bound(greatest_lower_bound(a,identity),multiply(inverse(b),greatest_lower_bound(a,identity))),
    inference(subst,[],[refute_0_728:[bind(X_110,$fot(greatest_lower_bound(a,identity))),bind(X_111,$fot(inverse(b)))]]) ).

cnf(refute_0_1291,plain,
    inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = greatest_lower_bound(identity,inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_299:[bind(Y,$fot(greatest_lower_bound(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_1292,plain,
    ( inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) != inverse(b)
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = greatest_lower_bound(identity,inverse(b)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))) ),[1,1],$fot(inverse(b))]]) ).

cnf(refute_0_1293,plain,
    ( inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != greatest_lower_bound(identity,inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = greatest_lower_bound(identity,inverse(b)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) )],[refute_0_1268,refute_0_1292]) ).

cnf(refute_0_1294,plain,
    inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = greatest_lower_bound(identity,inverse(b)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,inverse(greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_1291,refute_0_1293]) ).

cnf(refute_0_1295,plain,
    multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) = greatest_lower_bound(inverse(X_233),multiply(inverse(X_233),greatest_lower_bound(X_233,identity))),
    inference(subst,[],[refute_0_161:[bind(X_107,$fot(inverse(X_233))),bind(X_108,$fot(greatest_lower_bound(X_233,identity)))]]) ).

cnf(refute_0_1296,plain,
    multiply(inverse(X_232),greatest_lower_bound(X_232,identity)) = greatest_lower_bound(inverse(X_232),multiply(inverse(X_232),X_232)),
    inference(subst,[],[refute_0_161:[bind(X_107,$fot(inverse(X_232))),bind(X_108,$fot(X_232))]]) ).

cnf(refute_0_1297,plain,
    multiply(inverse(X_232),X_232) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_232))]]) ).

cnf(refute_0_1298,plain,
    ( multiply(inverse(X_232),X_232) != identity
    | multiply(inverse(X_232),greatest_lower_bound(X_232,identity)) != greatest_lower_bound(inverse(X_232),multiply(inverse(X_232),X_232))
    | multiply(inverse(X_232),greatest_lower_bound(X_232,identity)) = greatest_lower_bound(inverse(X_232),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_232),greatest_lower_bound(X_232,identity)),greatest_lower_bound(inverse(X_232),multiply(inverse(X_232),X_232))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1299,plain,
    ( multiply(inverse(X_232),greatest_lower_bound(X_232,identity)) != greatest_lower_bound(inverse(X_232),multiply(inverse(X_232),X_232))
    | multiply(inverse(X_232),greatest_lower_bound(X_232,identity)) = greatest_lower_bound(inverse(X_232),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_232),X_232),identity) )],[refute_0_1297,refute_0_1298]) ).

cnf(refute_0_1300,plain,
    multiply(inverse(X_232),greatest_lower_bound(X_232,identity)) = greatest_lower_bound(inverse(X_232),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_232),greatest_lower_bound(X_232,identity)),greatest_lower_bound(inverse(X_232),multiply(inverse(X_232),X_232))) )],[refute_0_1296,refute_0_1299]) ).

cnf(refute_0_1301,plain,
    greatest_lower_bound(identity,inverse(X_232)) = inverse(least_upper_bound(identity,X_232)),
    inference(subst,[],[refute_0_500:[bind(Y,$fot(X_232))]]) ).

cnf(refute_0_1302,plain,
    multiply(greatest_lower_bound(inverse(X_121),X_123),X_121) = greatest_lower_bound(multiply(inverse(X_121),X_121),multiply(X_123,X_121)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_121)),bind(Y,$fot(inverse(X_121))),bind(Z,$fot(X_123))]]) ).

cnf(refute_0_1303,plain,
    ( multiply(greatest_lower_bound(inverse(X_121),X_123),X_121) != greatest_lower_bound(multiply(inverse(X_121),X_121),multiply(X_123,X_121))
    | multiply(inverse(X_121),X_121) != identity
    | multiply(greatest_lower_bound(inverse(X_121),X_123),X_121) = greatest_lower_bound(identity,multiply(X_123,X_121)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),X_123),X_121),greatest_lower_bound(multiply(inverse(X_121),X_121),multiply(X_123,X_121))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1304,plain,
    ( multiply(greatest_lower_bound(inverse(X_121),X_123),X_121) != greatest_lower_bound(multiply(inverse(X_121),X_121),multiply(X_123,X_121))
    | multiply(greatest_lower_bound(inverse(X_121),X_123),X_121) = greatest_lower_bound(identity,multiply(X_123,X_121)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_121),X_121),identity) )],[refute_0_280,refute_0_1303]) ).

cnf(refute_0_1305,plain,
    multiply(greatest_lower_bound(inverse(X_121),X_123),X_121) = greatest_lower_bound(identity,multiply(X_123,X_121)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),X_123),X_121),greatest_lower_bound(multiply(inverse(X_121),X_121),multiply(X_123,X_121))) )],[refute_0_1302,refute_0_1304]) ).

cnf(refute_0_1306,plain,
    multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) = greatest_lower_bound(identity,multiply(inverse(X_59),multiply(X_59,X_60))),
    inference(subst,[],[refute_0_1305:[bind(X_121,$fot(multiply(X_59,X_60))),bind(X_123,$fot(inverse(X_59)))]]) ).

cnf(refute_0_1307,plain,
    ( X_60 != multiply(inverse(X_59),multiply(X_59,X_60))
    | multiply(inverse(X_59),multiply(X_59,X_60)) = X_60 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_60)),bind(Y0,$fot(multiply(inverse(X_59),multiply(X_59,X_60))))]]) ).

cnf(refute_0_1308,plain,
    multiply(inverse(X_59),multiply(X_59,X_60)) = X_60,
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(X_59),multiply(X_59,X_60))) )],[refute_0_8,refute_0_1307]) ).

cnf(refute_0_1309,plain,
    ( multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) != greatest_lower_bound(identity,multiply(inverse(X_59),multiply(X_59,X_60)))
    | multiply(inverse(X_59),multiply(X_59,X_60)) != X_60
    | multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) = greatest_lower_bound(identity,X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)),greatest_lower_bound(identity,multiply(inverse(X_59),multiply(X_59,X_60)))) ),[1,1],$fot(X_60)]]) ).

cnf(refute_0_1310,plain,
    ( multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) != greatest_lower_bound(identity,multiply(inverse(X_59),multiply(X_59,X_60)))
    | multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) = greatest_lower_bound(identity,X_60) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_59),multiply(X_59,X_60)),X_60) )],[refute_0_1308,refute_0_1309]) ).

cnf(refute_0_1311,plain,
    multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) = greatest_lower_bound(identity,X_60),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)),greatest_lower_bound(identity,multiply(inverse(X_59),multiply(X_59,X_60)))) )],[refute_0_1306,refute_0_1310]) ).

cnf(refute_0_1312,plain,
    multiply(multiply(greatest_lower_bound(X_125,inverse(Y)),Y),Z) = multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z)),
    inference(subst,[],[associativity:[bind(X,$fot(greatest_lower_bound(X_125,inverse(Y))))]]) ).

cnf(refute_0_1313,plain,
    multiply(greatest_lower_bound(X_125,inverse(Y)),Y) = greatest_lower_bound(identity,multiply(X_125,Y)),
    inference(subst,[],[refute_0_287:[bind(X_121,$fot(Y)),bind(X_122,$fot(X_125))]]) ).

cnf(refute_0_1314,plain,
    ( multiply(multiply(greatest_lower_bound(X_125,inverse(Y)),Y),Z) != multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z))
    | multiply(greatest_lower_bound(X_125,inverse(Y)),Y) != greatest_lower_bound(identity,multiply(X_125,Y))
    | multiply(greatest_lower_bound(identity,multiply(X_125,Y)),Z) = multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(greatest_lower_bound(X_125,inverse(Y)),Y),Z),multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z))) ),[0,0],$fot(greatest_lower_bound(identity,multiply(X_125,Y)))]]) ).

cnf(refute_0_1315,plain,
    ( multiply(multiply(greatest_lower_bound(X_125,inverse(Y)),Y),Z) != multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z))
    | multiply(greatest_lower_bound(identity,multiply(X_125,Y)),Z) = multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_125,inverse(Y)),Y),greatest_lower_bound(identity,multiply(X_125,Y))) )],[refute_0_1313,refute_0_1314]) ).

cnf(refute_0_1316,plain,
    multiply(greatest_lower_bound(identity,multiply(X_125,Y)),Z) = multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(X_125,inverse(Y)),Y),Z),multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z))) )],[refute_0_1312,refute_0_1315]) ).

cnf(refute_0_1317,plain,
    ( multiply(greatest_lower_bound(identity,multiply(X_125,Y)),Z) != multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z))
    | multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z)) = multiply(greatest_lower_bound(identity,multiply(X_125,Y)),Z) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(X_125,Y)),Z))),bind(Y0,$fot(multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z))))]]) ).

cnf(refute_0_1318,plain,
    multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z)) = multiply(greatest_lower_bound(identity,multiply(X_125,Y)),Z),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_125,Y)),Z),multiply(greatest_lower_bound(X_125,inverse(Y)),multiply(Y,Z))) )],[refute_0_1316,refute_0_1317]) ).

cnf(refute_0_1319,plain,
    multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) = multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),
    inference(subst,[],[refute_0_1318:[bind(Y,$fot(X_59)),bind(Z,$fot(X_60)),bind(X_125,$fot(inverse(multiply(X_59,X_60))))]]) ).

cnf(refute_0_1320,plain,
    ( multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) != multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60)
    | multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) != greatest_lower_bound(identity,X_60)
    | multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = greatest_lower_bound(identity,X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)),greatest_lower_bound(identity,X_60)) ),[0],$fot(multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60))]]) ).

cnf(refute_0_1321,plain,
    ( multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) != greatest_lower_bound(identity,X_60)
    | multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = greatest_lower_bound(identity,X_60) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)),multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60)) )],[refute_0_1319,refute_0_1320]) ).

cnf(refute_0_1322,plain,
    multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = greatest_lower_bound(identity,X_60),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)),greatest_lower_bound(identity,X_60)) )],[refute_0_1311,refute_0_1321]) ).

cnf(refute_0_1323,plain,
    greatest_lower_bound(identity,inverse(X_60)) = inverse(least_upper_bound(identity,X_60)),
    inference(subst,[],[refute_0_500:[bind(Y,$fot(X_60))]]) ).

cnf(refute_0_1324,plain,
    multiply(inverse(multiply(X_198,X_59)),inverse(multiply(X_59,inverse(multiply(X_198,X_59))))) = inverse(X_59),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(inverse(multiply(X_198,X_59))))]]) ).

cnf(refute_0_1325,plain,
    ( multiply(X_59,inverse(multiply(X_198,X_59))) != inverse(X_198)
    | multiply(inverse(multiply(X_198,X_59)),inverse(multiply(X_59,inverse(multiply(X_198,X_59))))) != inverse(X_59)
    | multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))) = inverse(X_59) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_198,X_59)),inverse(multiply(X_59,inverse(multiply(X_198,X_59))))),inverse(X_59)) ),[0,1,0],$fot(inverse(X_198))]]) ).

cnf(refute_0_1326,plain,
    ( multiply(inverse(multiply(X_198,X_59)),inverse(multiply(X_59,inverse(multiply(X_198,X_59))))) != inverse(X_59)
    | multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))) = inverse(X_59) ),
    inference(resolve,[$cnf( $equal(multiply(X_59,inverse(multiply(X_198,X_59))),inverse(X_198)) )],[refute_0_662,refute_0_1325]) ).

cnf(refute_0_1327,plain,
    multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))) = inverse(X_59),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_198,X_59)),inverse(multiply(X_59,inverse(multiply(X_198,X_59))))),inverse(X_59)) )],[refute_0_1324,refute_0_1326]) ).

cnf(refute_0_1328,plain,
    inverse(inverse(X_198)) = X_198,
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(X_198))]]) ).

cnf(refute_0_1329,plain,
    multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))) = multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))),
    introduced(tautology,[refl,[$fot(multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))))]]) ).

cnf(refute_0_1330,plain,
    ( multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))) != multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198)))
    | inverse(inverse(X_198)) != X_198
    | multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))) = multiply(inverse(multiply(X_198,X_59)),X_198) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))),multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198)))) ),[1,1],$fot(X_198)]]) ).

cnf(refute_0_1331,plain,
    ( inverse(inverse(X_198)) != X_198
    | multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))) = multiply(inverse(multiply(X_198,X_59)),X_198) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))),multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198)))) )],[refute_0_1329,refute_0_1330]) ).

cnf(refute_0_1332,plain,
    multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))) = multiply(inverse(multiply(X_198,X_59)),X_198),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_198)),X_198) )],[refute_0_1328,refute_0_1331]) ).

cnf(refute_0_1333,plain,
    ( multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))) != multiply(inverse(multiply(X_198,X_59)),X_198)
    | multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))) != inverse(X_59)
    | multiply(inverse(multiply(X_198,X_59)),X_198) = inverse(X_59) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))),inverse(X_59)) ),[0],$fot(multiply(inverse(multiply(X_198,X_59)),X_198))]]) ).

cnf(refute_0_1334,plain,
    ( multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))) != inverse(X_59)
    | multiply(inverse(multiply(X_198,X_59)),X_198) = inverse(X_59) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))),multiply(inverse(multiply(X_198,X_59)),X_198)) )],[refute_0_1332,refute_0_1333]) ).

cnf(refute_0_1335,plain,
    multiply(inverse(multiply(X_198,X_59)),X_198) = inverse(X_59),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_198,X_59)),inverse(inverse(X_198))),inverse(X_59)) )],[refute_0_1327,refute_0_1334]) ).

cnf(refute_0_1336,plain,
    multiply(inverse(multiply(X_59,X_60)),X_59) = inverse(X_60),
    inference(subst,[],[refute_0_1335:[bind(X_198,$fot(X_59)),bind(X_59,$fot(X_60))]]) ).

cnf(refute_0_1337,plain,
    greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)))]]) ).

cnf(refute_0_1338,plain,
    ( multiply(inverse(multiply(X_59,X_60)),X_59) != inverse(X_60)
    | greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) != greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59))
    | greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = greatest_lower_bound(identity,inverse(X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59))) ),[1,1],$fot(inverse(X_60))]]) ).

cnf(refute_0_1339,plain,
    ( multiply(inverse(multiply(X_59,X_60)),X_59) != inverse(X_60)
    | greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = greatest_lower_bound(identity,inverse(X_60)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59))) )],[refute_0_1337,refute_0_1338]) ).

cnf(refute_0_1340,plain,
    greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = greatest_lower_bound(identity,inverse(X_60)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_59,X_60)),X_59),inverse(X_60)) )],[refute_0_1336,refute_0_1339]) ).

cnf(refute_0_1341,plain,
    ( greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) != greatest_lower_bound(identity,inverse(X_60))
    | greatest_lower_bound(identity,inverse(X_60)) != inverse(least_upper_bound(identity,X_60))
    | greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = inverse(least_upper_bound(identity,X_60)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_60)))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_60))))]]) ).

cnf(refute_0_1342,plain,
    ( greatest_lower_bound(identity,inverse(X_60)) != inverse(least_upper_bound(identity,X_60))
    | greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = inverse(least_upper_bound(identity,X_60)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),greatest_lower_bound(identity,inverse(X_60))) )],[refute_0_1340,refute_0_1341]) ).

cnf(refute_0_1343,plain,
    greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = inverse(least_upper_bound(identity,X_60)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_60)),inverse(least_upper_bound(identity,X_60))) )],[refute_0_1323,refute_0_1342]) ).

cnf(refute_0_1344,plain,
    multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60))]]) ).

cnf(refute_0_1345,plain,
    ( multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) != multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60)
    | greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) != inverse(least_upper_bound(identity,X_60))
    | multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = multiply(inverse(least_upper_bound(identity,X_60)),X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60)) ),[1,0],$fot(inverse(least_upper_bound(identity,X_60)))]]) ).

cnf(refute_0_1346,plain,
    ( greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) != inverse(least_upper_bound(identity,X_60))
    | multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = multiply(inverse(least_upper_bound(identity,X_60)),X_60) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60)) )],[refute_0_1344,refute_0_1345]) ).

cnf(refute_0_1347,plain,
    multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = multiply(inverse(least_upper_bound(identity,X_60)),X_60),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),inverse(least_upper_bound(identity,X_60))) )],[refute_0_1343,refute_0_1346]) ).

cnf(refute_0_1348,plain,
    ( multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) != multiply(inverse(least_upper_bound(identity,X_60)),X_60)
    | multiply(inverse(least_upper_bound(identity,X_60)),X_60) != greatest_lower_bound(X_60,identity)
    | multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = greatest_lower_bound(X_60,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60))),bind(Y0,$fot(multiply(inverse(least_upper_bound(identity,X_60)),X_60))),bind(Z0,$fot(greatest_lower_bound(X_60,identity)))]]) ).

cnf(refute_0_1349,plain,
    ( multiply(inverse(least_upper_bound(identity,X_60)),X_60) != greatest_lower_bound(X_60,identity)
    | multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = greatest_lower_bound(X_60,identity) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),multiply(inverse(least_upper_bound(identity,X_60)),X_60)) )],[refute_0_1347,refute_0_1348]) ).

cnf(refute_0_1350,plain,
    multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = greatest_lower_bound(X_60,identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_60)),X_60),greatest_lower_bound(X_60,identity)) )],[refute_0_316,refute_0_1349]) ).

cnf(refute_0_1351,plain,
    ( multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) != greatest_lower_bound(X_60,identity)
    | multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) != greatest_lower_bound(identity,X_60)
    | greatest_lower_bound(X_60,identity) = greatest_lower_bound(identity,X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),greatest_lower_bound(identity,X_60)) ),[0],$fot(greatest_lower_bound(X_60,identity))]]) ).

cnf(refute_0_1352,plain,
    ( multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) != greatest_lower_bound(identity,X_60)
    | greatest_lower_bound(X_60,identity) = greatest_lower_bound(identity,X_60) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),greatest_lower_bound(X_60,identity)) )],[refute_0_1350,refute_0_1351]) ).

cnf(refute_0_1353,plain,
    greatest_lower_bound(X_60,identity) = greatest_lower_bound(identity,X_60),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),greatest_lower_bound(identity,X_60)) )],[refute_0_1322,refute_0_1352]) ).

cnf(refute_0_1354,plain,
    greatest_lower_bound(inverse(X_232),identity) = greatest_lower_bound(identity,inverse(X_232)),
    inference(subst,[],[refute_0_1353:[bind(X_60,$fot(inverse(X_232)))]]) ).

cnf(refute_0_1355,plain,
    ( greatest_lower_bound(identity,inverse(X_232)) != inverse(least_upper_bound(identity,X_232))
    | greatest_lower_bound(inverse(X_232),identity) != greatest_lower_bound(identity,inverse(X_232))
    | greatest_lower_bound(inverse(X_232),identity) = inverse(least_upper_bound(identity,X_232)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(inverse(X_232),identity))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_232)))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_232))))]]) ).

cnf(refute_0_1356,plain,
    ( greatest_lower_bound(identity,inverse(X_232)) != inverse(least_upper_bound(identity,X_232))
    | greatest_lower_bound(inverse(X_232),identity) = inverse(least_upper_bound(identity,X_232)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_232),identity),greatest_lower_bound(identity,inverse(X_232))) )],[refute_0_1354,refute_0_1355]) ).

cnf(refute_0_1357,plain,
    greatest_lower_bound(inverse(X_232),identity) = inverse(least_upper_bound(identity,X_232)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_232)),inverse(least_upper_bound(identity,X_232))) )],[refute_0_1301,refute_0_1356]) ).

cnf(refute_0_1358,plain,
    ( multiply(inverse(X_232),greatest_lower_bound(X_232,identity)) != greatest_lower_bound(inverse(X_232),identity)
    | greatest_lower_bound(inverse(X_232),identity) != inverse(least_upper_bound(identity,X_232))
    | multiply(inverse(X_232),greatest_lower_bound(X_232,identity)) = inverse(least_upper_bound(identity,X_232)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_232),greatest_lower_bound(X_232,identity)),inverse(least_upper_bound(identity,X_232))) ),[0],$fot(greatest_lower_bound(inverse(X_232),identity))]]) ).

cnf(refute_0_1359,plain,
    ( multiply(inverse(X_232),greatest_lower_bound(X_232,identity)) != greatest_lower_bound(inverse(X_232),identity)
    | multiply(inverse(X_232),greatest_lower_bound(X_232,identity)) = inverse(least_upper_bound(identity,X_232)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_232),identity),inverse(least_upper_bound(identity,X_232))) )],[refute_0_1357,refute_0_1358]) ).

cnf(refute_0_1360,plain,
    multiply(inverse(X_232),greatest_lower_bound(X_232,identity)) = inverse(least_upper_bound(identity,X_232)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_232),greatest_lower_bound(X_232,identity)),greatest_lower_bound(inverse(X_232),identity)) )],[refute_0_1300,refute_0_1359]) ).

cnf(refute_0_1361,plain,
    multiply(inverse(X_233),greatest_lower_bound(X_233,identity)) = inverse(least_upper_bound(identity,X_233)),
    inference(subst,[],[refute_0_1360:[bind(X_232,$fot(X_233))]]) ).

cnf(refute_0_1362,plain,
    ( multiply(inverse(X_233),greatest_lower_bound(X_233,identity)) != inverse(least_upper_bound(identity,X_233))
    | multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) != greatest_lower_bound(inverse(X_233),multiply(inverse(X_233),greatest_lower_bound(X_233,identity)))
    | multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) = greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)),greatest_lower_bound(inverse(X_233),multiply(inverse(X_233),greatest_lower_bound(X_233,identity)))) ),[1,1],$fot(inverse(least_upper_bound(identity,X_233)))]]) ).

cnf(refute_0_1363,plain,
    ( multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) != greatest_lower_bound(inverse(X_233),multiply(inverse(X_233),greatest_lower_bound(X_233,identity)))
    | multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) = greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233))) )],[refute_0_1361,refute_0_1362]) ).

cnf(refute_0_1364,plain,
    multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) = greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)),greatest_lower_bound(inverse(X_233),multiply(inverse(X_233),greatest_lower_bound(X_233,identity)))) )],[refute_0_1295,refute_0_1363]) ).

cnf(refute_0_1365,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_233,identity)) = greatest_lower_bound(identity,X_233),
    inference(subst,[],[refute_0_794:[bind(Y,$fot(X_233)),bind(X_23,$fot(identity))]]) ).

cnf(refute_0_1366,plain,
    multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))) = multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))),
    introduced(tautology,[refl,[$fot(multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))))]]) ).

cnf(refute_0_1367,plain,
    ( multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))) != multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity)))
    | greatest_lower_bound(identity,greatest_lower_bound(X_233,identity)) != greatest_lower_bound(identity,X_233)
    | multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))) = multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))),multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,X_233))]]) ).

cnf(refute_0_1368,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_233,identity)) != greatest_lower_bound(identity,X_233)
    | multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))) = multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))),multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity)))) )],[refute_0_1366,refute_0_1367]) ).

cnf(refute_0_1369,plain,
    multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))) = multiply(inverse(X_233),greatest_lower_bound(identity,X_233)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_233,identity)),greatest_lower_bound(identity,X_233)) )],[refute_0_1365,refute_0_1368]) ).

cnf(refute_0_1370,plain,
    multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) = multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))),
    inference(subst,[],[refute_0_925:[bind(X_232,$fot(greatest_lower_bound(X_233,identity))),bind(X_33,$fot(inverse(X_233)))]]) ).

cnf(refute_0_1371,plain,
    ( multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) != multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity)))
    | multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))) != multiply(inverse(X_233),greatest_lower_bound(identity,X_233))
    | multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) = multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)))),bind(Y0,$fot(multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))))),bind(Z0,$fot(multiply(inverse(X_233),greatest_lower_bound(identity,X_233))))]]) ).

cnf(refute_0_1372,plain,
    ( multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))) != multiply(inverse(X_233),greatest_lower_bound(identity,X_233))
    | multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) = multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)),multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity)))) )],[refute_0_1370,refute_0_1371]) ).

cnf(refute_0_1373,plain,
    multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) = multiply(inverse(X_233),greatest_lower_bound(identity,X_233)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(identity,greatest_lower_bound(X_233,identity))),multiply(inverse(X_233),greatest_lower_bound(identity,X_233))) )],[refute_0_1369,refute_0_1372]) ).

cnf(refute_0_1374,plain,
    ( multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) != multiply(inverse(X_233),greatest_lower_bound(identity,X_233))
    | multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) != greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233)))
    | multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) = greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)),greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233)))) ),[0],$fot(multiply(inverse(X_233),greatest_lower_bound(identity,X_233)))]]) ).

cnf(refute_0_1375,plain,
    ( multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) != greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233)))
    | multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) = greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)),multiply(inverse(X_233),greatest_lower_bound(identity,X_233))) )],[refute_0_1373,refute_0_1374]) ).

cnf(refute_0_1376,plain,
    greatest_lower_bound(identity,inverse(X_233)) = inverse(least_upper_bound(identity,X_233)),
    inference(subst,[],[refute_0_500:[bind(Y,$fot(X_233))]]) ).

cnf(refute_0_1377,plain,
    least_upper_bound(X_233,X_233) = X_233,
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_233))]]) ).

cnf(refute_0_1378,plain,
    inverse(least_upper_bound(X_233,X_233)) = inverse(least_upper_bound(X_233,X_233)),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(X_233,X_233)))]]) ).

cnf(refute_0_1379,plain,
    ( inverse(least_upper_bound(X_233,X_233)) != inverse(least_upper_bound(X_233,X_233))
    | least_upper_bound(X_233,X_233) != X_233
    | inverse(least_upper_bound(X_233,X_233)) = inverse(X_233) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_233,X_233)),inverse(least_upper_bound(X_233,X_233))) ),[1,0],$fot(X_233)]]) ).

cnf(refute_0_1380,plain,
    ( least_upper_bound(X_233,X_233) != X_233
    | inverse(least_upper_bound(X_233,X_233)) = inverse(X_233) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_233,X_233)),inverse(least_upper_bound(X_233,X_233))) )],[refute_0_1378,refute_0_1379]) ).

cnf(refute_0_1381,plain,
    inverse(least_upper_bound(X_233,X_233)) = inverse(X_233),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_233,X_233),X_233) )],[refute_0_1377,refute_0_1380]) ).

cnf(refute_0_1382,plain,
    greatest_lower_bound(inverse(X_233),inverse(X_233)) = inverse(least_upper_bound(X_233,X_233)),
    inference(subst,[],[refute_0_54:[bind(X,$fot(X_233)),bind(Y,$fot(X_233))]]) ).

cnf(refute_0_1383,plain,
    ( greatest_lower_bound(inverse(X_233),inverse(X_233)) != inverse(least_upper_bound(X_233,X_233))
    | inverse(least_upper_bound(X_233,X_233)) != inverse(X_233)
    | greatest_lower_bound(inverse(X_233),inverse(X_233)) = inverse(X_233) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(inverse(X_233),inverse(X_233)))),bind(Y0,$fot(inverse(least_upper_bound(X_233,X_233)))),bind(Z0,$fot(inverse(X_233)))]]) ).

cnf(refute_0_1384,plain,
    ( inverse(least_upper_bound(X_233,X_233)) != inverse(X_233)
    | greatest_lower_bound(inverse(X_233),inverse(X_233)) = inverse(X_233) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_233),inverse(X_233)),inverse(least_upper_bound(X_233,X_233))) )],[refute_0_1382,refute_0_1383]) ).

cnf(refute_0_1385,plain,
    greatest_lower_bound(inverse(X_233),inverse(X_233)) = inverse(X_233),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_233,X_233)),inverse(X_233)) )],[refute_0_1381,refute_0_1384]) ).

cnf(refute_0_1386,plain,
    greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))))]]) ).

cnf(refute_0_1387,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233)))
    | greatest_lower_bound(inverse(X_233),inverse(X_233)) != inverse(X_233)
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))) = greatest_lower_bound(identity,inverse(X_233)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233)))) ),[1,1],$fot(inverse(X_233))]]) ).

cnf(refute_0_1388,plain,
    ( greatest_lower_bound(inverse(X_233),inverse(X_233)) != inverse(X_233)
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))) = greatest_lower_bound(identity,inverse(X_233)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233)))) )],[refute_0_1386,refute_0_1387]) ).

cnf(refute_0_1389,plain,
    greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))) = greatest_lower_bound(identity,inverse(X_233)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_233),inverse(X_233)),inverse(X_233)) )],[refute_0_1385,refute_0_1388]) ).

cnf(refute_0_1390,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))) != greatest_lower_bound(identity,inverse(X_233))
    | greatest_lower_bound(identity,inverse(X_233)) != inverse(least_upper_bound(identity,X_233))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))) = inverse(least_upper_bound(identity,X_233)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_233)))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_233))))]]) ).

cnf(refute_0_1391,plain,
    ( greatest_lower_bound(identity,inverse(X_233)) != inverse(least_upper_bound(identity,X_233))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))) = inverse(least_upper_bound(identity,X_233)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))),greatest_lower_bound(identity,inverse(X_233))) )],[refute_0_1389,refute_0_1390]) ).

cnf(refute_0_1392,plain,
    greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))) = inverse(least_upper_bound(identity,X_233)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_233)),inverse(least_upper_bound(identity,X_233))) )],[refute_0_1376,refute_0_1391]) ).

cnf(refute_0_1393,plain,
    greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)) = greatest_lower_bound(X_76,greatest_lower_bound(identity,inverse(Y))),
    inference(subst,[],[refute_0_839:[bind(X,$fot(inverse(Y))),bind(X_36,$fot(X_76)),bind(X_37,$fot(identity))]]) ).

cnf(refute_0_1394,plain,
    ( greatest_lower_bound(identity,inverse(Y)) != inverse(least_upper_bound(identity,Y))
    | greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)) != greatest_lower_bound(X_76,greatest_lower_bound(identity,inverse(Y)))
    | greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)) = greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)),greatest_lower_bound(X_76,greatest_lower_bound(identity,inverse(Y)))) ),[1,1],$fot(inverse(least_upper_bound(identity,Y)))]]) ).

cnf(refute_0_1395,plain,
    ( greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)) != greatest_lower_bound(X_76,greatest_lower_bound(identity,inverse(Y)))
    | greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)) = greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(Y)),inverse(least_upper_bound(identity,Y))) )],[refute_0_500,refute_0_1394]) ).

cnf(refute_0_1396,plain,
    greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)) = greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)),greatest_lower_bound(X_76,greatest_lower_bound(identity,inverse(Y)))) )],[refute_0_1393,refute_0_1395]) ).

cnf(refute_0_1397,plain,
    greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y))),
    inference(subst,[],[refute_0_909:[bind(Y,$fot(inverse(Y))),bind(X_75,$fot(identity))]]) ).

cnf(refute_0_1398,plain,
    ( greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)) != greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y)))
    | greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y)))
    | greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y))) = greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)),greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y)))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y))))]]) ).

cnf(refute_0_1399,plain,
    ( greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)) != greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y)))
    | greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y))) = greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y)))) )],[refute_0_1397,refute_0_1398]) ).

cnf(refute_0_1400,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y))) = greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(Y),greatest_lower_bound(X_76,identity)),greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1396,refute_0_1399]) ).

cnf(refute_0_1401,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y))) != greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y)))
    | greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y))) = greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y))))),bind(Y0,$fot(greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y)))))]]) ).

cnf(refute_0_1402,plain,
    greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y))) = greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_76,inverse(Y))),greatest_lower_bound(X_76,inverse(least_upper_bound(identity,Y)))) )],[refute_0_1400,refute_0_1401]) ).

cnf(refute_0_1403,plain,
    greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))),
    inference(subst,[],[refute_0_1402:[bind(Y,$fot(X_233)),bind(X_76,$fot(inverse(X_233)))]]) ).

cnf(refute_0_1404,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))) != inverse(least_upper_bound(identity,X_233))
    | greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233)))
    | greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))) = inverse(least_upper_bound(identity,X_233)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_233))))]]) ).

cnf(refute_0_1405,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))) != inverse(least_upper_bound(identity,X_233))
    | greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))) = inverse(least_upper_bound(identity,X_233)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233)))) )],[refute_0_1403,refute_0_1404]) ).

cnf(refute_0_1406,plain,
    greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))) = inverse(least_upper_bound(identity,X_233)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_233),inverse(X_233))),inverse(least_upper_bound(identity,X_233))) )],[refute_0_1392,refute_0_1405]) ).

cnf(refute_0_1407,plain,
    ( multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) != greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233)))
    | greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))) != inverse(least_upper_bound(identity,X_233))
    | multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) = inverse(least_upper_bound(identity,X_233)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_233),greatest_lower_bound(identity,X_233)),inverse(least_upper_bound(identity,X_233))) ),[0],$fot(greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))))]]) ).

cnf(refute_0_1408,plain,
    ( multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) != greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233)))
    | multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) = inverse(least_upper_bound(identity,X_233)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233))),inverse(least_upper_bound(identity,X_233))) )],[refute_0_1406,refute_0_1407]) ).

cnf(refute_0_1409,plain,
    ( multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)) != greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233)))
    | multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) = inverse(least_upper_bound(identity,X_233)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(identity,X_233)),greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233)))) )],[refute_0_1375,refute_0_1408]) ).

cnf(refute_0_1410,plain,
    multiply(inverse(X_233),greatest_lower_bound(identity,X_233)) = inverse(least_upper_bound(identity,X_233)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(greatest_lower_bound(X_233,identity),identity)),greatest_lower_bound(inverse(X_233),inverse(least_upper_bound(identity,X_233)))) )],[refute_0_1364,refute_0_1409]) ).

cnf(refute_0_1411,plain,
    multiply(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_1410:[bind(X_233,$fot(greatest_lower_bound(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_1412,plain,
    ( multiply(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) != inverse(b)
    | multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) ),[0,0],$fot(inverse(b))]]) ).

cnf(refute_0_1413,plain,
    ( multiply(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) )],[refute_0_1268,refute_0_1412]) ).

cnf(refute_0_1414,plain,
    multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_1411,refute_0_1413]) ).

cnf(refute_0_1415,plain,
    greatest_lower_bound(identity,least_upper_bound(b,identity)) = identity,
    inference(subst,[],[refute_0_215:[bind(X_10,$fot(identity)),bind(X_11,$fot(b))]]) ).

cnf(refute_0_1416,plain,
    greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))) = greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_1417,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))) != greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity)))
    | greatest_lower_bound(identity,least_upper_bound(b,identity)) != identity
    | greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))) = greatest_lower_bound(a,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))),greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1418,plain,
    ( greatest_lower_bound(identity,least_upper_bound(b,identity)) != identity
    | greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))),greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity)))) )],[refute_0_1416,refute_0_1417]) ).

cnf(refute_0_1419,plain,
    greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(b,identity)),identity) )],[refute_0_1415,refute_0_1418]) ).

cnf(refute_0_1420,plain,
    greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75))) = greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y),
    inference(subst,[],[refute_0_794:[bind(X_23,$fot(greatest_lower_bound(X_77,X_75)))]]) ).

cnf(refute_0_1421,plain,
    greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77)) = greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75)),
    inference(subst,[],[refute_0_839:[bind(X,$fot(X_75)),bind(X_36,$fot(Y)),bind(X_37,$fot(X_77))]]) ).

cnf(refute_0_1422,plain,
    ( greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77)) != greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75))
    | greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75)) = greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75))))]]) ).

cnf(refute_0_1423,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75)) = greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77)),greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75))) )],[refute_0_1421,refute_0_1422]) ).

cnf(refute_0_1424,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75)) != greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))
    | greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75))) != greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)
    | greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) = greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75))),greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)) ),[0,1],$fot(greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77)))]]) ).

cnf(refute_0_1425,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75))) != greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)
    | greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) = greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75)),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) )],[refute_0_1423,refute_0_1424]) ).

cnf(refute_0_1426,plain,
    greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) = greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(Y,greatest_lower_bound(X_77,X_75))),greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)) )],[refute_0_1420,refute_0_1425]) ).

cnf(refute_0_1427,plain,
    greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23)) = greatest_lower_bound(X_23,greatest_lower_bound(X_36,X_37)),
    inference(subst,[],[refute_0_794:[bind(Y,$fot(greatest_lower_bound(X_36,X_37)))]]) ).

cnf(refute_0_1428,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_23))]]) ).

cnf(refute_0_1429,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23)
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23)))]]) ).

cnf(refute_0_1430,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23)) )],[refute_0_1428,refute_0_1429]) ).

cnf(refute_0_1431,plain,
    ( greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23)) != greatest_lower_bound(X_23,greatest_lower_bound(X_36,X_37))
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23))
    | greatest_lower_bound(X_23,greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23))) = greatest_lower_bound(X_23,greatest_lower_bound(X_36,X_37)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23)),greatest_lower_bound(X_23,greatest_lower_bound(X_36,X_37))) ),[0,1],$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23)))]]) ).

cnf(refute_0_1432,plain,
    ( greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23)) != greatest_lower_bound(X_23,greatest_lower_bound(X_36,X_37))
    | greatest_lower_bound(X_23,greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23))) = greatest_lower_bound(X_23,greatest_lower_bound(X_36,X_37)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23))) )],[refute_0_1430,refute_0_1431]) ).

cnf(refute_0_1433,plain,
    greatest_lower_bound(X_23,greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_23))) = greatest_lower_bound(X_23,greatest_lower_bound(X_36,X_37)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_23,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_23)),greatest_lower_bound(X_23,greatest_lower_bound(X_36,X_37))) )],[refute_0_1427,refute_0_1432]) ).

cnf(refute_0_1434,plain,
    greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)),
    inference(subst,[],[refute_0_1433:[bind(X_23,$fot(X_77)),bind(X_36,$fot(Y)),bind(X_37,$fot(X_75))]]) ).

cnf(refute_0_1435,plain,
    greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75)) = greatest_lower_bound(X_75,X_77),
    inference(subst,[],[refute_0_794:[bind(Y,$fot(X_77)),bind(X_23,$fot(X_75))]]) ).

cnf(refute_0_1436,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))) = greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))))]]) ).

cnf(refute_0_1437,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))) != greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75)))
    | greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75)) != greatest_lower_bound(X_75,X_77)
    | greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))) = greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))),greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75)))) ),[1,1],$fot(greatest_lower_bound(X_75,X_77))]]) ).

cnf(refute_0_1438,plain,
    ( greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75)) != greatest_lower_bound(X_75,X_77)
    | greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))) = greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))),greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75)))) )],[refute_0_1436,refute_0_1437]) ).

cnf(refute_0_1439,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))) = greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75)),greatest_lower_bound(X_75,X_77)) )],[refute_0_1435,refute_0_1438]) ).

cnf(refute_0_1440,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_1441,plain,
    greatest_lower_bound(X_38,X_37) = greatest_lower_bound(X_37,X_38),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_38)),bind(Y,$fot(X_37))]]) ).

cnf(refute_0_1442,plain,
    ( greatest_lower_bound(X_38,X_37) != greatest_lower_bound(X_37,X_38)
    | greatest_lower_bound(X_37,X_38) = greatest_lower_bound(X_38,X_37) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_38,X_37))),bind(Y0,$fot(greatest_lower_bound(X_37,X_38)))]]) ).

cnf(refute_0_1443,plain,
    greatest_lower_bound(X_37,X_38) = greatest_lower_bound(X_38,X_37),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_38,X_37),greatest_lower_bound(X_37,X_38)) )],[refute_0_1441,refute_0_1442]) ).

cnf(refute_0_1444,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38)
    | greatest_lower_bound(X_37,X_38) != greatest_lower_bound(X_38,X_37)
    | greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38)) ),[0,1],$fot(greatest_lower_bound(X_38,X_37))]]) ).

cnf(refute_0_1445,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38)
    | greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,X_38),greatest_lower_bound(X_38,X_37)) )],[refute_0_1443,refute_0_1444]) ).

cnf(refute_0_1446,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38)) )],[refute_0_1440,refute_0_1445]) ).

cnf(refute_0_1447,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_1448,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38)
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38))
    | greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38))]]) ).

cnf(refute_0_1449,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38)
    | greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38))) )],[refute_0_1447,refute_0_1448]) ).

cnf(refute_0_1450,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_38)) )],[refute_0_1446,refute_0_1449]) ).

cnf(refute_0_1451,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38))
    | greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38)) = greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)))),bind(Y0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38))))]]) ).

cnf(refute_0_1452,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38)) = greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_38,X_37)),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_38))) )],[refute_0_1450,refute_0_1451]) ).

cnf(refute_0_1453,plain,
    greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)) = greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))),
    inference(subst,[],[refute_0_1452:[bind(X_36,$fot(Y)),bind(X_37,$fot(greatest_lower_bound(X_77,X_75))),bind(X_38,$fot(X_75))]]) ).

cnf(refute_0_1454,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))) != greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))
    | greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)) != greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75)))
    | greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)) = greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))))]]) ).

cnf(refute_0_1455,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))) != greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))
    | greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)) = greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)),greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75)))) )],[refute_0_1453,refute_0_1454]) ).

cnf(refute_0_1456,plain,
    greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)) = greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_75,greatest_lower_bound(X_77,X_75))),greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))) )],[refute_0_1439,refute_0_1455]) ).

cnf(refute_0_1457,plain,
    greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))))]]) ).

cnf(refute_0_1458,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)) != greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))
    | greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))) != greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)))
    | greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))),greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77)))]]) ).

cnf(refute_0_1459,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)) != greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))
    | greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))),greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)))) )],[refute_0_1457,refute_0_1458]) ).

cnf(refute_0_1460,plain,
    greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)),greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))) )],[refute_0_1456,refute_0_1459]) ).

cnf(refute_0_1461,plain,
    ( greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))) != greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75))
    | greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))) != greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77)))
    | greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))))),bind(Y0,$fot(greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))))),bind(Z0,$fot(greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75))))]]) ).

cnf(refute_0_1462,plain,
    ( greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))) != greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75))
    | greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))),greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77)))) )],[refute_0_1460,refute_0_1461]) ).

cnf(refute_0_1463,plain,
    greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(X_75,X_77))),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75))) )],[refute_0_1434,refute_0_1462]) ).

cnf(refute_0_1464,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75))) = greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)),
    inference(subst,[],[refute_0_839:[bind(X_37,$fot(greatest_lower_bound(X_77,X_75)))]]) ).

cnf(refute_0_1465,plain,
    greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77)) = greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75)),
    inference(subst,[],[refute_0_839:[bind(X,$fot(X_75)),bind(X_37,$fot(X_77))]]) ).

cnf(refute_0_1466,plain,
    ( greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77)) != greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75))
    | greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75)) = greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77)))),bind(Y0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75))))]]) ).

cnf(refute_0_1467,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75)) = greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77)),greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75))) )],[refute_0_1465,refute_0_1466]) ).

cnf(refute_0_1468,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75))) != greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X))
    | greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75)) != greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))
    | greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))) = greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75))),greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X))) ),[0,1],$fot(greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77)))]]) ).

cnf(refute_0_1469,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75))) != greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X))
    | greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))) = greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75)),greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))) )],[refute_0_1467,refute_0_1468]) ).

cnf(refute_0_1470,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))) = greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_36,greatest_lower_bound(X_77,X_75))),greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X))) )],[refute_0_1464,refute_0_1469]) ).

cnf(refute_0_1471,plain,
    greatest_lower_bound(greatest_lower_bound(X_77,X_75),X) = greatest_lower_bound(X_77,greatest_lower_bound(X_75,X)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_77)),bind(Y,$fot(X_75)),bind(Z,$fot(X))]]) ).

cnf(refute_0_1472,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)) = greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)))]]) ).

cnf(refute_0_1473,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)) != greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X))
    | greatest_lower_bound(greatest_lower_bound(X_77,X_75),X) != greatest_lower_bound(X_77,greatest_lower_bound(X_75,X))
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)) = greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)),greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X))) ),[1,1],$fot(greatest_lower_bound(X_77,greatest_lower_bound(X_75,X)))]]) ).

cnf(refute_0_1474,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_77,X_75),X) != greatest_lower_bound(X_77,greatest_lower_bound(X_75,X))
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)) = greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)),greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X))) )],[refute_0_1472,refute_0_1473]) ).

cnf(refute_0_1475,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)) = greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_77,X_75),X),greatest_lower_bound(X_77,greatest_lower_bound(X_75,X))) )],[refute_0_1471,refute_0_1474]) ).

cnf(refute_0_1476,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))) != greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X))
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)) != greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X)))
    | greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))) = greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))),greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X)))) ),[0],$fot(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)))]]) ).

cnf(refute_0_1477,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))) != greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X))
    | greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))) = greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X)),greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X)))) )],[refute_0_1475,refute_0_1476]) ).

cnf(refute_0_1478,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))) = greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))),greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X))) )],[refute_0_1470,refute_0_1477]) ).

cnf(refute_0_1479,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))) != greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X)))
    | greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X))) = greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))))),bind(Y0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X)))))]]) ).

cnf(refute_0_1480,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X))) = greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_75,greatest_lower_bound(X_36,X_77))),greatest_lower_bound(X_36,greatest_lower_bound(X_77,greatest_lower_bound(X_75,X)))) )],[refute_0_1478,refute_0_1479]) ).

cnf(refute_0_1481,plain,
    greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))),
    inference(subst,[],[refute_0_1480:[bind(X,$fot(X_77)),bind(X_36,$fot(greatest_lower_bound(X_77,X_75))),bind(X_75,$fot(Y)),bind(X_77,$fot(X_75))]]) ).

cnf(refute_0_1482,plain,
    ( greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))) != greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75))
    | greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) != greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)))
    | greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))))),bind(Y0,$fot(greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))))),bind(Z0,$fot(greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75))))]]) ).

cnf(refute_0_1483,plain,
    ( greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))) != greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75))
    | greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))),greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75)))) )],[refute_0_1481,refute_0_1482]) ).

cnf(refute_0_1484,plain,
    greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) = greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(Y,greatest_lower_bound(greatest_lower_bound(X_77,X_75),X_75))),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75))) )],[refute_0_1463,refute_0_1483]) ).

cnf(refute_0_1485,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) != greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75))
    | greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) != greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)
    | greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) = greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))),greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)) ),[0],$fot(greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)))]]) ).

cnf(refute_0_1486,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) != greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)
    | greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) = greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))),greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75))) )],[refute_0_1484,refute_0_1485]) ).

cnf(refute_0_1487,plain,
    greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y) = greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_77)),bind(Y,$fot(X_75)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_1488,plain,
    ( greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) != greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)
    | greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y) != greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y))
    | greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) = greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)),greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y))]]) ).

cnf(refute_0_1489,plain,
    ( greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) != greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)
    | greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) = greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y),greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y))) )],[refute_0_1487,refute_0_1488]) ).

cnf(refute_0_1490,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))) != greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)
    | greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) = greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)),greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)) )],[refute_0_1486,refute_0_1489]) ).

cnf(refute_0_1491,plain,
    greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) = greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_77,X_75),greatest_lower_bound(X_75,greatest_lower_bound(Y,X_77))),greatest_lower_bound(greatest_lower_bound(X_77,X_75),Y)) )],[refute_0_1426,refute_0_1490]) ).

cnf(refute_0_1492,plain,
    ( greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) != greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y))
    | greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y)) = greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)))),bind(Y0,$fot(greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y))))]]) ).

cnf(refute_0_1493,plain,
    greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y)) = greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,greatest_lower_bound(Y,X_75)),greatest_lower_bound(X_77,greatest_lower_bound(X_75,Y))) )],[refute_0_1491,refute_0_1492]) ).

cnf(refute_0_1494,plain,
    greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)) = greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_1493:[bind(Y,$fot(identity)),bind(X_75,$fot(least_upper_bound(b,identity))),bind(X_77,$fot(a))]]) ).

cnf(refute_0_1495,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)) != greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity)))
    | greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)) = greatest_lower_bound(a,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))))),bind(Z0,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_1496,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity)))) )],[refute_0_1494,refute_0_1495]) ).

cnf(refute_0_1497,plain,
    greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_1419,refute_0_1496]) ).

cnf(refute_0_1498,plain,
    multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))) = multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))),
    introduced(tautology,[refl,[$fot(multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))))]]) ).

cnf(refute_0_1499,plain,
    ( multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))) != multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)))
    | greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)) != greatest_lower_bound(a,identity)
    | multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))) = multiply(inverse(b),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))),multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)))) ),[1,1],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_1500,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)) != greatest_lower_bound(a,identity)
    | multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))) = multiply(inverse(b),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))),multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)))) )],[refute_0_1498,refute_0_1499]) ).

cnf(refute_0_1501,plain,
    multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))) = multiply(inverse(b),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),greatest_lower_bound(a,identity)) )],[refute_0_1497,refute_0_1500]) ).

cnf(refute_0_1502,plain,
    multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity)) = greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))),
    inference(subst,[],[refute_0_161:[bind(X_107,$fot(X_231)),bind(X_108,$fot(greatest_lower_bound(X,Y)))]]) ).

cnf(refute_0_1503,plain,
    greatest_lower_bound(X,greatest_lower_bound(Y,identity)) = greatest_lower_bound(greatest_lower_bound(X,Y),identity),
    inference(subst,[],[associativity_of_glb:[bind(Z,$fot(identity))]]) ).

cnf(refute_0_1504,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(Y,identity)) != greatest_lower_bound(greatest_lower_bound(X,Y),identity)
    | greatest_lower_bound(greatest_lower_bound(X,Y),identity) = greatest_lower_bound(X,greatest_lower_bound(Y,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,identity)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),identity)))]]) ).

cnf(refute_0_1505,plain,
    greatest_lower_bound(greatest_lower_bound(X,Y),identity) = greatest_lower_bound(X,greatest_lower_bound(Y,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,identity)),greatest_lower_bound(greatest_lower_bound(X,Y),identity)) )],[refute_0_1503,refute_0_1504]) ).

cnf(refute_0_1506,plain,
    ( multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity)) != greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y)))
    | greatest_lower_bound(greatest_lower_bound(X,Y),identity) != greatest_lower_bound(X,greatest_lower_bound(Y,identity))
    | multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))) = greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity)),greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y)))) ),[0,1],$fot(greatest_lower_bound(X,greatest_lower_bound(Y,identity)))]]) ).

cnf(refute_0_1507,plain,
    ( multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity)) != greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y)))
    | multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))) = greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),identity),greatest_lower_bound(X,greatest_lower_bound(Y,identity))) )],[refute_0_1505,refute_0_1506]) ).

cnf(refute_0_1508,plain,
    multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))) = greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))),
    inference(resolve,[$cnf( $equal(multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity)),greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y)))) )],[refute_0_1502,refute_0_1507]) ).

cnf(refute_0_1509,plain,
    multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity)) = multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y))),
    inference(subst,[],[refute_0_925:[bind(X_232,$fot(greatest_lower_bound(X,Y))),bind(X_33,$fot(X_231))]]) ).

cnf(refute_0_1510,plain,
    greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))) = multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity)),
    inference(subst,[],[refute_0_308:[bind(X_107,$fot(X_231)),bind(X_108,$fot(greatest_lower_bound(X,Y)))]]) ).

cnf(refute_0_1511,plain,
    ( multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity)) != multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y)))
    | greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))) != multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity))
    | greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))) = multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))))),bind(Y0,$fot(multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity)))),bind(Z0,$fot(multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y)))))]]) ).

cnf(refute_0_1512,plain,
    ( multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity)) != multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y)))
    | greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))) = multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))),multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity))) )],[refute_0_1510,refute_0_1511]) ).

cnf(refute_0_1513,plain,
    greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))) = multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y))),
    inference(resolve,[$cnf( $equal(multiply(X_231,greatest_lower_bound(greatest_lower_bound(X,Y),identity)),multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y)))) )],[refute_0_1509,refute_0_1512]) ).

cnf(refute_0_1514,plain,
    ( multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))) != greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y)))
    | greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))) != multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y)))
    | multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))) = multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))),multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y)))) ),[0],$fot(greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))))]]) ).

cnf(refute_0_1515,plain,
    ( multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))) != greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y)))
    | multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))) = multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y))),multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y)))) )],[refute_0_1513,refute_0_1514]) ).

cnf(refute_0_1516,plain,
    multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))) = multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y))),
    inference(resolve,[$cnf( $equal(multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))),greatest_lower_bound(X_231,multiply(X_231,greatest_lower_bound(X,Y)))) )],[refute_0_1508,refute_0_1515]) ).

cnf(refute_0_1517,plain,
    ( multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))) != multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y)))
    | multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y))) = multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))))),bind(Y0,$fot(multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y)))))]]) ).

cnf(refute_0_1518,plain,
    multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y))) = multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(multiply(X_231,greatest_lower_bound(X,greatest_lower_bound(Y,identity))),multiply(X_231,greatest_lower_bound(identity,greatest_lower_bound(X,Y)))) )],[refute_0_1516,refute_0_1517]) ).

cnf(refute_0_1519,plain,
    multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))),
    inference(subst,[],[refute_0_1518:[bind(X,$fot(a)),bind(Y,$fot(least_upper_bound(b,identity))),bind(X_231,$fot(inverse(b)))]]) ).

cnf(refute_0_1520,plain,
    ( multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))) != multiply(inverse(b),greatest_lower_bound(a,identity))
    | multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)))
    | multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = multiply(inverse(b),greatest_lower_bound(a,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))))),bind(Y0,$fot(multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))))),bind(Z0,$fot(multiply(inverse(b),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_1521,plain,
    ( multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))) != multiply(inverse(b),greatest_lower_bound(a,identity))
    | multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = multiply(inverse(b),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)))) )],[refute_0_1519,refute_0_1520]) ).

cnf(refute_0_1522,plain,
    multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = multiply(inverse(b),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity))),multiply(inverse(b),greatest_lower_bound(a,identity))) )],[refute_0_1501,refute_0_1521]) ).

cnf(refute_0_1523,plain,
    ( multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != multiply(inverse(b),greatest_lower_bound(a,identity))
    | multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | multiply(inverse(b),greatest_lower_bound(a,identity)) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) ),[0],$fot(multiply(inverse(b),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_1524,plain,
    ( multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | multiply(inverse(b),greatest_lower_bound(a,identity)) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(inverse(b),greatest_lower_bound(a,identity))) )],[refute_0_1522,refute_0_1523]) ).

cnf(refute_0_1525,plain,
    multiply(inverse(b),greatest_lower_bound(a,identity)) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_1414,refute_0_1524]) ).

cnf(refute_0_1526,plain,
    ( multiply(inverse(b),greatest_lower_bound(a,identity)) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = multiply(inverse(b),greatest_lower_bound(a,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(inverse(b),greatest_lower_bound(a,identity)))),bind(Y0,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_1527,plain,
    inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = multiply(inverse(b),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_1525,refute_0_1526]) ).

cnf(refute_0_1528,plain,
    ( inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != multiply(inverse(b),greatest_lower_bound(a,identity))
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != greatest_lower_bound(identity,inverse(b))
    | multiply(inverse(b),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,inverse(b)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,inverse(b))) ),[0],$fot(multiply(inverse(b),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_1529,plain,
    ( inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != greatest_lower_bound(identity,inverse(b))
    | multiply(inverse(b),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,inverse(b)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(inverse(b),greatest_lower_bound(a,identity))) )],[refute_0_1527,refute_0_1528]) ).

cnf(refute_0_1530,plain,
    ( multiply(inverse(b),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,inverse(b))
    | greatest_lower_bound(identity,inverse(b)) != inverse(least_upper_bound(b,identity))
    | multiply(inverse(b),greatest_lower_bound(a,identity)) = inverse(least_upper_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(b),greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))) ),[0],$fot(greatest_lower_bound(identity,inverse(b)))]]) ).

cnf(refute_0_1531,plain,
    ( multiply(inverse(b),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,inverse(b))
    | multiply(inverse(b),greatest_lower_bound(a,identity)) = inverse(least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(b)),inverse(least_upper_bound(b,identity))) )],[refute_0_779,refute_0_1530]) ).

cnf(refute_0_1532,plain,
    ( inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != greatest_lower_bound(identity,inverse(b))
    | multiply(inverse(b),greatest_lower_bound(a,identity)) = inverse(least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,inverse(b))) )],[refute_0_1529,refute_0_1531]) ).

cnf(refute_0_1533,plain,
    multiply(inverse(b),greatest_lower_bound(a,identity)) = inverse(least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,inverse(b))) )],[refute_0_1294,refute_0_1532]) ).

cnf(refute_0_1534,plain,
    ( multiply(inverse(b),greatest_lower_bound(a,identity)) != inverse(least_upper_bound(b,identity))
    | multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) != least_upper_bound(greatest_lower_bound(a,identity),multiply(inverse(b),greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) = least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)),least_upper_bound(greatest_lower_bound(a,identity),multiply(inverse(b),greatest_lower_bound(a,identity)))) ),[1,1],$fot(inverse(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_1535,plain,
    ( multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) != least_upper_bound(greatest_lower_bound(a,identity),multiply(inverse(b),greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) = least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))) )],[refute_0_1533,refute_0_1534]) ).

cnf(refute_0_1536,plain,
    multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) = least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)),least_upper_bound(greatest_lower_bound(a,identity),multiply(inverse(b),greatest_lower_bound(a,identity)))) )],[refute_0_1290,refute_0_1535]) ).

cnf(refute_0_1537,plain,
    multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_1538,plain,
    inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_14,X_15))),
    inference(subst,[],[refute_0_299:[bind(Y,$fot(least_upper_bound(X_14,X_15)))]]) ).

cnf(refute_0_1539,plain,
    ( inverse(least_upper_bound(X_15,X_14)) != inverse(least_upper_bound(X_14,X_15))
    | inverse(least_upper_bound(X_14,X_15)) = inverse(least_upper_bound(X_15,X_14)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(least_upper_bound(X_15,X_14)))),bind(Y0,$fot(inverse(least_upper_bound(X_14,X_15))))]]) ).

cnf(refute_0_1540,plain,
    inverse(least_upper_bound(X_14,X_15)) = inverse(least_upper_bound(X_15,X_14)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_15,X_14)),inverse(least_upper_bound(X_14,X_15))) )],[refute_0_58,refute_0_1539]) ).

cnf(refute_0_1541,plain,
    ( inverse(least_upper_bound(X_14,X_15)) != inverse(least_upper_bound(X_15,X_14))
    | inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_14,X_15)))
    | inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_15,X_14))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))),greatest_lower_bound(identity,inverse(least_upper_bound(X_14,X_15)))) ),[1,1],$fot(inverse(least_upper_bound(X_15,X_14)))]]) ).

cnf(refute_0_1542,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_14,X_15)))
    | inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_15,X_14))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_15,X_14))) )],[refute_0_1540,refute_0_1541]) ).

cnf(refute_0_1543,plain,
    inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))) = greatest_lower_bound(identity,inverse(least_upper_bound(X_15,X_14))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))),greatest_lower_bound(identity,inverse(least_upper_bound(X_14,X_15)))) )],[refute_0_1538,refute_0_1542]) ).

cnf(refute_0_1544,plain,
    greatest_lower_bound(identity,inverse(least_upper_bound(X_15,X_14))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,X_14))),
    inference(subst,[],[refute_0_500:[bind(Y,$fot(least_upper_bound(X_15,X_14)))]]) ).

cnf(refute_0_1545,plain,
    ( greatest_lower_bound(identity,inverse(least_upper_bound(X_15,X_14))) != inverse(least_upper_bound(identity,least_upper_bound(X_15,X_14)))
    | inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_15,X_14)))
    | inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,X_14))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))),greatest_lower_bound(identity,inverse(least_upper_bound(X_15,X_14)))) ),[1],$fot(inverse(least_upper_bound(identity,least_upper_bound(X_15,X_14))))]]) ).

cnf(refute_0_1546,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))) != greatest_lower_bound(identity,inverse(least_upper_bound(X_15,X_14)))
    | inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,X_14))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_15,X_14))),inverse(least_upper_bound(identity,least_upper_bound(X_15,X_14)))) )],[refute_0_1544,refute_0_1545]) ).

cnf(refute_0_1547,plain,
    inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,X_14))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(X_14,X_15))),greatest_lower_bound(identity,inverse(least_upper_bound(X_15,X_14)))) )],[refute_0_1543,refute_0_1546]) ).

cnf(refute_0_1548,plain,
    inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) = inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))),
    inference(subst,[],[refute_0_1547:[bind(X_14,$fot(greatest_lower_bound(a,identity))),bind(X_15,$fot(inverse(b)))]]) ).

cnf(refute_0_1549,plain,
    inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) = inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12)))),
    inference(subst,[],[refute_0_140:[bind(X_13,$fot(inverse(greatest_lower_bound(identity,X_12))))]]) ).

cnf(refute_0_1550,plain,
    greatest_lower_bound(X_12,identity) = greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12))),
    inference(subst,[],[refute_0_625:[bind(X_204,$fot(X_12))]]) ).

cnf(refute_0_1551,plain,
    ( greatest_lower_bound(X_12,identity) != greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12)))
    | greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12))) = greatest_lower_bound(X_12,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_12,identity))),bind(Y0,$fot(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12)))))]]) ).

cnf(refute_0_1552,plain,
    greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12))) = greatest_lower_bound(X_12,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,identity),greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12)))) )],[refute_0_1550,refute_0_1551]) ).

cnf(refute_0_1553,plain,
    ( greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12))) != greatest_lower_bound(X_12,identity)
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) != inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12))))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) = inverse(greatest_lower_bound(X_12,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)),inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12))))) ),[1,0],$fot(greatest_lower_bound(X_12,identity))]]) ).

cnf(refute_0_1554,plain,
    ( inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) != inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12))))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) = inverse(greatest_lower_bound(X_12,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12))),greatest_lower_bound(X_12,identity)) )],[refute_0_1552,refute_0_1553]) ).

cnf(refute_0_1555,plain,
    inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) = inverse(greatest_lower_bound(X_12,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)),inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12))))) )],[refute_0_1549,refute_0_1554]) ).

cnf(refute_0_1556,plain,
    inverse(greatest_lower_bound(X,inverse(X_89))) = least_upper_bound(inverse(X),inverse(inverse(X_89))),
    inference(subst,[],[p12x_3:[bind(Y,$fot(inverse(X_89)))]]) ).

cnf(refute_0_1557,plain,
    ( inverse(greatest_lower_bound(X,inverse(X_89))) != least_upper_bound(inverse(X),inverse(inverse(X_89)))
    | inverse(inverse(X_89)) != X_89
    | inverse(greatest_lower_bound(X,inverse(X_89))) = least_upper_bound(inverse(X),X_89) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X,inverse(X_89))),least_upper_bound(inverse(X),inverse(inverse(X_89)))) ),[1,1],$fot(X_89)]]) ).

cnf(refute_0_1558,plain,
    ( inverse(greatest_lower_bound(X,inverse(X_89))) != least_upper_bound(inverse(X),inverse(inverse(X_89)))
    | inverse(greatest_lower_bound(X,inverse(X_89))) = least_upper_bound(inverse(X),X_89) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_89)),X_89) )],[refute_0_98,refute_0_1557]) ).

cnf(refute_0_1559,plain,
    inverse(greatest_lower_bound(X,inverse(X_89))) = least_upper_bound(inverse(X),X_89),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,inverse(X_89))),least_upper_bound(inverse(X),inverse(inverse(X_89)))) )],[refute_0_1556,refute_0_1558]) ).

cnf(refute_0_1560,plain,
    inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12)))) = least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12)),
    inference(subst,[],[refute_0_1559:[bind(X,$fot(X_12)),bind(X_89,$fot(greatest_lower_bound(identity,X_12)))]]) ).

cnf(refute_0_1561,plain,
    ( inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12)))) != least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) != inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12))))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) = least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12)))))),bind(Z0,$fot(least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12))))]]) ).

cnf(refute_0_1562,plain,
    ( inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12)))) != least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) = least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)),inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12))))) )],[refute_0_1549,refute_0_1561]) ).

cnf(refute_0_1563,plain,
    inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) = least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_12,inverse(greatest_lower_bound(identity,X_12)))),least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12))) )],[refute_0_1560,refute_0_1562]) ).

cnf(refute_0_1564,plain,
    ( inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) != inverse(greatest_lower_bound(X_12,identity))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) != least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12))
    | least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12)) = inverse(greatest_lower_bound(X_12,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)),inverse(greatest_lower_bound(X_12,identity))) ),[0],$fot(least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12)))]]) ).

cnf(refute_0_1565,plain,
    ( inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)) != inverse(greatest_lower_bound(X_12,identity))
    | least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12)) = inverse(greatest_lower_bound(X_12,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)),least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12))) )],[refute_0_1563,refute_0_1564]) ).

cnf(refute_0_1566,plain,
    least_upper_bound(inverse(X_12),greatest_lower_bound(identity,X_12)) = inverse(greatest_lower_bound(X_12,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_12)),X_12)),inverse(greatest_lower_bound(X_12,identity))) )],[refute_0_1555,refute_0_1565]) ).

cnf(refute_0_1567,plain,
    least_upper_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)),
    inference(subst,[],[refute_0_1566:[bind(X_12,$fot(greatest_lower_bound(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_1568,plain,
    ( inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) != inverse(b)
    | least_upper_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))
    | least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))) ),[0,0],$fot(inverse(b))]]) ).

cnf(refute_0_1569,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))
    | least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) )],[refute_0_1268,refute_0_1568]) ).

cnf(refute_0_1570,plain,
    least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))) )],[refute_0_1567,refute_0_1569]) ).

cnf(refute_0_1571,plain,
    inverse(inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)))) = greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))))]]) ).

cnf(refute_0_1572,plain,
    ( inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))) != inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))
    | inverse(inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)))) != greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))
    | inverse(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))) = greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)))),greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))) ),[0,0],$fot(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178))))]]) ).

cnf(refute_0_1573,plain,
    ( inverse(inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)))) != greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))
    | inverse(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))) = greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))),inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))) )],[refute_0_1014,refute_0_1572]) ).

cnf(refute_0_1574,plain,
    inverse(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))) = greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)))),greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))) )],[refute_0_1571,refute_0_1573]) ).

cnf(refute_0_1575,plain,
    inverse(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))) = greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178))))]]) ).

cnf(refute_0_1576,plain,
    ( inverse(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))) != greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178))
    | inverse(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))) != greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))
    | greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)) = greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))),greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))) ),[0],$fot(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))]]) ).

cnf(refute_0_1577,plain,
    ( inverse(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))) != greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))
    | greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)) = greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))),greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178))) )],[refute_0_1575,refute_0_1576]) ).

cnf(refute_0_1578,plain,
    greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)) = greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))),greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))) )],[refute_0_1574,refute_0_1577]) ).

cnf(refute_0_1579,plain,
    ( greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)) != greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))
    | greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)) = greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)))),bind(Y0,$fot(greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))))]]) ).

cnf(refute_0_1580,plain,
    greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178)) = greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_179,greatest_lower_bound(X_180,X_178)),greatest_lower_bound(X_180,greatest_lower_bound(X_179,X_178))) )],[refute_0_1578,refute_0_1579]) ).

cnf(refute_0_1581,plain,
    greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))) = greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_1580:[bind(X_178,$fot(least_upper_bound(b,identity))),bind(X_179,$fot(a)),bind(X_180,$fot(identity))]]) ).

cnf(refute_0_1582,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity)))
    | greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))) = greatest_lower_bound(a,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))))),bind(Z0,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_1583,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity)))) )],[refute_0_1581,refute_0_1582]) ).

cnf(refute_0_1584,plain,
    greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_1419,refute_0_1583]) ).

cnf(refute_0_1585,plain,
    least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_1586,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) ),[1,1],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_1587,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_1585,refute_0_1586]) ).

cnf(refute_0_1588,plain,
    least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = least_upper_bound(inverse(b),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_1584,refute_0_1587]) ).

cnf(refute_0_1589,plain,
    ( least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))
    | least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != least_upper_bound(inverse(b),greatest_lower_bound(a,identity))
    | least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) = inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))) ),[0],$fot(least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_1590,plain,
    ( least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))
    | least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) = inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),least_upper_bound(inverse(b),greatest_lower_bound(a,identity))) )],[refute_0_1588,refute_0_1589]) ).

cnf(refute_0_1591,plain,
    inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) = greatest_lower_bound(identity,least_upper_bound(X_273,X_274)),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))))]]) ).

cnf(refute_0_1592,plain,
    inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))) = least_upper_bound(identity,inverse(least_upper_bound(X_14,X_15))),
    inference(subst,[],[refute_0_486:[bind(Y,$fot(least_upper_bound(X_14,X_15)))]]) ).

cnf(refute_0_1593,plain,
    ( inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))) != least_upper_bound(identity,inverse(least_upper_bound(X_14,X_15)))
    | inverse(least_upper_bound(X_14,X_15)) != inverse(least_upper_bound(X_15,X_14))
    | inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))) = least_upper_bound(identity,inverse(least_upper_bound(X_15,X_14))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))),least_upper_bound(identity,inverse(least_upper_bound(X_14,X_15)))) ),[1,1],$fot(inverse(least_upper_bound(X_15,X_14)))]]) ).

cnf(refute_0_1594,plain,
    ( inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))) != least_upper_bound(identity,inverse(least_upper_bound(X_14,X_15)))
    | inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))) = least_upper_bound(identity,inverse(least_upper_bound(X_15,X_14))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_15,X_14))) )],[refute_0_1540,refute_0_1593]) ).

cnf(refute_0_1595,plain,
    inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))) = least_upper_bound(identity,inverse(least_upper_bound(X_15,X_14))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))),least_upper_bound(identity,inverse(least_upper_bound(X_14,X_15)))) )],[refute_0_1592,refute_0_1594]) ).

cnf(refute_0_1596,plain,
    least_upper_bound(identity,inverse(least_upper_bound(X_15,X_14))) = inverse(greatest_lower_bound(identity,least_upper_bound(X_15,X_14))),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(least_upper_bound(X_15,X_14)))]]) ).

cnf(refute_0_1597,plain,
    ( inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))) != least_upper_bound(identity,inverse(least_upper_bound(X_15,X_14)))
    | least_upper_bound(identity,inverse(least_upper_bound(X_15,X_14))) != inverse(greatest_lower_bound(identity,least_upper_bound(X_15,X_14)))
    | inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))) = inverse(greatest_lower_bound(identity,least_upper_bound(X_15,X_14))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))),inverse(greatest_lower_bound(identity,least_upper_bound(X_15,X_14)))) ),[0],$fot(least_upper_bound(identity,inverse(least_upper_bound(X_15,X_14))))]]) ).

cnf(refute_0_1598,plain,
    ( inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))) != least_upper_bound(identity,inverse(least_upper_bound(X_15,X_14)))
    | inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))) = inverse(greatest_lower_bound(identity,least_upper_bound(X_15,X_14))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(least_upper_bound(X_15,X_14))),inverse(greatest_lower_bound(identity,least_upper_bound(X_15,X_14)))) )],[refute_0_1596,refute_0_1597]) ).

cnf(refute_0_1599,plain,
    inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))) = inverse(greatest_lower_bound(identity,least_upper_bound(X_15,X_14))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(X_14,X_15))),least_upper_bound(identity,inverse(least_upper_bound(X_15,X_14)))) )],[refute_0_1595,refute_0_1598]) ).

cnf(refute_0_1600,plain,
    inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))) = inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273))),
    inference(subst,[],[refute_0_1599:[bind(X_14,$fot(X_273)),bind(X_15,$fot(X_274))]]) ).

cnf(refute_0_1601,plain,
    ( inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))) != inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))
    | inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) != greatest_lower_bound(identity,least_upper_bound(X_273,X_274))
    | inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) = greatest_lower_bound(identity,least_upper_bound(X_273,X_274)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))),greatest_lower_bound(identity,least_upper_bound(X_273,X_274))) ),[0,0],$fot(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273))))]]) ).

cnf(refute_0_1602,plain,
    ( inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) != greatest_lower_bound(identity,least_upper_bound(X_273,X_274))
    | inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) = greatest_lower_bound(identity,least_upper_bound(X_273,X_274)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) )],[refute_0_1600,refute_0_1601]) ).

cnf(refute_0_1603,plain,
    inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) = greatest_lower_bound(identity,least_upper_bound(X_273,X_274)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))),greatest_lower_bound(identity,least_upper_bound(X_273,X_274))) )],[refute_0_1591,refute_0_1602]) ).

cnf(refute_0_1604,plain,
    inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) = greatest_lower_bound(identity,least_upper_bound(X_274,X_273)),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(identity,least_upper_bound(X_274,X_273))))]]) ).

cnf(refute_0_1605,plain,
    ( inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) != greatest_lower_bound(identity,least_upper_bound(X_273,X_274))
    | inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) != greatest_lower_bound(identity,least_upper_bound(X_274,X_273))
    | greatest_lower_bound(identity,least_upper_bound(X_274,X_273)) = greatest_lower_bound(identity,least_upper_bound(X_273,X_274)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))),greatest_lower_bound(identity,least_upper_bound(X_273,X_274))) ),[0],$fot(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))]]) ).

cnf(refute_0_1606,plain,
    ( inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) != greatest_lower_bound(identity,least_upper_bound(X_273,X_274))
    | greatest_lower_bound(identity,least_upper_bound(X_274,X_273)) = greatest_lower_bound(identity,least_upper_bound(X_273,X_274)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))),greatest_lower_bound(identity,least_upper_bound(X_274,X_273))) )],[refute_0_1604,refute_0_1605]) ).

cnf(refute_0_1607,plain,
    greatest_lower_bound(identity,least_upper_bound(X_274,X_273)) = greatest_lower_bound(identity,least_upper_bound(X_273,X_274)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))),greatest_lower_bound(identity,least_upper_bound(X_273,X_274))) )],[refute_0_1603,refute_0_1606]) ).

cnf(refute_0_1608,plain,
    ( greatest_lower_bound(identity,least_upper_bound(X_274,X_273)) != greatest_lower_bound(identity,least_upper_bound(X_273,X_274))
    | greatest_lower_bound(identity,least_upper_bound(X_273,X_274)) = greatest_lower_bound(identity,least_upper_bound(X_274,X_273)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))))]]) ).

cnf(refute_0_1609,plain,
    greatest_lower_bound(identity,least_upper_bound(X_273,X_274)) = greatest_lower_bound(identity,least_upper_bound(X_274,X_273)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)),greatest_lower_bound(identity,least_upper_bound(X_273,X_274))) )],[refute_0_1607,refute_0_1608]) ).

cnf(refute_0_1610,plain,
    greatest_lower_bound(identity,least_upper_bound(identity,b)) = greatest_lower_bound(identity,least_upper_bound(b,identity)),
    inference(subst,[],[refute_0_1609:[bind(X_273,$fot(identity)),bind(X_274,$fot(b))]]) ).

cnf(refute_0_1611,plain,
    ( greatest_lower_bound(identity,least_upper_bound(b,identity)) != identity
    | greatest_lower_bound(identity,least_upper_bound(identity,b)) != greatest_lower_bound(identity,least_upper_bound(b,identity))
    | greatest_lower_bound(identity,least_upper_bound(identity,b)) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,least_upper_bound(identity,b)))),bind(Y0,$fot(greatest_lower_bound(identity,least_upper_bound(b,identity)))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_1612,plain,
    ( greatest_lower_bound(identity,least_upper_bound(b,identity)) != identity
    | greatest_lower_bound(identity,least_upper_bound(identity,b)) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,b)),greatest_lower_bound(identity,least_upper_bound(b,identity))) )],[refute_0_1610,refute_0_1611]) ).

cnf(refute_0_1613,plain,
    greatest_lower_bound(identity,least_upper_bound(identity,b)) = identity,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(b,identity)),identity) )],[refute_0_1415,refute_0_1612]) ).

cnf(refute_0_1614,plain,
    greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))) = greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))))]]) ).

cnf(refute_0_1615,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))) != greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))
    | greatest_lower_bound(identity,least_upper_bound(identity,b)) != identity
    | greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))) = greatest_lower_bound(a,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))),greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1616,plain,
    ( greatest_lower_bound(identity,least_upper_bound(identity,b)) != identity
    | greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))),greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))) )],[refute_0_1614,refute_0_1615]) ).

cnf(refute_0_1617,plain,
    greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,b)),identity) )],[refute_0_1613,refute_0_1616]) ).

cnf(refute_0_1618,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))))]]) ).

cnf(refute_0_1619,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))) != greatest_lower_bound(a,identity)
    | inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))) = inverse(greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))),inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))))) ),[1,0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_1620,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))) != greatest_lower_bound(a,identity)
    | inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))),inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))))) )],[refute_0_1618,refute_0_1619]) ).

cnf(refute_0_1621,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))),greatest_lower_bound(a,identity)) )],[refute_0_1617,refute_0_1620]) ).

cnf(refute_0_1622,plain,
    inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) = least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))),
    inference(subst,[],[p12x_3:[bind(Y,$fot(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))))]]) ).

cnf(refute_0_1623,plain,
    ( inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) != least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))))
    | inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))) != inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))
    | inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) = least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))),least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273))))]]) ).

cnf(refute_0_1624,plain,
    ( inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) != least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))))
    | inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) = least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) )],[refute_0_1600,refute_0_1623]) ).

cnf(refute_0_1625,plain,
    inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) = least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))),least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_273,X_274))))) )],[refute_0_1622,refute_0_1624]) ).

cnf(refute_0_1626,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(greatest_lower_bound(X,least_upper_bound(X_274,X_273))))]]) ).

cnf(refute_0_1627,plain,
    least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273))) = inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273))),
    inference(subst,[],[refute_0_136:[bind(Y,$fot(least_upper_bound(X_274,X_273)))]]) ).

cnf(refute_0_1628,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))) = least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))))]]) ).

cnf(refute_0_1629,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))) != least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273))))
    | least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273))) != inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273)))
    | least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))) = least_upper_bound(identity,inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))),least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273))))) ),[1,1],$fot(inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273))))]]) ).

cnf(refute_0_1630,plain,
    ( least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273))) != inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273)))
    | least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))) = least_upper_bound(identity,inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))),least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273))))) )],[refute_0_1628,refute_0_1629]) ).

cnf(refute_0_1631,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))) = least_upper_bound(identity,inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273))),inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) )],[refute_0_1627,refute_0_1630]) ).

cnf(refute_0_1632,plain,
    ( least_upper_bound(identity,inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))
    | least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))) != least_upper_bound(identity,inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273))))
    | least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))))]]) ).

cnf(refute_0_1633,plain,
    ( least_upper_bound(identity,inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))
    | least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))),least_upper_bound(identity,inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273))))) )],[refute_0_1631,refute_0_1632]) ).

cnf(refute_0_1634,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X,least_upper_bound(X_274,X_273)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))) )],[refute_0_1626,refute_0_1633]) ).

cnf(refute_0_1635,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)) = least_upper_bound(least_upper_bound(identity,inverse(X_64)),Z),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_64)))]]) ).

cnf(refute_0_1636,plain,
    inverse(greatest_lower_bound(identity,X_64)) = least_upper_bound(identity,inverse(X_64)),
    inference(subst,[],[refute_0_486:[bind(Y,$fot(X_64))]]) ).

cnf(refute_0_1637,plain,
    ( inverse(greatest_lower_bound(identity,X_64)) != least_upper_bound(identity,inverse(X_64))
    | least_upper_bound(identity,inverse(X_64)) = inverse(greatest_lower_bound(identity,X_64)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_64)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_64))))]]) ).

cnf(refute_0_1638,plain,
    least_upper_bound(identity,inverse(X_64)) = inverse(greatest_lower_bound(identity,X_64)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_64)),least_upper_bound(identity,inverse(X_64))) )],[refute_0_1636,refute_0_1637]) ).

cnf(refute_0_1639,plain,
    ( least_upper_bound(identity,inverse(X_64)) != inverse(greatest_lower_bound(identity,X_64))
    | least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)) != least_upper_bound(least_upper_bound(identity,inverse(X_64)),Z)
    | least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_64)),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)),least_upper_bound(least_upper_bound(identity,inverse(X_64)),Z)) ),[1,0],$fot(inverse(greatest_lower_bound(identity,X_64)))]]) ).

cnf(refute_0_1640,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)) != least_upper_bound(least_upper_bound(identity,inverse(X_64)),Z)
    | least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_64)),Z) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_64)),inverse(greatest_lower_bound(identity,X_64))) )],[refute_0_1638,refute_0_1639]) ).

cnf(refute_0_1641,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_64)),Z),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)),least_upper_bound(least_upper_bound(identity,inverse(X_64)),Z)) )],[refute_0_1635,refute_0_1640]) ).

cnf(refute_0_1642,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(identity,X_166))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)),
    inference(subst,[],[refute_0_1641:[bind(Z,$fot(least_upper_bound(identity,X_166))),bind(X_64,$fot(X_272))]]) ).

cnf(refute_0_1643,plain,
    least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))),X_211)) = least_upper_bound(least_upper_bound(identity,X_166),X_211),
    inference(subst,[],[refute_0_685:[bind(Y,$fot(inverse(greatest_lower_bound(identity,X_166)))),bind(X_43,$fot(least_upper_bound(identity,X_166))),bind(X_45,$fot(X_211))]]) ).

cnf(refute_0_1644,plain,
    ( greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))) != identity
    | least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))),X_211)) != least_upper_bound(least_upper_bound(identity,X_166),X_211)
    | least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) = least_upper_bound(least_upper_bound(identity,X_166),X_211) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))),X_211)),least_upper_bound(least_upper_bound(identity,X_166),X_211)) ),[0,1,0],$fot(identity)]]) ).

cnf(refute_0_1645,plain,
    ( least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))),X_211)) != least_upper_bound(least_upper_bound(identity,X_166),X_211)
    | least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) = least_upper_bound(least_upper_bound(identity,X_166),X_211) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))),identity) )],[refute_0_621,refute_0_1644]) ).

cnf(refute_0_1646,plain,
    least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) = least_upper_bound(least_upper_bound(identity,X_166),X_211),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X_166),inverse(greatest_lower_bound(identity,X_166))),X_211)),least_upper_bound(least_upper_bound(identity,X_166),X_211)) )],[refute_0_1643,refute_0_1645]) ).

cnf(refute_0_1647,plain,
    least_upper_bound(identity,least_upper_bound(X_211,least_upper_bound(identity,X_166))) = least_upper_bound(X_211,least_upper_bound(identity,X_166)),
    inference(subst,[],[refute_0_1086:[bind(Y,$fot(X_166)),bind(X_43,$fot(X_211)),bind(X_44,$fot(identity))]]) ).

cnf(refute_0_1648,plain,
    least_upper_bound(least_upper_bound(X_195,identity),Y) = least_upper_bound(Y,least_upper_bound(X_195,identity)),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(least_upper_bound(X_195,identity)))]]) ).

cnf(refute_0_1649,plain,
    X_60 = multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),multiply(inverse(greatest_lower_bound(identity,X_60)),X_60)),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(inverse(greatest_lower_bound(identity,X_60))))]]) ).

cnf(refute_0_1650,plain,
    multiply(least_upper_bound(identity,inverse(X_113)),X_113) = least_upper_bound(identity,multiply(identity,X_113)),
    inference(subst,[],[refute_0_92:[bind(X_110,$fot(X_113)),bind(X_111,$fot(identity))]]) ).

cnf(refute_0_1651,plain,
    inverse(greatest_lower_bound(identity,X_113)) = least_upper_bound(identity,inverse(X_113)),
    inference(subst,[],[refute_0_486:[bind(Y,$fot(X_113))]]) ).

cnf(refute_0_1652,plain,
    ( inverse(greatest_lower_bound(identity,X_113)) != least_upper_bound(identity,inverse(X_113))
    | least_upper_bound(identity,inverse(X_113)) = inverse(greatest_lower_bound(identity,X_113)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_113)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_113))))]]) ).

cnf(refute_0_1653,plain,
    least_upper_bound(identity,inverse(X_113)) = inverse(greatest_lower_bound(identity,X_113)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_113)),least_upper_bound(identity,inverse(X_113))) )],[refute_0_1651,refute_0_1652]) ).

cnf(refute_0_1654,plain,
    ( multiply(least_upper_bound(identity,inverse(X_113)),X_113) != least_upper_bound(identity,multiply(identity,X_113))
    | least_upper_bound(identity,inverse(X_113)) != inverse(greatest_lower_bound(identity,X_113))
    | multiply(inverse(greatest_lower_bound(identity,X_113)),X_113) = least_upper_bound(identity,multiply(identity,X_113)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_113)),X_113),least_upper_bound(identity,multiply(identity,X_113))) ),[0,0],$fot(inverse(greatest_lower_bound(identity,X_113)))]]) ).

cnf(refute_0_1655,plain,
    ( multiply(least_upper_bound(identity,inverse(X_113)),X_113) != least_upper_bound(identity,multiply(identity,X_113))
    | multiply(inverse(greatest_lower_bound(identity,X_113)),X_113) = least_upper_bound(identity,multiply(identity,X_113)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_113)),inverse(greatest_lower_bound(identity,X_113))) )],[refute_0_1653,refute_0_1654]) ).

cnf(refute_0_1656,plain,
    multiply(inverse(greatest_lower_bound(identity,X_113)),X_113) = least_upper_bound(identity,multiply(identity,X_113)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_113)),X_113),least_upper_bound(identity,multiply(identity,X_113))) )],[refute_0_1650,refute_0_1655]) ).

cnf(refute_0_1657,plain,
    multiply(identity,least_upper_bound(X_113,identity)) = least_upper_bound(X_113,identity),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_113,identity)))]]) ).

cnf(refute_0_1658,plain,
    least_upper_bound(identity,multiply(identity,X_113)) = multiply(identity,least_upper_bound(X_113,identity)),
    inference(subst,[],[refute_0_549:[bind(X_93,$fot(identity)),bind(X_94,$fot(X_113))]]) ).

cnf(refute_0_1659,plain,
    ( multiply(identity,least_upper_bound(X_113,identity)) != least_upper_bound(X_113,identity)
    | least_upper_bound(identity,multiply(identity,X_113)) != multiply(identity,least_upper_bound(X_113,identity))
    | least_upper_bound(identity,multiply(identity,X_113)) = least_upper_bound(X_113,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,X_113)))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_113,identity)))),bind(Z0,$fot(least_upper_bound(X_113,identity)))]]) ).

cnf(refute_0_1660,plain,
    ( multiply(identity,least_upper_bound(X_113,identity)) != least_upper_bound(X_113,identity)
    | least_upper_bound(identity,multiply(identity,X_113)) = least_upper_bound(X_113,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_113)),multiply(identity,least_upper_bound(X_113,identity))) )],[refute_0_1658,refute_0_1659]) ).

cnf(refute_0_1661,plain,
    least_upper_bound(identity,multiply(identity,X_113)) = least_upper_bound(X_113,identity),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_113,identity)),least_upper_bound(X_113,identity)) )],[refute_0_1657,refute_0_1660]) ).

cnf(refute_0_1662,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_113)),X_113) != least_upper_bound(identity,multiply(identity,X_113))
    | least_upper_bound(identity,multiply(identity,X_113)) != least_upper_bound(X_113,identity)
    | multiply(inverse(greatest_lower_bound(identity,X_113)),X_113) = least_upper_bound(X_113,identity) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(identity,X_113)),X_113),least_upper_bound(X_113,identity)) ),[0],$fot(least_upper_bound(identity,multiply(identity,X_113)))]]) ).

cnf(refute_0_1663,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_113)),X_113) != least_upper_bound(identity,multiply(identity,X_113))
    | multiply(inverse(greatest_lower_bound(identity,X_113)),X_113) = least_upper_bound(X_113,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_113)),least_upper_bound(X_113,identity)) )],[refute_0_1661,refute_0_1662]) ).

cnf(refute_0_1664,plain,
    multiply(inverse(greatest_lower_bound(identity,X_113)),X_113) = least_upper_bound(X_113,identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_113)),X_113),least_upper_bound(identity,multiply(identity,X_113))) )],[refute_0_1656,refute_0_1663]) ).

cnf(refute_0_1665,plain,
    multiply(inverse(greatest_lower_bound(identity,X_60)),X_60) = least_upper_bound(X_60,identity),
    inference(subst,[],[refute_0_1664:[bind(X_113,$fot(X_60))]]) ).

cnf(refute_0_1666,plain,
    ( X_60 != multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),multiply(inverse(greatest_lower_bound(identity,X_60)),X_60))
    | multiply(inverse(greatest_lower_bound(identity,X_60)),X_60) != least_upper_bound(X_60,identity)
    | X_60 = multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(X_60,multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),multiply(inverse(greatest_lower_bound(identity,X_60)),X_60))) ),[1,1],$fot(least_upper_bound(X_60,identity))]]) ).

cnf(refute_0_1667,plain,
    ( X_60 != multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),multiply(inverse(greatest_lower_bound(identity,X_60)),X_60))
    | X_60 = multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_60)),X_60),least_upper_bound(X_60,identity)) )],[refute_0_1665,refute_0_1666]) ).

cnf(refute_0_1668,plain,
    X_60 = multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)),
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),multiply(inverse(greatest_lower_bound(identity,X_60)),X_60))) )],[refute_0_1649,refute_0_1667]) ).

cnf(refute_0_1669,plain,
    inverse(inverse(greatest_lower_bound(identity,X_60))) = greatest_lower_bound(identity,X_60),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(identity,X_60)))]]) ).

cnf(refute_0_1670,plain,
    multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)) = multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)),
    introduced(tautology,[refl,[$fot(multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)))]]) ).

cnf(refute_0_1671,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)) != multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity))
    | inverse(inverse(greatest_lower_bound(identity,X_60))) != greatest_lower_bound(identity,X_60)
    | multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)) = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(X_60,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)),multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity))) ),[1,0],$fot(greatest_lower_bound(identity,X_60))]]) ).

cnf(refute_0_1672,plain,
    ( inverse(inverse(greatest_lower_bound(identity,X_60))) != greatest_lower_bound(identity,X_60)
    | multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)) = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(X_60,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)),multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity))) )],[refute_0_1670,refute_0_1671]) ).

cnf(refute_0_1673,plain,
    multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)) = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(X_60,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,X_60))),greatest_lower_bound(identity,X_60)) )],[refute_0_1669,refute_0_1672]) ).

cnf(refute_0_1674,plain,
    ( X_60 != multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity))
    | multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)) != multiply(greatest_lower_bound(identity,X_60),least_upper_bound(X_60,identity))
    | X_60 = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(X_60,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_60,multiply(greatest_lower_bound(identity,X_60),least_upper_bound(X_60,identity))) ),[0],$fot(multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)))]]) ).

cnf(refute_0_1675,plain,
    ( X_60 != multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity))
    | X_60 = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(X_60,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity)),multiply(greatest_lower_bound(identity,X_60),least_upper_bound(X_60,identity))) )],[refute_0_1673,refute_0_1674]) ).

cnf(refute_0_1676,plain,
    X_60 = multiply(greatest_lower_bound(identity,X_60),least_upper_bound(X_60,identity)),
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(inverse(greatest_lower_bound(identity,X_60))),least_upper_bound(X_60,identity))) )],[refute_0_1668,refute_0_1675]) ).

cnf(refute_0_1677,plain,
    least_upper_bound(X_192,least_upper_bound(X_193,identity)) = multiply(greatest_lower_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))),least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)),
    inference(subst,[],[refute_0_1676:[bind(X_60,$fot(least_upper_bound(X_192,least_upper_bound(X_193,identity))))]]) ).

cnf(refute_0_1678,plain,
    greatest_lower_bound(X_10,least_upper_bound(least_upper_bound(X_43,X_44),X_10)) = X_10,
    inference(subst,[],[refute_0_215:[bind(X_11,$fot(least_upper_bound(X_43,X_44)))]]) ).

cnf(refute_0_1679,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,X_10)) = least_upper_bound(least_upper_bound(X_43,X_44),X_10),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(X_10))]]) ).

cnf(refute_0_1680,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,X_10)) != least_upper_bound(least_upper_bound(X_43,X_44),X_10)
    | least_upper_bound(least_upper_bound(X_43,X_44),X_10) = least_upper_bound(X_43,least_upper_bound(X_44,X_10)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_43,least_upper_bound(X_44,X_10)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_43,X_44),X_10)))]]) ).

cnf(refute_0_1681,plain,
    least_upper_bound(least_upper_bound(X_43,X_44),X_10) = least_upper_bound(X_43,least_upper_bound(X_44,X_10)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,X_10)),least_upper_bound(least_upper_bound(X_43,X_44),X_10)) )],[refute_0_1679,refute_0_1680]) ).

cnf(refute_0_1682,plain,
    ( greatest_lower_bound(X_10,least_upper_bound(least_upper_bound(X_43,X_44),X_10)) != X_10
    | least_upper_bound(least_upper_bound(X_43,X_44),X_10) != least_upper_bound(X_43,least_upper_bound(X_44,X_10))
    | greatest_lower_bound(X_10,least_upper_bound(X_43,least_upper_bound(X_44,X_10))) = X_10 ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(least_upper_bound(X_43,X_44),X_10)),X_10) ),[0,1],$fot(least_upper_bound(X_43,least_upper_bound(X_44,X_10)))]]) ).

cnf(refute_0_1683,plain,
    ( greatest_lower_bound(X_10,least_upper_bound(least_upper_bound(X_43,X_44),X_10)) != X_10
    | greatest_lower_bound(X_10,least_upper_bound(X_43,least_upper_bound(X_44,X_10))) = X_10 ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_43,X_44),X_10),least_upper_bound(X_43,least_upper_bound(X_44,X_10))) )],[refute_0_1681,refute_0_1682]) ).

cnf(refute_0_1684,plain,
    greatest_lower_bound(X_10,least_upper_bound(X_43,least_upper_bound(X_44,X_10))) = X_10,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(least_upper_bound(X_43,X_44),X_10)),X_10) )],[refute_0_1678,refute_0_1683]) ).

cnf(refute_0_1685,plain,
    greatest_lower_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))) = identity,
    inference(subst,[],[refute_0_1684:[bind(X_10,$fot(identity)),bind(X_43,$fot(X_192)),bind(X_44,$fot(X_193))]]) ).

cnf(refute_0_1686,plain,
    ( greatest_lower_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))) != identity
    | least_upper_bound(X_192,least_upper_bound(X_193,identity)) != multiply(greatest_lower_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))),least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity))
    | least_upper_bound(X_192,least_upper_bound(X_193,identity)) = multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_192,least_upper_bound(X_193,identity)),multiply(greatest_lower_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))),least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1687,plain,
    ( least_upper_bound(X_192,least_upper_bound(X_193,identity)) != multiply(greatest_lower_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))),least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity))
    | least_upper_bound(X_192,least_upper_bound(X_193,identity)) = multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))),identity) )],[refute_0_1685,refute_0_1686]) ).

cnf(refute_0_1688,plain,
    least_upper_bound(X_192,least_upper_bound(X_193,identity)) = multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_192,least_upper_bound(X_193,identity)),multiply(greatest_lower_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))),least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity))) )],[refute_0_1677,refute_0_1687]) ).

cnf(refute_0_1689,plain,
    least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_43,X_44),X_21)) = least_upper_bound(X_21,least_upper_bound(X_43,X_44)),
    inference(subst,[],[refute_0_426:[bind(Y,$fot(least_upper_bound(X_43,X_44)))]]) ).

cnf(refute_0_1690,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,X_21)) = least_upper_bound(least_upper_bound(X_43,X_44),X_21),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(X_21))]]) ).

cnf(refute_0_1691,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,X_21)) != least_upper_bound(least_upper_bound(X_43,X_44),X_21)
    | least_upper_bound(least_upper_bound(X_43,X_44),X_21) = least_upper_bound(X_43,least_upper_bound(X_44,X_21)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_43,least_upper_bound(X_44,X_21)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_43,X_44),X_21)))]]) ).

cnf(refute_0_1692,plain,
    least_upper_bound(least_upper_bound(X_43,X_44),X_21) = least_upper_bound(X_43,least_upper_bound(X_44,X_21)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,X_21)),least_upper_bound(least_upper_bound(X_43,X_44),X_21)) )],[refute_0_1690,refute_0_1691]) ).

cnf(refute_0_1693,plain,
    ( least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_43,X_44),X_21)) != least_upper_bound(X_21,least_upper_bound(X_43,X_44))
    | least_upper_bound(least_upper_bound(X_43,X_44),X_21) != least_upper_bound(X_43,least_upper_bound(X_44,X_21))
    | least_upper_bound(X_21,least_upper_bound(X_43,least_upper_bound(X_44,X_21))) = least_upper_bound(X_21,least_upper_bound(X_43,X_44)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_43,X_44),X_21)),least_upper_bound(X_21,least_upper_bound(X_43,X_44))) ),[0,1],$fot(least_upper_bound(X_43,least_upper_bound(X_44,X_21)))]]) ).

cnf(refute_0_1694,plain,
    ( least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_43,X_44),X_21)) != least_upper_bound(X_21,least_upper_bound(X_43,X_44))
    | least_upper_bound(X_21,least_upper_bound(X_43,least_upper_bound(X_44,X_21))) = least_upper_bound(X_21,least_upper_bound(X_43,X_44)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_43,X_44),X_21),least_upper_bound(X_43,least_upper_bound(X_44,X_21))) )],[refute_0_1692,refute_0_1693]) ).

cnf(refute_0_1695,plain,
    least_upper_bound(X_21,least_upper_bound(X_43,least_upper_bound(X_44,X_21))) = least_upper_bound(X_21,least_upper_bound(X_43,X_44)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_21,least_upper_bound(least_upper_bound(X_43,X_44),X_21)),least_upper_bound(X_21,least_upper_bound(X_43,X_44))) )],[refute_0_1689,refute_0_1694]) ).

cnf(refute_0_1696,plain,
    least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))) = least_upper_bound(identity,least_upper_bound(X_192,X_193)),
    inference(subst,[],[refute_0_1695:[bind(X_21,$fot(identity)),bind(X_43,$fot(X_192)),bind(X_44,$fot(X_193))]]) ).

cnf(refute_0_1697,plain,
    multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))) = least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))))]]) ).

cnf(refute_0_1698,plain,
    ( multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))) != least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))
    | least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))) != least_upper_bound(identity,least_upper_bound(X_192,X_193))
    | multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))) = least_upper_bound(identity,least_upper_bound(X_192,X_193)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_192,X_193))))]]) ).

cnf(refute_0_1699,plain,
    ( least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))) != least_upper_bound(identity,least_upper_bound(X_192,X_193))
    | multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))) = least_upper_bound(identity,least_upper_bound(X_192,X_193)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))),least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))) )],[refute_0_1697,refute_0_1698]) ).

cnf(refute_0_1700,plain,
    multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))) = least_upper_bound(identity,least_upper_bound(X_192,X_193)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))),least_upper_bound(identity,least_upper_bound(X_192,X_193))) )],[refute_0_1696,refute_0_1699]) ).

cnf(refute_0_1701,plain,
    multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)) = multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))),
    inference(subst,[],[refute_0_564:[bind(X_165,$fot(least_upper_bound(X_192,least_upper_bound(X_193,identity)))),bind(X_31,$fot(identity))]]) ).

cnf(refute_0_1702,plain,
    ( multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))) != least_upper_bound(identity,least_upper_bound(X_192,X_193))
    | multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)) != multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))))
    | multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)) = least_upper_bound(identity,least_upper_bound(X_192,X_193)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_192,X_193))))]]) ).

cnf(refute_0_1703,plain,
    ( multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))) != least_upper_bound(identity,least_upper_bound(X_192,X_193))
    | multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)) = least_upper_bound(identity,least_upper_bound(X_192,X_193)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)),multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity))))) )],[refute_0_1701,refute_0_1702]) ).

cnf(refute_0_1704,plain,
    multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)) = least_upper_bound(identity,least_upper_bound(X_192,X_193)),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,identity)))),least_upper_bound(identity,least_upper_bound(X_192,X_193))) )],[refute_0_1700,refute_0_1703]) ).

cnf(refute_0_1705,plain,
    ( multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)) != least_upper_bound(identity,least_upper_bound(X_192,X_193))
    | least_upper_bound(X_192,least_upper_bound(X_193,identity)) != multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity))
    | least_upper_bound(X_192,least_upper_bound(X_193,identity)) = least_upper_bound(identity,least_upper_bound(X_192,X_193)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_192,least_upper_bound(X_193,identity)),multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity))) ),[1],$fot(least_upper_bound(identity,least_upper_bound(X_192,X_193)))]]) ).

cnf(refute_0_1706,plain,
    ( least_upper_bound(X_192,least_upper_bound(X_193,identity)) != multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity))
    | least_upper_bound(X_192,least_upper_bound(X_193,identity)) = least_upper_bound(identity,least_upper_bound(X_192,X_193)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)),least_upper_bound(identity,least_upper_bound(X_192,X_193))) )],[refute_0_1704,refute_0_1705]) ).

cnf(refute_0_1707,plain,
    least_upper_bound(X_192,least_upper_bound(X_193,identity)) = least_upper_bound(identity,least_upper_bound(X_192,X_193)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_192,least_upper_bound(X_193,identity)),multiply(identity,least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity))) )],[refute_0_1688,refute_0_1706]) ).

cnf(refute_0_1708,plain,
    least_upper_bound(Y,least_upper_bound(X_195,identity)) = least_upper_bound(identity,least_upper_bound(Y,X_195)),
    inference(subst,[],[refute_0_1707:[bind(X_192,$fot(Y)),bind(X_193,$fot(X_195))]]) ).

cnf(refute_0_1709,plain,
    ( least_upper_bound(Y,least_upper_bound(X_195,identity)) != least_upper_bound(identity,least_upper_bound(Y,X_195))
    | least_upper_bound(least_upper_bound(X_195,identity),Y) != least_upper_bound(Y,least_upper_bound(X_195,identity))
    | least_upper_bound(least_upper_bound(X_195,identity),Y) = least_upper_bound(identity,least_upper_bound(Y,X_195)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_195,identity),Y),least_upper_bound(Y,least_upper_bound(X_195,identity))) ),[1],$fot(least_upper_bound(identity,least_upper_bound(Y,X_195)))]]) ).

cnf(refute_0_1710,plain,
    ( least_upper_bound(least_upper_bound(X_195,identity),Y) != least_upper_bound(Y,least_upper_bound(X_195,identity))
    | least_upper_bound(least_upper_bound(X_195,identity),Y) = least_upper_bound(identity,least_upper_bound(Y,X_195)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_195,identity)),least_upper_bound(identity,least_upper_bound(Y,X_195))) )],[refute_0_1708,refute_0_1709]) ).

cnf(refute_0_1711,plain,
    least_upper_bound(least_upper_bound(X_195,identity),Y) = least_upper_bound(identity,least_upper_bound(Y,X_195)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_195,identity),Y),least_upper_bound(Y,least_upper_bound(X_195,identity))) )],[refute_0_1648,refute_0_1710]) ).

cnf(refute_0_1712,plain,
    least_upper_bound(least_upper_bound(X_195,identity),Y) = least_upper_bound(X_195,least_upper_bound(identity,Y)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(X_195)),bind(Y,$fot(identity)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_1713,plain,
    ( least_upper_bound(least_upper_bound(X_195,identity),Y) != least_upper_bound(X_195,least_upper_bound(identity,Y))
    | least_upper_bound(least_upper_bound(X_195,identity),Y) != least_upper_bound(identity,least_upper_bound(Y,X_195))
    | least_upper_bound(X_195,least_upper_bound(identity,Y)) = least_upper_bound(identity,least_upper_bound(Y,X_195)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_195,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_195))) ),[0],$fot(least_upper_bound(X_195,least_upper_bound(identity,Y)))]]) ).

cnf(refute_0_1714,plain,
    ( least_upper_bound(least_upper_bound(X_195,identity),Y) != least_upper_bound(identity,least_upper_bound(Y,X_195))
    | least_upper_bound(X_195,least_upper_bound(identity,Y)) = least_upper_bound(identity,least_upper_bound(Y,X_195)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_195,identity),Y),least_upper_bound(X_195,least_upper_bound(identity,Y))) )],[refute_0_1712,refute_0_1713]) ).

cnf(refute_0_1715,plain,
    least_upper_bound(X_195,least_upper_bound(identity,Y)) = least_upper_bound(identity,least_upper_bound(Y,X_195)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_195,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_195))) )],[refute_0_1711,refute_0_1714]) ).

cnf(refute_0_1716,plain,
    least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) = least_upper_bound(identity,least_upper_bound(X_211,least_upper_bound(identity,X_166))),
    inference(subst,[],[refute_0_1715:[bind(Y,$fot(X_211)),bind(X_195,$fot(least_upper_bound(identity,X_166)))]]) ).

cnf(refute_0_1717,plain,
    ( least_upper_bound(identity,least_upper_bound(X_211,least_upper_bound(identity,X_166))) != least_upper_bound(X_211,least_upper_bound(identity,X_166))
    | least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) != least_upper_bound(identity,least_upper_bound(X_211,least_upper_bound(identity,X_166)))
    | least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) = least_upper_bound(X_211,least_upper_bound(identity,X_166)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_211,least_upper_bound(identity,X_166))))),bind(Z0,$fot(least_upper_bound(X_211,least_upper_bound(identity,X_166))))]]) ).

cnf(refute_0_1718,plain,
    ( least_upper_bound(identity,least_upper_bound(X_211,least_upper_bound(identity,X_166))) != least_upper_bound(X_211,least_upper_bound(identity,X_166))
    | least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) = least_upper_bound(X_211,least_upper_bound(identity,X_166)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)),least_upper_bound(identity,least_upper_bound(X_211,least_upper_bound(identity,X_166)))) )],[refute_0_1716,refute_0_1717]) ).

cnf(refute_0_1719,plain,
    least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) = least_upper_bound(X_211,least_upper_bound(identity,X_166)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_211,least_upper_bound(identity,X_166))),least_upper_bound(X_211,least_upper_bound(identity,X_166))) )],[refute_0_1647,refute_0_1718]) ).

cnf(refute_0_1720,plain,
    ( least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) != least_upper_bound(X_211,least_upper_bound(identity,X_166))
    | least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) != least_upper_bound(least_upper_bound(identity,X_166),X_211)
    | least_upper_bound(X_211,least_upper_bound(identity,X_166)) = least_upper_bound(least_upper_bound(identity,X_166),X_211) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)),least_upper_bound(least_upper_bound(identity,X_166),X_211)) ),[0],$fot(least_upper_bound(X_211,least_upper_bound(identity,X_166)))]]) ).

cnf(refute_0_1721,plain,
    ( least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) != least_upper_bound(least_upper_bound(identity,X_166),X_211)
    | least_upper_bound(X_211,least_upper_bound(identity,X_166)) = least_upper_bound(least_upper_bound(identity,X_166),X_211) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)),least_upper_bound(X_211,least_upper_bound(identity,X_166))) )],[refute_0_1719,refute_0_1720]) ).

cnf(refute_0_1722,plain,
    least_upper_bound(least_upper_bound(identity,X_166),X_211) = least_upper_bound(identity,least_upper_bound(X_166,X_211)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(identity)),bind(Y,$fot(X_166)),bind(Z,$fot(X_211))]]) ).

cnf(refute_0_1723,plain,
    ( least_upper_bound(X_211,least_upper_bound(identity,X_166)) != least_upper_bound(least_upper_bound(identity,X_166),X_211)
    | least_upper_bound(least_upper_bound(identity,X_166),X_211) != least_upper_bound(identity,least_upper_bound(X_166,X_211))
    | least_upper_bound(X_211,least_upper_bound(identity,X_166)) = least_upper_bound(identity,least_upper_bound(X_166,X_211)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_211,least_upper_bound(identity,X_166)),least_upper_bound(identity,least_upper_bound(X_166,X_211))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,X_166),X_211))]]) ).

cnf(refute_0_1724,plain,
    ( least_upper_bound(X_211,least_upper_bound(identity,X_166)) != least_upper_bound(least_upper_bound(identity,X_166),X_211)
    | least_upper_bound(X_211,least_upper_bound(identity,X_166)) = least_upper_bound(identity,least_upper_bound(X_166,X_211)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_166),X_211),least_upper_bound(identity,least_upper_bound(X_166,X_211))) )],[refute_0_1722,refute_0_1723]) ).

cnf(refute_0_1725,plain,
    ( least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)) != least_upper_bound(least_upper_bound(identity,X_166),X_211)
    | least_upper_bound(X_211,least_upper_bound(identity,X_166)) = least_upper_bound(identity,least_upper_bound(X_166,X_211)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_211,least_upper_bound(identity,X_166)),least_upper_bound(least_upper_bound(identity,X_166),X_211)) )],[refute_0_1721,refute_0_1724]) ).

cnf(refute_0_1726,plain,
    least_upper_bound(X_211,least_upper_bound(identity,X_166)) = least_upper_bound(identity,least_upper_bound(X_166,X_211)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_166),least_upper_bound(identity,X_211)),least_upper_bound(least_upper_bound(identity,X_166),X_211)) )],[refute_0_1646,refute_0_1725]) ).

cnf(refute_0_1727,plain,
    least_upper_bound(inverse(X_272),least_upper_bound(identity,X_166)) = least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))),
    inference(subst,[],[refute_0_1726:[bind(X_211,$fot(inverse(X_272)))]]) ).

cnf(refute_0_1728,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(identity,X_166))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))
    | least_upper_bound(inverse(X_272),least_upper_bound(identity,X_166)) != least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))
    | least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(identity,X_166))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))) ),[0,1],$fot(least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))))]]) ).

cnf(refute_0_1729,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(identity,X_166))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))
    | least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_272),least_upper_bound(identity,X_166)),least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))) )],[refute_0_1727,refute_0_1728]) ).

cnf(refute_0_1730,plain,
    least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(identity,X_166))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))) )],[refute_0_1642,refute_0_1729]) ).

cnf(refute_0_1731,plain,
    least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))) = least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(least_upper_bound(X_166,inverse(X_272)))),bind(X_31,$fot(identity))]]) ).

cnf(refute_0_1732,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))) != least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))
    | least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))
    | least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))))]]) ).

cnf(refute_0_1733,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))
    | least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))),least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))) )],[refute_0_1731,refute_0_1732]) ).

cnf(refute_0_1734,plain,
    least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) = least_upper_bound(identity,least_upper_bound(X_185,least_upper_bound(identity,inverse(Y)))),
    inference(subst,[],[refute_0_1084:[bind(Y,$fot(inverse(Y))),bind(X_43,$fot(X_185)),bind(X_44,$fot(identity))]]) ).

cnf(refute_0_1735,plain,
    ( least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) != least_upper_bound(identity,least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))))
    | least_upper_bound(identity,inverse(Y)) != inverse(greatest_lower_bound(identity,Y))
    | least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) = least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))),least_upper_bound(identity,least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))))) ),[1,1,1],$fot(inverse(greatest_lower_bound(identity,Y)))]]) ).

cnf(refute_0_1736,plain,
    ( least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) != least_upper_bound(identity,least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))))
    | least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) = least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(Y)),inverse(greatest_lower_bound(identity,Y))) )],[refute_0_488,refute_0_1735]) ).

cnf(refute_0_1737,plain,
    least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) = least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))),least_upper_bound(identity,least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))))) )],[refute_0_1734,refute_0_1736]) ).

cnf(refute_0_1738,plain,
    least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) = least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))))]]) ).

cnf(refute_0_1739,plain,
    ( least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) != least_upper_bound(X_185,least_upper_bound(identity,inverse(Y)))
    | least_upper_bound(identity,inverse(Y)) != inverse(greatest_lower_bound(identity,Y))
    | least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) = least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))),least_upper_bound(X_185,least_upper_bound(identity,inverse(Y)))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,Y)))]]) ).

cnf(refute_0_1740,plain,
    ( least_upper_bound(identity,inverse(Y)) != inverse(greatest_lower_bound(identity,Y))
    | least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) = least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))),least_upper_bound(X_185,least_upper_bound(identity,inverse(Y)))) )],[refute_0_1738,refute_0_1739]) ).

cnf(refute_0_1741,plain,
    least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) = least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(Y)),inverse(greatest_lower_bound(identity,Y))) )],[refute_0_488,refute_0_1740]) ).

cnf(refute_0_1742,plain,
    ( least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) != least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y)))
    | least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) != least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))))
    | least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))),least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))))) ),[0],$fot(least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))))]]) ).

cnf(refute_0_1743,plain,
    ( least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))) != least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))))
    | least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))),least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_1741,refute_0_1742]) ).

cnf(refute_0_1744,plain,
    least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_185,least_upper_bound(identity,inverse(Y))),least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))))) )],[refute_0_1737,refute_0_1743]) ).

cnf(refute_0_1745,plain,
    ( least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))) != least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))))
    | least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y)))) = least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))))))]]) ).

cnf(refute_0_1746,plain,
    least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y)))) = least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))),least_upper_bound(identity,least_upper_bound(X_185,inverse(greatest_lower_bound(identity,Y))))) )],[refute_0_1744,refute_0_1745]) ).

cnf(refute_0_1747,plain,
    least_upper_bound(identity,least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))) = least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))),
    inference(subst,[],[refute_0_1746:[bind(Y,$fot(X_272)),bind(X_185,$fot(X_166))]]) ).

cnf(refute_0_1748,plain,
    multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(multiply(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))),least_upper_bound(X_247,least_upper_bound(X_248,X_246))))) = inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248)))),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(least_upper_bound(X_247,least_upper_bound(X_248,X_246)))),bind(X_59,$fot(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248)))))]]) ).

cnf(refute_0_1749,plain,
    multiply(inverse(least_upper_bound(X_16,least_upper_bound(X_43,X_44))),least_upper_bound(least_upper_bound(X_43,X_44),X_16)) = identity,
    inference(subst,[],[refute_0_62:[bind(X_17,$fot(least_upper_bound(X_43,X_44)))]]) ).

cnf(refute_0_1750,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,X_16)) = least_upper_bound(least_upper_bound(X_43,X_44),X_16),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_1751,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,X_16)) != least_upper_bound(least_upper_bound(X_43,X_44),X_16)
    | least_upper_bound(least_upper_bound(X_43,X_44),X_16) = least_upper_bound(X_43,least_upper_bound(X_44,X_16)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_43,least_upper_bound(X_44,X_16)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_43,X_44),X_16)))]]) ).

cnf(refute_0_1752,plain,
    least_upper_bound(least_upper_bound(X_43,X_44),X_16) = least_upper_bound(X_43,least_upper_bound(X_44,X_16)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,X_16)),least_upper_bound(least_upper_bound(X_43,X_44),X_16)) )],[refute_0_1750,refute_0_1751]) ).

cnf(refute_0_1753,plain,
    ( multiply(inverse(least_upper_bound(X_16,least_upper_bound(X_43,X_44))),least_upper_bound(least_upper_bound(X_43,X_44),X_16)) != identity
    | least_upper_bound(least_upper_bound(X_43,X_44),X_16) != least_upper_bound(X_43,least_upper_bound(X_44,X_16))
    | multiply(inverse(least_upper_bound(X_16,least_upper_bound(X_43,X_44))),least_upper_bound(X_43,least_upper_bound(X_44,X_16))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,least_upper_bound(X_43,X_44))),least_upper_bound(least_upper_bound(X_43,X_44),X_16)),identity) ),[0,1],$fot(least_upper_bound(X_43,least_upper_bound(X_44,X_16)))]]) ).

cnf(refute_0_1754,plain,
    ( multiply(inverse(least_upper_bound(X_16,least_upper_bound(X_43,X_44))),least_upper_bound(least_upper_bound(X_43,X_44),X_16)) != identity
    | multiply(inverse(least_upper_bound(X_16,least_upper_bound(X_43,X_44))),least_upper_bound(X_43,least_upper_bound(X_44,X_16))) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_43,X_44),X_16),least_upper_bound(X_43,least_upper_bound(X_44,X_16))) )],[refute_0_1752,refute_0_1753]) ).

cnf(refute_0_1755,plain,
    multiply(inverse(least_upper_bound(X_16,least_upper_bound(X_43,X_44))),least_upper_bound(X_43,least_upper_bound(X_44,X_16))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,least_upper_bound(X_43,X_44))),least_upper_bound(least_upper_bound(X_43,X_44),X_16)),identity) )],[refute_0_1749,refute_0_1754]) ).

cnf(refute_0_1756,plain,
    multiply(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))),least_upper_bound(X_247,least_upper_bound(X_248,X_246))) = identity,
    inference(subst,[],[refute_0_1755:[bind(X_16,$fot(X_246)),bind(X_43,$fot(X_247)),bind(X_44,$fot(X_248))]]) ).

cnf(refute_0_1757,plain,
    ( multiply(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))),least_upper_bound(X_247,least_upper_bound(X_248,X_246))) != identity
    | multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(multiply(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))),least_upper_bound(X_247,least_upper_bound(X_248,X_246))))) != inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))
    | multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) = inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(multiply(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))),least_upper_bound(X_247,least_upper_bound(X_248,X_246))))),inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))) ),[0,1,0],$fot(identity)]]) ).

cnf(refute_0_1758,plain,
    ( multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(multiply(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))),least_upper_bound(X_247,least_upper_bound(X_248,X_246))))) != inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))
    | multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) = inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))),least_upper_bound(X_247,least_upper_bound(X_248,X_246))),identity) )],[refute_0_1756,refute_0_1757]) ).

cnf(refute_0_1759,plain,
    multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) = inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(multiply(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))),least_upper_bound(X_247,least_upper_bound(X_248,X_246))))),inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))) )],[refute_0_1748,refute_0_1758]) ).

cnf(refute_0_1760,plain,
    multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),identity) = least_upper_bound(X_247,least_upper_bound(X_248,X_246)),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(least_upper_bound(X_247,least_upper_bound(X_248,X_246))))]]) ).

cnf(refute_0_1761,plain,
    multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) = multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)))]]) ).

cnf(refute_0_1762,plain,
    ( multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) != multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity))
    | inverse(identity) != identity
    | multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) = multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)),multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_1763,plain,
    ( inverse(identity) != identity
    | multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) = multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)),multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity))) )],[refute_0_1761,refute_0_1762]) ).

cnf(refute_0_1764,plain,
    multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) = multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),identity),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_1763]) ).

cnf(refute_0_1765,plain,
    ( multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),identity) != least_upper_bound(X_247,least_upper_bound(X_248,X_246))
    | multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) != multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),identity)
    | multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) = least_upper_bound(X_247,least_upper_bound(X_248,X_246)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),identity))),bind(Z0,$fot(least_upper_bound(X_247,least_upper_bound(X_248,X_246))))]]) ).

cnf(refute_0_1766,plain,
    ( multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),identity) != least_upper_bound(X_247,least_upper_bound(X_248,X_246))
    | multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) = least_upper_bound(X_247,least_upper_bound(X_248,X_246)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)),multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),identity)) )],[refute_0_1764,refute_0_1765]) ).

cnf(refute_0_1767,plain,
    multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) = least_upper_bound(X_247,least_upper_bound(X_248,X_246)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),identity),least_upper_bound(X_247,least_upper_bound(X_248,X_246))) )],[refute_0_1760,refute_0_1766]) ).

cnf(refute_0_1768,plain,
    ( multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) != inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))
    | multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) != least_upper_bound(X_247,least_upper_bound(X_248,X_246))
    | least_upper_bound(X_247,least_upper_bound(X_248,X_246)) = inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)),inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))) ),[0],$fot(least_upper_bound(X_247,least_upper_bound(X_248,X_246)))]]) ).

cnf(refute_0_1769,plain,
    ( multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) != inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))
    | least_upper_bound(X_247,least_upper_bound(X_248,X_246)) = inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)),least_upper_bound(X_247,least_upper_bound(X_248,X_246))) )],[refute_0_1767,refute_0_1768]) ).

cnf(refute_0_1770,plain,
    inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248)))) = least_upper_bound(X_246,least_upper_bound(X_247,X_248)),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))]]) ).

cnf(refute_0_1771,plain,
    ( inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248)))) != least_upper_bound(X_246,least_upper_bound(X_247,X_248))
    | least_upper_bound(X_247,least_upper_bound(X_248,X_246)) != inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))
    | least_upper_bound(X_247,least_upper_bound(X_248,X_246)) = least_upper_bound(X_246,least_upper_bound(X_247,X_248)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))) ),[1],$fot(least_upper_bound(X_246,least_upper_bound(X_247,X_248)))]]) ).

cnf(refute_0_1772,plain,
    ( least_upper_bound(X_247,least_upper_bound(X_248,X_246)) != inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))
    | least_upper_bound(X_247,least_upper_bound(X_248,X_246)) = least_upper_bound(X_246,least_upper_bound(X_247,X_248)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248)))),least_upper_bound(X_246,least_upper_bound(X_247,X_248))) )],[refute_0_1770,refute_0_1771]) ).

cnf(refute_0_1773,plain,
    ( multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)) != inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))
    | least_upper_bound(X_247,least_upper_bound(X_248,X_246)) = least_upper_bound(X_246,least_upper_bound(X_247,X_248)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))) )],[refute_0_1769,refute_0_1772]) ).

cnf(refute_0_1774,plain,
    least_upper_bound(X_247,least_upper_bound(X_248,X_246)) = least_upper_bound(X_246,least_upper_bound(X_247,X_248)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),inverse(identity)),inverse(inverse(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))) )],[refute_0_1759,refute_0_1773]) ).

cnf(refute_0_1775,plain,
    ( least_upper_bound(X_247,least_upper_bound(X_248,X_246)) != least_upper_bound(X_246,least_upper_bound(X_247,X_248))
    | least_upper_bound(X_246,least_upper_bound(X_247,X_248)) = least_upper_bound(X_247,least_upper_bound(X_248,X_246)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_247,least_upper_bound(X_248,X_246)))),bind(Y0,$fot(least_upper_bound(X_246,least_upper_bound(X_247,X_248))))]]) ).

cnf(refute_0_1776,plain,
    least_upper_bound(X_246,least_upper_bound(X_247,X_248)) = least_upper_bound(X_247,least_upper_bound(X_248,X_246)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_247,least_upper_bound(X_248,X_246)),least_upper_bound(X_246,least_upper_bound(X_247,X_248))) )],[refute_0_1774,refute_0_1775]) ).

cnf(refute_0_1777,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)) = least_upper_bound(identity,least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))),
    inference(subst,[],[refute_0_1776:[bind(X_246,$fot(inverse(greatest_lower_bound(identity,X_272)))),bind(X_247,$fot(identity)),bind(X_248,$fot(X_166))]]) ).

cnf(refute_0_1778,plain,
    ( least_upper_bound(identity,least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))) != least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)) != least_upper_bound(identity,least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)) = least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))))),bind(Z0,$fot(least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))))]]) ).

cnf(refute_0_1779,plain,
    ( least_upper_bound(identity,least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))) != least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)) = least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)),least_upper_bound(identity,least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))))) )],[refute_0_1777,refute_0_1778]) ).

cnf(refute_0_1780,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)) = least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))),least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))) )],[refute_0_1747,refute_0_1779]) ).

cnf(refute_0_1781,plain,
    ( least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)) != least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))
    | least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))) = least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))),least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)))]]) ).

cnf(refute_0_1782,plain,
    ( least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))
    | least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))) = least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166)),least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))) )],[refute_0_1780,refute_0_1781]) ).

cnf(refute_0_1783,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))
    | least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))) = least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))) )],[refute_0_1733,refute_0_1782]) ).

cnf(refute_0_1784,plain,
    least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))) = least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272)))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(identity,X_166))) )],[refute_0_1730,refute_0_1783]) ).

cnf(refute_0_1785,plain,
    ( least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))) != least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))
    | least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))) = least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))))),bind(Y0,$fot(least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))))]]) ).

cnf(refute_0_1786,plain,
    least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272))) = least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_166,inverse(X_272))),least_upper_bound(X_166,inverse(greatest_lower_bound(identity,X_272)))) )],[refute_0_1784,refute_0_1785]) ).

cnf(refute_0_1787,plain,
    least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) = least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))),
    inference(subst,[],[refute_0_1786:[bind(X_166,$fot(inverse(X))),bind(X_272,$fot(least_upper_bound(X_274,X_273)))]]) ).

cnf(refute_0_1788,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))
    | least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) != least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273))))
    | least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))))]]) ).

cnf(refute_0_1789,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))
    | least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))),least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273))))) )],[refute_0_1787,refute_0_1788]) ).

cnf(refute_0_1790,plain,
    least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X),inverse(least_upper_bound(X_274,X_273)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))) )],[refute_0_1634,refute_0_1789]) ).

cnf(refute_0_1791,plain,
    ( inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) != least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273))))
    | least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))
    | inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))) ),[0],$fot(least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))))]]) ).

cnf(refute_0_1792,plain,
    ( inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) != least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273))))
    | inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))) )],[refute_0_1790,refute_0_1791]) ).

cnf(refute_0_1793,plain,
    inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))),least_upper_bound(inverse(X),inverse(greatest_lower_bound(identity,least_upper_bound(X_274,X_273))))) )],[refute_0_1625,refute_0_1792]) ).

cnf(refute_0_1794,plain,
    ( inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) = inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))))]]) ).

cnf(refute_0_1795,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273)))) = inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,greatest_lower_bound(identity,least_upper_bound(X_273,X_274)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X,least_upper_bound(X_274,X_273))))) )],[refute_0_1793,refute_0_1794]) ).

cnf(refute_0_1796,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))),
    inference(subst,[],[refute_0_1795:[bind(X,$fot(a)),bind(X_273,$fot(identity)),bind(X_274,$fot(b))]]) ).

cnf(refute_0_1797,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,X_95)) = least_upper_bound(multiply(inverse(X_94),X_94),multiply(inverse(X_94),X_95)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_94))),bind(Y,$fot(X_94)),bind(Z,$fot(X_95))]]) ).

cnf(refute_0_1798,plain,
    multiply(inverse(X_94),X_94) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_94))]]) ).

cnf(refute_0_1799,plain,
    ( multiply(inverse(X_94),X_94) != identity
    | multiply(inverse(X_94),least_upper_bound(X_94,X_95)) != least_upper_bound(multiply(inverse(X_94),X_94),multiply(inverse(X_94),X_95))
    | multiply(inverse(X_94),least_upper_bound(X_94,X_95)) = least_upper_bound(identity,multiply(inverse(X_94),X_95)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,X_95)),least_upper_bound(multiply(inverse(X_94),X_94),multiply(inverse(X_94),X_95))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1800,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,X_95)) != least_upper_bound(multiply(inverse(X_94),X_94),multiply(inverse(X_94),X_95))
    | multiply(inverse(X_94),least_upper_bound(X_94,X_95)) = least_upper_bound(identity,multiply(inverse(X_94),X_95)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),X_94),identity) )],[refute_0_1798,refute_0_1799]) ).

cnf(refute_0_1801,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,X_95)) = least_upper_bound(identity,multiply(inverse(X_94),X_95)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,X_95)),least_upper_bound(multiply(inverse(X_94),X_94),multiply(inverse(X_94),X_95))) )],[refute_0_1797,refute_0_1800]) ).

cnf(refute_0_1802,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity)))) = least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))),
    inference(subst,[],[refute_0_1801:[bind(X_95,$fot(inverse(least_upper_bound(X_94,identity))))]]) ).

cnf(refute_0_1803,plain,
    least_upper_bound(X_210,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity)))) = least_upper_bound(X_210,inverse(least_upper_bound(X_210,identity))),
    inference(subst,[],[refute_0_685:[bind(Y,$fot(identity)),bind(X_43,$fot(X_210)),bind(X_45,$fot(inverse(least_upper_bound(X_210,identity))))]]) ).

cnf(refute_0_1804,plain,
    multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)) = least_upper_bound(inverse(least_upper_bound(identity,X_165)),multiply(inverse(least_upper_bound(identity,X_165)),X_165)),
    inference(subst,[],[refute_0_480:[bind(X_93,$fot(inverse(least_upper_bound(identity,X_165)))),bind(X_94,$fot(X_165))]]) ).

cnf(refute_0_1805,plain,
    multiply(inverse(least_upper_bound(identity,X_165)),X_165) = greatest_lower_bound(X_165,identity),
    inference(subst,[],[refute_0_315:[bind(X_124,$fot(X_165))]]) ).

cnf(refute_0_1806,plain,
    ( multiply(inverse(least_upper_bound(identity,X_165)),X_165) != greatest_lower_bound(X_165,identity)
    | multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)) != least_upper_bound(inverse(least_upper_bound(identity,X_165)),multiply(inverse(least_upper_bound(identity,X_165)),X_165))
    | multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)) = least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)),least_upper_bound(inverse(least_upper_bound(identity,X_165)),multiply(inverse(least_upper_bound(identity,X_165)),X_165))) ),[1,1],$fot(greatest_lower_bound(X_165,identity))]]) ).

cnf(refute_0_1807,plain,
    ( multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)) != least_upper_bound(inverse(least_upper_bound(identity,X_165)),multiply(inverse(least_upper_bound(identity,X_165)),X_165))
    | multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)) = least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_165)),X_165),greatest_lower_bound(X_165,identity)) )],[refute_0_1805,refute_0_1806]) ).

cnf(refute_0_1808,plain,
    multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)) = least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity)),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)),least_upper_bound(inverse(least_upper_bound(identity,X_165)),multiply(inverse(least_upper_bound(identity,X_165)),X_165))) )],[refute_0_1804,refute_0_1807]) ).

cnf(refute_0_1809,plain,
    multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)) = identity,
    inference(subst,[],[refute_0_62:[bind(X_16,$fot(identity)),bind(X_17,$fot(X_165))]]) ).

cnf(refute_0_1810,plain,
    ( multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)) != identity
    | multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)) != least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity))
    | identity = least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)),least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity))) ),[0],$fot(identity)]]) ).

cnf(refute_0_1811,plain,
    ( multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)) != least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity))
    | identity = least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)),identity) )],[refute_0_1809,refute_0_1810]) ).

cnf(refute_0_1812,plain,
    least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) = multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))))),
    inference(subst,[],[refute_0_68:[bind(X_60,$fot(least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16)))))]]) ).

cnf(refute_0_1813,plain,
    multiply(least_upper_bound(X_17,X_16),least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16)))) = least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97)),
    inference(subst,[],[refute_0_251:[bind(X_93,$fot(least_upper_bound(X_17,X_16))),bind(X_94,$fot(X_97))]]) ).

cnf(refute_0_1814,plain,
    ( multiply(least_upper_bound(X_17,X_16),least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16)))) != least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))
    | least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) != multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16)))))
    | least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) = multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))),multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16)))))) ),[1,1],$fot(least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97)))]]) ).

cnf(refute_0_1815,plain,
    ( least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) != multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16)))))
    | least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) = multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_17,X_16),least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16)))),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))) )],[refute_0_1813,refute_0_1814]) ).

cnf(refute_0_1816,plain,
    least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) = multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))),multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16)))))) )],[refute_0_1812,refute_0_1815]) ).

cnf(refute_0_1817,plain,
    multiply(inverse(least_upper_bound(X_16,X_17)),identity) = inverse(least_upper_bound(X_16,X_17)),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(inverse(least_upper_bound(X_16,X_17))))]]) ).

cnf(refute_0_1818,plain,
    least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97) = least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97),
    introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97))]]) ).

cnf(refute_0_1819,plain,
    ( multiply(inverse(least_upper_bound(X_16,X_17)),identity) != inverse(least_upper_bound(X_16,X_17))
    | least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97) != least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97)
    | least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97) = least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97),least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97)) ),[1,0],$fot(inverse(least_upper_bound(X_16,X_17)))]]) ).

cnf(refute_0_1820,plain,
    ( multiply(inverse(least_upper_bound(X_16,X_17)),identity) != inverse(least_upper_bound(X_16,X_17))
    | least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97) = least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97),least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97)) )],[refute_0_1818,refute_0_1819]) ).

cnf(refute_0_1821,plain,
    least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97) = least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,X_17)),identity),inverse(least_upper_bound(X_16,X_17))) )],[refute_0_1817,refute_0_1820]) ).

cnf(refute_0_1822,plain,
    multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_94,multiply(least_upper_bound(X_17,X_16),X_60))) = least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),X_94),multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(least_upper_bound(X_16,X_17)))),bind(Y,$fot(X_94)),bind(Z,$fot(multiply(least_upper_bound(X_17,X_16),X_60)))]]) ).

cnf(refute_0_1823,plain,
    ( X_60 != multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))
    | multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)) = X_60 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_60)),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))))]]) ).

cnf(refute_0_1824,plain,
    multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)) = X_60,
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60))) )],[refute_0_68,refute_0_1823]) ).

cnf(refute_0_1825,plain,
    ( multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)) != X_60
    | multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_94,multiply(least_upper_bound(X_17,X_16),X_60))) != least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),X_94),multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)))
    | multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_94,multiply(least_upper_bound(X_17,X_16),X_60))) = least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),X_94),X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_94,multiply(least_upper_bound(X_17,X_16),X_60))),least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),X_94),multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)))) ),[1,1],$fot(X_60)]]) ).

cnf(refute_0_1826,plain,
    ( multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_94,multiply(least_upper_bound(X_17,X_16),X_60))) != least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),X_94),multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)))
    | multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_94,multiply(least_upper_bound(X_17,X_16),X_60))) = least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),X_94),X_60) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)),X_60) )],[refute_0_1824,refute_0_1825]) ).

cnf(refute_0_1827,plain,
    multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_94,multiply(least_upper_bound(X_17,X_16),X_60))) = least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),X_94),X_60),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(X_94,multiply(least_upper_bound(X_17,X_16),X_60))),least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),X_94),multiply(inverse(least_upper_bound(X_16,X_17)),multiply(least_upper_bound(X_17,X_16),X_60)))) )],[refute_0_1822,refute_0_1826]) ).

cnf(refute_0_1828,plain,
    multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))) = least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97),
    inference(subst,[],[refute_0_1827:[bind(X_60,$fot(X_97)),bind(X_94,$fot(identity))]]) ).

cnf(refute_0_1829,plain,
    ( multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))) != least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97)
    | least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97) != least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97)
    | multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))) = least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))))),bind(Y0,$fot(least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97))),bind(Z0,$fot(least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97)))]]) ).

cnf(refute_0_1830,plain,
    ( least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97) != least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97)
    | multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))) = least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))),least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97)) )],[refute_0_1828,refute_0_1829]) ).

cnf(refute_0_1831,plain,
    multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))) = least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(least_upper_bound(X_16,X_17)),identity),X_97),least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97)) )],[refute_0_1821,refute_0_1830]) ).

cnf(refute_0_1832,plain,
    ( multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))) != least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97)
    | least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) != multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97)))
    | least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) = least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))),multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97)))) ),[1],$fot(least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97))]]) ).

cnf(refute_0_1833,plain,
    ( least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) != multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97)))
    | least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) = least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97))),least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97)) )],[refute_0_1831,refute_0_1832]) ).

cnf(refute_0_1834,plain,
    least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) = least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))),multiply(inverse(least_upper_bound(X_16,X_17)),least_upper_bound(identity,multiply(least_upper_bound(X_17,X_16),X_97)))) )],[refute_0_1816,refute_0_1833]) ).

cnf(refute_0_1835,plain,
    ( least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) != least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97)
    | least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97) = least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97)))]]) ).

cnf(refute_0_1836,plain,
    least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97) = least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_97,inverse(least_upper_bound(X_17,X_16))),least_upper_bound(inverse(least_upper_bound(X_16,X_17)),X_97)) )],[refute_0_1834,refute_0_1835]) ).

cnf(refute_0_1837,plain,
    least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity)) = least_upper_bound(greatest_lower_bound(X_165,identity),inverse(least_upper_bound(X_165,identity))),
    inference(subst,[],[refute_0_1836:[bind(X_16,$fot(identity)),bind(X_17,$fot(X_165)),bind(X_97,$fot(greatest_lower_bound(X_165,identity)))]]) ).

cnf(refute_0_1838,plain,
    ( identity != least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity))
    | least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity)) != least_upper_bound(greatest_lower_bound(X_165,identity),inverse(least_upper_bound(X_165,identity)))
    | identity = least_upper_bound(greatest_lower_bound(X_165,identity),inverse(least_upper_bound(X_165,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(identity,least_upper_bound(greatest_lower_bound(X_165,identity),inverse(least_upper_bound(X_165,identity)))) ),[0],$fot(least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity)))]]) ).

cnf(refute_0_1839,plain,
    ( identity != least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity))
    | identity = least_upper_bound(greatest_lower_bound(X_165,identity),inverse(least_upper_bound(X_165,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity)),least_upper_bound(greatest_lower_bound(X_165,identity),inverse(least_upper_bound(X_165,identity)))) )],[refute_0_1837,refute_0_1838]) ).

cnf(refute_0_1840,plain,
    ( multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)) != least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity))
    | identity = least_upper_bound(greatest_lower_bound(X_165,identity),inverse(least_upper_bound(X_165,identity))) ),
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity))) )],[refute_0_1811,refute_0_1839]) ).

cnf(refute_0_1841,plain,
    identity = least_upper_bound(greatest_lower_bound(X_165,identity),inverse(least_upper_bound(X_165,identity))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,X_165)),least_upper_bound(X_165,identity)),least_upper_bound(inverse(least_upper_bound(identity,X_165)),greatest_lower_bound(X_165,identity))) )],[refute_0_1808,refute_0_1840]) ).

cnf(refute_0_1842,plain,
    identity = least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity))),
    inference(subst,[],[refute_0_1841:[bind(X_165,$fot(X_210))]]) ).

cnf(refute_0_1843,plain,
    ( identity != least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity)))
    | least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity)))))]]) ).

cnf(refute_0_1844,plain,
    least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity))) = identity,
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity)))) )],[refute_0_1842,refute_0_1843]) ).

cnf(refute_0_1845,plain,
    ( least_upper_bound(X_210,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity)))) != least_upper_bound(X_210,inverse(least_upper_bound(X_210,identity)))
    | least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity))) != identity
    | least_upper_bound(X_210,identity) = least_upper_bound(X_210,inverse(least_upper_bound(X_210,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_210,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity)))),least_upper_bound(X_210,inverse(least_upper_bound(X_210,identity)))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_1846,plain,
    ( least_upper_bound(X_210,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity)))) != least_upper_bound(X_210,inverse(least_upper_bound(X_210,identity)))
    | least_upper_bound(X_210,identity) = least_upper_bound(X_210,inverse(least_upper_bound(X_210,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity))),identity) )],[refute_0_1844,refute_0_1845]) ).

cnf(refute_0_1847,plain,
    least_upper_bound(X_210,identity) = least_upper_bound(X_210,inverse(least_upper_bound(X_210,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_210,least_upper_bound(greatest_lower_bound(X_210,identity),inverse(least_upper_bound(X_210,identity)))),least_upper_bound(X_210,inverse(least_upper_bound(X_210,identity)))) )],[refute_0_1803,refute_0_1846]) ).

cnf(refute_0_1848,plain,
    least_upper_bound(X_94,identity) = least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity))),
    inference(subst,[],[refute_0_1847:[bind(X_210,$fot(X_94))]]) ).

cnf(refute_0_1849,plain,
    ( least_upper_bound(X_94,identity) != least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity)))
    | least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity))) = least_upper_bound(X_94,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_94,identity))),bind(Y0,$fot(least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity)))))]]) ).

cnf(refute_0_1850,plain,
    least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity))) = least_upper_bound(X_94,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_94,identity),least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity)))) )],[refute_0_1848,refute_0_1849]) ).

cnf(refute_0_1851,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity)))) != least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))
    | least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity))) != least_upper_bound(X_94,identity)
    | multiply(inverse(X_94),least_upper_bound(X_94,identity)) = least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity)))),least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))) ),[0,1],$fot(least_upper_bound(X_94,identity))]]) ).

cnf(refute_0_1852,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity)))) != least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))
    | multiply(inverse(X_94),least_upper_bound(X_94,identity)) = least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity))),least_upper_bound(X_94,identity)) )],[refute_0_1850,refute_0_1851]) ).

cnf(refute_0_1853,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,identity)) = least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(least_upper_bound(X_94,identity)))),least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))) )],[refute_0_1802,refute_0_1852]) ).

cnf(refute_0_1854,plain,
    multiply(inverse(X_103),least_upper_bound(X_103,identity)) = least_upper_bound(identity,multiply(inverse(X_103),identity)),
    inference(subst,[],[refute_0_1801:[bind(X_94,$fot(X_103)),bind(X_95,$fot(identity))]]) ).

cnf(refute_0_1855,plain,
    inverse(X_103) = multiply(inverse(X_103),identity),
    inference(subst,[],[refute_0_29:[bind(X_62,$fot(inverse(X_103)))]]) ).

cnf(refute_0_1856,plain,
    ( inverse(X_103) != multiply(inverse(X_103),identity)
    | multiply(inverse(X_103),identity) = inverse(X_103) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(X_103))),bind(Y0,$fot(multiply(inverse(X_103),identity)))]]) ).

cnf(refute_0_1857,plain,
    multiply(inverse(X_103),identity) = inverse(X_103),
    inference(resolve,[$cnf( $equal(inverse(X_103),multiply(inverse(X_103),identity)) )],[refute_0_1855,refute_0_1856]) ).

cnf(refute_0_1858,plain,
    ( multiply(inverse(X_103),identity) != inverse(X_103)
    | multiply(inverse(X_103),least_upper_bound(X_103,identity)) != least_upper_bound(identity,multiply(inverse(X_103),identity))
    | multiply(inverse(X_103),least_upper_bound(X_103,identity)) = least_upper_bound(identity,inverse(X_103)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_103),least_upper_bound(X_103,identity)),least_upper_bound(identity,multiply(inverse(X_103),identity))) ),[1,1],$fot(inverse(X_103))]]) ).

cnf(refute_0_1859,plain,
    ( multiply(inverse(X_103),least_upper_bound(X_103,identity)) != least_upper_bound(identity,multiply(inverse(X_103),identity))
    | multiply(inverse(X_103),least_upper_bound(X_103,identity)) = least_upper_bound(identity,inverse(X_103)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_103),identity),inverse(X_103)) )],[refute_0_1857,refute_0_1858]) ).

cnf(refute_0_1860,plain,
    multiply(inverse(X_103),least_upper_bound(X_103,identity)) = least_upper_bound(identity,inverse(X_103)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_103),least_upper_bound(X_103,identity)),least_upper_bound(identity,multiply(inverse(X_103),identity))) )],[refute_0_1854,refute_0_1859]) ).

cnf(refute_0_1861,plain,
    least_upper_bound(identity,inverse(X_103)) = inverse(greatest_lower_bound(identity,X_103)),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(X_103))]]) ).

cnf(refute_0_1862,plain,
    ( multiply(inverse(X_103),least_upper_bound(X_103,identity)) != least_upper_bound(identity,inverse(X_103))
    | least_upper_bound(identity,inverse(X_103)) != inverse(greatest_lower_bound(identity,X_103))
    | multiply(inverse(X_103),least_upper_bound(X_103,identity)) = inverse(greatest_lower_bound(identity,X_103)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_103),least_upper_bound(X_103,identity)),inverse(greatest_lower_bound(identity,X_103))) ),[0],$fot(least_upper_bound(identity,inverse(X_103)))]]) ).

cnf(refute_0_1863,plain,
    ( multiply(inverse(X_103),least_upper_bound(X_103,identity)) != least_upper_bound(identity,inverse(X_103))
    | multiply(inverse(X_103),least_upper_bound(X_103,identity)) = inverse(greatest_lower_bound(identity,X_103)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_103)),inverse(greatest_lower_bound(identity,X_103))) )],[refute_0_1861,refute_0_1862]) ).

cnf(refute_0_1864,plain,
    multiply(inverse(X_103),least_upper_bound(X_103,identity)) = inverse(greatest_lower_bound(identity,X_103)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_103),least_upper_bound(X_103,identity)),least_upper_bound(identity,inverse(X_103))) )],[refute_0_1860,refute_0_1863]) ).

cnf(refute_0_1865,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,identity)) = inverse(greatest_lower_bound(identity,X_94)),
    inference(subst,[],[refute_0_1864:[bind(X_103,$fot(X_94))]]) ).

cnf(refute_0_1866,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,identity)) != inverse(greatest_lower_bound(identity,X_94))
    | multiply(inverse(X_94),least_upper_bound(X_94,identity)) != least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))
    | inverse(greatest_lower_bound(identity,X_94)) = least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,identity)),least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))) ),[0],$fot(inverse(greatest_lower_bound(identity,X_94)))]]) ).

cnf(refute_0_1867,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,identity)) != least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))
    | inverse(greatest_lower_bound(identity,X_94)) = least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,identity)),inverse(greatest_lower_bound(identity,X_94))) )],[refute_0_1865,refute_0_1866]) ).

cnf(refute_0_1868,plain,
    least_upper_bound(identity,inverse(multiply(least_upper_bound(X_94,identity),X_94))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(multiply(least_upper_bound(X_94,identity),X_94)))]]) ).

cnf(refute_0_1869,plain,
    multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))) = inverse(multiply(least_upper_bound(X_94,identity),X_94)),
    inference(subst,[],[refute_0_667:[bind(X_198,$fot(least_upper_bound(X_94,identity))),bind(X_59,$fot(X_94))]]) ).

cnf(refute_0_1870,plain,
    least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) = least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))))]]) ).

cnf(refute_0_1871,plain,
    ( multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))) != inverse(multiply(least_upper_bound(X_94,identity),X_94))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) != least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) = least_upper_bound(identity,inverse(multiply(least_upper_bound(X_94,identity),X_94))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))),least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))) ),[1,1],$fot(inverse(multiply(least_upper_bound(X_94,identity),X_94)))]]) ).

cnf(refute_0_1872,plain,
    ( multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))) != inverse(multiply(least_upper_bound(X_94,identity),X_94))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) = least_upper_bound(identity,inverse(multiply(least_upper_bound(X_94,identity),X_94))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))),least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))) )],[refute_0_1870,refute_0_1871]) ).

cnf(refute_0_1873,plain,
    least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) = least_upper_bound(identity,inverse(multiply(least_upper_bound(X_94,identity),X_94))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))),inverse(multiply(least_upper_bound(X_94,identity),X_94))) )],[refute_0_1869,refute_0_1872]) ).

cnf(refute_0_1874,plain,
    ( least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) != least_upper_bound(identity,inverse(multiply(least_upper_bound(X_94,identity),X_94)))
    | least_upper_bound(identity,inverse(multiply(least_upper_bound(X_94,identity),X_94))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(least_upper_bound(X_94,identity),X_94))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))))]]) ).

cnf(refute_0_1875,plain,
    ( least_upper_bound(identity,inverse(multiply(least_upper_bound(X_94,identity),X_94))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))),least_upper_bound(identity,inverse(multiply(least_upper_bound(X_94,identity),X_94)))) )],[refute_0_1873,refute_0_1874]) ).

cnf(refute_0_1876,plain,
    least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(least_upper_bound(X_94,identity),X_94))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))) )],[refute_0_1868,refute_0_1875]) ).

cnf(refute_0_1877,plain,
    ( inverse(greatest_lower_bound(identity,X_94)) != least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))
    | inverse(greatest_lower_bound(identity,X_94)) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,X_94)),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))))]]) ).

cnf(refute_0_1878,plain,
    ( inverse(greatest_lower_bound(identity,X_94)) != least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))
    | inverse(greatest_lower_bound(identity,X_94)) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity)))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))) )],[refute_0_1876,refute_0_1877]) ).

cnf(refute_0_1879,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,identity)) != least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))
    | inverse(greatest_lower_bound(identity,X_94)) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_94)),least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))) )],[refute_0_1867,refute_0_1878]) ).

cnf(refute_0_1880,plain,
    inverse(greatest_lower_bound(identity,X_94)) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,identity)),least_upper_bound(identity,multiply(inverse(X_94),inverse(least_upper_bound(X_94,identity))))) )],[refute_0_1853,refute_0_1879]) ).

cnf(refute_0_1881,plain,
    multiply(X_94,least_upper_bound(X_94,identity)) = least_upper_bound(X_94,multiply(X_94,X_94)),
    inference(subst,[],[refute_0_480:[bind(X_93,$fot(X_94))]]) ).

cnf(refute_0_1882,plain,
    multiply(least_upper_bound(X_94,identity),X_94) = least_upper_bound(X_94,multiply(X_94,X_94)),
    inference(subst,[],[refute_0_728:[bind(X_110,$fot(X_94)),bind(X_111,$fot(X_94))]]) ).

cnf(refute_0_1883,plain,
    ( multiply(least_upper_bound(X_94,identity),X_94) != least_upper_bound(X_94,multiply(X_94,X_94))
    | least_upper_bound(X_94,multiply(X_94,X_94)) = multiply(least_upper_bound(X_94,identity),X_94) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_94,identity),X_94))),bind(Y0,$fot(least_upper_bound(X_94,multiply(X_94,X_94))))]]) ).

cnf(refute_0_1884,plain,
    least_upper_bound(X_94,multiply(X_94,X_94)) = multiply(least_upper_bound(X_94,identity),X_94),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_94,identity),X_94),least_upper_bound(X_94,multiply(X_94,X_94))) )],[refute_0_1882,refute_0_1883]) ).

cnf(refute_0_1885,plain,
    ( multiply(X_94,least_upper_bound(X_94,identity)) != least_upper_bound(X_94,multiply(X_94,X_94))
    | least_upper_bound(X_94,multiply(X_94,X_94)) != multiply(least_upper_bound(X_94,identity),X_94)
    | multiply(X_94,least_upper_bound(X_94,identity)) = multiply(least_upper_bound(X_94,identity),X_94) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_94,least_upper_bound(X_94,identity)),multiply(least_upper_bound(X_94,identity),X_94)) ),[0],$fot(least_upper_bound(X_94,multiply(X_94,X_94)))]]) ).

cnf(refute_0_1886,plain,
    ( multiply(X_94,least_upper_bound(X_94,identity)) != least_upper_bound(X_94,multiply(X_94,X_94))
    | multiply(X_94,least_upper_bound(X_94,identity)) = multiply(least_upper_bound(X_94,identity),X_94) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_94,multiply(X_94,X_94)),multiply(least_upper_bound(X_94,identity),X_94)) )],[refute_0_1884,refute_0_1885]) ).

cnf(refute_0_1887,plain,
    multiply(X_94,least_upper_bound(X_94,identity)) = multiply(least_upper_bound(X_94,identity),X_94),
    inference(resolve,[$cnf( $equal(multiply(X_94,least_upper_bound(X_94,identity)),least_upper_bound(X_94,multiply(X_94,X_94))) )],[refute_0_1881,refute_0_1886]) ).

cnf(refute_0_1888,plain,
    ( multiply(X_94,least_upper_bound(X_94,identity)) != multiply(least_upper_bound(X_94,identity),X_94)
    | multiply(least_upper_bound(X_94,identity),X_94) = multiply(X_94,least_upper_bound(X_94,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_94,least_upper_bound(X_94,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_94,identity),X_94)))]]) ).

cnf(refute_0_1889,plain,
    multiply(least_upper_bound(X_94,identity),X_94) = multiply(X_94,least_upper_bound(X_94,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_94,least_upper_bound(X_94,identity)),multiply(least_upper_bound(X_94,identity),X_94)) )],[refute_0_1887,refute_0_1888]) ).

cnf(refute_0_1890,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)) = greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))]]) ).

cnf(refute_0_1891,plain,
    ( multiply(least_upper_bound(X_94,identity),X_94) != multiply(X_94,least_upper_bound(X_94,identity))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)) != greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)) = greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)),greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) ),[1,1],$fot(multiply(X_94,least_upper_bound(X_94,identity)))]]) ).

cnf(refute_0_1892,plain,
    ( multiply(least_upper_bound(X_94,identity),X_94) != multiply(X_94,least_upper_bound(X_94,identity))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)) = greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)),greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) )],[refute_0_1890,refute_0_1891]) ).

cnf(refute_0_1893,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)) = greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_94,identity),X_94),multiply(X_94,least_upper_bound(X_94,identity))) )],[refute_0_1889,refute_0_1892]) ).

cnf(refute_0_1894,plain,
    inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))))]]) ).

cnf(refute_0_1895,plain,
    ( greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)) != greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))
    | inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))
    | inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) = inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))))]]) ).

cnf(refute_0_1896,plain,
    ( greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)) != greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))
    | inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) = inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))) )],[refute_0_1894,refute_0_1895]) ).

cnf(refute_0_1897,plain,
    inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) = inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)),greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))) )],[refute_0_1893,refute_0_1896]) ).

cnf(refute_0_1898,plain,
    ( inverse(greatest_lower_bound(identity,X_94)) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))
    | inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))) != inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))))
    | inverse(greatest_lower_bound(identity,X_94)) = inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,X_94)),inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))))]]) ).

cnf(refute_0_1899,plain,
    ( inverse(greatest_lower_bound(identity,X_94)) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))
    | inverse(greatest_lower_bound(identity,X_94)) = inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94))),inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))))) )],[refute_0_1897,refute_0_1898]) ).

cnf(refute_0_1900,plain,
    inverse(greatest_lower_bound(identity,X_94)) = inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_94)),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(X_94,identity),X_94)))) )],[refute_0_1880,refute_0_1899]) ).

cnf(refute_0_1901,plain,
    multiply(greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity))),X_121) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)),
    inference(subst,[],[refute_0_1305:[bind(X_123,$fot(inverse(greatest_lower_bound(inverse(X_121),identity))))]]) ).

cnf(refute_0_1902,plain,
    greatest_lower_bound(X_204,greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(X_204,identity)))) = greatest_lower_bound(X_204,inverse(greatest_lower_bound(X_204,identity))),
    inference(subst,[],[refute_0_467:[bind(X_11,$fot(identity)),bind(X_36,$fot(X_204)),bind(X_38,$fot(inverse(greatest_lower_bound(X_204,identity))))]]) ).

cnf(refute_0_1903,plain,
    multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))) = identity,
    inference(subst,[],[refute_0_62:[bind(X_16,$fot(inverse(least_upper_bound(identity,X_167)))),bind(X_17,$fot(greatest_lower_bound(X_167,identity)))]]) ).

cnf(refute_0_1904,plain,
    identity = least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167))),
    inference(subst,[],[refute_0_706:[bind(X_132,$fot(X_167))]]) ).

cnf(refute_0_1905,plain,
    ( identity != least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))
    | least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))))]]) ).

cnf(refute_0_1906,plain,
    least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167))) = identity,
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))) )],[refute_0_1904,refute_0_1905]) ).

cnf(refute_0_1907,plain,
    ( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))) != identity
    | least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167))) != identity
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_1908,plain,
    ( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))) != identity
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167))),identity) )],[refute_0_1906,refute_0_1907]) ).

cnf(refute_0_1909,plain,
    multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity) )],[refute_0_1903,refute_0_1908]) ).

cnf(refute_0_1910,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(X_167,identity)),least_upper_bound(identity,X_167)) = greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(inverse(greatest_lower_bound(X_167,identity)))),bind(X_25,$fot(least_upper_bound(identity,X_167)))]]) ).

cnf(refute_0_1911,plain,
    inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))) = greatest_lower_bound(inverse(greatest_lower_bound(X_167,identity)),least_upper_bound(identity,X_167)),
    inference(subst,[],[refute_0_582:[bind(X,$fot(greatest_lower_bound(X_167,identity))),bind(X_89,$fot(least_upper_bound(identity,X_167)))]]) ).

cnf(refute_0_1912,plain,
    ( greatest_lower_bound(inverse(greatest_lower_bound(X_167,identity)),least_upper_bound(identity,X_167)) != greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))
    | inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))) != greatest_lower_bound(inverse(greatest_lower_bound(X_167,identity)),least_upper_bound(identity,X_167))
    | inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))) = greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_167,identity)),least_upper_bound(identity,X_167)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))))]]) ).

cnf(refute_0_1913,plain,
    ( greatest_lower_bound(inverse(greatest_lower_bound(X_167,identity)),least_upper_bound(identity,X_167)) != greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))
    | inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))) = greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),greatest_lower_bound(inverse(greatest_lower_bound(X_167,identity)),least_upper_bound(identity,X_167))) )],[refute_0_1911,refute_0_1912]) ).

cnf(refute_0_1914,plain,
    inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))) = greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_167,identity)),least_upper_bound(identity,X_167)),greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))) )],[refute_0_1910,refute_0_1913]) ).

cnf(refute_0_1915,plain,
    multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity) = inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167))))))]]) ).

cnf(refute_0_1916,plain,
    ( multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity) != inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167))))
    | inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))) != greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))
    | multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity) = greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity))),bind(Y0,$fot(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))))]]) ).

cnf(refute_0_1917,plain,
    ( inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))) != greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))
    | multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity) = greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity),inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167))))) )],[refute_0_1915,refute_0_1916]) ).

cnf(refute_0_1918,plain,
    multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity) = greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))) )],[refute_0_1914,refute_0_1917]) ).

cnf(refute_0_1919,plain,
    multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity) = multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity),
    inference(subst,[],[refute_0_614:[bind(X,$fot(inverse(least_upper_bound(identity,X_167)))),bind(Y,$fot(greatest_lower_bound(X_167,identity))),bind(X_88,$fot(identity))]]) ).

cnf(refute_0_1920,plain,
    ( multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity) != greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity) != multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity)
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity) = greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity))),bind(Y0,$fot(multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))))]]) ).

cnf(refute_0_1921,plain,
    ( multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity) != greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity) = greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity),multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity)) )],[refute_0_1919,refute_0_1920]) ).

cnf(refute_0_1922,plain,
    multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity) = greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(greatest_lower_bound(X_167,identity),inverse(least_upper_bound(identity,X_167)))),identity),greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))) )],[refute_0_1918,refute_0_1921]) ).

cnf(refute_0_1923,plain,
    ( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity) != greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))
    | multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity) != identity
    | greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity),identity) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))))]]) ).

cnf(refute_0_1924,plain,
    ( multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity) != identity
    | greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity),greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity)))) )],[refute_0_1922,refute_0_1923]) ).

cnf(refute_0_1925,plain,
    greatest_lower_bound(least_upper_bound(identity,X_167),inverse(greatest_lower_bound(X_167,identity))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(least_upper_bound(identity,X_167)),greatest_lower_bound(X_167,identity))),identity),identity) )],[refute_0_1909,refute_0_1924]) ).

cnf(refute_0_1926,plain,
    greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(X_204,identity))) = identity,
    inference(subst,[],[refute_0_1925:[bind(X_167,$fot(X_204))]]) ).

cnf(refute_0_1927,plain,
    ( greatest_lower_bound(X_204,greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(X_204,identity)))) != greatest_lower_bound(X_204,inverse(greatest_lower_bound(X_204,identity)))
    | greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(X_204,identity))) != identity
    | greatest_lower_bound(X_204,identity) = greatest_lower_bound(X_204,inverse(greatest_lower_bound(X_204,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_204,greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(X_204,identity)))),greatest_lower_bound(X_204,inverse(greatest_lower_bound(X_204,identity)))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_1928,plain,
    ( greatest_lower_bound(X_204,greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(X_204,identity)))) != greatest_lower_bound(X_204,inverse(greatest_lower_bound(X_204,identity)))
    | greatest_lower_bound(X_204,identity) = greatest_lower_bound(X_204,inverse(greatest_lower_bound(X_204,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(X_204,identity))),identity) )],[refute_0_1926,refute_0_1927]) ).

cnf(refute_0_1929,plain,
    greatest_lower_bound(X_204,identity) = greatest_lower_bound(X_204,inverse(greatest_lower_bound(X_204,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_204,greatest_lower_bound(least_upper_bound(identity,X_204),inverse(greatest_lower_bound(X_204,identity)))),greatest_lower_bound(X_204,inverse(greatest_lower_bound(X_204,identity)))) )],[refute_0_1902,refute_0_1928]) ).

cnf(refute_0_1930,plain,
    greatest_lower_bound(inverse(X_121),identity) = greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity))),
    inference(subst,[],[refute_0_1929:[bind(X_204,$fot(inverse(X_121)))]]) ).

cnf(refute_0_1931,plain,
    ( greatest_lower_bound(inverse(X_121),identity) != greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity)))
    | greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity))) = greatest_lower_bound(inverse(X_121),identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(inverse(X_121),identity))),bind(Y0,$fot(greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity)))))]]) ).

cnf(refute_0_1932,plain,
    greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity))) = greatest_lower_bound(inverse(X_121),identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_121),identity),greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity)))) )],[refute_0_1930,refute_0_1931]) ).

cnf(refute_0_1933,plain,
    ( multiply(greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity))),X_121) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))
    | greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity))) != greatest_lower_bound(inverse(X_121),identity)
    | multiply(greatest_lower_bound(inverse(X_121),identity),X_121) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity))),X_121),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))) ),[0,0],$fot(greatest_lower_bound(inverse(X_121),identity))]]) ).

cnf(refute_0_1934,plain,
    ( multiply(greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity))),X_121) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))
    | multiply(greatest_lower_bound(inverse(X_121),identity),X_121) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity))),greatest_lower_bound(inverse(X_121),identity)) )],[refute_0_1932,refute_0_1933]) ).

cnf(refute_0_1935,plain,
    multiply(greatest_lower_bound(inverse(X_121),identity),X_121) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),inverse(greatest_lower_bound(inverse(X_121),identity))),X_121),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))) )],[refute_0_1901,refute_0_1934]) ).

cnf(refute_0_1936,plain,
    multiply(identity,greatest_lower_bound(X_121,identity)) = greatest_lower_bound(X_121,identity),
    inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_121,identity)))]]) ).

cnf(refute_0_1937,plain,
    greatest_lower_bound(identity,multiply(identity,X_121)) = multiply(identity,greatest_lower_bound(X_121,identity)),
    inference(subst,[],[refute_0_308:[bind(X_107,$fot(identity)),bind(X_108,$fot(X_121))]]) ).

cnf(refute_0_1938,plain,
    ( multiply(identity,greatest_lower_bound(X_121,identity)) != greatest_lower_bound(X_121,identity)
    | greatest_lower_bound(identity,multiply(identity,X_121)) != multiply(identity,greatest_lower_bound(X_121,identity))
    | greatest_lower_bound(identity,multiply(identity,X_121)) = greatest_lower_bound(X_121,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,X_121)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(X_121,identity)))),bind(Z0,$fot(greatest_lower_bound(X_121,identity)))]]) ).

cnf(refute_0_1939,plain,
    ( multiply(identity,greatest_lower_bound(X_121,identity)) != greatest_lower_bound(X_121,identity)
    | greatest_lower_bound(identity,multiply(identity,X_121)) = greatest_lower_bound(X_121,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_121)),multiply(identity,greatest_lower_bound(X_121,identity))) )],[refute_0_1937,refute_0_1938]) ).

cnf(refute_0_1940,plain,
    greatest_lower_bound(identity,multiply(identity,X_121)) = greatest_lower_bound(X_121,identity),
    inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_121,identity)),greatest_lower_bound(X_121,identity)) )],[refute_0_1936,refute_0_1939]) ).

cnf(refute_0_1941,plain,
    multiply(greatest_lower_bound(inverse(X_121),identity),X_121) = greatest_lower_bound(identity,multiply(identity,X_121)),
    inference(subst,[],[refute_0_1305:[bind(X_123,$fot(identity))]]) ).

cnf(refute_0_1942,plain,
    ( multiply(greatest_lower_bound(inverse(X_121),identity),X_121) != greatest_lower_bound(identity,multiply(identity,X_121))
    | greatest_lower_bound(identity,multiply(identity,X_121)) != greatest_lower_bound(X_121,identity)
    | multiply(greatest_lower_bound(inverse(X_121),identity),X_121) = greatest_lower_bound(X_121,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(X_121),identity),X_121))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(identity,X_121)))),bind(Z0,$fot(greatest_lower_bound(X_121,identity)))]]) ).

cnf(refute_0_1943,plain,
    ( greatest_lower_bound(identity,multiply(identity,X_121)) != greatest_lower_bound(X_121,identity)
    | multiply(greatest_lower_bound(inverse(X_121),identity),X_121) = greatest_lower_bound(X_121,identity) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),identity),X_121),greatest_lower_bound(identity,multiply(identity,X_121))) )],[refute_0_1941,refute_0_1942]) ).

cnf(refute_0_1944,plain,
    multiply(greatest_lower_bound(inverse(X_121),identity),X_121) = greatest_lower_bound(X_121,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,X_121)),greatest_lower_bound(X_121,identity)) )],[refute_0_1940,refute_0_1943]) ).

cnf(refute_0_1945,plain,
    ( multiply(greatest_lower_bound(inverse(X_121),identity),X_121) != greatest_lower_bound(X_121,identity)
    | multiply(greatest_lower_bound(inverse(X_121),identity),X_121) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))
    | greatest_lower_bound(X_121,identity) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),identity),X_121),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))) ),[0],$fot(greatest_lower_bound(X_121,identity))]]) ).

cnf(refute_0_1946,plain,
    ( multiply(greatest_lower_bound(inverse(X_121),identity),X_121) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))
    | greatest_lower_bound(X_121,identity) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),identity),X_121),greatest_lower_bound(X_121,identity)) )],[refute_0_1944,refute_0_1945]) ).

cnf(refute_0_1947,plain,
    least_upper_bound(inverse(identity),X_121) = least_upper_bound(inverse(identity),X_121),
    introduced(tautology,[refl,[$fot(least_upper_bound(inverse(identity),X_121))]]) ).

cnf(refute_0_1948,plain,
    ( inverse(identity) != identity
    | least_upper_bound(inverse(identity),X_121) != least_upper_bound(inverse(identity),X_121)
    | least_upper_bound(inverse(identity),X_121) = least_upper_bound(identity,X_121) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(identity),X_121),least_upper_bound(inverse(identity),X_121)) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_1949,plain,
    ( inverse(identity) != identity
    | least_upper_bound(inverse(identity),X_121) = least_upper_bound(identity,X_121) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),X_121),least_upper_bound(inverse(identity),X_121)) )],[refute_0_1947,refute_0_1948]) ).

cnf(refute_0_1950,plain,
    least_upper_bound(inverse(identity),X_121) = least_upper_bound(identity,X_121),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_1949]) ).

cnf(refute_0_1951,plain,
    inverse(greatest_lower_bound(identity,inverse(X_121))) = least_upper_bound(inverse(identity),X_121),
    inference(subst,[],[refute_0_1559:[bind(X,$fot(identity)),bind(X_89,$fot(X_121))]]) ).

cnf(refute_0_1952,plain,
    multiply(inverse(greatest_lower_bound(X_168,identity)),least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity)))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))),
    inference(subst,[],[refute_0_1801:[bind(X_94,$fot(greatest_lower_bound(X_168,identity))),bind(X_95,$fot(inverse(least_upper_bound(X_168,identity))))]]) ).

cnf(refute_0_1953,plain,
    identity = least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity))),
    inference(subst,[],[refute_0_1841:[bind(X_165,$fot(X_168))]]) ).

cnf(refute_0_1954,plain,
    ( identity != least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity)))
    | least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity)))))]]) ).

cnf(refute_0_1955,plain,
    least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity))) = identity,
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity)))) )],[refute_0_1953,refute_0_1954]) ).

cnf(refute_0_1956,plain,
    ( multiply(inverse(greatest_lower_bound(X_168,identity)),least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity)))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))
    | least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity))) != identity
    | multiply(inverse(greatest_lower_bound(X_168,identity)),identity) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_168,identity)),least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_1957,plain,
    ( multiply(inverse(greatest_lower_bound(X_168,identity)),least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity)))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))
    | multiply(inverse(greatest_lower_bound(X_168,identity)),identity) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity))),identity) )],[refute_0_1955,refute_0_1956]) ).

cnf(refute_0_1958,plain,
    multiply(inverse(greatest_lower_bound(X_168,identity)),identity) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_168,identity)),least_upper_bound(greatest_lower_bound(X_168,identity),inverse(least_upper_bound(X_168,identity)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))) )],[refute_0_1952,refute_0_1957]) ).

cnf(refute_0_1959,plain,
    multiply(inverse(greatest_lower_bound(X_168,identity)),identity) = inverse(greatest_lower_bound(X_168,identity)),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(inverse(greatest_lower_bound(X_168,identity))))]]) ).

cnf(refute_0_1960,plain,
    ( multiply(inverse(greatest_lower_bound(X_168,identity)),identity) != inverse(greatest_lower_bound(X_168,identity))
    | multiply(inverse(greatest_lower_bound(X_168,identity)),identity) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))
    | inverse(greatest_lower_bound(X_168,identity)) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_168,identity)),identity),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))) ),[0],$fot(inverse(greatest_lower_bound(X_168,identity)))]]) ).

cnf(refute_0_1961,plain,
    ( multiply(inverse(greatest_lower_bound(X_168,identity)),identity) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))
    | inverse(greatest_lower_bound(X_168,identity)) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_168,identity)),identity),inverse(greatest_lower_bound(X_168,identity))) )],[refute_0_1959,refute_0_1960]) ).

cnf(refute_0_1962,plain,
    inverse(greatest_lower_bound(X_168,identity)) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_168,identity)),identity),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))) )],[refute_0_1958,refute_0_1961]) ).

cnf(refute_0_1963,plain,
    least_upper_bound(identity,inverse(X_168)) = inverse(greatest_lower_bound(identity,X_168)),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(X_168))]]) ).

cnf(refute_0_1964,plain,
    least_upper_bound(X_129,identity) = least_upper_bound(identity,X_129),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_129)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_1965,plain,
    ( least_upper_bound(X_129,identity) != least_upper_bound(identity,X_129)
    | least_upper_bound(identity,X_129) = least_upper_bound(X_129,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_129,identity))),bind(Y0,$fot(least_upper_bound(identity,X_129)))]]) ).

cnf(refute_0_1966,plain,
    least_upper_bound(identity,X_129) = least_upper_bound(X_129,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_129,identity),least_upper_bound(identity,X_129)) )],[refute_0_1964,refute_0_1965]) ).

cnf(refute_0_1967,plain,
    ( X_129 != multiply(least_upper_bound(identity,X_129),greatest_lower_bound(X_129,identity))
    | least_upper_bound(identity,X_129) != least_upper_bound(X_129,identity)
    | X_129 = multiply(least_upper_bound(X_129,identity),greatest_lower_bound(X_129,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(X_129,multiply(least_upper_bound(identity,X_129),greatest_lower_bound(X_129,identity))) ),[1,0],$fot(least_upper_bound(X_129,identity))]]) ).

cnf(refute_0_1968,plain,
    ( X_129 != multiply(least_upper_bound(identity,X_129),greatest_lower_bound(X_129,identity))
    | X_129 = multiply(least_upper_bound(X_129,identity),greatest_lower_bound(X_129,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_129),least_upper_bound(X_129,identity)) )],[refute_0_1966,refute_0_1967]) ).

cnf(refute_0_1969,plain,
    X_129 = multiply(least_upper_bound(X_129,identity),greatest_lower_bound(X_129,identity)),
    inference(resolve,[$cnf( $equal(X_129,multiply(least_upper_bound(identity,X_129),greatest_lower_bound(X_129,identity))) )],[refute_0_328,refute_0_1968]) ).

cnf(refute_0_1970,plain,
    ( X_129 != multiply(least_upper_bound(X_129,identity),greatest_lower_bound(X_129,identity))
    | multiply(least_upper_bound(X_129,identity),greatest_lower_bound(X_129,identity)) = X_129 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_129)),bind(Y0,$fot(multiply(least_upper_bound(X_129,identity),greatest_lower_bound(X_129,identity))))]]) ).

cnf(refute_0_1971,plain,
    multiply(least_upper_bound(X_129,identity),greatest_lower_bound(X_129,identity)) = X_129,
    inference(resolve,[$cnf( $equal(X_129,multiply(least_upper_bound(X_129,identity),greatest_lower_bound(X_129,identity))) )],[refute_0_1969,refute_0_1970]) ).

cnf(refute_0_1972,plain,
    multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity)) = X_168,
    inference(subst,[],[refute_0_1971:[bind(X_129,$fot(X_168))]]) ).

cnf(refute_0_1973,plain,
    inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))) = inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))),
    introduced(tautology,[refl,[$fot(inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))))]]) ).

cnf(refute_0_1974,plain,
    ( multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity)) != X_168
    | inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))) != inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity)))
    | inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))) = inverse(X_168) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))),inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity)))) ),[1,0],$fot(X_168)]]) ).

cnf(refute_0_1975,plain,
    ( multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity)) != X_168
    | inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))) = inverse(X_168) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))),inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity)))) )],[refute_0_1973,refute_0_1974]) ).

cnf(refute_0_1976,plain,
    inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))) = inverse(X_168),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity)),X_168) )],[refute_0_1972,refute_0_1975]) ).

cnf(refute_0_1977,plain,
    multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))) = inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))),
    inference(subst,[],[refute_0_667:[bind(X_198,$fot(least_upper_bound(X_168,identity))),bind(X_59,$fot(greatest_lower_bound(X_168,identity)))]]) ).

cnf(refute_0_1978,plain,
    ( multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))) != inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity)))
    | inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))) != inverse(X_168)
    | multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))) = inverse(X_168) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))))),bind(Z0,$fot(inverse(X_168)))]]) ).

cnf(refute_0_1979,plain,
    ( inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))) != inverse(X_168)
    | multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))) = inverse(X_168) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))),inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity)))) )],[refute_0_1977,refute_0_1978]) ).

cnf(refute_0_1980,plain,
    multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))) = inverse(X_168),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_168,identity),greatest_lower_bound(X_168,identity))),inverse(X_168)) )],[refute_0_1976,refute_0_1979]) ).

cnf(refute_0_1981,plain,
    least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) = least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))))]]) ).

cnf(refute_0_1982,plain,
    ( multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))) != inverse(X_168)
    | least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))
    | least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) = least_upper_bound(identity,inverse(X_168)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))) ),[1,1],$fot(inverse(X_168))]]) ).

cnf(refute_0_1983,plain,
    ( multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))) != inverse(X_168)
    | least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) = least_upper_bound(identity,inverse(X_168)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))) )],[refute_0_1981,refute_0_1982]) ).

cnf(refute_0_1984,plain,
    least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) = least_upper_bound(identity,inverse(X_168)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))),inverse(X_168)) )],[refute_0_1980,refute_0_1983]) ).

cnf(refute_0_1985,plain,
    ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) != least_upper_bound(identity,inverse(X_168))
    | least_upper_bound(identity,inverse(X_168)) != inverse(greatest_lower_bound(identity,X_168))
    | least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) = inverse(greatest_lower_bound(identity,X_168)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_168)))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,X_168))))]]) ).

cnf(refute_0_1986,plain,
    ( least_upper_bound(identity,inverse(X_168)) != inverse(greatest_lower_bound(identity,X_168))
    | least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) = inverse(greatest_lower_bound(identity,X_168)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))),least_upper_bound(identity,inverse(X_168))) )],[refute_0_1984,refute_0_1985]) ).

cnf(refute_0_1987,plain,
    least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) = inverse(greatest_lower_bound(identity,X_168)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_168)),inverse(greatest_lower_bound(identity,X_168))) )],[refute_0_1963,refute_0_1986]) ).

cnf(refute_0_1988,plain,
    ( inverse(greatest_lower_bound(X_168,identity)) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))
    | least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))) != inverse(greatest_lower_bound(identity,X_168))
    | inverse(greatest_lower_bound(X_168,identity)) = inverse(greatest_lower_bound(identity,X_168)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_168,identity)),inverse(greatest_lower_bound(identity,X_168))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))))]]) ).

cnf(refute_0_1989,plain,
    ( inverse(greatest_lower_bound(X_168,identity)) != least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))
    | inverse(greatest_lower_bound(X_168,identity)) = inverse(greatest_lower_bound(identity,X_168)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity)))),inverse(greatest_lower_bound(identity,X_168))) )],[refute_0_1987,refute_0_1988]) ).

cnf(refute_0_1990,plain,
    inverse(greatest_lower_bound(X_168,identity)) = inverse(greatest_lower_bound(identity,X_168)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_168,identity)),least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X_168,identity)),inverse(least_upper_bound(X_168,identity))))) )],[refute_0_1962,refute_0_1989]) ).

cnf(refute_0_1991,plain,
    inverse(greatest_lower_bound(inverse(X_121),identity)) = inverse(greatest_lower_bound(identity,inverse(X_121))),
    inference(subst,[],[refute_0_1990:[bind(X_168,$fot(inverse(X_121)))]]) ).

cnf(refute_0_1992,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_121))) != least_upper_bound(inverse(identity),X_121)
    | inverse(greatest_lower_bound(inverse(X_121),identity)) != inverse(greatest_lower_bound(identity,inverse(X_121)))
    | inverse(greatest_lower_bound(inverse(X_121),identity)) = least_upper_bound(inverse(identity),X_121) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(X_121),identity)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,inverse(X_121))))),bind(Z0,$fot(least_upper_bound(inverse(identity),X_121)))]]) ).

cnf(refute_0_1993,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_121))) != least_upper_bound(inverse(identity),X_121)
    | inverse(greatest_lower_bound(inverse(X_121),identity)) = least_upper_bound(inverse(identity),X_121) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_121),identity)),inverse(greatest_lower_bound(identity,inverse(X_121)))) )],[refute_0_1991,refute_0_1992]) ).

cnf(refute_0_1994,plain,
    inverse(greatest_lower_bound(inverse(X_121),identity)) = least_upper_bound(inverse(identity),X_121),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_121))),least_upper_bound(inverse(identity),X_121)) )],[refute_0_1951,refute_0_1993]) ).

cnf(refute_0_1995,plain,
    ( inverse(greatest_lower_bound(inverse(X_121),identity)) != least_upper_bound(inverse(identity),X_121)
    | least_upper_bound(inverse(identity),X_121) != least_upper_bound(identity,X_121)
    | inverse(greatest_lower_bound(inverse(X_121),identity)) = least_upper_bound(identity,X_121) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(X_121),identity)))),bind(Y0,$fot(least_upper_bound(inverse(identity),X_121))),bind(Z0,$fot(least_upper_bound(identity,X_121)))]]) ).

cnf(refute_0_1996,plain,
    ( least_upper_bound(inverse(identity),X_121) != least_upper_bound(identity,X_121)
    | inverse(greatest_lower_bound(inverse(X_121),identity)) = least_upper_bound(identity,X_121) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_121),identity)),least_upper_bound(inverse(identity),X_121)) )],[refute_0_1994,refute_0_1995]) ).

cnf(refute_0_1997,plain,
    inverse(greatest_lower_bound(inverse(X_121),identity)) = least_upper_bound(identity,X_121),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),X_121),least_upper_bound(identity,X_121)) )],[refute_0_1950,refute_0_1996]) ).

cnf(refute_0_1998,plain,
    multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121) = multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))]]) ).

cnf(refute_0_1999,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121) != multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)
    | inverse(greatest_lower_bound(inverse(X_121),identity)) != least_upper_bound(identity,X_121)
    | multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121) = multiply(least_upper_bound(identity,X_121),X_121) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121),multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) ),[1,0],$fot(least_upper_bound(identity,X_121))]]) ).

cnf(refute_0_2000,plain,
    ( inverse(greatest_lower_bound(inverse(X_121),identity)) != least_upper_bound(identity,X_121)
    | multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121) = multiply(least_upper_bound(identity,X_121),X_121) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121),multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) )],[refute_0_1998,refute_0_1999]) ).

cnf(refute_0_2001,plain,
    multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121) = multiply(least_upper_bound(identity,X_121),X_121),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_121),identity)),least_upper_bound(identity,X_121)) )],[refute_0_1997,refute_0_2000]) ).

cnf(refute_0_2002,plain,
    greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)))]]) ).

cnf(refute_0_2003,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121) != multiply(least_upper_bound(identity,X_121),X_121)
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_121),X_121)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))) ),[1,1],$fot(multiply(least_upper_bound(identity,X_121),X_121))]]) ).

cnf(refute_0_2004,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121) != multiply(least_upper_bound(identity,X_121),X_121)
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_121),X_121)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))) )],[refute_0_2002,refute_0_2003]) ).

cnf(refute_0_2005,plain,
    greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_121),X_121)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121),multiply(least_upper_bound(identity,X_121),X_121)) )],[refute_0_2001,refute_0_2004]) ).

cnf(refute_0_2006,plain,
    ( greatest_lower_bound(X_121,identity) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_121),X_121))
    | greatest_lower_bound(X_121,identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_121),X_121)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_121,identity),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_121),X_121))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)))]]) ).

cnf(refute_0_2007,plain,
    ( greatest_lower_bound(X_121,identity) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))
    | greatest_lower_bound(X_121,identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_121),X_121)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121)),greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_121),X_121))) )],[refute_0_2005,refute_0_2006]) ).

cnf(refute_0_2008,plain,
    ( multiply(greatest_lower_bound(inverse(X_121),identity),X_121) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))
    | greatest_lower_bound(X_121,identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_121),X_121)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_121,identity),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))) )],[refute_0_1946,refute_0_2007]) ).

cnf(refute_0_2009,plain,
    greatest_lower_bound(X_121,identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,X_121),X_121)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_121),identity),X_121),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(inverse(X_121),identity)),X_121))) )],[refute_0_1935,refute_0_2008]) ).

cnf(refute_0_2010,plain,
    greatest_lower_bound(multiply(X_111,identity),identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(X_111,identity)),multiply(X_111,identity))),
    inference(subst,[],[refute_0_2009:[bind(X_121,$fot(multiply(X_111,identity)))]]) ).

cnf(refute_0_2011,plain,
    multiply(least_upper_bound(X_111,identity),identity) = least_upper_bound(identity,multiply(X_111,identity)),
    inference(subst,[],[refute_0_728:[bind(X_110,$fot(identity))]]) ).

cnf(refute_0_2012,plain,
    ( multiply(least_upper_bound(X_111,identity),identity) != least_upper_bound(identity,multiply(X_111,identity))
    | least_upper_bound(identity,multiply(X_111,identity)) = multiply(least_upper_bound(X_111,identity),identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_111,identity),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_111,identity))))]]) ).

cnf(refute_0_2013,plain,
    least_upper_bound(identity,multiply(X_111,identity)) = multiply(least_upper_bound(X_111,identity),identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,identity),identity),least_upper_bound(identity,multiply(X_111,identity))) )],[refute_0_2011,refute_0_2012]) ).

cnf(refute_0_2014,plain,
    ( greatest_lower_bound(multiply(X_111,identity),identity) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(X_111,identity)),multiply(X_111,identity)))
    | least_upper_bound(identity,multiply(X_111,identity)) != multiply(least_upper_bound(X_111,identity),identity)
    | greatest_lower_bound(multiply(X_111,identity),identity) = greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_111,identity),identity),greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(X_111,identity)),multiply(X_111,identity)))) ),[1,1,0],$fot(multiply(least_upper_bound(X_111,identity),identity))]]) ).

cnf(refute_0_2015,plain,
    ( greatest_lower_bound(multiply(X_111,identity),identity) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(X_111,identity)),multiply(X_111,identity)))
    | greatest_lower_bound(multiply(X_111,identity),identity) = greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_111,identity)),multiply(least_upper_bound(X_111,identity),identity)) )],[refute_0_2013,refute_0_2014]) ).

cnf(refute_0_2016,plain,
    greatest_lower_bound(multiply(X_111,identity),identity) = greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_111,identity),identity),greatest_lower_bound(identity,multiply(least_upper_bound(identity,multiply(X_111,identity)),multiply(X_111,identity)))) )],[refute_0_2010,refute_0_2015]) ).

cnf(refute_0_2017,plain,
    multiply(greatest_lower_bound(X_111,identity),identity) = greatest_lower_bound(X_111,identity),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(greatest_lower_bound(X_111,identity)))]]) ).

cnf(refute_0_2018,plain,
    multiply(greatest_lower_bound(X_122,identity),X_121) = greatest_lower_bound(multiply(X_122,X_121),multiply(identity,X_121)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_121)),bind(Y,$fot(X_122)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_2019,plain,
    multiply(identity,X_121) = X_121,
    inference(subst,[],[left_identity:[bind(X,$fot(X_121))]]) ).

cnf(refute_0_2020,plain,
    ( multiply(greatest_lower_bound(X_122,identity),X_121) != greatest_lower_bound(multiply(X_122,X_121),multiply(identity,X_121))
    | multiply(identity,X_121) != X_121
    | multiply(greatest_lower_bound(X_122,identity),X_121) = greatest_lower_bound(multiply(X_122,X_121),X_121) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(identity,X_121))) ),[1,1],$fot(X_121)]]) ).

cnf(refute_0_2021,plain,
    ( multiply(greatest_lower_bound(X_122,identity),X_121) != greatest_lower_bound(multiply(X_122,X_121),multiply(identity,X_121))
    | multiply(greatest_lower_bound(X_122,identity),X_121) = greatest_lower_bound(multiply(X_122,X_121),X_121) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_121),X_121) )],[refute_0_2019,refute_0_2020]) ).

cnf(refute_0_2022,plain,
    multiply(greatest_lower_bound(X_122,identity),X_121) = greatest_lower_bound(multiply(X_122,X_121),X_121),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(identity,X_121))) )],[refute_0_2018,refute_0_2021]) ).

cnf(refute_0_2023,plain,
    greatest_lower_bound(multiply(X_122,X_121),X_121) = greatest_lower_bound(X_121,multiply(X_122,X_121)),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(multiply(X_122,X_121))),bind(X_25,$fot(X_121))]]) ).

cnf(refute_0_2024,plain,
    ( multiply(greatest_lower_bound(X_122,identity),X_121) != greatest_lower_bound(multiply(X_122,X_121),X_121)
    | greatest_lower_bound(multiply(X_122,X_121),X_121) != greatest_lower_bound(X_121,multiply(X_122,X_121))
    | multiply(greatest_lower_bound(X_122,identity),X_121) = greatest_lower_bound(X_121,multiply(X_122,X_121)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_122,identity),X_121),greatest_lower_bound(X_121,multiply(X_122,X_121))) ),[0],$fot(greatest_lower_bound(multiply(X_122,X_121),X_121))]]) ).

cnf(refute_0_2025,plain,
    ( multiply(greatest_lower_bound(X_122,identity),X_121) != greatest_lower_bound(multiply(X_122,X_121),X_121)
    | multiply(greatest_lower_bound(X_122,identity),X_121) = greatest_lower_bound(X_121,multiply(X_122,X_121)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),X_121),greatest_lower_bound(X_121,multiply(X_122,X_121))) )],[refute_0_2023,refute_0_2024]) ).

cnf(refute_0_2026,plain,
    multiply(greatest_lower_bound(X_122,identity),X_121) = greatest_lower_bound(X_121,multiply(X_122,X_121)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),X_121),greatest_lower_bound(multiply(X_122,X_121),X_121)) )],[refute_0_2022,refute_0_2025]) ).

cnf(refute_0_2027,plain,
    ( multiply(greatest_lower_bound(X_122,identity),X_121) != greatest_lower_bound(X_121,multiply(X_122,X_121))
    | greatest_lower_bound(X_121,multiply(X_122,X_121)) = multiply(greatest_lower_bound(X_122,identity),X_121) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(X_122,identity),X_121))),bind(Y0,$fot(greatest_lower_bound(X_121,multiply(X_122,X_121))))]]) ).

cnf(refute_0_2028,plain,
    greatest_lower_bound(X_121,multiply(X_122,X_121)) = multiply(greatest_lower_bound(X_122,identity),X_121),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),X_121),greatest_lower_bound(X_121,multiply(X_122,X_121))) )],[refute_0_2026,refute_0_2027]) ).

cnf(refute_0_2029,plain,
    greatest_lower_bound(identity,multiply(X_111,identity)) = multiply(greatest_lower_bound(X_111,identity),identity),
    inference(subst,[],[refute_0_2028:[bind(X_121,$fot(identity)),bind(X_122,$fot(X_111))]]) ).

cnf(refute_0_2030,plain,
    ( multiply(greatest_lower_bound(X_111,identity),identity) != greatest_lower_bound(X_111,identity)
    | greatest_lower_bound(identity,multiply(X_111,identity)) != multiply(greatest_lower_bound(X_111,identity),identity)
    | greatest_lower_bound(identity,multiply(X_111,identity)) = greatest_lower_bound(X_111,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_111,identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_111,identity),identity))),bind(Z0,$fot(greatest_lower_bound(X_111,identity)))]]) ).

cnf(refute_0_2031,plain,
    ( multiply(greatest_lower_bound(X_111,identity),identity) != greatest_lower_bound(X_111,identity)
    | greatest_lower_bound(identity,multiply(X_111,identity)) = greatest_lower_bound(X_111,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_111,identity)),multiply(greatest_lower_bound(X_111,identity),identity)) )],[refute_0_2029,refute_0_2030]) ).

cnf(refute_0_2032,plain,
    greatest_lower_bound(identity,multiply(X_111,identity)) = greatest_lower_bound(X_111,identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_111,identity),identity),greatest_lower_bound(X_111,identity)) )],[refute_0_2017,refute_0_2031]) ).

cnf(refute_0_2033,plain,
    greatest_lower_bound(multiply(X_111,identity),identity) = greatest_lower_bound(identity,multiply(X_111,identity)),
    inference(subst,[],[refute_0_1353:[bind(X_60,$fot(multiply(X_111,identity)))]]) ).

cnf(refute_0_2034,plain,
    ( greatest_lower_bound(multiply(X_111,identity),identity) != greatest_lower_bound(identity,multiply(X_111,identity))
    | greatest_lower_bound(identity,multiply(X_111,identity)) != greatest_lower_bound(X_111,identity)
    | greatest_lower_bound(multiply(X_111,identity),identity) = greatest_lower_bound(X_111,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(X_111,identity),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_111,identity)))),bind(Z0,$fot(greatest_lower_bound(X_111,identity)))]]) ).

cnf(refute_0_2035,plain,
    ( greatest_lower_bound(identity,multiply(X_111,identity)) != greatest_lower_bound(X_111,identity)
    | greatest_lower_bound(multiply(X_111,identity),identity) = greatest_lower_bound(X_111,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_111,identity),identity),greatest_lower_bound(identity,multiply(X_111,identity))) )],[refute_0_2033,refute_0_2034]) ).

cnf(refute_0_2036,plain,
    greatest_lower_bound(multiply(X_111,identity),identity) = greatest_lower_bound(X_111,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_111,identity)),greatest_lower_bound(X_111,identity)) )],[refute_0_2032,refute_0_2035]) ).

cnf(refute_0_2037,plain,
    ( greatest_lower_bound(multiply(X_111,identity),identity) != greatest_lower_bound(X_111,identity)
    | greatest_lower_bound(multiply(X_111,identity),identity) != greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity)))
    | greatest_lower_bound(X_111,identity) = greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_111,identity),identity),greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity)))) ),[0],$fot(greatest_lower_bound(X_111,identity))]]) ).

cnf(refute_0_2038,plain,
    ( greatest_lower_bound(multiply(X_111,identity),identity) != greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity)))
    | greatest_lower_bound(X_111,identity) = greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_111,identity),identity),greatest_lower_bound(X_111,identity)) )],[refute_0_2036,refute_0_2037]) ).

cnf(refute_0_2039,plain,
    multiply(least_upper_bound(X_111,identity),X_111) = multiply(X_111,least_upper_bound(X_111,identity)),
    inference(subst,[],[refute_0_1889:[bind(X_94,$fot(X_111))]]) ).

cnf(refute_0_2040,plain,
    multiply(identity,X_111) = X_111,
    inference(subst,[],[left_identity:[bind(X,$fot(X_111))]]) ).

cnf(refute_0_2041,plain,
    multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)) = multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)))]]) ).

cnf(refute_0_2042,plain,
    ( multiply(identity,X_111) != X_111
    | multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)) != multiply(least_upper_bound(X_111,identity),multiply(identity,X_111))
    | multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)) = multiply(least_upper_bound(X_111,identity),X_111) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)),multiply(least_upper_bound(X_111,identity),multiply(identity,X_111))) ),[1,1],$fot(X_111)]]) ).

cnf(refute_0_2043,plain,
    ( multiply(identity,X_111) != X_111
    | multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)) = multiply(least_upper_bound(X_111,identity),X_111) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)),multiply(least_upper_bound(X_111,identity),multiply(identity,X_111))) )],[refute_0_2041,refute_0_2042]) ).

cnf(refute_0_2044,plain,
    multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)) = multiply(least_upper_bound(X_111,identity),X_111),
    inference(resolve,[$cnf( $equal(multiply(identity,X_111),X_111) )],[refute_0_2040,refute_0_2043]) ).

cnf(refute_0_2045,plain,
    ( multiply(least_upper_bound(X_111,identity),X_111) != multiply(X_111,least_upper_bound(X_111,identity))
    | multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)) != multiply(least_upper_bound(X_111,identity),X_111)
    | multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)) = multiply(X_111,least_upper_bound(X_111,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)))),bind(Y0,$fot(multiply(least_upper_bound(X_111,identity),X_111))),bind(Z0,$fot(multiply(X_111,least_upper_bound(X_111,identity))))]]) ).

cnf(refute_0_2046,plain,
    ( multiply(least_upper_bound(X_111,identity),X_111) != multiply(X_111,least_upper_bound(X_111,identity))
    | multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)) = multiply(X_111,least_upper_bound(X_111,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)),multiply(least_upper_bound(X_111,identity),X_111)) )],[refute_0_2044,refute_0_2045]) ).

cnf(refute_0_2047,plain,
    multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)) = multiply(X_111,least_upper_bound(X_111,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,identity),X_111),multiply(X_111,least_upper_bound(X_111,identity))) )],[refute_0_2039,refute_0_2046]) ).

cnf(refute_0_2048,plain,
    multiply(multiply(least_upper_bound(X_111,identity),identity),X_111) = multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)),
    inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(X_111,identity))),bind(Y,$fot(identity)),bind(Z,$fot(X_111))]]) ).

cnf(refute_0_2049,plain,
    ( multiply(multiply(least_upper_bound(X_111,identity),identity),X_111) != multiply(least_upper_bound(X_111,identity),multiply(identity,X_111))
    | multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)) != multiply(X_111,least_upper_bound(X_111,identity))
    | multiply(multiply(least_upper_bound(X_111,identity),identity),X_111) = multiply(X_111,least_upper_bound(X_111,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(least_upper_bound(X_111,identity),identity),X_111))),bind(Y0,$fot(multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)))),bind(Z0,$fot(multiply(X_111,least_upper_bound(X_111,identity))))]]) ).

cnf(refute_0_2050,plain,
    ( multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)) != multiply(X_111,least_upper_bound(X_111,identity))
    | multiply(multiply(least_upper_bound(X_111,identity),identity),X_111) = multiply(X_111,least_upper_bound(X_111,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_111,identity),identity),X_111),multiply(least_upper_bound(X_111,identity),multiply(identity,X_111))) )],[refute_0_2048,refute_0_2049]) ).

cnf(refute_0_2051,plain,
    multiply(multiply(least_upper_bound(X_111,identity),identity),X_111) = multiply(X_111,least_upper_bound(X_111,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,identity),multiply(identity,X_111)),multiply(X_111,least_upper_bound(X_111,identity))) )],[refute_0_2047,refute_0_2050]) ).

cnf(refute_0_2052,plain,
    greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)) = greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)))]]) ).

cnf(refute_0_2053,plain,
    ( multiply(multiply(least_upper_bound(X_111,identity),identity),X_111) != multiply(X_111,least_upper_bound(X_111,identity))
    | greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)) != greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111))
    | greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)) = greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111))) ),[1,1],$fot(multiply(X_111,least_upper_bound(X_111,identity)))]]) ).

cnf(refute_0_2054,plain,
    ( multiply(multiply(least_upper_bound(X_111,identity),identity),X_111) != multiply(X_111,least_upper_bound(X_111,identity))
    | greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)) = greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111))) )],[refute_0_2052,refute_0_2053]) ).

cnf(refute_0_2055,plain,
    greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)) = greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_111,identity),identity),X_111),multiply(X_111,least_upper_bound(X_111,identity))) )],[refute_0_2051,refute_0_2054]) ).

cnf(refute_0_2056,plain,
    multiply(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),identity) = greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111))))]]) ).

cnf(refute_0_2057,plain,
    multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) = greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),multiply(inverse(X_59),multiply(X_59,X_60))),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(multiply(X_59,X_60))),bind(Y,$fot(X_122)),bind(Z,$fot(inverse(X_59)))]]) ).

cnf(refute_0_2058,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) != greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),multiply(inverse(X_59),multiply(X_59,X_60)))
    | multiply(inverse(X_59),multiply(X_59,X_60)) != X_60
    | multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) = greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)),greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),multiply(inverse(X_59),multiply(X_59,X_60)))) ),[1,1],$fot(X_60)]]) ).

cnf(refute_0_2059,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) != greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),multiply(inverse(X_59),multiply(X_59,X_60)))
    | multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) = greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),X_60) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_59),multiply(X_59,X_60)),X_60) )],[refute_0_1308,refute_0_2058]) ).

cnf(refute_0_2060,plain,
    multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) = greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),X_60),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)),greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),multiply(inverse(X_59),multiply(X_59,X_60)))) )],[refute_0_2057,refute_0_2059]) ).

cnf(refute_0_2061,plain,
    greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),X_60) = greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60))),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(multiply(X_122,multiply(X_59,X_60)))),bind(X_25,$fot(X_60))]]) ).

cnf(refute_0_2062,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) != greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),X_60)
    | greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),X_60) != greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60)))
    | multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) = greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)),greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60)))) ),[0],$fot(greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),X_60))]]) ).

cnf(refute_0_2063,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) != greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),X_60)
    | multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) = greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),X_60),greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60)))) )],[refute_0_2061,refute_0_2062]) ).

cnf(refute_0_2064,plain,
    multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) = greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)),greatest_lower_bound(multiply(X_122,multiply(X_59,X_60)),X_60)) )],[refute_0_2060,refute_0_2063]) ).

cnf(refute_0_2065,plain,
    multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) = multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60),
    inference(subst,[],[refute_0_1318:[bind(Y,$fot(X_59)),bind(Z,$fot(X_60)),bind(X_125,$fot(X_122))]]) ).

cnf(refute_0_2066,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) != multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60)
    | multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) != greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60)))
    | multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60) = greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)),greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60)))) ),[0],$fot(multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60))]]) ).

cnf(refute_0_2067,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)) != greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60)))
    | multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60) = greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)),multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60)) )],[refute_0_2065,refute_0_2066]) ).

cnf(refute_0_2068,plain,
    multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60) = greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(X_59)),multiply(X_59,X_60)),greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60)))) )],[refute_0_2064,refute_0_2067]) ).

cnf(refute_0_2069,plain,
    ( multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60) != greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60)))
    | greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60))) = multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60))),bind(Y0,$fot(greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60)))))]]) ).

cnf(refute_0_2070,plain,
    greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60))) = multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_122,X_59)),X_60),greatest_lower_bound(X_60,multiply(X_122,multiply(X_59,X_60)))) )],[refute_0_2068,refute_0_2069]) ).

cnf(refute_0_2071,plain,
    greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) = multiply(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),identity),
    inference(subst,[],[refute_0_2070:[bind(X_122,$fot(multiply(least_upper_bound(X_111,identity),identity))),bind(X_59,$fot(X_111)),bind(X_60,$fot(identity))]]) ).

cnf(refute_0_2072,plain,
    ( multiply(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),identity) != greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111))
    | greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) != multiply(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),identity)
    | greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) = greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),identity))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111))))]]) ).

cnf(refute_0_2073,plain,
    ( multiply(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),identity) != greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111))
    | greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) = greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))),multiply(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),identity)) )],[refute_0_2071,refute_0_2072]) ).

cnf(refute_0_2074,plain,
    greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) = greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),identity),greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111))) )],[refute_0_2056,refute_0_2073]) ).

cnf(refute_0_2075,plain,
    ( greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)) != greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity)))
    | greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) != greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111))
    | greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) = greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity)))))]]) ).

cnf(refute_0_2076,plain,
    ( greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)) != greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity)))
    | greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) = greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))),greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111))) )],[refute_0_2074,refute_0_2075]) ).

cnf(refute_0_2077,plain,
    greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) = greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),X_111)),greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity)))) )],[refute_0_2055,refute_0_2076]) ).

cnf(refute_0_2078,plain,
    ( greatest_lower_bound(X_111,identity) != greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity)))
    | greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))) != greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity)))
    | greatest_lower_bound(X_111,identity) = greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_111,identity),greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity)))) ),[0],$fot(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))))]]) ).

cnf(refute_0_2079,plain,
    ( greatest_lower_bound(X_111,identity) != greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity)))
    | greatest_lower_bound(X_111,identity) = greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity))),greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity)))) )],[refute_0_2077,refute_0_2078]) ).

cnf(refute_0_2080,plain,
    ( greatest_lower_bound(multiply(X_111,identity),identity) != greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity)))
    | greatest_lower_bound(X_111,identity) = greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_111,identity),greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity)))) )],[refute_0_2038,refute_0_2079]) ).

cnf(refute_0_2081,plain,
    greatest_lower_bound(X_111,identity) = greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_111,identity),identity),greatest_lower_bound(identity,multiply(multiply(least_upper_bound(X_111,identity),identity),multiply(X_111,identity)))) )],[refute_0_2016,refute_0_2080]) ).

cnf(refute_0_2082,plain,
    ( greatest_lower_bound(X_111,identity) != greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity)))
    | greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))) = greatest_lower_bound(X_111,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_111,identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity)))))]]) ).

cnf(refute_0_2083,plain,
    greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity))) = greatest_lower_bound(X_111,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_111,identity),greatest_lower_bound(identity,multiply(X_111,least_upper_bound(X_111,identity)))) )],[refute_0_2081,refute_0_2082]) ).

cnf(refute_0_2084,plain,
    greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))) = greatest_lower_bound(X_94,identity),
    inference(subst,[],[refute_0_2083:[bind(X_111,$fot(X_94))]]) ).

cnf(refute_0_2085,plain,
    inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))) = inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))))]]) ).

cnf(refute_0_2086,plain,
    ( greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))) != greatest_lower_bound(X_94,identity)
    | inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))) != inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))))
    | inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))) = inverse(greatest_lower_bound(X_94,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))),inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))))) ),[1,0],$fot(greatest_lower_bound(X_94,identity))]]) ).

cnf(refute_0_2087,plain,
    ( greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))) != greatest_lower_bound(X_94,identity)
    | inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))) = inverse(greatest_lower_bound(X_94,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))),inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))))) )],[refute_0_2085,refute_0_2086]) ).

cnf(refute_0_2088,plain,
    inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))) = inverse(greatest_lower_bound(X_94,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))),greatest_lower_bound(X_94,identity)) )],[refute_0_2084,refute_0_2087]) ).

cnf(refute_0_2089,plain,
    ( inverse(greatest_lower_bound(identity,X_94)) != inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))))
    | inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))) != inverse(greatest_lower_bound(X_94,identity))
    | inverse(greatest_lower_bound(identity,X_94)) = inverse(greatest_lower_bound(X_94,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,X_94)),inverse(greatest_lower_bound(X_94,identity))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))))]]) ).

cnf(refute_0_2090,plain,
    ( inverse(greatest_lower_bound(identity,X_94)) != inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))))
    | inverse(greatest_lower_bound(identity,X_94)) = inverse(greatest_lower_bound(X_94,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity)))),inverse(greatest_lower_bound(X_94,identity))) )],[refute_0_2088,refute_0_2089]) ).

cnf(refute_0_2091,plain,
    inverse(greatest_lower_bound(identity,X_94)) = inverse(greatest_lower_bound(X_94,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_94)),inverse(greatest_lower_bound(identity,multiply(X_94,least_upper_bound(X_94,identity))))) )],[refute_0_1900,refute_0_2090]) ).

cnf(refute_0_2092,plain,
    ( inverse(greatest_lower_bound(identity,X_94)) != inverse(greatest_lower_bound(X_94,identity))
    | inverse(greatest_lower_bound(X_94,identity)) = inverse(greatest_lower_bound(identity,X_94)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_94)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_94,identity))))]]) ).

cnf(refute_0_2093,plain,
    inverse(greatest_lower_bound(X_94,identity)) = inverse(greatest_lower_bound(identity,X_94)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_94)),inverse(greatest_lower_bound(X_94,identity))) )],[refute_0_2091,refute_0_2092]) ).

cnf(refute_0_2094,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) = inverse(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_2093:[bind(X_94,$fot(greatest_lower_bound(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2095,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) != inverse(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))))
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))))),bind(Z0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))))))]]) ).

cnf(refute_0_2096,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))))
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_2094,refute_0_2095]) ).

cnf(refute_0_2097,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))))) )],[refute_0_1796,refute_0_2096]) ).

cnf(refute_0_2098,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))) != inverse(greatest_lower_bound(a,identity))
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))))
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) = inverse(greatest_lower_bound(a,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)))),bind(Y0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))))),bind(Z0,$fot(inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_2099,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))) != inverse(greatest_lower_bound(a,identity))
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)),inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b))))) )],[refute_0_2097,refute_0_2098]) ).

cnf(refute_0_2100,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,least_upper_bound(identity,b)))),inverse(greatest_lower_bound(a,identity))) )],[refute_0_1621,refute_0_2099]) ).

cnf(refute_0_2101,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) != inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))
    | least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) = inverse(greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))) ),[1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_2102,plain,
    ( least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) != inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))
    | least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2100,refute_0_2101]) ).

cnf(refute_0_2103,plain,
    ( least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))
    | least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))) )],[refute_0_1590,refute_0_2102]) ).

cnf(refute_0_2104,plain,
    least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),identity))) )],[refute_0_1570,refute_0_2103]) ).

cnf(refute_0_2105,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) != inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity))))
    | least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) != inverse(greatest_lower_bound(a,identity))
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))),inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity))))) ),[1,0,1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_2106,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) != inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity))))
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2104,refute_0_2105]) ).

cnf(refute_0_2107,plain,
    inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))),inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity))))) )],[refute_0_1548,refute_0_2106]) ).

cnf(refute_0_2108,plain,
    least_upper_bound(identity,greatest_lower_bound(a,identity)) = identity,
    inference(subst,[],[refute_0_117:[bind(X_8,$fot(identity)),bind(X_9,$fot(a))]]) ).

cnf(refute_0_2109,plain,
    inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_2110,plain,
    ( inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,identity)))
    | least_upper_bound(identity,greatest_lower_bound(a,identity)) != identity
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))) = inverse(identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))),inverse(least_upper_bound(identity,greatest_lower_bound(a,identity)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_2111,plain,
    ( least_upper_bound(identity,greatest_lower_bound(a,identity)) != identity
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))) = inverse(identity) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))),inverse(least_upper_bound(identity,greatest_lower_bound(a,identity)))) )],[refute_0_2109,refute_0_2110]) ).

cnf(refute_0_2112,plain,
    inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))) = inverse(identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,identity)),identity) )],[refute_0_2108,refute_0_2111]) ).

cnf(refute_0_2113,plain,
    ( inverse(identity) != identity
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))) != inverse(identity)
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_2114,plain,
    ( inverse(identity) != identity
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))) = identity ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))),inverse(identity)) )],[refute_0_2112,refute_0_2113]) ).

cnf(refute_0_2115,plain,
    inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))) = identity,
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_2114]) ).

cnf(refute_0_2116,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))),
    inference(subst,[],[refute_0_500:[bind(Y,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_2117,plain,
    ( greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,identity)))
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))) != identity
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))),bind(Y0,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_2118,plain,
    ( inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))) != identity
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))),inverse(least_upper_bound(identity,greatest_lower_bound(a,identity)))) )],[refute_0_2116,refute_0_2117]) ).

cnf(refute_0_2119,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))) = identity,
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,identity))),identity) )],[refute_0_2115,refute_0_2118]) ).

cnf(refute_0_2120,plain,
    greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_2121,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))) != identity
    | greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(b,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))),greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_2122,plain,
    ( greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))) != identity
    | greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))),greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_2120,refute_0_2121]) ).

cnf(refute_0_2123,plain,
    greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(b,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))),identity) )],[refute_0_2119,refute_0_2122]) ).

cnf(refute_0_2124,plain,
    greatest_lower_bound(identity,greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))),
    inference(subst,[],[refute_0_1580:[bind(X_178,$fot(inverse(greatest_lower_bound(a,identity)))),bind(X_179,$fot(b)),bind(X_180,$fot(identity))]]) ).

cnf(refute_0_2125,plain,
    inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) = greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)),
    inference(subst,[],[p12x_4:[bind(X,$fot(inverse(greatest_lower_bound(identity,X_272))))]]) ).

cnf(refute_0_2126,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),Y)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y),
    inference(subst,[],[refute_0_1641:[bind(Z,$fot(Y)),bind(X_64,$fot(X_272))]]) ).

cnf(refute_0_2127,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),Y)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y) = least_upper_bound(identity,least_upper_bound(inverse(X_272),Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)))]]) ).

cnf(refute_0_2128,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y) = least_upper_bound(identity,least_upper_bound(inverse(X_272),Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) )],[refute_0_2126,refute_0_2127]) ).

cnf(refute_0_2129,plain,
    ( inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) != greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y) != least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))) = greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)),greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))) ),[0,0],$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y)))]]) ).

cnf(refute_0_2130,plain,
    ( inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) != greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))) = greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y),least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))) )],[refute_0_2128,refute_0_2129]) ).

cnf(refute_0_2131,plain,
    inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))) = greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)),greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))) )],[refute_0_2125,refute_0_2130]) ).

cnf(refute_0_2132,plain,
    inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) = inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15)),
    inference(subst,[],[refute_0_58:[bind(X_14,$fot(inverse(greatest_lower_bound(identity,X_272))))]]) ).

cnf(refute_0_2133,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15),
    inference(subst,[],[refute_0_1641:[bind(Z,$fot(X_15)),bind(X_64,$fot(X_272))]]) ).

cnf(refute_0_2134,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15)
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15) = least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15)))]]) ).

cnf(refute_0_2135,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15) = least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15)) )],[refute_0_2133,refute_0_2134]) ).

cnf(refute_0_2136,plain,
    ( inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) != inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15) != least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15))
    | inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) = inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))),inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15))) ),[1,0],$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)))]]) ).

cnf(refute_0_2137,plain,
    ( inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) != inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15))
    | inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) = inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15),least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15))) )],[refute_0_2135,refute_0_2136]) ).

cnf(refute_0_2138,plain,
    inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) = inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))),inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_15))) )],[refute_0_2132,refute_0_2137]) ).

cnf(refute_0_2139,plain,
    greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_272)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)),
    inference(subst,[],[refute_0_1580:[bind(X_178,$fot(X_272)),bind(X_179,$fot(identity)),bind(X_180,$fot(inverse(X_15)))]]) ).

cnf(refute_0_2140,plain,
    inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) = greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_272)),
    inference(subst,[],[refute_0_582:[bind(X,$fot(X_15)),bind(X_89,$fot(greatest_lower_bound(identity,X_272)))]]) ).

cnf(refute_0_2141,plain,
    ( greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_272)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272))
    | inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) != greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_272))
    | inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))))),bind(Y0,$fot(greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_272)))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272))))]]) ).

cnf(refute_0_2142,plain,
    ( greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_272)) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272))
    | inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))),greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_272))) )],[refute_0_2140,refute_0_2141]) ).

cnf(refute_0_2143,plain,
    inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_272)),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272))) )],[refute_0_2139,refute_0_2142]) ).

cnf(refute_0_2144,plain,
    ( inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272))
    | inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) != inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)) = inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))),inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)))]]) ).

cnf(refute_0_2145,plain,
    ( inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))) != inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)) = inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272))) )],[refute_0_2143,refute_0_2144]) ).

cnf(refute_0_2146,plain,
    greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)) = inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_272)))),inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)))) )],[refute_0_2138,refute_0_2145]) ).

cnf(refute_0_2147,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)) != inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)))),bind(Y0,$fot(inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)))))]]) ).

cnf(refute_0_2148,plain,
    inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),X_272)),inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_15)))) )],[refute_0_2146,refute_0_2147]) ).

cnf(refute_0_2149,plain,
    inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)),
    inference(subst,[],[refute_0_2148:[bind(X_15,$fot(Y))]]) ).

cnf(refute_0_2150,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))) != greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)) = greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))),greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)))]]) ).

cnf(refute_0_2151,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))) != greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)) = greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))),greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272))) )],[refute_0_2149,refute_0_2150]) ).

cnf(refute_0_2152,plain,
    greatest_lower_bound(greatest_lower_bound(identity,X_272),inverse(Y)) = greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y))),
    inference(subst,[],[refute_0_790:[bind(X,$fot(identity)),bind(Y,$fot(X_272)),bind(Z,$fot(inverse(Y)))]]) ).

cnf(refute_0_2153,plain,
    inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) = greatest_lower_bound(greatest_lower_bound(identity,X_272),inverse(Y)),
    inference(subst,[],[refute_0_101:[bind(X_89,$fot(greatest_lower_bound(identity,X_272)))]]) ).

cnf(refute_0_2154,plain,
    ( greatest_lower_bound(greatest_lower_bound(identity,X_272),inverse(Y)) != greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y)))
    | inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) != greatest_lower_bound(greatest_lower_bound(identity,X_272),inverse(Y))
    | inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) = greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(identity,X_272),inverse(Y)))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y)))))]]) ).

cnf(refute_0_2155,plain,
    ( greatest_lower_bound(greatest_lower_bound(identity,X_272),inverse(Y)) != greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y)))
    | inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) = greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)),greatest_lower_bound(greatest_lower_bound(identity,X_272),inverse(Y))) )],[refute_0_2153,refute_0_2154]) ).

cnf(refute_0_2156,plain,
    inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) = greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,X_272),inverse(Y)),greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y)))) )],[refute_0_2152,refute_0_2155]) ).

cnf(refute_0_2157,plain,
    greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)) = inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)),
    inference(subst,[],[refute_0_54:[bind(X,$fot(inverse(greatest_lower_bound(identity,X_272))))]]) ).

cnf(refute_0_2158,plain,
    ( greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)) != inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y))
    | inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) != greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y)))
    | greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)) = greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)))),bind(Y0,$fot(inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y)))))]]) ).

cnf(refute_0_2159,plain,
    ( inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) != greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y)))
    | greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)) = greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)),inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y))) )],[refute_0_2157,refute_0_2158]) ).

cnf(refute_0_2160,plain,
    greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)) = greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)),greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y)))) )],[refute_0_2156,refute_0_2159]) ).

cnf(refute_0_2161,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)) != greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))
    | greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)) != greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y)))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)) = greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)),greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y)))) ),[0],$fot(greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)))]]) ).

cnf(refute_0_2162,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)) != greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)) = greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y)),greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y)))) )],[refute_0_2160,refute_0_2161]) ).

cnf(refute_0_2163,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))) != greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)) = greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)),greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))) )],[refute_0_2151,refute_0_2162]) ).

cnf(refute_0_2164,plain,
    greatest_lower_bound(identity,greatest_lower_bound(inverse(Y),X_272)) = greatest_lower_bound(identity,greatest_lower_bound(X_272,inverse(Y))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))),greatest_lower_bound(inverse(inverse(greatest_lower_bound(identity,X_272))),inverse(Y))) )],[refute_0_2131,refute_0_2163]) ).

cnf(refute_0_2165,plain,
    greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)) = greatest_lower_bound(identity,greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))),
    inference(subst,[],[refute_0_2164:[bind(Y,$fot(greatest_lower_bound(a,identity))),bind(X_272,$fot(b))]]) ).

cnf(refute_0_2166,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)) != greatest_lower_bound(identity,greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_2167,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)),greatest_lower_bound(identity,greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_2165,refute_0_2166]) ).

cnf(refute_0_2168,plain,
    greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))),greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_2124,refute_0_2167]) ).

cnf(refute_0_2169,plain,
    inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)),
    inference(subst,[],[refute_0_2148:[bind(X_15,$fot(greatest_lower_bound(a,identity))),bind(X_272,$fot(b))]]) ).

cnf(refute_0_2170,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)) != greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_2171,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)) != greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))),greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b))) )],[refute_0_2169,refute_0_2170]) ).

cnf(refute_0_2172,plain,
    inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)),greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_2168,refute_0_2171]) ).

cnf(refute_0_2173,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) != inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity))))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))) != greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))))),bind(Y0,$fot(inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_2174,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))) != greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))),inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity))))) )],[refute_0_1548,refute_0_2173]) ).

cnf(refute_0_2175,plain,
    inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) = greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))),greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_2172,refute_0_2174]) ).

cnf(refute_0_2176,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(b,identity)
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) != greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) = greatest_lower_bound(b,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))))),bind(Z0,$fot(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2177,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(b,identity)
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) = greatest_lower_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))),greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_2175,refute_0_2176]) ).

cnf(refute_0_2178,plain,
    inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) = greatest_lower_bound(b,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,identity)))),greatest_lower_bound(b,identity)) )],[refute_0_2123,refute_0_2177]) ).

cnf(refute_0_2179,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) != greatest_lower_bound(b,identity)
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | greatest_lower_bound(b,identity) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).

cnf(refute_0_2180,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | greatest_lower_bound(b,identity) = inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))),greatest_lower_bound(b,identity)) )],[refute_0_2178,refute_0_2179]) ).

cnf(refute_0_2181,plain,
    least_upper_bound(identity,identity) = identity,
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(identity))]]) ).

cnf(refute_0_2182,plain,
    inverse(least_upper_bound(identity,identity)) = inverse(least_upper_bound(identity,identity)),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,identity)))]]) ).

cnf(refute_0_2183,plain,
    ( inverse(least_upper_bound(identity,identity)) != inverse(least_upper_bound(identity,identity))
    | least_upper_bound(identity,identity) != identity
    | inverse(least_upper_bound(identity,identity)) = inverse(identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,identity)),inverse(least_upper_bound(identity,identity))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_2184,plain,
    ( least_upper_bound(identity,identity) != identity
    | inverse(least_upper_bound(identity,identity)) = inverse(identity) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,identity)),inverse(least_upper_bound(identity,identity))) )],[refute_0_2182,refute_0_2183]) ).

cnf(refute_0_2185,plain,
    inverse(least_upper_bound(identity,identity)) = inverse(identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,identity),identity) )],[refute_0_2181,refute_0_2184]) ).

cnf(refute_0_2186,plain,
    ( inverse(identity) != identity
    | inverse(least_upper_bound(identity,identity)) != inverse(identity)
    | inverse(least_upper_bound(identity,identity)) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(identity,identity)))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_2187,plain,
    ( inverse(identity) != identity
    | inverse(least_upper_bound(identity,identity)) = identity ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,identity)),inverse(identity)) )],[refute_0_2185,refute_0_2186]) ).

cnf(refute_0_2188,plain,
    inverse(least_upper_bound(identity,identity)) = identity,
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_2187]) ).

cnf(refute_0_2189,plain,
    greatest_lower_bound(identity,inverse(identity)) = inverse(least_upper_bound(identity,identity)),
    inference(subst,[],[refute_0_500:[bind(Y,$fot(identity))]]) ).

cnf(refute_0_2190,plain,
    ( greatest_lower_bound(identity,inverse(identity)) != inverse(least_upper_bound(identity,identity))
    | inverse(least_upper_bound(identity,identity)) != identity
    | greatest_lower_bound(identity,inverse(identity)) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,inverse(identity)))),bind(Y0,$fot(inverse(least_upper_bound(identity,identity)))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_2191,plain,
    ( inverse(least_upper_bound(identity,identity)) != identity
    | greatest_lower_bound(identity,inverse(identity)) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(identity)),inverse(least_upper_bound(identity,identity))) )],[refute_0_2189,refute_0_2190]) ).

cnf(refute_0_2192,plain,
    greatest_lower_bound(identity,inverse(identity)) = identity,
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,identity)),identity) )],[refute_0_2188,refute_0_2191]) ).

cnf(refute_0_2193,plain,
    greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))) = greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))))]]) ).

cnf(refute_0_2194,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))) != greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))
    | greatest_lower_bound(identity,inverse(identity)) != identity
    | greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))) = greatest_lower_bound(a,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))),greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_2195,plain,
    ( greatest_lower_bound(identity,inverse(identity)) != identity
    | greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))),greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))) )],[refute_0_2193,refute_0_2194]) ).

cnf(refute_0_2196,plain,
    greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(identity)),identity) )],[refute_0_2192,refute_0_2195]) ).

cnf(refute_0_2197,plain,
    greatest_lower_bound(a,greatest_lower_bound(inverse(identity),identity)) = greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))),
    inference(subst,[],[refute_0_1493:[bind(Y,$fot(identity)),bind(X_75,$fot(inverse(identity))),bind(X_77,$fot(a))]]) ).

cnf(refute_0_2198,plain,
    greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(a,greatest_lower_bound(inverse(identity),identity)),
    inference(subst,[],[refute_0_1580:[bind(X_178,$fot(identity)),bind(X_179,$fot(a)),bind(X_180,$fot(inverse(identity)))]]) ).

cnf(refute_0_2199,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(inverse(identity),identity)) != greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))
    | greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(a,greatest_lower_bound(inverse(identity),identity))
    | greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(inverse(identity),identity)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))))]]) ).

cnf(refute_0_2200,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(inverse(identity),identity)) != greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))
    | greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)),greatest_lower_bound(a,greatest_lower_bound(inverse(identity),identity))) )],[refute_0_2198,refute_0_2199]) ).

cnf(refute_0_2201,plain,
    greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(inverse(identity),identity)),greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))) )],[refute_0_2197,refute_0_2200]) ).

cnf(refute_0_2202,plain,
    inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)),
    inference(subst,[],[refute_0_582:[bind(X,$fot(identity)),bind(X_89,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_2203,plain,
    ( greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))
    | inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity))
    | inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))))),bind(Y0,$fot(greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))))]]) ).

cnf(refute_0_2204,plain,
    ( greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))
    | inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))),greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity))) )],[refute_0_2202,refute_0_2203]) ).

cnf(refute_0_2205,plain,
    inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(identity),greatest_lower_bound(a,identity)),greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))) )],[refute_0_2201,refute_0_2204]) ).

cnf(refute_0_2206,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))) != greatest_lower_bound(a,identity)
    | inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))
    | inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(a,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))))),bind(Z0,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_2207,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))) != greatest_lower_bound(a,identity)
    | inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))),greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity)))) )],[refute_0_2205,refute_0_2206]) ).

cnf(refute_0_2208,plain,
    inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,inverse(identity))),greatest_lower_bound(a,identity)) )],[refute_0_2196,refute_0_2207]) ).

cnf(refute_0_2209,plain,
    ( greatest_lower_bound(b,identity) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(b,identity) = greatest_lower_bound(a,identity) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,identity),greatest_lower_bound(a,identity)) ),[0],$fot(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_2210,plain,
    ( greatest_lower_bound(b,identity) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))),greatest_lower_bound(a,identity)) )],[refute_0_2208,refute_0_2209]) ).

cnf(refute_0_2211,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))) != inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_2180,refute_0_2210]) ).

cnf(refute_0_2212,plain,
    greatest_lower_bound(b,identity) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(b)))),inverse(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_2107,refute_0_2211]) ).

cnf(refute_0_2213,plain,
    inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(b,identity)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2214,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(a,identity)
    | inverse(greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(b,identity))
    | inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(b,identity))) ),[1,0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_2215,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(a,identity)
    | inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2213,refute_0_2214]) ).

cnf(refute_0_2216,plain,
    inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(a,identity)) )],[refute_0_2212,refute_0_2215]) ).

cnf(refute_0_2217,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) = least_upper_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(Y)),
    inference(subst,[],[p12x_3:[bind(X,$fot(greatest_lower_bound(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2218,plain,
    ( inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) != inverse(b)
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) != least_upper_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) = least_upper_bound(inverse(b),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)),least_upper_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(Y))) ),[1,0],$fot(inverse(b))]]) ).

cnf(refute_0_2219,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) != least_upper_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) = least_upper_bound(inverse(b),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) )],[refute_0_1268,refute_0_2218]) ).

cnf(refute_0_2220,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) = least_upper_bound(inverse(b),inverse(Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)),least_upper_bound(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(Y))) )],[refute_0_2217,refute_0_2219]) ).

cnf(refute_0_2221,plain,
    greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y) = greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(a)),bind(Y,$fot(least_upper_bound(b,identity))),bind(Z,$fot(Y))]]) ).

cnf(refute_0_2222,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) = inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)))]]) ).

cnf(refute_0_2223,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y) != greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) != inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) = inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)),inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y))) ),[1,0],$fot(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y)))]]) ).

cnf(refute_0_2224,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y) != greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) = inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)),inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y))) )],[refute_0_2222,refute_0_2223]) ).

cnf(refute_0_2225,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) = inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) )],[refute_0_2221,refute_0_2224]) ).

cnf(refute_0_2226,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) != inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y)))
    | inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) != least_upper_bound(inverse(b),inverse(Y))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) = least_upper_bound(inverse(b),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)),least_upper_bound(inverse(b),inverse(Y))) ),[0],$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))))]]) ).

cnf(refute_0_2227,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) != least_upper_bound(inverse(b),inverse(Y))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) = least_upper_bound(inverse(b),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)),inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y)))) )],[refute_0_2225,refute_0_2226]) ).

cnf(refute_0_2228,plain,
    least_upper_bound(inverse(b),inverse(Y)) = inverse(greatest_lower_bound(b,Y)),
    inference(subst,[],[refute_0_136:[bind(X,$fot(b))]]) ).

cnf(refute_0_2229,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) != least_upper_bound(inverse(b),inverse(Y))
    | least_upper_bound(inverse(b),inverse(Y)) != inverse(greatest_lower_bound(b,Y))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) = inverse(greatest_lower_bound(b,Y)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))),inverse(greatest_lower_bound(b,Y))) ),[0],$fot(least_upper_bound(inverse(b),inverse(Y)))]]) ).

cnf(refute_0_2230,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) != least_upper_bound(inverse(b),inverse(Y))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) = inverse(greatest_lower_bound(b,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),inverse(Y)),inverse(greatest_lower_bound(b,Y))) )],[refute_0_2228,refute_0_2229]) ).

cnf(refute_0_2231,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)) != least_upper_bound(inverse(b),inverse(Y))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) = inverse(greatest_lower_bound(b,Y)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))),least_upper_bound(inverse(b),inverse(Y))) )],[refute_0_2227,refute_0_2230]) ).

cnf(refute_0_2232,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) = inverse(greatest_lower_bound(b,Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(a,least_upper_bound(b,identity)),Y)),least_upper_bound(inverse(b),inverse(Y))) )],[refute_0_2220,refute_0_2231]) ).

cnf(refute_0_2233,plain,
    greatest_lower_bound(X,greatest_lower_bound(a,least_upper_bound(b,identity))) = greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X)),
    inference(subst,[],[refute_0_839:[bind(X_36,$fot(a)),bind(X_37,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2234,plain,
    ( b != greatest_lower_bound(a,least_upper_bound(b,identity))
    | greatest_lower_bound(a,least_upper_bound(b,identity)) = b ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(b)),bind(Y0,$fot(greatest_lower_bound(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2235,plain,
    greatest_lower_bound(a,least_upper_bound(b,identity)) = b,
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(a,least_upper_bound(b,identity))) )],[refute_0_1275,refute_0_2234]) ).

cnf(refute_0_2236,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X))
    | greatest_lower_bound(a,least_upper_bound(b,identity)) != b
    | greatest_lower_bound(X,b) = greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X))) ),[0,1],$fot(b)]]) ).

cnf(refute_0_2237,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X))
    | greatest_lower_bound(X,b) = greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(b,identity)),b) )],[refute_0_2235,refute_0_2236]) ).

cnf(refute_0_2238,plain,
    greatest_lower_bound(X,b) = greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(a,least_upper_bound(b,identity))),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X))) )],[refute_0_2233,refute_0_2237]) ).

cnf(refute_0_2239,plain,
    ( greatest_lower_bound(X,b) != greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X))
    | greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X)) = greatest_lower_bound(X,b) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,b))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X))))]]) ).

cnf(refute_0_2240,plain,
    greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X)) = greatest_lower_bound(X,b),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,b),greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),X))) )],[refute_0_2238,refute_0_2239]) ).

cnf(refute_0_2241,plain,
    greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y)) = greatest_lower_bound(Y,b),
    inference(subst,[],[refute_0_2240:[bind(X,$fot(Y))]]) ).

cnf(refute_0_2242,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) = inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))))]]) ).

cnf(refute_0_2243,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y)) != greatest_lower_bound(Y,b)
    | inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) != inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) = inverse(greatest_lower_bound(Y,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))),inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y)))) ),[1,0],$fot(greatest_lower_bound(Y,b))]]) ).

cnf(refute_0_2244,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y)) != greatest_lower_bound(Y,b)
    | inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) = inverse(greatest_lower_bound(Y,b)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))),inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y)))) )],[refute_0_2242,refute_0_2243]) ).

cnf(refute_0_2245,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) = inverse(greatest_lower_bound(Y,b)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y)),greatest_lower_bound(Y,b)) )],[refute_0_2241,refute_0_2244]) ).

cnf(refute_0_2246,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) != inverse(greatest_lower_bound(Y,b))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) != inverse(greatest_lower_bound(b,Y))
    | inverse(greatest_lower_bound(Y,b)) = inverse(greatest_lower_bound(b,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))),inverse(greatest_lower_bound(b,Y))) ),[0],$fot(inverse(greatest_lower_bound(Y,b)))]]) ).

cnf(refute_0_2247,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))) != inverse(greatest_lower_bound(b,Y))
    | inverse(greatest_lower_bound(Y,b)) = inverse(greatest_lower_bound(b,Y)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))),inverse(greatest_lower_bound(Y,b))) )],[refute_0_2245,refute_0_2246]) ).

cnf(refute_0_2248,plain,
    inverse(greatest_lower_bound(Y,b)) = inverse(greatest_lower_bound(b,Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),Y))),inverse(greatest_lower_bound(b,Y))) )],[refute_0_2232,refute_0_2247]) ).

cnf(refute_0_2249,plain,
    inverse(greatest_lower_bound(identity,b)) = inverse(greatest_lower_bound(b,identity)),
    inference(subst,[],[refute_0_2248:[bind(Y,$fot(identity))]]) ).

cnf(refute_0_2250,plain,
    least_upper_bound(identity,inverse(b)) = inverse(greatest_lower_bound(identity,b)),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(b))]]) ).

cnf(refute_0_2251,plain,
    ( inverse(greatest_lower_bound(identity,b)) != inverse(greatest_lower_bound(b,identity))
    | least_upper_bound(identity,inverse(b)) != inverse(greatest_lower_bound(identity,b))
    | least_upper_bound(identity,inverse(b)) = inverse(greatest_lower_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,inverse(b)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,b)))),bind(Z0,$fot(inverse(greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_2252,plain,
    ( inverse(greatest_lower_bound(identity,b)) != inverse(greatest_lower_bound(b,identity))
    | least_upper_bound(identity,inverse(b)) = inverse(greatest_lower_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(b)),inverse(greatest_lower_bound(identity,b))) )],[refute_0_2250,refute_0_2251]) ).

cnf(refute_0_2253,plain,
    least_upper_bound(identity,inverse(b)) = inverse(greatest_lower_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,b)),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2249,refute_0_2252]) ).

cnf(refute_0_2254,plain,
    ( inverse(greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(identity,inverse(b)) != inverse(greatest_lower_bound(b,identity))
    | least_upper_bound(identity,inverse(b)) = inverse(greatest_lower_bound(a,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,inverse(b)))),bind(Y0,$fot(inverse(greatest_lower_bound(b,identity)))),bind(Z0,$fot(inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_2255,plain,
    ( inverse(greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(identity,inverse(b)) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(b)),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2253,refute_0_2254]) ).

cnf(refute_0_2256,plain,
    least_upper_bound(identity,inverse(b)) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2216,refute_0_2255]) ).

cnf(refute_0_2257,plain,
    multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)) = multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_2258,plain,
    ( multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)) != multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity))
    | least_upper_bound(identity,inverse(b)) != inverse(greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)) = multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)),multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity))) ),[1,0],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_2259,plain,
    ( least_upper_bound(identity,inverse(b)) != inverse(greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)) = multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)),multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity))) )],[refute_0_2257,refute_0_2258]) ).

cnf(refute_0_2260,plain,
    multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)) = multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(b)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2256,refute_0_2259]) ).

cnf(refute_0_2261,plain,
    ( multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)) != identity
    | multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)) != multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_2262,plain,
    ( multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)) != identity
    | multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)) = identity ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)),multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity))) )],[refute_0_2260,refute_0_2261]) ).

cnf(refute_0_2263,plain,
    multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,identity)),greatest_lower_bound(a,identity)),identity) )],[refute_0_1537,refute_0_2262]) ).

cnf(refute_0_2264,plain,
    least_upper_bound(X_31,least_upper_bound(X_31,multiply(X_230,X_31))) = least_upper_bound(X_31,multiply(X_230,X_31)),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(multiply(X_230,X_31)))]]) ).

cnf(refute_0_2265,plain,
    multiply(least_upper_bound(X_230,identity),X_31) = least_upper_bound(X_31,multiply(X_230,X_31)),
    inference(subst,[],[refute_0_728:[bind(X_110,$fot(X_31)),bind(X_111,$fot(X_230))]]) ).

cnf(refute_0_2266,plain,
    ( multiply(least_upper_bound(X_230,identity),X_31) != least_upper_bound(X_31,multiply(X_230,X_31))
    | least_upper_bound(X_31,multiply(X_230,X_31)) = multiply(least_upper_bound(X_230,identity),X_31) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_230,identity),X_31))),bind(Y0,$fot(least_upper_bound(X_31,multiply(X_230,X_31))))]]) ).

cnf(refute_0_2267,plain,
    least_upper_bound(X_31,multiply(X_230,X_31)) = multiply(least_upper_bound(X_230,identity),X_31),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_230,identity),X_31),least_upper_bound(X_31,multiply(X_230,X_31))) )],[refute_0_2265,refute_0_2266]) ).

cnf(refute_0_2268,plain,
    ( least_upper_bound(X_31,multiply(X_230,X_31)) != multiply(least_upper_bound(X_230,identity),X_31)
    | least_upper_bound(X_31,least_upper_bound(X_31,multiply(X_230,X_31))) != least_upper_bound(X_31,multiply(X_230,X_31))
    | least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) = least_upper_bound(X_31,multiply(X_230,X_31)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_31,multiply(X_230,X_31))),least_upper_bound(X_31,multiply(X_230,X_31))) ),[0,1],$fot(multiply(least_upper_bound(X_230,identity),X_31))]]) ).

cnf(refute_0_2269,plain,
    ( least_upper_bound(X_31,least_upper_bound(X_31,multiply(X_230,X_31))) != least_upper_bound(X_31,multiply(X_230,X_31))
    | least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) = least_upper_bound(X_31,multiply(X_230,X_31)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(X_230,X_31)),multiply(least_upper_bound(X_230,identity),X_31)) )],[refute_0_2267,refute_0_2268]) ).

cnf(refute_0_2270,plain,
    least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) = least_upper_bound(X_31,multiply(X_230,X_31)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,least_upper_bound(X_31,multiply(X_230,X_31))),least_upper_bound(X_31,multiply(X_230,X_31))) )],[refute_0_2264,refute_0_2269]) ).

cnf(refute_0_2271,plain,
    least_upper_bound(identity,least_upper_bound(X_230,identity)) = least_upper_bound(identity,X_230),
    inference(subst,[],[refute_0_426:[bind(Y,$fot(X_230)),bind(X_21,$fot(identity))]]) ).

cnf(refute_0_2272,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31) = multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31))]]) ).

cnf(refute_0_2273,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31) != multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31)
    | least_upper_bound(identity,least_upper_bound(X_230,identity)) != least_upper_bound(identity,X_230)
    | multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31) = multiply(least_upper_bound(identity,X_230),X_31) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31),multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31)) ),[1,0],$fot(least_upper_bound(identity,X_230))]]) ).

cnf(refute_0_2274,plain,
    ( least_upper_bound(identity,least_upper_bound(X_230,identity)) != least_upper_bound(identity,X_230)
    | multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31) = multiply(least_upper_bound(identity,X_230),X_31) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31),multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31)) )],[refute_0_2272,refute_0_2273]) ).

cnf(refute_0_2275,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31) = multiply(least_upper_bound(identity,X_230),X_31),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_230,identity)),least_upper_bound(identity,X_230)) )],[refute_0_2271,refute_0_2274]) ).

cnf(refute_0_2276,plain,
    multiply(least_upper_bound(least_upper_bound(X_230,identity),identity),X_31) = multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31),
    inference(subst,[],[refute_0_411:[bind(X_110,$fot(X_31)),bind(X_111,$fot(least_upper_bound(X_230,identity))),bind(X_112,$fot(identity))]]) ).

cnf(refute_0_2277,plain,
    least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) = multiply(least_upper_bound(least_upper_bound(X_230,identity),identity),X_31),
    inference(subst,[],[refute_0_730:[bind(X_110,$fot(X_31)),bind(X_111,$fot(least_upper_bound(X_230,identity)))]]) ).

cnf(refute_0_2278,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_230,identity),identity),X_31) != multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31)
    | least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) != multiply(least_upper_bound(least_upper_bound(X_230,identity),identity),X_31)
    | least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) = multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_230,identity),identity),X_31))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31)))]]) ).

cnf(refute_0_2279,plain,
    ( multiply(least_upper_bound(least_upper_bound(X_230,identity),identity),X_31) != multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31)
    | least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) = multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)),multiply(least_upper_bound(least_upper_bound(X_230,identity),identity),X_31)) )],[refute_0_2277,refute_0_2278]) ).

cnf(refute_0_2280,plain,
    least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) = multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_230,identity),identity),X_31),multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31)) )],[refute_0_2276,refute_0_2279]) ).

cnf(refute_0_2281,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31) != multiply(least_upper_bound(identity,X_230),X_31)
    | least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) != multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31)
    | least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) = multiply(least_upper_bound(identity,X_230),X_31) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_230),X_31)))]]) ).

cnf(refute_0_2282,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31) != multiply(least_upper_bound(identity,X_230),X_31)
    | least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) = multiply(least_upper_bound(identity,X_230),X_31) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)),multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31)) )],[refute_0_2280,refute_0_2281]) ).

cnf(refute_0_2283,plain,
    least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) = multiply(least_upper_bound(identity,X_230),X_31),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_230,identity)),X_31),multiply(least_upper_bound(identity,X_230),X_31)) )],[refute_0_2275,refute_0_2282]) ).

cnf(refute_0_2284,plain,
    ( least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) != multiply(least_upper_bound(identity,X_230),X_31)
    | least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) != least_upper_bound(X_31,multiply(X_230,X_31))
    | multiply(least_upper_bound(identity,X_230),X_31) = least_upper_bound(X_31,multiply(X_230,X_31)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)),least_upper_bound(X_31,multiply(X_230,X_31))) ),[0],$fot(multiply(least_upper_bound(identity,X_230),X_31))]]) ).

cnf(refute_0_2285,plain,
    ( least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) != least_upper_bound(X_31,multiply(X_230,X_31))
    | multiply(least_upper_bound(identity,X_230),X_31) = least_upper_bound(X_31,multiply(X_230,X_31)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)),multiply(least_upper_bound(identity,X_230),X_31)) )],[refute_0_2283,refute_0_2284]) ).

cnf(refute_0_2286,plain,
    ( multiply(least_upper_bound(identity,X_230),X_31) != least_upper_bound(X_31,multiply(X_230,X_31))
    | least_upper_bound(X_31,multiply(X_230,X_31)) != multiply(least_upper_bound(X_230,identity),X_31)
    | multiply(least_upper_bound(identity,X_230),X_31) = multiply(least_upper_bound(X_230,identity),X_31) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_230),X_31),multiply(least_upper_bound(X_230,identity),X_31)) ),[0],$fot(least_upper_bound(X_31,multiply(X_230,X_31)))]]) ).

cnf(refute_0_2287,plain,
    ( multiply(least_upper_bound(identity,X_230),X_31) != least_upper_bound(X_31,multiply(X_230,X_31))
    | multiply(least_upper_bound(identity,X_230),X_31) = multiply(least_upper_bound(X_230,identity),X_31) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(X_230,X_31)),multiply(least_upper_bound(X_230,identity),X_31)) )],[refute_0_2267,refute_0_2286]) ).

cnf(refute_0_2288,plain,
    ( least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)) != least_upper_bound(X_31,multiply(X_230,X_31))
    | multiply(least_upper_bound(identity,X_230),X_31) = multiply(least_upper_bound(X_230,identity),X_31) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_230),X_31),least_upper_bound(X_31,multiply(X_230,X_31))) )],[refute_0_2285,refute_0_2287]) ).

cnf(refute_0_2289,plain,
    multiply(least_upper_bound(identity,X_230),X_31) = multiply(least_upper_bound(X_230,identity),X_31),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_31,multiply(least_upper_bound(X_230,identity),X_31)),least_upper_bound(X_31,multiply(X_230,X_31))) )],[refute_0_2270,refute_0_2288]) ).

cnf(refute_0_2290,plain,
    ( multiply(least_upper_bound(identity,X_230),X_31) != multiply(least_upper_bound(X_230,identity),X_31)
    | multiply(least_upper_bound(X_230,identity),X_31) = multiply(least_upper_bound(identity,X_230),X_31) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(identity,X_230),X_31))),bind(Y0,$fot(multiply(least_upper_bound(X_230,identity),X_31)))]]) ).

cnf(refute_0_2291,plain,
    multiply(least_upper_bound(X_230,identity),X_31) = multiply(least_upper_bound(identity,X_230),X_31),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_230),X_31),multiply(least_upper_bound(X_230,identity),X_31)) )],[refute_0_2289,refute_0_2290]) ).

cnf(refute_0_2292,plain,
    multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) = multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)),
    inference(subst,[],[refute_0_2291:[bind(X_230,$fot(inverse(b))),bind(X_31,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_2293,plain,
    ( multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)) != identity
    | multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) != multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_2294,plain,
    ( multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)) != identity
    | multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) = identity ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)),multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity))) )],[refute_0_2292,refute_0_2293]) ).

cnf(refute_0_2295,plain,
    multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) = identity,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(a,identity)),identity) )],[refute_0_2263,refute_0_2294]) ).

cnf(refute_0_2296,plain,
    ( multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) != identity
    | multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) != least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))
    | identity = least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)),least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))) ),[0],$fot(identity)]]) ).

cnf(refute_0_2297,plain,
    ( multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)) != least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))
    | identity = least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)),identity) )],[refute_0_2295,refute_0_2296]) ).

cnf(refute_0_2298,plain,
    identity = least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(b),identity),greatest_lower_bound(a,identity)),least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))) )],[refute_0_1536,refute_0_2297]) ).

cnf(refute_0_2299,plain,
    ( identity != least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))
    | least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2300,plain,
    least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity))) = identity,
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))) )],[refute_0_2298,refute_0_2299]) ).

cnf(refute_0_2301,plain,
    ( least_upper_bound(a,least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))) != least_upper_bound(a,inverse(least_upper_bound(b,identity)))
    | least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity))) != identity
    | least_upper_bound(a,identity) = least_upper_bound(a,inverse(least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))),least_upper_bound(a,inverse(least_upper_bound(b,identity)))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_2302,plain,
    ( least_upper_bound(a,least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))) != least_upper_bound(a,inverse(least_upper_bound(b,identity)))
    | least_upper_bound(a,identity) = least_upper_bound(a,inverse(least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity))),identity) )],[refute_0_2300,refute_0_2301]) ).

cnf(refute_0_2303,plain,
    least_upper_bound(a,identity) = least_upper_bound(a,inverse(least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(greatest_lower_bound(a,identity),inverse(least_upper_bound(b,identity)))),least_upper_bound(a,inverse(least_upper_bound(b,identity)))) )],[refute_0_1289,refute_0_2302]) ).

cnf(refute_0_2304,plain,
    ( least_upper_bound(a,identity) != least_upper_bound(a,inverse(least_upper_bound(b,identity)))
    | least_upper_bound(a,inverse(least_upper_bound(b,identity))) = least_upper_bound(a,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(a,identity))),bind(Y0,$fot(least_upper_bound(a,inverse(least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2305,plain,
    least_upper_bound(a,inverse(least_upper_bound(b,identity))) = least_upper_bound(a,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),least_upper_bound(a,inverse(least_upper_bound(b,identity)))) )],[refute_0_2303,refute_0_2304]) ).

cnf(refute_0_2306,plain,
    ( inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) != inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity))))
    | least_upper_bound(a,inverse(least_upper_bound(b,identity))) != least_upper_bound(a,identity)
    | inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) = inverse(least_upper_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)),inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity))))) ),[1,0],$fot(least_upper_bound(a,identity))]]) ).

cnf(refute_0_2307,plain,
    ( inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) != inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity))))
    | inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) = inverse(least_upper_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,inverse(least_upper_bound(b,identity))),least_upper_bound(a,identity)) )],[refute_0_2305,refute_0_2306]) ).

cnf(refute_0_2308,plain,
    inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) = inverse(least_upper_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)),inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity))))) )],[refute_0_1288,refute_0_2307]) ).

cnf(refute_0_2309,plain,
    inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity)))) = greatest_lower_bound(inverse(a),least_upper_bound(b,identity)),
    inference(subst,[],[refute_0_582:[bind(X,$fot(a)),bind(X_89,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2310,plain,
    ( inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity)))) != greatest_lower_bound(inverse(a),least_upper_bound(b,identity))
    | inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) != inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity))))
    | inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) = greatest_lower_bound(inverse(a),least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)))),bind(Y0,$fot(inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity)))))),bind(Z0,$fot(greatest_lower_bound(inverse(a),least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2311,plain,
    ( inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity)))) != greatest_lower_bound(inverse(a),least_upper_bound(b,identity))
    | inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) = greatest_lower_bound(inverse(a),least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)),inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity))))) )],[refute_0_1288,refute_0_2310]) ).

cnf(refute_0_2312,plain,
    inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) = greatest_lower_bound(inverse(a),least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,inverse(least_upper_bound(b,identity)))),greatest_lower_bound(inverse(a),least_upper_bound(b,identity))) )],[refute_0_2309,refute_0_2311]) ).

cnf(refute_0_2313,plain,
    ( inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) != greatest_lower_bound(inverse(a),least_upper_bound(b,identity))
    | inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) != inverse(least_upper_bound(a,identity))
    | greatest_lower_bound(inverse(a),least_upper_bound(b,identity)) = inverse(least_upper_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)),inverse(least_upper_bound(a,identity))) ),[0],$fot(greatest_lower_bound(inverse(a),least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2314,plain,
    ( inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)) != inverse(least_upper_bound(a,identity))
    | greatest_lower_bound(inverse(a),least_upper_bound(b,identity)) = inverse(least_upper_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)),greatest_lower_bound(inverse(a),least_upper_bound(b,identity))) )],[refute_0_2312,refute_0_2313]) ).

cnf(refute_0_2315,plain,
    greatest_lower_bound(inverse(a),least_upper_bound(b,identity)) = inverse(least_upper_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(b,identity)),a)),inverse(least_upper_bound(a,identity))) )],[refute_0_2308,refute_0_2314]) ).

cnf(refute_0_2316,plain,
    ( multiply(a,greatest_lower_bound(inverse(a),least_upper_bound(b,identity))) != greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(inverse(a),least_upper_bound(b,identity)) != inverse(least_upper_bound(a,identity))
    | multiply(a,inverse(least_upper_bound(a,identity))) = greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,greatest_lower_bound(inverse(a),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) ),[0,1],$fot(inverse(least_upper_bound(a,identity)))]]) ).

cnf(refute_0_2317,plain,
    ( multiply(a,greatest_lower_bound(inverse(a),least_upper_bound(b,identity))) != greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))
    | multiply(a,inverse(least_upper_bound(a,identity))) = greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(a),least_upper_bound(b,identity)),inverse(least_upper_bound(a,identity))) )],[refute_0_2315,refute_0_2316]) ).

cnf(refute_0_2318,plain,
    multiply(a,inverse(least_upper_bound(a,identity))) = greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(inverse(a),least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) )],[refute_0_1287,refute_0_2317]) ).

cnf(refute_0_2319,plain,
    greatest_lower_bound(X,greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)),
    inference(subst,[],[refute_0_839:[bind(X_36,$fot(identity)),bind(X_37,$fot(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2320,plain,
    multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_36,X_37))) = identity,
    inference(subst,[],[refute_0_144:[bind(X_24,$fot(greatest_lower_bound(X_36,X_37)))]]) ).

cnf(refute_0_2321,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_25))]]) ).

cnf(refute_0_2322,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25)
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25)))]]) ).

cnf(refute_0_2323,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25)) )],[refute_0_2321,refute_0_2322]) ).

cnf(refute_0_2324,plain,
    ( multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_36,X_37))) != identity
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25))
    | multiply(inverse(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25))),greatest_lower_bound(X_25,greatest_lower_bound(X_36,X_37))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_36,X_37))),identity) ),[0,0,0],$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25)))]]) ).

cnf(refute_0_2325,plain,
    ( multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_36,X_37))) != identity
    | multiply(inverse(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25))),greatest_lower_bound(X_25,greatest_lower_bound(X_36,X_37))) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25))) )],[refute_0_2323,refute_0_2324]) ).

cnf(refute_0_2326,plain,
    multiply(inverse(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_25))),greatest_lower_bound(X_25,greatest_lower_bound(X_36,X_37))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_36,X_37))),identity) )],[refute_0_2320,refute_0_2325]) ).

cnf(refute_0_2327,plain,
    multiply(inverse(greatest_lower_bound(X_238,greatest_lower_bound(X_237,X_237))),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))) = identity,
    inference(subst,[],[refute_0_2326:[bind(X_25,$fot(X_237)),bind(X_36,$fot(X_238)),bind(X_37,$fot(X_237))]]) ).

cnf(refute_0_2328,plain,
    greatest_lower_bound(X_237,X_237) = X_237,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(X_237))]]) ).

cnf(refute_0_2329,plain,
    ( multiply(inverse(greatest_lower_bound(X_238,greatest_lower_bound(X_237,X_237))),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))) != identity
    | greatest_lower_bound(X_237,X_237) != X_237
    | multiply(inverse(greatest_lower_bound(X_238,X_237)),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_238,greatest_lower_bound(X_237,X_237))),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))),identity) ),[0,0,0,1],$fot(X_237)]]) ).

cnf(refute_0_2330,plain,
    ( multiply(inverse(greatest_lower_bound(X_238,greatest_lower_bound(X_237,X_237))),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))) != identity
    | multiply(inverse(greatest_lower_bound(X_238,X_237)),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_237,X_237),X_237) )],[refute_0_2328,refute_0_2329]) ).

cnf(refute_0_2331,plain,
    multiply(inverse(greatest_lower_bound(X_238,X_237)),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_238,greatest_lower_bound(X_237,X_237))),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))),identity) )],[refute_0_2327,refute_0_2330]) ).

cnf(refute_0_2332,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(greatest_lower_bound(X_24,X_25)))),bind(Y,$fot(greatest_lower_bound(X_25,X_24))),bind(Z,$fot(X_109))]]) ).

cnf(refute_0_2333,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)) != identity
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_2334,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),identity) )],[refute_0_144,refute_0_2333]) ).

cnf(refute_0_2335,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109))) )],[refute_0_2332,refute_0_2334]) ).

cnf(refute_0_2336,plain,
    greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109) = greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_25)),bind(Y,$fot(X_24)),bind(Z,$fot(X_109))]]) ).

cnf(refute_0_2337,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) = multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)))]]) ).

cnf(refute_0_2338,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) != multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109))
    | greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109) != greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) = multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109))) ),[1,1],$fot(greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109)))]]) ).

cnf(refute_0_2339,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109) != greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) = multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109))) )],[refute_0_2337,refute_0_2338]) ).

cnf(refute_0_2340,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) = multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109),greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109))) )],[refute_0_2336,refute_0_2339]) ).

cnf(refute_0_2341,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) != multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109)))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109))) ),[0],$fot(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109))))]]) ).

cnf(refute_0_2342,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109)))) )],[refute_0_2340,refute_0_2341]) ).

cnf(refute_0_2343,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,greatest_lower_bound(X_24,X_109))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(greatest_lower_bound(X_25,X_24),X_109)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_24,X_25)),X_109))) )],[refute_0_2335,refute_0_2342]) ).

cnf(refute_0_2344,plain,
    multiply(inverse(greatest_lower_bound(X_238,X_237)),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_238,X_237)),X_237)),
    inference(subst,[],[refute_0_2343:[bind(X_109,$fot(X_237)),bind(X_24,$fot(X_238)),bind(X_25,$fot(X_237))]]) ).

cnf(refute_0_2345,plain,
    ( multiply(inverse(greatest_lower_bound(X_238,X_237)),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_238,X_237)),X_237))
    | multiply(inverse(greatest_lower_bound(X_238,X_237)),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))) != identity
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_238,X_237)),X_237)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_238,X_237)),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_238,X_237)),X_237)))]]) ).

cnf(refute_0_2346,plain,
    ( multiply(inverse(greatest_lower_bound(X_238,X_237)),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))) != identity
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_238,X_237)),X_237)) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_238,X_237)),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_238,X_237)),X_237))) )],[refute_0_2344,refute_0_2345]) ).

cnf(refute_0_2347,plain,
    greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_238,X_237)),X_237)) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_238,X_237)),greatest_lower_bound(X_237,greatest_lower_bound(X_238,X_237))),identity) )],[refute_0_2331,refute_0_2346]) ).

cnf(refute_0_2348,plain,
    greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = identity,
    inference(subst,[],[refute_0_2347:[bind(X_237,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),bind(X_238,$fot(identity))]]) ).

cnf(refute_0_2349,plain,
    multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b)) = least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))),
    inference(subst,[],[refute_0_170:[bind(X_116,$fot(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),bind(X_87,$fot(b))]]) ).

cnf(refute_0_2350,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_685:[bind(Y,$fot(identity)),bind(X_43,$fot(b)),bind(X_45,$fot(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2351,plain,
    identity = least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))),
    inference(subst,[],[refute_0_571:[bind(Y,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))]]) ).

cnf(refute_0_2352,plain,
    multiply(greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(inverse(b))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))),
    inference(subst,[],[refute_0_340:[bind(X_122,$fot(inverse(b))),bind(X_123,$fot(least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2353,plain,
    inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) = inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_58:[bind(X_14,$fot(b)),bind(X_15,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2354,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_45)) = least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_45),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(b)),bind(Y,$fot(greatest_lower_bound(a,c))),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_2355,plain,
    least_upper_bound(b,greatest_lower_bound(b,c)) = b,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).

cnf(refute_0_2356,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | least_upper_bound(b,greatest_lower_bound(b,c)) != b
    | least_upper_bound(b,greatest_lower_bound(a,c)) = b ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,c)),b) ),[0,1],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_2357,plain,
    ( least_upper_bound(b,greatest_lower_bound(b,c)) != b
    | least_upper_bound(b,greatest_lower_bound(a,c)) = b ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_178,refute_0_2356]) ).

cnf(refute_0_2358,plain,
    least_upper_bound(b,greatest_lower_bound(a,c)) = b,
    inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,c)),b) )],[refute_0_2355,refute_0_2357]) ).

cnf(refute_0_2359,plain,
    ( least_upper_bound(b,greatest_lower_bound(a,c)) != b
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_45)) != least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_45)
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_45)) = least_upper_bound(b,X_45) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_45)),least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_45)) ),[1,0],$fot(b)]]) ).

cnf(refute_0_2360,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_45)) != least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_45)
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_45)) = least_upper_bound(b,X_45) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,c)),b) )],[refute_0_2358,refute_0_2359]) ).

cnf(refute_0_2361,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_45)) = least_upper_bound(b,X_45),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_45)),least_upper_bound(least_upper_bound(b,greatest_lower_bound(a,c)),X_45)) )],[refute_0_2354,refute_0_2360]) ).

cnf(refute_0_2362,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_2361:[bind(X_45,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2363,plain,
    least_upper_bound(greatest_lower_bound(a,c),identity) = least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_712:[bind(X_210,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2364,plain,
    ( least_upper_bound(greatest_lower_bound(a,c),identity) != least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))
    | least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) = least_upper_bound(greatest_lower_bound(a,c),identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(a,c),identity))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_2365,plain,
    least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) = least_upper_bound(greatest_lower_bound(a,c),identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),identity),least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) )],[refute_0_2363,refute_0_2364]) ).

cnf(refute_0_2366,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))
    | least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) != least_upper_bound(greatest_lower_bound(a,c),identity)
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)) = least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),[0,1],$fot(least_upper_bound(greatest_lower_bound(a,c),identity))]]) ).

cnf(refute_0_2367,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)) = least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(greatest_lower_bound(a,c),identity)) )],[refute_0_2365,refute_0_2366]) ).

cnf(refute_0_2368,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)) = least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) )],[refute_0_2362,refute_0_2367]) ).

cnf(refute_0_2369,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46))) = least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b),
    inference(subst,[],[refute_0_426:[bind(Y,$fot(b)),bind(X_21,$fot(least_upper_bound(greatest_lower_bound(a,c),X_46)))]]) ).

cnf(refute_0_2370,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46)) = least_upper_bound(b,X_46),
    inference(subst,[],[refute_0_2361:[bind(X_45,$fot(X_46))]]) ).

cnf(refute_0_2371,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46)) != least_upper_bound(b,X_46)
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46))) != least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) = least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46))),least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)) ),[0,1],$fot(least_upper_bound(b,X_46))]]) ).

cnf(refute_0_2372,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46))) != least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) = least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46)),least_upper_bound(b,X_46)) )],[refute_0_2370,refute_0_2371]) ).

cnf(refute_0_2373,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) = least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46))),least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)) )],[refute_0_2369,refute_0_2372]) ).

cnf(refute_0_2374,plain,
    least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)) = least_upper_bound(X_46,greatest_lower_bound(a,c)),
    inference(subst,[],[refute_0_426:[bind(Y,$fot(greatest_lower_bound(a,c))),bind(X_21,$fot(X_46))]]) ).

cnf(refute_0_2375,plain,
    least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))) = least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))),
    introduced(tautology,[refl,[$fot(least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))))]]) ).

cnf(refute_0_2376,plain,
    ( least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)) != least_upper_bound(X_46,greatest_lower_bound(a,c))
    | least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))) != least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)))
    | least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))) = least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))),least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)))) ),[1,1],$fot(least_upper_bound(X_46,greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2377,plain,
    ( least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)) != least_upper_bound(X_46,greatest_lower_bound(a,c))
    | least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))) = least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))),least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)))) )],[refute_0_2375,refute_0_2376]) ).

cnf(refute_0_2378,plain,
    least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))) = least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)),least_upper_bound(X_46,greatest_lower_bound(a,c))) )],[refute_0_2374,refute_0_2377]) ).

cnf(refute_0_2379,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,X_45)) = least_upper_bound(least_upper_bound(X_43,X_44),X_45),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_2380,plain,
    least_upper_bound(X_45,X_44) = least_upper_bound(X_44,X_45),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_45)),bind(Y,$fot(X_44))]]) ).

cnf(refute_0_2381,plain,
    ( least_upper_bound(X_45,X_44) != least_upper_bound(X_44,X_45)
    | least_upper_bound(X_44,X_45) = least_upper_bound(X_45,X_44) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_45,X_44))),bind(Y0,$fot(least_upper_bound(X_44,X_45)))]]) ).

cnf(refute_0_2382,plain,
    least_upper_bound(X_44,X_45) = least_upper_bound(X_45,X_44),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,X_44),least_upper_bound(X_44,X_45)) )],[refute_0_2380,refute_0_2381]) ).

cnf(refute_0_2383,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,X_45)) != least_upper_bound(least_upper_bound(X_43,X_44),X_45)
    | least_upper_bound(X_44,X_45) != least_upper_bound(X_45,X_44)
    | least_upper_bound(X_43,least_upper_bound(X_45,X_44)) = least_upper_bound(least_upper_bound(X_43,X_44),X_45) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,X_45)),least_upper_bound(least_upper_bound(X_43,X_44),X_45)) ),[0,1],$fot(least_upper_bound(X_45,X_44))]]) ).

cnf(refute_0_2384,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,X_45)) != least_upper_bound(least_upper_bound(X_43,X_44),X_45)
    | least_upper_bound(X_43,least_upper_bound(X_45,X_44)) = least_upper_bound(least_upper_bound(X_43,X_44),X_45) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_44,X_45),least_upper_bound(X_45,X_44)) )],[refute_0_2382,refute_0_2383]) ).

cnf(refute_0_2385,plain,
    least_upper_bound(X_43,least_upper_bound(X_45,X_44)) = least_upper_bound(least_upper_bound(X_43,X_44),X_45),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,X_45)),least_upper_bound(least_upper_bound(X_43,X_44),X_45)) )],[refute_0_2379,refute_0_2384]) ).

cnf(refute_0_2386,plain,
    least_upper_bound(least_upper_bound(X_43,X_44),X_45) = least_upper_bound(X_43,least_upper_bound(X_44,X_45)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_2387,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_45,X_44)) != least_upper_bound(least_upper_bound(X_43,X_44),X_45)
    | least_upper_bound(least_upper_bound(X_43,X_44),X_45) != least_upper_bound(X_43,least_upper_bound(X_44,X_45))
    | least_upper_bound(X_43,least_upper_bound(X_45,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,X_45)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_43,least_upper_bound(X_45,X_44)),least_upper_bound(X_43,least_upper_bound(X_44,X_45))) ),[0],$fot(least_upper_bound(least_upper_bound(X_43,X_44),X_45))]]) ).

cnf(refute_0_2388,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_45,X_44)) != least_upper_bound(least_upper_bound(X_43,X_44),X_45)
    | least_upper_bound(X_43,least_upper_bound(X_45,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_43,X_44),X_45),least_upper_bound(X_43,least_upper_bound(X_44,X_45))) )],[refute_0_2386,refute_0_2387]) ).

cnf(refute_0_2389,plain,
    least_upper_bound(X_43,least_upper_bound(X_45,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_45,X_44)),least_upper_bound(least_upper_bound(X_43,X_44),X_45)) )],[refute_0_2385,refute_0_2388]) ).

cnf(refute_0_2390,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_45,X_44)) != least_upper_bound(X_43,least_upper_bound(X_44,X_45))
    | least_upper_bound(X_43,least_upper_bound(X_44,X_45)) = least_upper_bound(X_43,least_upper_bound(X_45,X_44)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_43,least_upper_bound(X_45,X_44)))),bind(Y0,$fot(least_upper_bound(X_43,least_upper_bound(X_44,X_45))))]]) ).

cnf(refute_0_2391,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,X_45)) = least_upper_bound(X_43,least_upper_bound(X_45,X_44)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_45,X_44)),least_upper_bound(X_43,least_upper_bound(X_44,X_45))) )],[refute_0_2389,refute_0_2390]) ).

cnf(refute_0_2392,plain,
    least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),X_46)) = least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))),
    inference(subst,[],[refute_0_2391:[bind(X_43,$fot(b)),bind(X_44,$fot(least_upper_bound(greatest_lower_bound(a,c),X_46))),bind(X_45,$fot(X_46))]]) ).

cnf(refute_0_2393,plain,
    ( least_upper_bound(Y,least_upper_bound(X_43,X_45)) != least_upper_bound(X_43,least_upper_bound(Y,X_45))
    | least_upper_bound(X_43,least_upper_bound(Y,X_45)) = least_upper_bound(Y,least_upper_bound(X_43,X_45)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_43,X_45)))),bind(Y0,$fot(least_upper_bound(X_43,least_upper_bound(Y,X_45))))]]) ).

cnf(refute_0_2394,plain,
    least_upper_bound(X_43,least_upper_bound(Y,X_45)) = least_upper_bound(Y,least_upper_bound(X_43,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_43,X_45)),least_upper_bound(X_43,least_upper_bound(Y,X_45))) )],[refute_0_1102,refute_0_2393]) ).

cnf(refute_0_2395,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) = least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),X_46)),
    inference(subst,[],[refute_0_2394:[bind(Y,$fot(b)),bind(X_43,$fot(least_upper_bound(greatest_lower_bound(a,c),X_46))),bind(X_45,$fot(X_46))]]) ).

cnf(refute_0_2396,plain,
    ( least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),X_46)) != least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) != least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),X_46))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) = least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),X_46)))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)))))]]) ).

cnf(refute_0_2397,plain,
    ( least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),X_46)) != least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) = least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)),least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),X_46))) )],[refute_0_2395,refute_0_2396]) ).

cnf(refute_0_2398,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) = least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),X_46)),least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)))) )],[refute_0_2392,refute_0_2397]) ).

cnf(refute_0_2399,plain,
    ( least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))) != least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c)))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) != least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) = least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2400,plain,
    ( least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))) != least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c)))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) = least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)),least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46)))) )],[refute_0_2398,refute_0_2399]) ).

cnf(refute_0_2401,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) = least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(X_46,least_upper_bound(greatest_lower_bound(a,c),X_46))),least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c)))) )],[refute_0_2378,refute_0_2400]) ).

cnf(refute_0_2402,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) != least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c)))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) != least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)
    | least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) = least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)),least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)) ),[0],$fot(least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2403,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) != least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)
    | least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) = least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)),least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c)))) )],[refute_0_2401,refute_0_2402]) ).

cnf(refute_0_2404,plain,
    least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)) = least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46)),
    inference(subst,[],[refute_0_1077:[bind(X,$fot(b)),bind(X_43,$fot(greatest_lower_bound(a,c))),bind(X_44,$fot(X_46))]]) ).

cnf(refute_0_2405,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46)) != least_upper_bound(b,X_46)
    | least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)) != least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46))
    | least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)) = least_upper_bound(b,X_46) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46)))),bind(Z0,$fot(least_upper_bound(b,X_46)))]]) ).

cnf(refute_0_2406,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46)) != least_upper_bound(b,X_46)
    | least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)) = least_upper_bound(b,X_46) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)),least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46))) )],[refute_0_2404,refute_0_2405]) ).

cnf(refute_0_2407,plain,
    least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)) = least_upper_bound(b,X_46),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X_46)),least_upper_bound(b,X_46)) )],[refute_0_2370,refute_0_2406]) ).

cnf(refute_0_2408,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(greatest_lower_bound(a,c))),bind(Y,$fot(X_46)),bind(Z,$fot(b))]]) ).

cnf(refute_0_2409,plain,
    ( least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)) != least_upper_bound(b,X_46)
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b) != least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b) = least_upper_bound(b,X_46) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)))),bind(Z0,$fot(least_upper_bound(b,X_46)))]]) ).

cnf(refute_0_2410,plain,
    ( least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)) != least_upper_bound(b,X_46)
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b) = least_upper_bound(b,X_46) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b),least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b))) )],[refute_0_2408,refute_0_2409]) ).

cnf(refute_0_2411,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b) = least_upper_bound(b,X_46),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X_46,b)),least_upper_bound(b,X_46)) )],[refute_0_2407,refute_0_2410]) ).

cnf(refute_0_2412,plain,
    ( least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) != least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)
    | least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b) != least_upper_bound(b,X_46)
    | least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) = least_upper_bound(b,X_46) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))),least_upper_bound(b,X_46)) ),[0],$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b))]]) ).

cnf(refute_0_2413,plain,
    ( least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) != least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)
    | least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) = least_upper_bound(b,X_46) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b),least_upper_bound(b,X_46)) )],[refute_0_2411,refute_0_2412]) ).

cnf(refute_0_2414,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)) != least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)
    | least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) = least_upper_bound(b,X_46) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))),least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)) )],[refute_0_2403,refute_0_2413]) ).

cnf(refute_0_2415,plain,
    least_upper_bound(b,least_upper_bound(X_46,greatest_lower_bound(a,c))) = least_upper_bound(b,X_46),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),least_upper_bound(b,X_46)),least_upper_bound(least_upper_bound(greatest_lower_bound(a,c),X_46),b)) )],[refute_0_2373,refute_0_2414]) ).

cnf(refute_0_2416,plain,
    least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(a,c))) = least_upper_bound(b,identity),
    inference(subst,[],[refute_0_2415:[bind(X_46,$fot(identity))]]) ).

cnf(refute_0_2417,plain,
    multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_194,X_195))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))),
    inference(subst,[],[refute_0_1801:[bind(X_94,$fot(identity)),bind(X_95,$fot(least_upper_bound(X_194,X_195)))]]) ).

cnf(refute_0_2418,plain,
    least_upper_bound(X_194,least_upper_bound(X_195,identity)) = least_upper_bound(identity,least_upper_bound(X_194,X_195)),
    inference(subst,[],[refute_0_1707:[bind(X_192,$fot(X_194)),bind(X_193,$fot(X_195))]]) ).

cnf(refute_0_2419,plain,
    ( least_upper_bound(X_194,least_upper_bound(X_195,identity)) != least_upper_bound(identity,least_upper_bound(X_194,X_195))
    | least_upper_bound(identity,least_upper_bound(X_194,X_195)) = least_upper_bound(X_194,least_upper_bound(X_195,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_194,least_upper_bound(X_195,identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_194,X_195))))]]) ).

cnf(refute_0_2420,plain,
    least_upper_bound(identity,least_upper_bound(X_194,X_195)) = least_upper_bound(X_194,least_upper_bound(X_195,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_194,least_upper_bound(X_195,identity)),least_upper_bound(identity,least_upper_bound(X_194,X_195))) )],[refute_0_2418,refute_0_2419]) ).

cnf(refute_0_2421,plain,
    ( multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_194,X_195))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))
    | least_upper_bound(identity,least_upper_bound(X_194,X_195)) != least_upper_bound(X_194,least_upper_bound(X_195,identity))
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_194,X_195))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))) ),[0,1],$fot(least_upper_bound(X_194,least_upper_bound(X_195,identity)))]]) ).

cnf(refute_0_2422,plain,
    ( multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_194,X_195))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_194,X_195)),least_upper_bound(X_194,least_upper_bound(X_195,identity))) )],[refute_0_2420,refute_0_2421]) ).

cnf(refute_0_2423,plain,
    multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_194,X_195))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))) )],[refute_0_2417,refute_0_2422]) ).

cnf(refute_0_2424,plain,
    multiply(identity,least_upper_bound(X_194,least_upper_bound(X_195,identity))) = least_upper_bound(X_194,least_upper_bound(X_195,identity)),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_194,least_upper_bound(X_195,identity))))]]) ).

cnf(refute_0_2425,plain,
    multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) = multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))),
    introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))))]]) ).

cnf(refute_0_2426,plain,
    ( multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) != multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity)))
    | inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) = multiply(identity,least_upper_bound(X_194,least_upper_bound(X_195,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))),multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_2427,plain,
    ( inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) = multiply(identity,least_upper_bound(X_194,least_upper_bound(X_195,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))),multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity)))) )],[refute_0_2425,refute_0_2426]) ).

cnf(refute_0_2428,plain,
    multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) = multiply(identity,least_upper_bound(X_194,least_upper_bound(X_195,identity))),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_2427]) ).

cnf(refute_0_2429,plain,
    ( multiply(identity,least_upper_bound(X_194,least_upper_bound(X_195,identity))) != least_upper_bound(X_194,least_upper_bound(X_195,identity))
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) != multiply(identity,least_upper_bound(X_194,least_upper_bound(X_195,identity)))
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) = least_upper_bound(X_194,least_upper_bound(X_195,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_194,least_upper_bound(X_195,identity))))),bind(Z0,$fot(least_upper_bound(X_194,least_upper_bound(X_195,identity))))]]) ).

cnf(refute_0_2430,plain,
    ( multiply(identity,least_upper_bound(X_194,least_upper_bound(X_195,identity))) != least_upper_bound(X_194,least_upper_bound(X_195,identity))
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) = least_upper_bound(X_194,least_upper_bound(X_195,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))),multiply(identity,least_upper_bound(X_194,least_upper_bound(X_195,identity)))) )],[refute_0_2428,refute_0_2429]) ).

cnf(refute_0_2431,plain,
    multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) = least_upper_bound(X_194,least_upper_bound(X_195,identity)),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_194,least_upper_bound(X_195,identity))),least_upper_bound(X_194,least_upper_bound(X_195,identity))) )],[refute_0_2424,refute_0_2430]) ).

cnf(refute_0_2432,plain,
    ( multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) != least_upper_bound(X_194,least_upper_bound(X_195,identity))
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))
    | least_upper_bound(X_194,least_upper_bound(X_195,identity)) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))) ),[0],$fot(least_upper_bound(X_194,least_upper_bound(X_195,identity)))]]) ).

cnf(refute_0_2433,plain,
    ( multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))
    | least_upper_bound(X_194,least_upper_bound(X_195,identity)) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))),least_upper_bound(X_194,least_upper_bound(X_195,identity))) )],[refute_0_2431,refute_0_2432]) ).

cnf(refute_0_2434,plain,
    multiply(identity,least_upper_bound(X_194,least_upper_bound(identity,X_195))) = least_upper_bound(X_194,least_upper_bound(identity,X_195)),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_194,least_upper_bound(identity,X_195))))]]) ).

cnf(refute_0_2435,plain,
    multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))) = multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))),
    introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))))]]) ).

cnf(refute_0_2436,plain,
    ( multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))) != multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195)))
    | inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))) = multiply(identity,least_upper_bound(X_194,least_upper_bound(identity,X_195))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))),multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_2437,plain,
    ( inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))) = multiply(identity,least_upper_bound(X_194,least_upper_bound(identity,X_195))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))),multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195)))) )],[refute_0_2435,refute_0_2436]) ).

cnf(refute_0_2438,plain,
    multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))) = multiply(identity,least_upper_bound(X_194,least_upper_bound(identity,X_195))),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_2437]) ).

cnf(refute_0_2439,plain,
    ( multiply(identity,least_upper_bound(X_194,least_upper_bound(identity,X_195))) != least_upper_bound(X_194,least_upper_bound(identity,X_195))
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))) != multiply(identity,least_upper_bound(X_194,least_upper_bound(identity,X_195)))
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))) = least_upper_bound(X_194,least_upper_bound(identity,X_195)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_194,least_upper_bound(identity,X_195))))),bind(Z0,$fot(least_upper_bound(X_194,least_upper_bound(identity,X_195))))]]) ).

cnf(refute_0_2440,plain,
    ( multiply(identity,least_upper_bound(X_194,least_upper_bound(identity,X_195))) != least_upper_bound(X_194,least_upper_bound(identity,X_195))
    | multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))) = least_upper_bound(X_194,least_upper_bound(identity,X_195)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))),multiply(identity,least_upper_bound(X_194,least_upper_bound(identity,X_195)))) )],[refute_0_2438,refute_0_2439]) ).

cnf(refute_0_2441,plain,
    multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))) = least_upper_bound(X_194,least_upper_bound(identity,X_195)),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_194,least_upper_bound(identity,X_195))),least_upper_bound(X_194,least_upper_bound(identity,X_195))) )],[refute_0_2434,refute_0_2440]) ).

cnf(refute_0_2442,plain,
    multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) = least_upper_bound(multiply(inverse(X_103),Y),multiply(inverse(X_103),least_upper_bound(X_103,X_104))),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_103))),bind(Z,$fot(least_upper_bound(X_103,X_104)))]]) ).

cnf(refute_0_2443,plain,
    multiply(inverse(X_103),least_upper_bound(X_103,X_104)) = least_upper_bound(identity,multiply(inverse(X_103),X_104)),
    inference(subst,[],[refute_0_1801:[bind(X_94,$fot(X_103)),bind(X_95,$fot(X_104))]]) ).

cnf(refute_0_2444,plain,
    ( multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) != least_upper_bound(multiply(inverse(X_103),Y),multiply(inverse(X_103),least_upper_bound(X_103,X_104)))
    | multiply(inverse(X_103),least_upper_bound(X_103,X_104)) != least_upper_bound(identity,multiply(inverse(X_103),X_104))
    | multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) = least_upper_bound(multiply(inverse(X_103),Y),least_upper_bound(identity,multiply(inverse(X_103),X_104))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))),least_upper_bound(multiply(inverse(X_103),Y),multiply(inverse(X_103),least_upper_bound(X_103,X_104)))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_103),X_104)))]]) ).

cnf(refute_0_2445,plain,
    ( multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) != least_upper_bound(multiply(inverse(X_103),Y),multiply(inverse(X_103),least_upper_bound(X_103,X_104)))
    | multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) = least_upper_bound(multiply(inverse(X_103),Y),least_upper_bound(identity,multiply(inverse(X_103),X_104))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_103),least_upper_bound(X_103,X_104)),least_upper_bound(identity,multiply(inverse(X_103),X_104))) )],[refute_0_2443,refute_0_2444]) ).

cnf(refute_0_2446,plain,
    multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) = least_upper_bound(multiply(inverse(X_103),Y),least_upper_bound(identity,multiply(inverse(X_103),X_104))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))),least_upper_bound(multiply(inverse(X_103),Y),multiply(inverse(X_103),least_upper_bound(X_103,X_104)))) )],[refute_0_2442,refute_0_2445]) ).

cnf(refute_0_2447,plain,
    least_upper_bound(multiply(X_93,X_94),least_upper_bound(X_43,multiply(X_93,X_95))) = least_upper_bound(X_43,least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95))),
    inference(subst,[],[refute_0_1102:[bind(Y,$fot(multiply(X_93,X_94))),bind(X_45,$fot(multiply(X_93,X_95)))]]) ).

cnf(refute_0_2448,plain,
    ( least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)) != multiply(X_93,least_upper_bound(X_94,X_95))
    | least_upper_bound(multiply(X_93,X_94),least_upper_bound(X_43,multiply(X_93,X_95))) != least_upper_bound(X_43,least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)))
    | least_upper_bound(multiply(X_93,X_94),least_upper_bound(X_43,multiply(X_93,X_95))) = least_upper_bound(X_43,multiply(X_93,least_upper_bound(X_94,X_95))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_93,X_94),least_upper_bound(X_43,multiply(X_93,X_95))),least_upper_bound(X_43,least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)))) ),[1,1],$fot(multiply(X_93,least_upper_bound(X_94,X_95)))]]) ).

cnf(refute_0_2449,plain,
    ( least_upper_bound(multiply(X_93,X_94),least_upper_bound(X_43,multiply(X_93,X_95))) != least_upper_bound(X_43,least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)))
    | least_upper_bound(multiply(X_93,X_94),least_upper_bound(X_43,multiply(X_93,X_95))) = least_upper_bound(X_43,multiply(X_93,least_upper_bound(X_94,X_95))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)),multiply(X_93,least_upper_bound(X_94,X_95))) )],[refute_0_535,refute_0_2448]) ).

cnf(refute_0_2450,plain,
    least_upper_bound(multiply(X_93,X_94),least_upper_bound(X_43,multiply(X_93,X_95))) = least_upper_bound(X_43,multiply(X_93,least_upper_bound(X_94,X_95))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_93,X_94),least_upper_bound(X_43,multiply(X_93,X_95))),least_upper_bound(X_43,least_upper_bound(multiply(X_93,X_94),multiply(X_93,X_95)))) )],[refute_0_2447,refute_0_2449]) ).

cnf(refute_0_2451,plain,
    least_upper_bound(multiply(inverse(X_103),Y),least_upper_bound(identity,multiply(inverse(X_103),X_104))) = least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104))),
    inference(subst,[],[refute_0_2450:[bind(X_43,$fot(identity)),bind(X_93,$fot(inverse(X_103))),bind(X_94,$fot(Y)),bind(X_95,$fot(X_104))]]) ).

cnf(refute_0_2452,plain,
    ( multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) != least_upper_bound(multiply(inverse(X_103),Y),least_upper_bound(identity,multiply(inverse(X_103),X_104)))
    | least_upper_bound(multiply(inverse(X_103),Y),least_upper_bound(identity,multiply(inverse(X_103),X_104))) != least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104)))
    | multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) = least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))),least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104)))) ),[0],$fot(least_upper_bound(multiply(inverse(X_103),Y),least_upper_bound(identity,multiply(inverse(X_103),X_104))))]]) ).

cnf(refute_0_2453,plain,
    ( multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) != least_upper_bound(multiply(inverse(X_103),Y),least_upper_bound(identity,multiply(inverse(X_103),X_104)))
    | multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) = least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_103),Y),least_upper_bound(identity,multiply(inverse(X_103),X_104))),least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104)))) )],[refute_0_2451,refute_0_2452]) ).

cnf(refute_0_2454,plain,
    multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) = least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))),least_upper_bound(multiply(inverse(X_103),Y),least_upper_bound(identity,multiply(inverse(X_103),X_104)))) )],[refute_0_2446,refute_0_2453]) ).

cnf(refute_0_2455,plain,
    ( multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) != least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104)))
    | least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104))) = multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104)))))]]) ).

cnf(refute_0_2456,plain,
    least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104))) = multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_103),least_upper_bound(Y,least_upper_bound(X_103,X_104))),least_upper_bound(identity,multiply(inverse(X_103),least_upper_bound(Y,X_104)))) )],[refute_0_2454,refute_0_2455]) ).

cnf(refute_0_2457,plain,
    least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))) = multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))),
    inference(subst,[],[refute_0_2456:[bind(Y,$fot(X_194)),bind(X_103,$fot(identity)),bind(X_104,$fot(X_195))]]) ).

cnf(refute_0_2458,plain,
    ( multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))) != least_upper_bound(X_194,least_upper_bound(identity,X_195))
    | least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))) != multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195)))
    | least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))) = least_upper_bound(X_194,least_upper_bound(identity,X_195)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))))),bind(Y0,$fot(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))))),bind(Z0,$fot(least_upper_bound(X_194,least_upper_bound(identity,X_195))))]]) ).

cnf(refute_0_2459,plain,
    ( multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))) != least_upper_bound(X_194,least_upper_bound(identity,X_195))
    | least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))) = least_upper_bound(X_194,least_upper_bound(identity,X_195)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))),multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195)))) )],[refute_0_2457,refute_0_2458]) ).

cnf(refute_0_2460,plain,
    least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))) = least_upper_bound(X_194,least_upper_bound(identity,X_195)),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(identity,X_195))),least_upper_bound(X_194,least_upper_bound(identity,X_195))) )],[refute_0_2441,refute_0_2459]) ).

cnf(refute_0_2461,plain,
    ( least_upper_bound(X_194,least_upper_bound(X_195,identity)) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))
    | least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))) != least_upper_bound(X_194,least_upper_bound(identity,X_195))
    | least_upper_bound(X_194,least_upper_bound(X_195,identity)) = least_upper_bound(X_194,least_upper_bound(identity,X_195)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_194,least_upper_bound(X_195,identity)),least_upper_bound(X_194,least_upper_bound(identity,X_195))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))))]]) ).

cnf(refute_0_2462,plain,
    ( least_upper_bound(X_194,least_upper_bound(X_195,identity)) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))
    | least_upper_bound(X_194,least_upper_bound(X_195,identity)) = least_upper_bound(X_194,least_upper_bound(identity,X_195)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195))),least_upper_bound(X_194,least_upper_bound(identity,X_195))) )],[refute_0_2460,refute_0_2461]) ).

cnf(refute_0_2463,plain,
    ( multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))
    | least_upper_bound(X_194,least_upper_bound(X_195,identity)) = least_upper_bound(X_194,least_upper_bound(identity,X_195)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_194,least_upper_bound(X_195,identity)),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))) )],[refute_0_2433,refute_0_2462]) ).

cnf(refute_0_2464,plain,
    least_upper_bound(X_194,least_upper_bound(X_195,identity)) = least_upper_bound(X_194,least_upper_bound(identity,X_195)),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_194,least_upper_bound(X_195,identity))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_194,X_195)))) )],[refute_0_2423,refute_0_2463]) ).

cnf(refute_0_2465,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)) = least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_2464:[bind(X_194,$fot(b)),bind(X_195,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2466,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)) != least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(a,c)))
    | least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(a,c))) != least_upper_bound(b,identity)
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)) = least_upper_bound(b,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),bind(Z0,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2467,plain,
    ( least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(a,c))) != least_upper_bound(b,identity)
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)) = least_upper_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)),least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(a,c)))) )],[refute_0_2465,refute_0_2466]) ).

cnf(refute_0_2468,plain,
    least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,greatest_lower_bound(a,c))),least_upper_bound(b,identity)) )],[refute_0_2416,refute_0_2467]) ).

cnf(refute_0_2469,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)) != least_upper_bound(b,identity)
    | least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)) != least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))
    | least_upper_bound(b,identity) = least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)),least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),[0],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_2470,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)) != least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))
    | least_upper_bound(b,identity) = least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)),least_upper_bound(b,identity)) )],[refute_0_2468,refute_0_2469]) ).

cnf(refute_0_2471,plain,
    least_upper_bound(b,identity) = least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),identity)),least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) )],[refute_0_2368,refute_0_2470]) ).

cnf(refute_0_2472,plain,
    ( least_upper_bound(b,identity) != least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))
    | least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) = least_upper_bound(b,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(b,identity))),bind(Y0,$fot(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_2473,plain,
    least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) )],[refute_0_2471,refute_0_2472]) ).

cnf(refute_0_2474,plain,
    ( inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) != inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) != least_upper_bound(b,identity)
    | inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) = inverse(least_upper_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),[1,0],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_2475,plain,
    ( inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) != inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) = inverse(least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) )],[refute_0_2473,refute_0_2474]) ).

cnf(refute_0_2476,plain,
    inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) = inverse(least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_2353,refute_0_2475]) ).

cnf(refute_0_2477,plain,
    inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) = greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_582:[bind(X,$fot(b)),bind(X_89,$fot(least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2478,plain,
    ( inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) != greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))
    | inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) != inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) = greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)))),bind(Y0,$fot(inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Z0,$fot(greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2479,plain,
    ( inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) != greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))
    | inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) = greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_2353,refute_0_2478]) ).

cnf(refute_0_2480,plain,
    inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) = greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))) )],[refute_0_2477,refute_0_2479]) ).

cnf(refute_0_2481,plain,
    ( inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) != greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))
    | inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) != inverse(least_upper_bound(b,identity))
    | greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) = inverse(least_upper_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),inverse(least_upper_bound(b,identity))) ),[0],$fot(greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2482,plain,
    ( inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) != inverse(least_upper_bound(b,identity))
    | greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) = inverse(least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))) )],[refute_0_2480,refute_0_2481]) ).

cnf(refute_0_2483,plain,
    greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) = inverse(least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),inverse(least_upper_bound(b,identity))) )],[refute_0_2476,refute_0_2482]) ).

cnf(refute_0_2484,plain,
    ( multiply(greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(inverse(b))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))
    | greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) != inverse(least_upper_bound(b,identity))
    | multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(inverse(b))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))) ),[0,0],$fot(inverse(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2485,plain,
    ( multiply(greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(inverse(b))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))
    | multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(least_upper_bound(b,identity))) )],[refute_0_2483,refute_0_2484]) ).

cnf(refute_0_2486,plain,
    multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(inverse(b))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))) )],[refute_0_2352,refute_0_2485]) ).

cnf(refute_0_2487,plain,
    inverse(inverse(greatest_lower_bound(b,identity))) = greatest_lower_bound(b,identity),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2488,plain,
    multiply(inverse(b),least_upper_bound(b,identity)) = inverse(greatest_lower_bound(identity,b)),
    inference(subst,[],[refute_0_1864:[bind(X_103,$fot(b))]]) ).

cnf(refute_0_2489,plain,
    ( multiply(inverse(b),least_upper_bound(b,identity)) != inverse(greatest_lower_bound(identity,b))
    | inverse(greatest_lower_bound(identity,b)) != inverse(greatest_lower_bound(b,identity))
    | multiply(inverse(b),least_upper_bound(b,identity)) = inverse(greatest_lower_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(b),least_upper_bound(b,identity)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,b)))),bind(Z0,$fot(inverse(greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_2490,plain,
    ( inverse(greatest_lower_bound(identity,b)) != inverse(greatest_lower_bound(b,identity))
    | multiply(inverse(b),least_upper_bound(b,identity)) = inverse(greatest_lower_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),least_upper_bound(b,identity)),inverse(greatest_lower_bound(identity,b))) )],[refute_0_2488,refute_0_2489]) ).

cnf(refute_0_2491,plain,
    multiply(inverse(b),least_upper_bound(b,identity)) = inverse(greatest_lower_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,b)),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2249,refute_0_2490]) ).

cnf(refute_0_2492,plain,
    inverse(multiply(inverse(b),least_upper_bound(b,identity))) = inverse(multiply(inverse(b),least_upper_bound(b,identity))),
    introduced(tautology,[refl,[$fot(inverse(multiply(inverse(b),least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2493,plain,
    ( multiply(inverse(b),least_upper_bound(b,identity)) != inverse(greatest_lower_bound(b,identity))
    | inverse(multiply(inverse(b),least_upper_bound(b,identity))) != inverse(multiply(inverse(b),least_upper_bound(b,identity)))
    | inverse(multiply(inverse(b),least_upper_bound(b,identity))) = inverse(inverse(greatest_lower_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(b),least_upper_bound(b,identity))),inverse(multiply(inverse(b),least_upper_bound(b,identity)))) ),[1,0],$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2494,plain,
    ( multiply(inverse(b),least_upper_bound(b,identity)) != inverse(greatest_lower_bound(b,identity))
    | inverse(multiply(inverse(b),least_upper_bound(b,identity))) = inverse(inverse(greatest_lower_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(b),least_upper_bound(b,identity))),inverse(multiply(inverse(b),least_upper_bound(b,identity)))) )],[refute_0_2492,refute_0_2493]) ).

cnf(refute_0_2495,plain,
    inverse(multiply(inverse(b),least_upper_bound(b,identity))) = inverse(inverse(greatest_lower_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2491,refute_0_2494]) ).

cnf(refute_0_2496,plain,
    ( inverse(multiply(inverse(b),least_upper_bound(b,identity))) != inverse(inverse(greatest_lower_bound(b,identity)))
    | inverse(inverse(greatest_lower_bound(b,identity))) != greatest_lower_bound(b,identity)
    | inverse(multiply(inverse(b),least_upper_bound(b,identity))) = greatest_lower_bound(b,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(multiply(inverse(b),least_upper_bound(b,identity))))),bind(Y0,$fot(inverse(inverse(greatest_lower_bound(b,identity))))),bind(Z0,$fot(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2497,plain,
    ( inverse(inverse(greatest_lower_bound(b,identity))) != greatest_lower_bound(b,identity)
    | inverse(multiply(inverse(b),least_upper_bound(b,identity))) = greatest_lower_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(b),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(b,identity)))) )],[refute_0_2495,refute_0_2496]) ).

cnf(refute_0_2498,plain,
    inverse(multiply(inverse(b),least_upper_bound(b,identity))) = greatest_lower_bound(b,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(b,identity))),greatest_lower_bound(b,identity)) )],[refute_0_2487,refute_0_2497]) ).

cnf(refute_0_2499,plain,
    multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) = inverse(multiply(inverse(b),least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_667:[bind(X_198,$fot(inverse(b))),bind(X_59,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2500,plain,
    ( multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) != inverse(multiply(inverse(b),least_upper_bound(b,identity)))
    | inverse(multiply(inverse(b),least_upper_bound(b,identity))) != greatest_lower_bound(b,identity)
    | multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) = greatest_lower_bound(b,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))))),bind(Y0,$fot(inverse(multiply(inverse(b),least_upper_bound(b,identity))))),bind(Z0,$fot(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2501,plain,
    ( inverse(multiply(inverse(b),least_upper_bound(b,identity))) != greatest_lower_bound(b,identity)
    | multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) = greatest_lower_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))),inverse(multiply(inverse(b),least_upper_bound(b,identity)))) )],[refute_0_2499,refute_0_2500]) ).

cnf(refute_0_2502,plain,
    multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) = greatest_lower_bound(b,identity),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(b),least_upper_bound(b,identity))),greatest_lower_bound(b,identity)) )],[refute_0_2498,refute_0_2501]) ).

cnf(refute_0_2503,plain,
    ( multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) != greatest_lower_bound(b,identity)
    | multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).

cnf(refute_0_2504,plain,
    ( multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))),greatest_lower_bound(b,identity)) )],[refute_0_2502,refute_0_2503]) ).

cnf(refute_0_2505,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))]]) ).

cnf(refute_0_2506,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))
    | inverse(inverse(b)) != b
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) ),[1,1],$fot(b)]]) ).

cnf(refute_0_2507,plain,
    ( inverse(inverse(b)) != b
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) )],[refute_0_2505,refute_0_2506]) ).

cnf(refute_0_2508,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),b) )],[refute_0_1272,refute_0_2507]) ).

cnf(refute_0_2509,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))))]]) ).

cnf(refute_0_2510,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)
    | greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))
    | greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))) ),[1,1],$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))]]) ).

cnf(refute_0_2511,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)
    | greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))) )],[refute_0_2509,refute_0_2510]) ).

cnf(refute_0_2512,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) )],[refute_0_2508,refute_0_2511]) ).

cnf(refute_0_2513,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))
    | greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) ),[0],$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))))]]) ).

cnf(refute_0_2514,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b)))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) )],[refute_0_2512,refute_0_2513]) ).

cnf(refute_0_2515,plain,
    ( multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))) )],[refute_0_2504,refute_0_2514]) ).

cnf(refute_0_2516,plain,
    greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(b,identity)),inverse(inverse(b))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(inverse(b))))) )],[refute_0_2486,refute_0_2515]) ).

cnf(refute_0_2517,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))
    | greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) = greatest_lower_bound(b,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(b,identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))]]) ).

cnf(refute_0_2518,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) = greatest_lower_bound(b,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) )],[refute_0_2516,refute_0_2517]) ).

cnf(refute_0_2519,plain,
    ( greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) != greatest_lower_bound(b,identity)
    | identity != least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))
    | identity = least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) ),
    introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))) ),[1,0],$fot(greatest_lower_bound(b,identity))]]) ).

cnf(refute_0_2520,plain,
    ( identity != least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))
    | identity = least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),greatest_lower_bound(b,identity)) )],[refute_0_2518,refute_0_2519]) ).

cnf(refute_0_2521,plain,
    identity = least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))),
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))) )],[refute_0_2351,refute_0_2520]) ).

cnf(refute_0_2522,plain,
    multiply(inverse(X_95),least_upper_bound(X_94,X_95)) = least_upper_bound(multiply(inverse(X_95),X_94),multiply(inverse(X_95),X_95)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_95))),bind(Y,$fot(X_94)),bind(Z,$fot(X_95))]]) ).

cnf(refute_0_2523,plain,
    multiply(inverse(X_95),X_95) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_95))]]) ).

cnf(refute_0_2524,plain,
    ( multiply(inverse(X_95),X_95) != identity
    | multiply(inverse(X_95),least_upper_bound(X_94,X_95)) != least_upper_bound(multiply(inverse(X_95),X_94),multiply(inverse(X_95),X_95))
    | multiply(inverse(X_95),least_upper_bound(X_94,X_95)) = least_upper_bound(multiply(inverse(X_95),X_94),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(X_94,X_95)),least_upper_bound(multiply(inverse(X_95),X_94),multiply(inverse(X_95),X_95))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_2525,plain,
    ( multiply(inverse(X_95),least_upper_bound(X_94,X_95)) != least_upper_bound(multiply(inverse(X_95),X_94),multiply(inverse(X_95),X_95))
    | multiply(inverse(X_95),least_upper_bound(X_94,X_95)) = least_upper_bound(multiply(inverse(X_95),X_94),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_95),X_95),identity) )],[refute_0_2523,refute_0_2524]) ).

cnf(refute_0_2526,plain,
    multiply(inverse(X_95),least_upper_bound(X_94,X_95)) = least_upper_bound(multiply(inverse(X_95),X_94),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(X_94,X_95)),least_upper_bound(multiply(inverse(X_95),X_94),multiply(inverse(X_95),X_95))) )],[refute_0_2522,refute_0_2525]) ).

cnf(refute_0_2527,plain,
    least_upper_bound(multiply(inverse(X_95),X_94),identity) = least_upper_bound(identity,multiply(inverse(X_95),X_94)),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(multiply(inverse(X_95),X_94))),bind(X_17,$fot(identity))]]) ).

cnf(refute_0_2528,plain,
    ( multiply(inverse(X_95),least_upper_bound(X_94,X_95)) != least_upper_bound(multiply(inverse(X_95),X_94),identity)
    | least_upper_bound(multiply(inverse(X_95),X_94),identity) != least_upper_bound(identity,multiply(inverse(X_95),X_94))
    | multiply(inverse(X_95),least_upper_bound(X_94,X_95)) = least_upper_bound(identity,multiply(inverse(X_95),X_94)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_95),least_upper_bound(X_94,X_95)),least_upper_bound(identity,multiply(inverse(X_95),X_94))) ),[0],$fot(least_upper_bound(multiply(inverse(X_95),X_94),identity))]]) ).

cnf(refute_0_2529,plain,
    ( multiply(inverse(X_95),least_upper_bound(X_94,X_95)) != least_upper_bound(multiply(inverse(X_95),X_94),identity)
    | multiply(inverse(X_95),least_upper_bound(X_94,X_95)) = least_upper_bound(identity,multiply(inverse(X_95),X_94)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_95),X_94),identity),least_upper_bound(identity,multiply(inverse(X_95),X_94))) )],[refute_0_2527,refute_0_2528]) ).

cnf(refute_0_2530,plain,
    multiply(inverse(X_95),least_upper_bound(X_94,X_95)) = least_upper_bound(identity,multiply(inverse(X_95),X_94)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_95),least_upper_bound(X_94,X_95)),least_upper_bound(multiply(inverse(X_95),X_94),identity)) )],[refute_0_2526,refute_0_2529]) ).

cnf(refute_0_2531,plain,
    multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)),
    inference(subst,[],[refute_0_2530:[bind(X_94,$fot(b)),bind(X_95,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2532,plain,
    ( multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))
    | least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) != least_upper_bound(b,identity)
    | multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))) ),[0,1],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_2533,plain,
    ( multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))
    | multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) )],[refute_0_2473,refute_0_2532]) ).

cnf(refute_0_2534,plain,
    multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))) )],[refute_0_2531,refute_0_2533]) ).

cnf(refute_0_2535,plain,
    inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) = least_upper_bound(identity,greatest_lower_bound(a,c)),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2536,plain,
    multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) = multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)),
    introduced(tautology,[refl,[$fot(multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2537,plain,
    ( multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) != multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity))
    | inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) != least_upper_bound(identity,greatest_lower_bound(a,c))
    | multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)),multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity))) ),[1,0],$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2538,plain,
    ( inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) != least_upper_bound(identity,greatest_lower_bound(a,c))
    | multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)),multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity))) )],[refute_0_2536,refute_0_2537]) ).

cnf(refute_0_2539,plain,
    multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(identity,greatest_lower_bound(a,c))) )],[refute_0_2535,refute_0_2538]) ).

cnf(refute_0_2540,plain,
    ( multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))
    | multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) != least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)),least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))) ),[0],$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2541,plain,
    ( multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) != least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) )],[refute_0_2539,refute_0_2540]) ).

cnf(refute_0_2542,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) = least_upper_bound(multiply(inverse(greatest_lower_bound(identity,X)),X),multiply(Z,X)),
    inference(subst,[],[monotony_lub2:[bind(Y,$fot(inverse(greatest_lower_bound(identity,X))))]]) ).

cnf(refute_0_2543,plain,
    multiply(inverse(greatest_lower_bound(identity,X)),X) = least_upper_bound(X,identity),
    inference(subst,[],[refute_0_1664:[bind(X_113,$fot(X))]]) ).

cnf(refute_0_2544,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X)),X) != least_upper_bound(X,identity)
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) != least_upper_bound(multiply(inverse(greatest_lower_bound(identity,X)),X),multiply(Z,X))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) = least_upper_bound(least_upper_bound(X,identity),multiply(Z,X)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X),least_upper_bound(multiply(inverse(greatest_lower_bound(identity,X)),X),multiply(Z,X))) ),[1,0],$fot(least_upper_bound(X,identity))]]) ).

cnf(refute_0_2545,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) != least_upper_bound(multiply(inverse(greatest_lower_bound(identity,X)),X),multiply(Z,X))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) = least_upper_bound(least_upper_bound(X,identity),multiply(Z,X)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X)),X),least_upper_bound(X,identity)) )],[refute_0_2543,refute_0_2544]) ).

cnf(refute_0_2546,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) = least_upper_bound(least_upper_bound(X,identity),multiply(Z,X)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X),least_upper_bound(multiply(inverse(greatest_lower_bound(identity,X)),X),multiply(Z,X))) )],[refute_0_2542,refute_0_2545]) ).

cnf(refute_0_2547,plain,
    multiply(least_upper_bound(identity,least_upper_bound(inverse(X),Z)),X) = least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)),
    inference(subst,[],[refute_0_397:[bind(X_114,$fot(identity))]]) ).

cnf(refute_0_2548,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_64)),Z)
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_64)),Z) = least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_64)),Z)))]]) ).

cnf(refute_0_2549,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_64)),Z) = least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_64),Z)),least_upper_bound(inverse(greatest_lower_bound(identity,X_64)),Z)) )],[refute_0_1641,refute_0_2548]) ).

cnf(refute_0_2550,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z) = least_upper_bound(identity,least_upper_bound(inverse(X),Z)),
    inference(subst,[],[refute_0_2549:[bind(X_64,$fot(X))]]) ).

cnf(refute_0_2551,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) = multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X))]]) ).

cnf(refute_0_2552,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) != multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X)
    | least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z) != least_upper_bound(identity,least_upper_bound(inverse(X),Z))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) = multiply(least_upper_bound(identity,least_upper_bound(inverse(X),Z)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X),multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X)) ),[1,0],$fot(least_upper_bound(identity,least_upper_bound(inverse(X),Z)))]]) ).

cnf(refute_0_2553,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z) != least_upper_bound(identity,least_upper_bound(inverse(X),Z))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) = multiply(least_upper_bound(identity,least_upper_bound(inverse(X),Z)),X) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X),multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X)) )],[refute_0_2551,refute_0_2552]) ).

cnf(refute_0_2554,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) = multiply(least_upper_bound(identity,least_upper_bound(inverse(X),Z)),X),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),least_upper_bound(identity,least_upper_bound(inverse(X),Z))) )],[refute_0_2550,refute_0_2553]) ).

cnf(refute_0_2555,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) != multiply(least_upper_bound(identity,least_upper_bound(inverse(X),Z)),X)
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) = least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(inverse(X),Z)),X))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X))))]]) ).

cnf(refute_0_2556,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(inverse(X),Z)),X) != least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) = least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X),multiply(least_upper_bound(identity,least_upper_bound(inverse(X),Z)),X)) )],[refute_0_2554,refute_0_2555]) ).

cnf(refute_0_2557,plain,
    multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) = least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(inverse(X),Z)),X),least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X))) )],[refute_0_2547,refute_0_2556]) ).

cnf(refute_0_2558,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) != least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X))
    | multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) != least_upper_bound(least_upper_bound(X,identity),multiply(Z,X))
    | least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)) = least_upper_bound(least_upper_bound(X,identity),multiply(Z,X)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X),least_upper_bound(least_upper_bound(X,identity),multiply(Z,X))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)))]]) ).

cnf(refute_0_2559,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) != least_upper_bound(least_upper_bound(X,identity),multiply(Z,X))
    | least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)) = least_upper_bound(least_upper_bound(X,identity),multiply(Z,X)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X),least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X))) )],[refute_0_2557,refute_0_2558]) ).

cnf(refute_0_2560,plain,
    least_upper_bound(least_upper_bound(X,identity),multiply(Z,X)) = least_upper_bound(X,least_upper_bound(identity,multiply(Z,X))),
    inference(subst,[],[refute_0_375:[bind(Y,$fot(identity)),bind(Z,$fot(multiply(Z,X)))]]) ).

cnf(refute_0_2561,plain,
    ( least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)) != least_upper_bound(least_upper_bound(X,identity),multiply(Z,X))
    | least_upper_bound(least_upper_bound(X,identity),multiply(Z,X)) != least_upper_bound(X,least_upper_bound(identity,multiply(Z,X)))
    | least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)) = least_upper_bound(X,least_upper_bound(identity,multiply(Z,X))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)),least_upper_bound(X,least_upper_bound(identity,multiply(Z,X)))) ),[0],$fot(least_upper_bound(least_upper_bound(X,identity),multiply(Z,X)))]]) ).

cnf(refute_0_2562,plain,
    ( least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)) != least_upper_bound(least_upper_bound(X,identity),multiply(Z,X))
    | least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)) = least_upper_bound(X,least_upper_bound(identity,multiply(Z,X))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,identity),multiply(Z,X)),least_upper_bound(X,least_upper_bound(identity,multiply(Z,X)))) )],[refute_0_2560,refute_0_2561]) ).

cnf(refute_0_2563,plain,
    ( multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X) != least_upper_bound(least_upper_bound(X,identity),multiply(Z,X))
    | least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)) = least_upper_bound(X,least_upper_bound(identity,multiply(Z,X))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)),least_upper_bound(least_upper_bound(X,identity),multiply(Z,X))) )],[refute_0_2559,refute_0_2562]) ).

cnf(refute_0_2564,plain,
    least_upper_bound(identity,multiply(least_upper_bound(identity,Z),X)) = least_upper_bound(X,least_upper_bound(identity,multiply(Z,X))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(greatest_lower_bound(identity,X)),Z),X),least_upper_bound(least_upper_bound(X,identity),multiply(Z,X))) )],[refute_0_2546,refute_0_2563]) ).

cnf(refute_0_2565,plain,
    least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))),
    inference(subst,[],[refute_0_2564:[bind(X,$fot(b)),bind(Z,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2566,plain,
    multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b) = least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),
    inference(subst,[],[refute_0_397:[bind(X,$fot(b)),bind(Z,$fot(greatest_lower_bound(a,c))),bind(X_114,$fot(identity))]]) ).

cnf(refute_0_2567,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b) != least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))
    | least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) != least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))
    | multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b))),bind(Y0,$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))))]]) ).

cnf(refute_0_2568,plain,
    ( least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) != least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))
    | multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b),least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) )],[refute_0_2566,refute_0_2567]) ).

cnf(refute_0_2569,plain,
    multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))) )],[refute_0_2565,refute_0_2568]) ).

cnf(refute_0_2570,plain,
    least_upper_bound(X_185,least_upper_bound(X_186,X_184)) = least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184))),
    inference(subst,[],[refute_0_1084:[bind(Y,$fot(X_184)),bind(X_43,$fot(X_185)),bind(X_44,$fot(X_186))]]) ).

cnf(refute_0_2571,plain,
    least_upper_bound(X_184,X_186) = least_upper_bound(X_186,X_184),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_184)),bind(Y,$fot(X_186))]]) ).

cnf(refute_0_2572,plain,
    ( least_upper_bound(X_184,X_186) != least_upper_bound(X_186,X_184)
    | least_upper_bound(X_186,X_184) = least_upper_bound(X_184,X_186) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_184,X_186))),bind(Y0,$fot(least_upper_bound(X_186,X_184)))]]) ).

cnf(refute_0_2573,plain,
    least_upper_bound(X_186,X_184) = least_upper_bound(X_184,X_186),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_184,X_186),least_upper_bound(X_186,X_184)) )],[refute_0_2571,refute_0_2572]) ).

cnf(refute_0_2574,plain,
    ( least_upper_bound(X_185,least_upper_bound(X_186,X_184)) != least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184)))
    | least_upper_bound(X_186,X_184) != least_upper_bound(X_184,X_186)
    | least_upper_bound(X_185,least_upper_bound(X_184,X_186)) = least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_185,least_upper_bound(X_186,X_184)),least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184)))) ),[0,1],$fot(least_upper_bound(X_184,X_186))]]) ).

cnf(refute_0_2575,plain,
    ( least_upper_bound(X_185,least_upper_bound(X_186,X_184)) != least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184)))
    | least_upper_bound(X_185,least_upper_bound(X_184,X_186)) = least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_186,X_184),least_upper_bound(X_184,X_186)) )],[refute_0_2573,refute_0_2574]) ).

cnf(refute_0_2576,plain,
    least_upper_bound(X_185,least_upper_bound(X_184,X_186)) = least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_185,least_upper_bound(X_186,X_184)),least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184)))) )],[refute_0_2570,refute_0_2575]) ).

cnf(refute_0_2577,plain,
    least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184))) = least_upper_bound(X_185,least_upper_bound(X_186,X_184)),
    inference(subst,[],[refute_0_1086:[bind(Y,$fot(X_184)),bind(X_43,$fot(X_185)),bind(X_44,$fot(X_186))]]) ).

cnf(refute_0_2578,plain,
    ( least_upper_bound(X_185,least_upper_bound(X_184,X_186)) != least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184)))
    | least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184))) != least_upper_bound(X_185,least_upper_bound(X_186,X_184))
    | least_upper_bound(X_185,least_upper_bound(X_184,X_186)) = least_upper_bound(X_185,least_upper_bound(X_186,X_184)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_185,least_upper_bound(X_184,X_186)),least_upper_bound(X_185,least_upper_bound(X_186,X_184))) ),[0],$fot(least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184))))]]) ).

cnf(refute_0_2579,plain,
    ( least_upper_bound(X_185,least_upper_bound(X_184,X_186)) != least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184)))
    | least_upper_bound(X_185,least_upper_bound(X_184,X_186)) = least_upper_bound(X_185,least_upper_bound(X_186,X_184)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184))),least_upper_bound(X_185,least_upper_bound(X_186,X_184))) )],[refute_0_2577,refute_0_2578]) ).

cnf(refute_0_2580,plain,
    least_upper_bound(X_185,least_upper_bound(X_184,X_186)) = least_upper_bound(X_185,least_upper_bound(X_186,X_184)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_185,least_upper_bound(X_184,X_186)),least_upper_bound(X_186,least_upper_bound(X_185,least_upper_bound(X_186,X_184)))) )],[refute_0_2576,refute_0_2579]) ).

cnf(refute_0_2581,plain,
    ( least_upper_bound(X_185,least_upper_bound(X_184,X_186)) != least_upper_bound(X_185,least_upper_bound(X_186,X_184))
    | least_upper_bound(X_185,least_upper_bound(X_186,X_184)) = least_upper_bound(X_185,least_upper_bound(X_184,X_186)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_185,least_upper_bound(X_184,X_186)))),bind(Y0,$fot(least_upper_bound(X_185,least_upper_bound(X_186,X_184))))]]) ).

cnf(refute_0_2582,plain,
    least_upper_bound(X_185,least_upper_bound(X_186,X_184)) = least_upper_bound(X_185,least_upper_bound(X_184,X_186)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_185,least_upper_bound(X_184,X_186)),least_upper_bound(X_185,least_upper_bound(X_186,X_184))) )],[refute_0_2580,refute_0_2581]) ).

cnf(refute_0_2583,plain,
    least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(b))) = least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_2582:[bind(X_184,$fot(inverse(b))),bind(X_185,$fot(identity)),bind(X_186,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_2584,plain,
    least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(b))),
    inference(subst,[],[refute_0_1726:[bind(X_166,$fot(greatest_lower_bound(a,c))),bind(X_211,$fot(inverse(b)))]]) ).

cnf(refute_0_2585,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(b))) != least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))
    | least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(b)))
    | least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) = least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(b))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2586,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(b))) != least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))
    | least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) = least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(b)))) )],[refute_0_2584,refute_0_2585]) ).

cnf(refute_0_2587,plain,
    least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) = least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(b))),least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))) )],[refute_0_2583,refute_0_2586]) ).

cnf(refute_0_2588,plain,
    inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_1559:[bind(X,$fot(b)),bind(X_89,$fot(least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2589,plain,
    ( inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))
    | least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) != least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))
    | inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Y0,$fot(least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2590,plain,
    ( least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) != least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))
    | inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))) )],[refute_0_2588,refute_0_2589]) ).

cnf(refute_0_2591,plain,
    inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))) )],[refute_0_2587,refute_0_2590]) ).

cnf(refute_0_2592,plain,
    ( inverse(greatest_lower_bound(X_25,X_24)) != inverse(greatest_lower_bound(X_24,X_25))
    | inverse(greatest_lower_bound(X_24,X_25)) = inverse(greatest_lower_bound(X_25,X_24)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(X_25,X_24)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_24,X_25))))]]) ).

cnf(refute_0_2593,plain,
    inverse(greatest_lower_bound(X_24,X_25)) = inverse(greatest_lower_bound(X_25,X_24)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_25,X_24)),inverse(greatest_lower_bound(X_24,X_25))) )],[refute_0_141,refute_0_2592]) ).

cnf(refute_0_2594,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) = inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_2593:[bind(X_24,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),bind(X_25,$fot(b))]]) ).

cnf(refute_0_2595,plain,
    ( inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) != inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) = least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)))),bind(Y0,$fot(inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2596,plain,
    ( inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) = least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_2594,refute_0_2595]) ).

cnf(refute_0_2597,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) = least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))) )],[refute_0_2591,refute_0_2596]) ).

cnf(refute_0_2598,plain,
    multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b) = multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b))]]) ).

cnf(refute_0_2599,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b)
    | inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) != least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))
    | multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b) = multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b)) ),[1,0],$fot(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2600,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)) != least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))
    | multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b) = multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b)) )],[refute_0_2598,refute_0_2599]) ).

cnf(refute_0_2601,plain,
    multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b) = multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c)))) )],[refute_0_2597,refute_0_2600]) ).

cnf(refute_0_2602,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b) != multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b)
    | multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b) != least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))
    | multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))))]]) ).

cnf(refute_0_2603,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b) != least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))
    | multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b),multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b)) )],[refute_0_2601,refute_0_2602]) ).

cnf(refute_0_2604,plain,
    multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(inverse(b),greatest_lower_bound(a,c))),b),least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))) )],[refute_0_2569,refute_0_2603]) ).

cnf(refute_0_2605,plain,
    multiply(least_upper_bound(inverse(X),inverse(Y)),inverse(inverse(Y))) = least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))),
    inference(subst,[],[refute_0_363:[bind(X_111,$fot(inverse(X))),bind(X_112,$fot(inverse(Y)))]]) ).

cnf(refute_0_2606,plain,
    ( multiply(least_upper_bound(inverse(X),inverse(Y)),inverse(inverse(Y))) != least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))
    | least_upper_bound(inverse(X),inverse(Y)) != inverse(greatest_lower_bound(X,Y))
    | multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) = least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X),inverse(Y)),inverse(inverse(Y))),least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))) ),[0,0],$fot(inverse(greatest_lower_bound(X,Y)))]]) ).

cnf(refute_0_2607,plain,
    ( multiply(least_upper_bound(inverse(X),inverse(Y)),inverse(inverse(Y))) != least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))
    | multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) = least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(Y)),inverse(greatest_lower_bound(X,Y))) )],[refute_0_136,refute_0_2606]) ).

cnf(refute_0_2608,plain,
    multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) = least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X),inverse(Y)),inverse(inverse(Y))),least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))) )],[refute_0_2605,refute_0_2607]) ).

cnf(refute_0_2609,plain,
    inverse(inverse(Y)) = Y,
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(Y))]]) ).

cnf(refute_0_2610,plain,
    multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) = multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))))]]) ).

cnf(refute_0_2611,plain,
    ( multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) != multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y)))
    | inverse(inverse(Y)) != Y
    | multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) = multiply(inverse(greatest_lower_bound(X,Y)),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))),multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y)))) ),[1,1],$fot(Y)]]) ).

cnf(refute_0_2612,plain,
    ( inverse(inverse(Y)) != Y
    | multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) = multiply(inverse(greatest_lower_bound(X,Y)),Y) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))),multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y)))) )],[refute_0_2610,refute_0_2611]) ).

cnf(refute_0_2613,plain,
    multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) = multiply(inverse(greatest_lower_bound(X,Y)),Y),
    inference(resolve,[$cnf( $equal(inverse(inverse(Y)),Y) )],[refute_0_2609,refute_0_2612]) ).

cnf(refute_0_2614,plain,
    ( multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) != multiply(inverse(greatest_lower_bound(X,Y)),Y)
    | multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) != least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))
    | multiply(inverse(greatest_lower_bound(X,Y)),Y) = least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))),least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))) ),[0],$fot(multiply(inverse(greatest_lower_bound(X,Y)),Y))]]) ).

cnf(refute_0_2615,plain,
    ( multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) != least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))
    | multiply(inverse(greatest_lower_bound(X,Y)),Y) = least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))),multiply(inverse(greatest_lower_bound(X,Y)),Y)) )],[refute_0_2613,refute_0_2614]) ).

cnf(refute_0_2616,plain,
    multiply(inverse(X),inverse(inverse(Y))) = multiply(inverse(X),inverse(inverse(Y))),
    introduced(tautology,[refl,[$fot(multiply(inverse(X),inverse(inverse(Y))))]]) ).

cnf(refute_0_2617,plain,
    ( multiply(inverse(X),inverse(inverse(Y))) != multiply(inverse(X),inverse(inverse(Y)))
    | inverse(inverse(Y)) != Y
    | multiply(inverse(X),inverse(inverse(Y))) = multiply(inverse(X),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X),inverse(inverse(Y))),multiply(inverse(X),inverse(inverse(Y)))) ),[1,1],$fot(Y)]]) ).

cnf(refute_0_2618,plain,
    ( inverse(inverse(Y)) != Y
    | multiply(inverse(X),inverse(inverse(Y))) = multiply(inverse(X),Y) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X),inverse(inverse(Y))),multiply(inverse(X),inverse(inverse(Y)))) )],[refute_0_2616,refute_0_2617]) ).

cnf(refute_0_2619,plain,
    multiply(inverse(X),inverse(inverse(Y))) = multiply(inverse(X),Y),
    inference(resolve,[$cnf( $equal(inverse(inverse(Y)),Y) )],[refute_0_2609,refute_0_2618]) ).

cnf(refute_0_2620,plain,
    least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))) = least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))))]]) ).

cnf(refute_0_2621,plain,
    ( multiply(inverse(X),inverse(inverse(Y))) != multiply(inverse(X),Y)
    | least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))) != least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))
    | least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))) = least_upper_bound(identity,multiply(inverse(X),Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))),least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))) ),[1,1],$fot(multiply(inverse(X),Y))]]) ).

cnf(refute_0_2622,plain,
    ( multiply(inverse(X),inverse(inverse(Y))) != multiply(inverse(X),Y)
    | least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))) = least_upper_bound(identity,multiply(inverse(X),Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))),least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))) )],[refute_0_2620,refute_0_2621]) ).

cnf(refute_0_2623,plain,
    least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))) = least_upper_bound(identity,multiply(inverse(X),Y)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X),inverse(inverse(Y))),multiply(inverse(X),Y)) )],[refute_0_2619,refute_0_2622]) ).

cnf(refute_0_2624,plain,
    ( multiply(inverse(greatest_lower_bound(X,Y)),Y) != least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))
    | least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))) != least_upper_bound(identity,multiply(inverse(X),Y))
    | multiply(inverse(greatest_lower_bound(X,Y)),Y) = least_upper_bound(identity,multiply(inverse(X),Y)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(X,Y)),Y),least_upper_bound(identity,multiply(inverse(X),Y))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))))]]) ).

cnf(refute_0_2625,plain,
    ( multiply(inverse(greatest_lower_bound(X,Y)),Y) != least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))
    | multiply(inverse(greatest_lower_bound(X,Y)),Y) = least_upper_bound(identity,multiply(inverse(X),Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y)))),least_upper_bound(identity,multiply(inverse(X),Y))) )],[refute_0_2623,refute_0_2624]) ).

cnf(refute_0_2626,plain,
    ( multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))) != least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))
    | multiply(inverse(greatest_lower_bound(X,Y)),Y) = least_upper_bound(identity,multiply(inverse(X),Y)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X,Y)),Y),least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))) )],[refute_0_2615,refute_0_2625]) ).

cnf(refute_0_2627,plain,
    multiply(inverse(greatest_lower_bound(X,Y)),Y) = least_upper_bound(identity,multiply(inverse(X),Y)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X,Y)),inverse(inverse(Y))),least_upper_bound(identity,multiply(inverse(X),inverse(inverse(Y))))) )],[refute_0_2608,refute_0_2626]) ).

cnf(refute_0_2628,plain,
    ( multiply(inverse(greatest_lower_bound(X,Y)),Y) != least_upper_bound(identity,multiply(inverse(X),Y))
    | least_upper_bound(identity,multiply(inverse(X),Y)) = multiply(inverse(greatest_lower_bound(X,Y)),Y) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X,Y)),Y))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X),Y))))]]) ).

cnf(refute_0_2629,plain,
    least_upper_bound(identity,multiply(inverse(X),Y)) = multiply(inverse(greatest_lower_bound(X,Y)),Y),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X,Y)),Y),least_upper_bound(identity,multiply(inverse(X),Y))) )],[refute_0_2627,refute_0_2628]) ).

cnf(refute_0_2630,plain,
    least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)) = multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b),
    inference(subst,[],[refute_0_2629:[bind(X,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),bind(Y,$fot(b))]]) ).

cnf(refute_0_2631,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b) != least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))
    | least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)) != multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b)
    | least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))))]]) ).

cnf(refute_0_2632,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b) != least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))
    | least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)),multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b)) )],[refute_0_2630,refute_0_2631]) ).

cnf(refute_0_2633,plain,
    least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),b)),b),least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))) )],[refute_0_2604,refute_0_2632]) ).

cnf(refute_0_2634,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) != least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))
    | least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)) != least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)))]]) ).

cnf(refute_0_2635,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) != least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b)),least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))) )],[refute_0_2633,refute_0_2634]) ).

cnf(refute_0_2636,plain,
    ( multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) != least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))) )],[refute_0_2541,refute_0_2635]) ).

cnf(refute_0_2637,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) = least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)),least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),b))) )],[refute_0_2534,refute_0_2636]) ).

cnf(refute_0_2638,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) != least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))
    | least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))))]]) ).

cnf(refute_0_2639,plain,
    least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))) )],[refute_0_2637,refute_0_2638]) ).

cnf(refute_0_2640,plain,
    ( least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))
    | least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) != least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))
    | least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))))),bind(Z0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2641,plain,
    ( least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))
    | least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b)))) )],[refute_0_2565,refute_0_2640]) ).

cnf(refute_0_2642,plain,
    least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),b))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) )],[refute_0_2639,refute_0_2641]) ).

cnf(refute_0_2643,plain,
    inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) = inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))]]) ).

cnf(refute_0_2644,plain,
    ( inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) != inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))
    | least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))
    | inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) = inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) ),[1,0],$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2645,plain,
    ( least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))
    | inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) = inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) )],[refute_0_2643,refute_0_2644]) ).

cnf(refute_0_2646,plain,
    inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) = inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) )],[refute_0_2642,refute_0_2645]) ).

cnf(refute_0_2647,plain,
    least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) = least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))))]]) ).

cnf(refute_0_2648,plain,
    ( inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) != inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) != least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) = least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))),least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))) ),[1,1],$fot(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2649,plain,
    ( inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) != inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) = least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))),least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))) )],[refute_0_2647,refute_0_2648]) ).

cnf(refute_0_2650,plain,
    least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) = least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) )],[refute_0_2646,refute_0_2649]) ).

cnf(refute_0_2651,plain,
    ( identity != least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) != least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | identity = least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(identity,least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),[0],$fot(least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))))]]) ).

cnf(refute_0_2652,plain,
    ( identity != least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))
    | identity = least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))),least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2650,refute_0_2651]) ).

cnf(refute_0_2653,plain,
    identity = least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(greatest_lower_bound(b,identity),inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))) )],[refute_0_2521,refute_0_2652]) ).

cnf(refute_0_2654,plain,
    ( identity != least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_2655,plain,
    least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = identity,
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2653,refute_0_2654]) ).

cnf(refute_0_2656,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != identity
    | least_upper_bound(b,identity) = least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_2657,plain,
    ( least_upper_bound(b,least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | least_upper_bound(b,identity) = least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),identity) )],[refute_0_2655,refute_0_2656]) ).

cnf(refute_0_2658,plain,
    least_upper_bound(b,identity) = least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2350,refute_0_2657]) ).

cnf(refute_0_2659,plain,
    ( least_upper_bound(b,identity) != least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = least_upper_bound(b,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(b,identity))),bind(Y0,$fot(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_2660,plain,
    least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2658,refute_0_2659]) ).

cnf(refute_0_2661,plain,
    ( multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b)) != least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))
    | least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != least_upper_bound(b,identity)
    | multiply(least_upper_bound(b,identity),inverse(b)) = least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b)),least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))) ),[0,0],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_2662,plain,
    ( multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b)) != least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))
    | multiply(least_upper_bound(b,identity),inverse(b)) = least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),least_upper_bound(b,identity)) )],[refute_0_2660,refute_0_2661]) ).

cnf(refute_0_2663,plain,
    multiply(least_upper_bound(b,identity),inverse(b)) = least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b)),least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))) )],[refute_0_2349,refute_0_2662]) ).

cnf(refute_0_2664,plain,
    multiply(identity,inverse(greatest_lower_bound(b,identity))) = inverse(greatest_lower_bound(b,identity)),
    inference(subst,[],[left_identity:[bind(X,$fot(inverse(greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_2665,plain,
    multiply(identity,inverse(greatest_lower_bound(identity,b))) = multiply(identity,inverse(greatest_lower_bound(b,identity))),
    inference(subst,[],[refute_0_264:[bind(Y,$fot(b)),bind(X_99,$fot(identity))]]) ).

cnf(refute_0_2666,plain,
    ( multiply(identity,inverse(greatest_lower_bound(b,identity))) != inverse(greatest_lower_bound(b,identity))
    | multiply(identity,inverse(greatest_lower_bound(identity,b))) != multiply(identity,inverse(greatest_lower_bound(b,identity)))
    | multiply(identity,inverse(greatest_lower_bound(identity,b))) = inverse(greatest_lower_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(identity,inverse(greatest_lower_bound(identity,b))))),bind(Y0,$fot(multiply(identity,inverse(greatest_lower_bound(b,identity))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_2667,plain,
    ( multiply(identity,inverse(greatest_lower_bound(b,identity))) != inverse(greatest_lower_bound(b,identity))
    | multiply(identity,inverse(greatest_lower_bound(identity,b))) = inverse(greatest_lower_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(greatest_lower_bound(identity,b))),multiply(identity,inverse(greatest_lower_bound(b,identity)))) )],[refute_0_2665,refute_0_2666]) ).

cnf(refute_0_2668,plain,
    multiply(identity,inverse(greatest_lower_bound(identity,b))) = inverse(greatest_lower_bound(b,identity)),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(greatest_lower_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2664,refute_0_2667]) ).

cnf(refute_0_2669,plain,
    multiply(least_upper_bound(b,identity),inverse(b)) = multiply(identity,inverse(greatest_lower_bound(identity,b))),
    inference(subst,[],[refute_0_273:[bind(Y,$fot(b)),bind(X_99,$fot(identity))]]) ).

cnf(refute_0_2670,plain,
    ( multiply(identity,inverse(greatest_lower_bound(identity,b))) != inverse(greatest_lower_bound(b,identity))
    | multiply(least_upper_bound(b,identity),inverse(b)) != multiply(identity,inverse(greatest_lower_bound(identity,b)))
    | multiply(least_upper_bound(b,identity),inverse(b)) = inverse(greatest_lower_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(b,identity),inverse(b)))),bind(Y0,$fot(multiply(identity,inverse(greatest_lower_bound(identity,b))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_2671,plain,
    ( multiply(identity,inverse(greatest_lower_bound(identity,b))) != inverse(greatest_lower_bound(b,identity))
    | multiply(least_upper_bound(b,identity),inverse(b)) = inverse(greatest_lower_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(b)),multiply(identity,inverse(greatest_lower_bound(identity,b)))) )],[refute_0_2669,refute_0_2670]) ).

cnf(refute_0_2672,plain,
    multiply(least_upper_bound(b,identity),inverse(b)) = inverse(greatest_lower_bound(b,identity)),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(greatest_lower_bound(identity,b))),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2668,refute_0_2671]) ).

cnf(refute_0_2673,plain,
    ( multiply(least_upper_bound(b,identity),inverse(b)) != inverse(greatest_lower_bound(b,identity))
    | multiply(least_upper_bound(b,identity),inverse(b)) != least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))
    | inverse(greatest_lower_bound(b,identity)) = least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(b)),least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))) ),[0],$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2674,plain,
    ( multiply(least_upper_bound(b,identity),inverse(b)) != least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))
    | inverse(greatest_lower_bound(b,identity)) = least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(b)),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2672,refute_0_2673]) ).

cnf(refute_0_2675,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))) = least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278))),
    inference(subst,[],[refute_0_1801:[bind(X_95,$fot(inverse(X_278)))]]) ).

cnf(refute_0_2676,plain,
    multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)) = least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278))),
    inference(subst,[],[refute_0_170:[bind(X_116,$fot(inverse(X_94))),bind(X_87,$fot(X_278))]]) ).

cnf(refute_0_2677,plain,
    ( multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)) != least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278)))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278))) = multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278)))))]]) ).

cnf(refute_0_2678,plain,
    least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278))) = multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)),least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278)))) )],[refute_0_2676,refute_0_2677]) ).

cnf(refute_0_2679,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))) != least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278)))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278))) != multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))) = multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))),multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278))))]]) ).

cnf(refute_0_2680,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))) != least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278)))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))) = multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278))),multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278))) )],[refute_0_2678,refute_0_2679]) ).

cnf(refute_0_2681,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))) = multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))),least_upper_bound(identity,multiply(inverse(X_94),inverse(X_278)))) )],[refute_0_2675,refute_0_2680]) ).

cnf(refute_0_2682,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) = least_upper_bound(identity,multiply(inverse(X_94),inverse(greatest_lower_bound(inverse(X_94),X_219)))),
    inference(subst,[],[refute_0_1801:[bind(X_95,$fot(inverse(greatest_lower_bound(inverse(X_94),X_219))))]]) ).

cnf(refute_0_2683,plain,
    multiply(inverse(X_94),inverse(greatest_lower_bound(inverse(X_94),X_219))) = least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))),
    inference(subst,[],[refute_0_243:[bind(Y,$fot(X_219)),bind(X_99,$fot(inverse(X_94)))]]) ).

cnf(refute_0_2684,plain,
    ( multiply(inverse(X_94),inverse(greatest_lower_bound(inverse(X_94),X_219))) != least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) != least_upper_bound(identity,multiply(inverse(X_94),inverse(greatest_lower_bound(inverse(X_94),X_219))))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))),least_upper_bound(identity,multiply(inverse(X_94),inverse(greatest_lower_bound(inverse(X_94),X_219))))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))]]) ).

cnf(refute_0_2685,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) != least_upper_bound(identity,multiply(inverse(X_94),inverse(greatest_lower_bound(inverse(X_94),X_219))))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),inverse(greatest_lower_bound(inverse(X_94),X_219))),least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) )],[refute_0_2683,refute_0_2684]) ).

cnf(refute_0_2686,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))),least_upper_bound(identity,multiply(inverse(X_94),inverse(greatest_lower_bound(inverse(X_94),X_219))))) )],[refute_0_2682,refute_0_2685]) ).

cnf(refute_0_2687,plain,
    least_upper_bound(X_94,least_upper_bound(X_94,inverse(X_219))) = least_upper_bound(X_94,inverse(X_219)),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(inverse(X_219))),bind(X_31,$fot(X_94))]]) ).

cnf(refute_0_2688,plain,
    inverse(greatest_lower_bound(inverse(X_89),Y)) = least_upper_bound(inverse(inverse(X_89)),inverse(Y)),
    inference(subst,[],[p12x_3:[bind(X,$fot(inverse(X_89)))]]) ).

cnf(refute_0_2689,plain,
    ( inverse(greatest_lower_bound(inverse(X_89),Y)) != least_upper_bound(inverse(inverse(X_89)),inverse(Y))
    | inverse(inverse(X_89)) != X_89
    | inverse(greatest_lower_bound(inverse(X_89),Y)) = least_upper_bound(X_89,inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_89),Y)),least_upper_bound(inverse(inverse(X_89)),inverse(Y))) ),[1,0],$fot(X_89)]]) ).

cnf(refute_0_2690,plain,
    ( inverse(greatest_lower_bound(inverse(X_89),Y)) != least_upper_bound(inverse(inverse(X_89)),inverse(Y))
    | inverse(greatest_lower_bound(inverse(X_89),Y)) = least_upper_bound(X_89,inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_89)),X_89) )],[refute_0_98,refute_0_2689]) ).

cnf(refute_0_2691,plain,
    inverse(greatest_lower_bound(inverse(X_89),Y)) = least_upper_bound(X_89,inverse(Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_89),Y)),least_upper_bound(inverse(inverse(X_89)),inverse(Y))) )],[refute_0_2688,refute_0_2690]) ).

cnf(refute_0_2692,plain,
    inverse(greatest_lower_bound(inverse(X_94),X_219)) = least_upper_bound(X_94,inverse(X_219)),
    inference(subst,[],[refute_0_2691:[bind(Y,$fot(X_219)),bind(X_89,$fot(X_94))]]) ).

cnf(refute_0_2693,plain,
    least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))) = least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))))]]) ).

cnf(refute_0_2694,plain,
    ( inverse(greatest_lower_bound(inverse(X_94),X_219)) != least_upper_bound(X_94,inverse(X_219))
    | least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))) != least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))
    | least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))) = least_upper_bound(X_94,least_upper_bound(X_94,inverse(X_219))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) ),[1,1],$fot(least_upper_bound(X_94,inverse(X_219)))]]) ).

cnf(refute_0_2695,plain,
    ( inverse(greatest_lower_bound(inverse(X_94),X_219)) != least_upper_bound(X_94,inverse(X_219))
    | least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))) = least_upper_bound(X_94,least_upper_bound(X_94,inverse(X_219))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) )],[refute_0_2693,refute_0_2694]) ).

cnf(refute_0_2696,plain,
    least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))) = least_upper_bound(X_94,least_upper_bound(X_94,inverse(X_219))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_94),X_219)),least_upper_bound(X_94,inverse(X_219))) )],[refute_0_2692,refute_0_2695]) ).

cnf(refute_0_2697,plain,
    ( least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))) != least_upper_bound(X_94,least_upper_bound(X_94,inverse(X_219)))
    | least_upper_bound(X_94,least_upper_bound(X_94,inverse(X_219))) != least_upper_bound(X_94,inverse(X_219))
    | least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))) = least_upper_bound(X_94,inverse(X_219)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))))),bind(Y0,$fot(least_upper_bound(X_94,least_upper_bound(X_94,inverse(X_219))))),bind(Z0,$fot(least_upper_bound(X_94,inverse(X_219))))]]) ).

cnf(refute_0_2698,plain,
    ( least_upper_bound(X_94,least_upper_bound(X_94,inverse(X_219))) != least_upper_bound(X_94,inverse(X_219))
    | least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))) = least_upper_bound(X_94,inverse(X_219)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))),least_upper_bound(X_94,least_upper_bound(X_94,inverse(X_219)))) )],[refute_0_2696,refute_0_2697]) ).

cnf(refute_0_2699,plain,
    least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))) = least_upper_bound(X_94,inverse(X_219)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_94,least_upper_bound(X_94,inverse(X_219))),least_upper_bound(X_94,inverse(X_219))) )],[refute_0_2687,refute_0_2698]) ).

cnf(refute_0_2700,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) = multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))),
    introduced(tautology,[refl,[$fot(multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))))]]) ).

cnf(refute_0_2701,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) != multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))))
    | least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))) != least_upper_bound(X_94,inverse(X_219))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) = multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))),multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))))) ),[1,1],$fot(least_upper_bound(X_94,inverse(X_219)))]]) ).

cnf(refute_0_2702,plain,
    ( least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))) != least_upper_bound(X_94,inverse(X_219))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) = multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))),multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))))) )],[refute_0_2700,refute_0_2701]) ).

cnf(refute_0_2703,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) = multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219))),least_upper_bound(X_94,inverse(X_219))) )],[refute_0_2699,refute_0_2702]) ).

cnf(refute_0_2704,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) != multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219)))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))) ),[0],$fot(multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))))]]) ).

cnf(refute_0_2705,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))),multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219)))) )],[refute_0_2703,refute_0_2704]) ).

cnf(refute_0_2706,plain,
    least_upper_bound(identity,inverse(multiply(X_219,X_94))) = inverse(greatest_lower_bound(identity,multiply(X_219,X_94))),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(multiply(X_219,X_94)))]]) ).

cnf(refute_0_2707,plain,
    multiply(inverse(X_94),inverse(X_219)) = inverse(multiply(X_219,X_94)),
    inference(subst,[],[refute_0_667:[bind(X_198,$fot(X_219)),bind(X_59,$fot(X_94))]]) ).

cnf(refute_0_2708,plain,
    least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))) = least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))]]) ).

cnf(refute_0_2709,plain,
    ( multiply(inverse(X_94),inverse(X_219)) != inverse(multiply(X_219,X_94))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))) != least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))) = least_upper_bound(identity,inverse(multiply(X_219,X_94))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))),least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) ),[1,1],$fot(inverse(multiply(X_219,X_94)))]]) ).

cnf(refute_0_2710,plain,
    ( multiply(inverse(X_94),inverse(X_219)) != inverse(multiply(X_219,X_94))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))) = least_upper_bound(identity,inverse(multiply(X_219,X_94))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))),least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) )],[refute_0_2708,refute_0_2709]) ).

cnf(refute_0_2711,plain,
    least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))) = least_upper_bound(identity,inverse(multiply(X_219,X_94))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),inverse(X_219)),inverse(multiply(X_219,X_94))) )],[refute_0_2707,refute_0_2710]) ).

cnf(refute_0_2712,plain,
    ( least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))) != least_upper_bound(identity,inverse(multiply(X_219,X_94)))
    | least_upper_bound(identity,inverse(multiply(X_219,X_94))) != inverse(greatest_lower_bound(identity,multiply(X_219,X_94)))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))) = inverse(greatest_lower_bound(identity,multiply(X_219,X_94))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(X_219,X_94))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(X_219,X_94)))))]]) ).

cnf(refute_0_2713,plain,
    ( least_upper_bound(identity,inverse(multiply(X_219,X_94))) != inverse(greatest_lower_bound(identity,multiply(X_219,X_94)))
    | least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))) = inverse(greatest_lower_bound(identity,multiply(X_219,X_94))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))),least_upper_bound(identity,inverse(multiply(X_219,X_94)))) )],[refute_0_2711,refute_0_2712]) ).

cnf(refute_0_2714,plain,
    least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))) = inverse(greatest_lower_bound(identity,multiply(X_219,X_94))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_219,X_94))),inverse(greatest_lower_bound(identity,multiply(X_219,X_94)))) )],[refute_0_2706,refute_0_2713]) ).

cnf(refute_0_2715,plain,
    least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) = least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(multiply(inverse(X_94),inverse(X_219)))),bind(X_31,$fot(identity))]]) ).

cnf(refute_0_2716,plain,
    ( least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))) != inverse(greatest_lower_bound(identity,multiply(X_219,X_94)))
    | least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) != least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))
    | least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) = inverse(greatest_lower_bound(identity,multiply(X_219,X_94))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(X_219,X_94)))))]]) ).

cnf(refute_0_2717,plain,
    ( least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))) != inverse(greatest_lower_bound(identity,multiply(X_219,X_94)))
    | least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) = inverse(greatest_lower_bound(identity,multiply(X_219,X_94))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))),least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) )],[refute_0_2715,refute_0_2716]) ).

cnf(refute_0_2718,plain,
    least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) = inverse(greatest_lower_bound(identity,multiply(X_219,X_94))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))),inverse(greatest_lower_bound(identity,multiply(X_219,X_94)))) )],[refute_0_2714,refute_0_2717]) ).

cnf(refute_0_2719,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))
    | least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))) != inverse(greatest_lower_bound(identity,multiply(X_219,X_94)))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))) = inverse(greatest_lower_bound(identity,multiply(X_219,X_94))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))),inverse(greatest_lower_bound(identity,multiply(X_219,X_94)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))))]]) ).

cnf(refute_0_2720,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))) = inverse(greatest_lower_bound(identity,multiply(X_219,X_94))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219)))),inverse(greatest_lower_bound(identity,multiply(X_219,X_94)))) )],[refute_0_2718,refute_0_2719]) ).

cnf(refute_0_2721,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))) = inverse(greatest_lower_bound(identity,multiply(X_219,X_94))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))) )],[refute_0_2705,refute_0_2720]) ).

cnf(refute_0_2722,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_219))) = inverse(greatest_lower_bound(identity,multiply(X_219,X_94))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(greatest_lower_bound(inverse(X_94),X_219)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(X_94),inverse(X_219))))) )],[refute_0_2686,refute_0_2721]) ).

cnf(refute_0_2723,plain,
    multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))) = inverse(greatest_lower_bound(identity,multiply(X_278,X_94))),
    inference(subst,[],[refute_0_2722:[bind(X_219,$fot(X_278))]]) ).

cnf(refute_0_2724,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))) != multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278))
    | multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))) != inverse(greatest_lower_bound(identity,multiply(X_278,X_94)))
    | inverse(greatest_lower_bound(identity,multiply(X_278,X_94))) = multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))),multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(X_278,X_94))))]]) ).

cnf(refute_0_2725,plain,
    ( multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))) != multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278))
    | inverse(greatest_lower_bound(identity,multiply(X_278,X_94))) = multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))),inverse(greatest_lower_bound(identity,multiply(X_278,X_94)))) )],[refute_0_2723,refute_0_2724]) ).

cnf(refute_0_2726,plain,
    inverse(greatest_lower_bound(identity,multiply(X_278,X_94))) = multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_94),least_upper_bound(X_94,inverse(X_278))),multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278))) )],[refute_0_2681,refute_0_2725]) ).

cnf(refute_0_2727,plain,
    ( inverse(greatest_lower_bound(identity,multiply(X_278,X_94))) != multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278))
    | multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)) = inverse(greatest_lower_bound(identity,multiply(X_278,X_94))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(X_278,X_94))))),bind(Y0,$fot(multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278))))]]) ).

cnf(refute_0_2728,plain,
    multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278)) = inverse(greatest_lower_bound(identity,multiply(X_278,X_94))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_278,X_94))),multiply(least_upper_bound(X_278,inverse(X_94)),inverse(X_278))) )],[refute_0_2726,refute_0_2727]) ).

cnf(refute_0_2729,plain,
    multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b)) = inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),
    inference(subst,[],[refute_0_2728:[bind(X_278,$fot(b)),bind(X_94,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2730,plain,
    least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))) = multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b)),
    inference(subst,[],[refute_0_448:[bind(Y,$fot(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),bind(X_132,$fot(b))]]) ).

cnf(refute_0_2731,plain,
    ( multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b)) != inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))
    | least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))) != multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b))
    | least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))) = inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))))),bind(Y0,$fot(multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b)))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))))]]) ).

cnf(refute_0_2732,plain,
    ( multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b)) != inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))
    | least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))) = inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))),multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b))) )],[refute_0_2730,refute_0_2731]) ).

cnf(refute_0_2733,plain,
    least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))) = inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(b)),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) )],[refute_0_2729,refute_0_2732]) ).

cnf(refute_0_2734,plain,
    ( inverse(greatest_lower_bound(b,identity)) != least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))
    | least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))) != inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))
    | inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))))]]) ).

cnf(refute_0_2735,plain,
    ( inverse(greatest_lower_bound(b,identity)) != least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))
    | inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b))),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) )],[refute_0_2733,refute_0_2734]) ).

cnf(refute_0_2736,plain,
    ( multiply(least_upper_bound(b,identity),inverse(b)) != least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))
    | inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,identity)),least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))) )],[refute_0_2674,refute_0_2735]) ).

cnf(refute_0_2737,plain,
    inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(b)),least_upper_bound(identity,multiply(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(b)))) )],[refute_0_2663,refute_0_2736]) ).

cnf(refute_0_2738,plain,
    ( inverse(greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))
    | inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = inverse(greatest_lower_bound(b,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(b,identity)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))))]]) ).

cnf(refute_0_2739,plain,
    inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = inverse(greatest_lower_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) )],[refute_0_2737,refute_0_2738]) ).

cnf(refute_0_2740,plain,
    ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != identity
    | inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(b,identity))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),identity) ),[0,1,0],$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2741,plain,
    ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != identity
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = identity ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2739,refute_0_2740]) ).

cnf(refute_0_2742,plain,
    greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = identity,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),identity) )],[refute_0_2348,refute_0_2741]) ).

cnf(refute_0_2743,plain,
    multiply(multiply(inverse(greatest_lower_bound(Y,identity)),Y),Z) = multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(greatest_lower_bound(Y,identity))))]]) ).

cnf(refute_0_2744,plain,
    multiply(inverse(greatest_lower_bound(identity,X_117)),X_117) = least_upper_bound(X_117,identity),
    inference(subst,[],[refute_0_1664:[bind(X_113,$fot(X_117))]]) ).

cnf(refute_0_2745,plain,
    greatest_lower_bound(X_117,identity) = greatest_lower_bound(identity,X_117),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_117)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_2746,plain,
    ( greatest_lower_bound(X_117,identity) != greatest_lower_bound(identity,X_117)
    | greatest_lower_bound(identity,X_117) = greatest_lower_bound(X_117,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_117,identity))),bind(Y0,$fot(greatest_lower_bound(identity,X_117)))]]) ).

cnf(refute_0_2747,plain,
    greatest_lower_bound(identity,X_117) = greatest_lower_bound(X_117,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_117,identity),greatest_lower_bound(identity,X_117)) )],[refute_0_2745,refute_0_2746]) ).

cnf(refute_0_2748,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_117)),X_117) != least_upper_bound(X_117,identity)
    | greatest_lower_bound(identity,X_117) != greatest_lower_bound(X_117,identity)
    | multiply(inverse(greatest_lower_bound(X_117,identity)),X_117) = least_upper_bound(X_117,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_117)),X_117),least_upper_bound(X_117,identity)) ),[0,0,0],$fot(greatest_lower_bound(X_117,identity))]]) ).

cnf(refute_0_2749,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_117)),X_117) != least_upper_bound(X_117,identity)
    | multiply(inverse(greatest_lower_bound(X_117,identity)),X_117) = least_upper_bound(X_117,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_117),greatest_lower_bound(X_117,identity)) )],[refute_0_2747,refute_0_2748]) ).

cnf(refute_0_2750,plain,
    multiply(inverse(greatest_lower_bound(X_117,identity)),X_117) = least_upper_bound(X_117,identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_117)),X_117),least_upper_bound(X_117,identity)) )],[refute_0_2744,refute_0_2749]) ).

cnf(refute_0_2751,plain,
    multiply(inverse(greatest_lower_bound(Y,identity)),Y) = least_upper_bound(Y,identity),
    inference(subst,[],[refute_0_2750:[bind(X_117,$fot(Y))]]) ).

cnf(refute_0_2752,plain,
    ( multiply(multiply(inverse(greatest_lower_bound(Y,identity)),Y),Z) != multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z))
    | multiply(inverse(greatest_lower_bound(Y,identity)),Y) != least_upper_bound(Y,identity)
    | multiply(least_upper_bound(Y,identity),Z) = multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(greatest_lower_bound(Y,identity)),Y),Z),multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z))) ),[0,0],$fot(least_upper_bound(Y,identity))]]) ).

cnf(refute_0_2753,plain,
    ( multiply(multiply(inverse(greatest_lower_bound(Y,identity)),Y),Z) != multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z))
    | multiply(least_upper_bound(Y,identity),Z) = multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,identity)),Y),least_upper_bound(Y,identity)) )],[refute_0_2751,refute_0_2752]) ).

cnf(refute_0_2754,plain,
    multiply(least_upper_bound(Y,identity),Z) = multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(greatest_lower_bound(Y,identity)),Y),Z),multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z))) )],[refute_0_2743,refute_0_2753]) ).

cnf(refute_0_2755,plain,
    ( multiply(least_upper_bound(Y,identity),Z) != multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z))
    | multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z)) = multiply(least_upper_bound(Y,identity),Z) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(Y,identity),Z))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z))))]]) ).

cnf(refute_0_2756,plain,
    multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z)) = multiply(least_upper_bound(Y,identity),Z),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,identity),Z),multiply(inverse(greatest_lower_bound(Y,identity)),multiply(Y,Z))) )],[refute_0_2754,refute_0_2755]) ).

cnf(refute_0_2757,plain,
    multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_2756:[bind(Y,$fot(b)),bind(Z,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2758,plain,
    greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_2759,plain,
    ( multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) ),[1,1],$fot(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2760,plain,
    ( multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) )],[refute_0_2758,refute_0_2759]) ).

cnf(refute_0_2761,plain,
    greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) )],[refute_0_2757,refute_0_2760]) ).

cnf(refute_0_2762,plain,
    ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != identity
    | greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2763,plain,
    ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != identity
    | greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2761,refute_0_2762]) ).

cnf(refute_0_2764,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = identity,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),identity) )],[refute_0_2742,refute_0_2763]) ).

cnf(refute_0_2765,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))
    | greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != identity
    | greatest_lower_bound(X,identity) = greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_2766,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))
    | greatest_lower_bound(X,identity) = greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),identity) )],[refute_0_2764,refute_0_2765]) ).

cnf(refute_0_2767,plain,
    greatest_lower_bound(X,identity) = greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))) )],[refute_0_2319,refute_0_2766]) ).

cnf(refute_0_2768,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) = greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_38),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(least_upper_bound(X_36,Y))),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_2769,plain,
    greatest_lower_bound(X_36,least_upper_bound(X_36,Y)) = X_36,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_36))]]) ).

cnf(refute_0_2770,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_38)
    | greatest_lower_bound(X_36,least_upper_bound(X_36,Y)) != X_36
    | greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) = greatest_lower_bound(X_36,X_38) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)),greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_38)) ),[1,0],$fot(X_36)]]) ).

cnf(refute_0_2771,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_38)
    | greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) = greatest_lower_bound(X_36,X_38) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_36) )],[refute_0_2769,refute_0_2770]) ).

cnf(refute_0_2772,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) = greatest_lower_bound(X_36,X_38),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)),greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_38)) )],[refute_0_2768,refute_0_2771]) ).

cnf(refute_0_2773,plain,
    greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X)) = greatest_lower_bound(identity,X),
    inference(subst,[],[refute_0_2772:[bind(Y,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))),bind(X_36,$fot(identity)),bind(X_38,$fot(X))]]) ).

cnf(refute_0_2774,plain,
    multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))),
    inference(subst,[],[refute_0_258:[bind(X,$fot(inverse(greatest_lower_bound(a,identity)))),bind(X_96,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2775,plain,
    greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) = greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))),
    inference(subst,[],[refute_0_625:[bind(X_204,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2776,plain,
    ( greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) != greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))
    | inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(b,identity))
    | greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) = greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))) ),[1,1],$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2777,plain,
    ( greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) != greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))
    | greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) = greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2739,refute_0_2776]) ).

cnf(refute_0_2778,plain,
    greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) = greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))) )],[refute_0_2775,refute_0_2777]) ).

cnf(refute_0_2779,plain,
    inverse(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) = greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_2780,plain,
    ( inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(b,identity))
    | inverse(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) != greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | inverse(inverse(greatest_lower_bound(b,identity))) = greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))),greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),[0,0],$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2781,plain,
    ( inverse(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) != greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | inverse(inverse(greatest_lower_bound(b,identity))) = greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2739,refute_0_2780]) ).

cnf(refute_0_2782,plain,
    inverse(inverse(greatest_lower_bound(b,identity))) = greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))),greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2779,refute_0_2781]) ).

cnf(refute_0_2783,plain,
    ( inverse(inverse(greatest_lower_bound(b,identity))) != greatest_lower_bound(b,identity)
    | inverse(inverse(greatest_lower_bound(b,identity))) != greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(b,identity))),greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).

cnf(refute_0_2784,plain,
    ( inverse(inverse(greatest_lower_bound(b,identity))) != greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(b,identity))),greatest_lower_bound(b,identity)) )],[refute_0_2487,refute_0_2783]) ).

cnf(refute_0_2785,plain,
    greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(b,identity))),greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2782,refute_0_2784]) ).

cnf(refute_0_2786,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(b,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(b,identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_2787,plain,
    greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(b,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2785,refute_0_2786]) ).

cnf(refute_0_2788,plain,
    greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) = greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_1353:[bind(X_60,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2789,plain,
    ( greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) != greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != greatest_lower_bound(b,identity)
    | greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) = greatest_lower_bound(b,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))),bind(Z0,$fot(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2790,plain,
    ( greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != greatest_lower_bound(b,identity)
    | greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) = greatest_lower_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2788,refute_0_2789]) ).

cnf(refute_0_2791,plain,
    greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) = greatest_lower_bound(b,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),greatest_lower_bound(b,identity)) )],[refute_0_2787,refute_0_2790]) ).

cnf(refute_0_2792,plain,
    ( greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) != greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity)))
    | greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) != greatest_lower_bound(b,identity)
    | greatest_lower_bound(b,identity) = greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity)))) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).

cnf(refute_0_2793,plain,
    ( greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) != greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity)))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),greatest_lower_bound(b,identity)) )],[refute_0_2791,refute_0_2792]) ).

cnf(refute_0_2794,plain,
    greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),bind(X_25,$fot(inverse(greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_2795,plain,
    ( greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) != greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(b,identity) != greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity)))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity)))) ),[1],$fot(greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2796,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity)))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))),greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2794,refute_0_2795]) ).

cnf(refute_0_2797,plain,
    ( greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) != greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity)))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity)))) )],[refute_0_2793,refute_0_2796]) ).

cnf(refute_0_2798,plain,
    greatest_lower_bound(b,identity) = greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity)))) )],[refute_0_2778,refute_0_2797]) ).

cnf(refute_0_2799,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2800,plain,
    ( greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | inverse(greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(a,identity))
    | greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),[1,0],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_2801,plain,
    ( inverse(greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(a,identity))
    | greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2799,refute_0_2800]) ).

cnf(refute_0_2802,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2216,refute_0_2801]) ).

cnf(refute_0_2803,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),[0],$fot(greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2804,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2802,refute_0_2803]) ).

cnf(refute_0_2805,plain,
    greatest_lower_bound(b,identity) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(inverse(greatest_lower_bound(b,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2798,refute_0_2804]) ).

cnf(refute_0_2806,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(b,identity) != greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(a,identity) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),[0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_2807,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(a,identity) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(a,identity)) )],[refute_0_2212,refute_0_2806]) ).

cnf(refute_0_2808,plain,
    greatest_lower_bound(a,identity) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2805,refute_0_2807]) ).

cnf(refute_0_2809,plain,
    ( greatest_lower_bound(a,identity) != greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(a,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(a,identity))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_2810,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_2808,refute_0_2809]) ).

cnf(refute_0_2811,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))
    | greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != greatest_lower_bound(a,identity)
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))) ),[0,1,0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_2812,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),greatest_lower_bound(a,identity)) )],[refute_0_2810,refute_0_2811]) ).

cnf(refute_0_2813,plain,
    multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_2774,refute_0_2812]) ).

cnf(refute_0_2814,plain,
    multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))),
    inference(subst,[],[refute_0_258:[bind(X,$fot(identity)),bind(X_96,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_2815,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))
    | inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(b,identity))
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))) ),[0,1],$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2816,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2739,refute_0_2815]) ).

cnf(refute_0_2817,plain,
    multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))) )],[refute_0_2814,refute_0_2816]) ).

cnf(refute_0_2818,plain,
    inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,X_37))) = inverse(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13)),
    inference(subst,[],[refute_0_140:[bind(X_12,$fot(greatest_lower_bound(X_36,X_37)))]]) ).

cnf(refute_0_2819,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_13))]]) ).

cnf(refute_0_2820,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13)
    | greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13)))]]) ).

cnf(refute_0_2821,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13)) )],[refute_0_2819,refute_0_2820]) ).

cnf(refute_0_2822,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13))
    | inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,X_37))) != inverse(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13))
    | inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,X_37))) = inverse(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,X_37))),inverse(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13))) ),[1,0],$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13)))]]) ).

cnf(refute_0_2823,plain,
    ( inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,X_37))) != inverse(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13))
    | inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,X_37))) = inverse(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13))) )],[refute_0_2821,refute_0_2822]) ).

cnf(refute_0_2824,plain,
    inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,X_37))) = inverse(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_13))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,X_37))),inverse(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_13))) )],[refute_0_2818,refute_0_2823]) ).

cnf(refute_0_2825,plain,
    inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) = inverse(greatest_lower_bound(X_36,greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_2824:[bind(X_13,$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))),bind(X_37,$fot(inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2826,plain,
    greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))) = greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)),
    inference(subst,[],[refute_0_794:[bind(Y,$fot(inverse(b))),bind(X_23,$fot(least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2827,plain,
    ( greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) != inverse(least_upper_bound(b,identity))
    | greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))) != greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))
    | greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(least_upper_bound(b,identity))) = greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))) ),[0,1],$fot(inverse(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2828,plain,
    ( greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))) != greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))
    | greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(least_upper_bound(b,identity))) = greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(least_upper_bound(b,identity))) )],[refute_0_2483,refute_0_2827]) ).

cnf(refute_0_2829,plain,
    greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(least_upper_bound(b,identity))) = greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))) )],[refute_0_2826,refute_0_2828]) ).

cnf(refute_0_2830,plain,
    greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(least_upper_bound(b,identity))) = greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))),bind(X_25,$fot(inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2831,plain,
    ( greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(least_upper_bound(b,identity))) != greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c)))
    | greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(least_upper_bound(b,identity))) != greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))
    | greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(least_upper_bound(b,identity))),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))) ),[0],$fot(greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_2832,plain,
    ( greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(least_upper_bound(b,identity))) != greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))
    | greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))) = greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(least_upper_bound(b,identity))),greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c)))) )],[refute_0_2830,refute_0_2831]) ).

cnf(refute_0_2833,plain,
    greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)) = greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))),bind(X_25,$fot(inverse(b)))]]) ).

cnf(refute_0_2834,plain,
    ( greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) != inverse(least_upper_bound(b,identity))
    | greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)) != greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))
    | greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)) = inverse(least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)))),bind(Y0,$fot(greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))))),bind(Z0,$fot(inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2835,plain,
    ( greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))) != inverse(least_upper_bound(b,identity))
    | greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)) = inverse(least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)),greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c)))) )],[refute_0_2833,refute_0_2834]) ).

cnf(refute_0_2836,plain,
    greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)) = inverse(least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(b),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(least_upper_bound(b,identity))) )],[refute_0_2483,refute_0_2835]) ).

cnf(refute_0_2837,plain,
    ( greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))) != greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))
    | greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)) != inverse(least_upper_bound(b,identity))
    | greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))) = inverse(least_upper_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(least_upper_bound(b,identity))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)))]]) ).

cnf(refute_0_2838,plain,
    ( greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))) != greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))
    | greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))) = inverse(least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b)),inverse(least_upper_bound(b,identity))) )],[refute_0_2836,refute_0_2837]) ).

cnf(refute_0_2839,plain,
    ( greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(least_upper_bound(b,identity))) != greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))
    | greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))) = inverse(least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))) )],[refute_0_2832,refute_0_2838]) ).

cnf(refute_0_2840,plain,
    greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))) = inverse(least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(least_upper_bound(b,identity))),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(b))) )],[refute_0_2829,refute_0_2839]) ).

cnf(refute_0_2841,plain,
    ( greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))) != inverse(least_upper_bound(b,identity))
    | inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(X_36,greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) = inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))),inverse(greatest_lower_bound(X_36,greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),[1,0,1],$fot(inverse(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2842,plain,
    ( inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(X_36,greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) = inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(least_upper_bound(b,identity))) )],[refute_0_2840,refute_0_2841]) ).

cnf(refute_0_2843,plain,
    inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) = inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))),inverse(greatest_lower_bound(X_36,greatest_lower_bound(inverse(least_upper_bound(b,identity)),least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_2825,refute_0_2842]) ).

cnf(refute_0_2844,plain,
    greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)) = greatest_lower_bound(X_76,greatest_lower_bound(X_77,least_upper_bound(X_77,Y))),
    inference(subst,[],[refute_0_839:[bind(X,$fot(least_upper_bound(X_77,Y))),bind(X_36,$fot(X_76)),bind(X_37,$fot(X_77))]]) ).

cnf(refute_0_2845,plain,
    greatest_lower_bound(X_77,least_upper_bound(X_77,Y)) = X_77,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_77))]]) ).

cnf(refute_0_2846,plain,
    ( greatest_lower_bound(X_77,least_upper_bound(X_77,Y)) != X_77
    | greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)) != greatest_lower_bound(X_76,greatest_lower_bound(X_77,least_upper_bound(X_77,Y)))
    | greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)) = greatest_lower_bound(X_76,X_77) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)),greatest_lower_bound(X_76,greatest_lower_bound(X_77,least_upper_bound(X_77,Y)))) ),[1,1],$fot(X_77)]]) ).

cnf(refute_0_2847,plain,
    ( greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)) != greatest_lower_bound(X_76,greatest_lower_bound(X_77,least_upper_bound(X_77,Y)))
    | greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)) = greatest_lower_bound(X_76,X_77) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_77,least_upper_bound(X_77,Y)),X_77) )],[refute_0_2845,refute_0_2846]) ).

cnf(refute_0_2848,plain,
    greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)) = greatest_lower_bound(X_76,X_77),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)),greatest_lower_bound(X_76,greatest_lower_bound(X_77,least_upper_bound(X_77,Y)))) )],[refute_0_2844,refute_0_2847]) ).

cnf(refute_0_2849,plain,
    greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)) = greatest_lower_bound(X_77,greatest_lower_bound(X_76,least_upper_bound(X_77,Y))),
    inference(subst,[],[refute_0_909:[bind(Y,$fot(least_upper_bound(X_77,Y))),bind(X_75,$fot(X_77))]]) ).

cnf(refute_0_2850,plain,
    ( greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)) != greatest_lower_bound(X_76,X_77)
    | greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)) != greatest_lower_bound(X_77,greatest_lower_bound(X_76,least_upper_bound(X_77,Y)))
    | greatest_lower_bound(X_77,greatest_lower_bound(X_76,least_upper_bound(X_77,Y))) = greatest_lower_bound(X_76,X_77) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)),greatest_lower_bound(X_76,X_77)) ),[0],$fot(greatest_lower_bound(X_77,greatest_lower_bound(X_76,least_upper_bound(X_77,Y))))]]) ).

cnf(refute_0_2851,plain,
    ( greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)) != greatest_lower_bound(X_76,X_77)
    | greatest_lower_bound(X_77,greatest_lower_bound(X_76,least_upper_bound(X_77,Y))) = greatest_lower_bound(X_76,X_77) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)),greatest_lower_bound(X_77,greatest_lower_bound(X_76,least_upper_bound(X_77,Y)))) )],[refute_0_2849,refute_0_2850]) ).

cnf(refute_0_2852,plain,
    greatest_lower_bound(X_77,greatest_lower_bound(X_76,least_upper_bound(X_77,Y))) = greatest_lower_bound(X_76,X_77),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_77,Y),greatest_lower_bound(X_76,X_77)),greatest_lower_bound(X_76,X_77)) )],[refute_0_2848,refute_0_2851]) ).

cnf(refute_0_2853,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))) = greatest_lower_bound(X_36,identity),
    inference(subst,[],[refute_0_2852:[bind(Y,$fot(greatest_lower_bound(a,c))),bind(X_76,$fot(X_36)),bind(X_77,$fot(identity))]]) ).

cnf(refute_0_2854,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_2855,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))) != greatest_lower_bound(X_36,identity)
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(X_36,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),[1,0],$fot(greatest_lower_bound(X_36,identity))]]) ).

cnf(refute_0_2856,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))) != greatest_lower_bound(X_36,identity)
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(X_36,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_2854,refute_0_2855]) ).

cnf(refute_0_2857,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(X_36,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(X_36,identity)) )],[refute_0_2853,refute_0_2856]) ).

cnf(refute_0_2858,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_2859,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(X_36,identity))
    | least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(X_36,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_36,identity))))]]) ).

cnf(refute_0_2860,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(X_36,identity))
    | least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(X_36,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_2858,refute_0_2859]) ).

cnf(refute_0_2861,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(X_36,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(X_36,identity))) )],[refute_0_2857,refute_0_2860]) ).

cnf(refute_0_2862,plain,
    least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) = least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_2863,plain,
    ( least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) != least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))
    | least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(X_36,identity))
    | least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) = least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))) ),[1,1],$fot(inverse(greatest_lower_bound(X_36,identity)))]]) ).

cnf(refute_0_2864,plain,
    ( least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(X_36,identity))
    | least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) = least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))) )],[refute_0_2862,refute_0_2863]) ).

cnf(refute_0_2865,plain,
    least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) = least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(X_36,identity))) )],[refute_0_2861,refute_0_2864]) ).

cnf(refute_0_2866,plain,
    least_upper_bound(least_upper_bound(b,identity),inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))),
    inference(subst,[],[refute_0_375:[bind(X,$fot(b)),bind(Y,$fot(identity)),bind(Z,$fot(inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_2867,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(least_upper_bound(b,identity),inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_2691:[bind(Y,$fot(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),bind(X_89,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_2868,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(least_upper_bound(b,identity),inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | least_upper_bound(least_upper_bound(b,identity),inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Y0,$fot(least_upper_bound(least_upper_bound(b,identity),inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_2869,plain,
    ( least_upper_bound(least_upper_bound(b,identity),inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(least_upper_bound(b,identity),inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_2867,refute_0_2868]) ).

cnf(refute_0_2870,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,identity),inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))) )],[refute_0_2866,refute_0_2869]) ).

cnf(refute_0_2871,plain,
    inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))),
    inference(subst,[],[refute_0_2824:[bind(X_13,$fot(Y)),bind(X_36,$fot(X_24)),bind(X_37,$fot(X_25))]]) ).

cnf(refute_0_2872,plain,
    ( inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))
    | inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))))),bind(Y0,$fot(inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))))]]) ).

cnf(refute_0_2873,plain,
    inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))) )],[refute_0_2871,refute_0_2872]) ).

cnf(refute_0_2874,plain,
    ( inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) != inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25)))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))) ),[1],$fot(inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))))]]) ).

cnf(refute_0_2875,plain,
    ( inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))),inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25)))) )],[refute_0_2873,refute_0_2874]) ).

cnf(refute_0_2876,plain,
    inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))) )],[refute_0_1013,refute_0_2875]) ).

cnf(refute_0_2877,plain,
    ( inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) != inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25)))
    | inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))) = inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))))),bind(Y0,$fot(inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25)))))]]) ).

cnf(refute_0_2878,plain,
    inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25))) = inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))),inverse(greatest_lower_bound(Y,greatest_lower_bound(X_24,X_25)))) )],[refute_0_2876,refute_0_2877]) ).

cnf(refute_0_2879,plain,
    inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) = inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_2878:[bind(Y,$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))),bind(X_24,$fot(X_36)),bind(X_25,$fot(inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_2880,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))
    | inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) = least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))))),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_2881,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))
    | inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) = least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))),inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_2879,refute_0_2880]) ).

cnf(refute_0_2882,plain,
    inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) = least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))) )],[refute_0_2870,refute_0_2881]) ).

cnf(refute_0_2883,plain,
    ( inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) != least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))
    | least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) != least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity)))
    | inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) = least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))))),bind(Z0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity)))))]]) ).

cnf(refute_0_2884,plain,
    ( least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))) != least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity)))
    | inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) = least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))),least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c))))))) )],[refute_0_2882,refute_0_2883]) ).

cnf(refute_0_2885,plain,
    inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) = least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(X_36,least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity)))) )],[refute_0_2865,refute_0_2884]) ).

cnf(refute_0_2886,plain,
    ( inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))
    | inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) != least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity)))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) = inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))),inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) ),[0],$fot(least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))))]]) ).

cnf(refute_0_2887,plain,
    ( inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) = inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))),least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity)))) )],[refute_0_2885,refute_0_2886]) ).

cnf(refute_0_2888,plain,
    least_upper_bound(identity,inverse(X_36)) = inverse(greatest_lower_bound(identity,X_36)),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(X_36))]]) ).

cnf(refute_0_2889,plain,
    least_upper_bound(b,least_upper_bound(identity,inverse(X_36))) = least_upper_bound(b,least_upper_bound(identity,inverse(X_36))),
    introduced(tautology,[refl,[$fot(least_upper_bound(b,least_upper_bound(identity,inverse(X_36))))]]) ).

cnf(refute_0_2890,plain,
    ( least_upper_bound(b,least_upper_bound(identity,inverse(X_36))) != least_upper_bound(b,least_upper_bound(identity,inverse(X_36)))
    | least_upper_bound(identity,inverse(X_36)) != inverse(greatest_lower_bound(identity,X_36))
    | least_upper_bound(b,least_upper_bound(identity,inverse(X_36))) = least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(X_36))),least_upper_bound(b,least_upper_bound(identity,inverse(X_36)))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,X_36)))]]) ).

cnf(refute_0_2891,plain,
    ( least_upper_bound(identity,inverse(X_36)) != inverse(greatest_lower_bound(identity,X_36))
    | least_upper_bound(b,least_upper_bound(identity,inverse(X_36))) = least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(X_36))),least_upper_bound(b,least_upper_bound(identity,inverse(X_36)))) )],[refute_0_2889,refute_0_2890]) ).

cnf(refute_0_2892,plain,
    least_upper_bound(b,least_upper_bound(identity,inverse(X_36))) = least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_36)),inverse(greatest_lower_bound(identity,X_36))) )],[refute_0_2888,refute_0_2891]) ).

cnf(refute_0_2893,plain,
    least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) = least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)))),
    inference(subst,[],[refute_0_1084:[bind(Y,$fot(multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))),bind(X_44,$fot(identity))]]) ).

cnf(refute_0_2894,plain,
    multiply(least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))),b) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)),
    inference(subst,[],[refute_0_166:[bind(X_110,$fot(b)),bind(X_112,$fot(greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).

cnf(refute_0_2895,plain,
    inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) = inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))),
    inference(subst,[],[refute_0_140:[bind(X_12,$fot(b)),bind(X_13,$fot(inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))))]]) ).

cnf(refute_0_2896,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_38)) = greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_38),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(least_upper_bound(a,c))),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_2897,plain,
    greatest_lower_bound(b,least_upper_bound(b,c)) = b,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).

cnf(refute_0_2898,plain,
    ( greatest_lower_bound(b,least_upper_bound(b,c)) != b
    | least_upper_bound(b,c) != least_upper_bound(a,c)
    | greatest_lower_bound(b,least_upper_bound(a,c)) = b ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,c)),b) ),[0,1],$fot(least_upper_bound(a,c))]]) ).

cnf(refute_0_2899,plain,
    ( greatest_lower_bound(b,least_upper_bound(b,c)) != b
    | greatest_lower_bound(b,least_upper_bound(a,c)) = b ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,c),least_upper_bound(a,c)) )],[refute_0_173,refute_0_2898]) ).

cnf(refute_0_2900,plain,
    greatest_lower_bound(b,least_upper_bound(a,c)) = b,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(b,c)),b) )],[refute_0_2897,refute_0_2899]) ).

cnf(refute_0_2901,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_38)) != greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_38)
    | greatest_lower_bound(b,least_upper_bound(a,c)) != b
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_38)) = greatest_lower_bound(b,X_38) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_38)),greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_38)) ),[1,0],$fot(b)]]) ).

cnf(refute_0_2902,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_38)) != greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_38)
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_38)) = greatest_lower_bound(b,X_38) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,c)),b) )],[refute_0_2900,refute_0_2901]) ).

cnf(refute_0_2903,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_38)) = greatest_lower_bound(b,X_38),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_38)),greatest_lower_bound(greatest_lower_bound(b,least_upper_bound(a,c)),X_38)) )],[refute_0_2896,refute_0_2902]) ).

cnf(refute_0_2904,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))) = greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))),
    inference(subst,[],[refute_0_2903:[bind(X_38,$fot(inverse(greatest_lower_bound(least_upper_bound(a,c),identity))))]]) ).

cnf(refute_0_2905,plain,
    greatest_lower_bound(least_upper_bound(a,c),identity) = greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity))),
    inference(subst,[],[refute_0_1929:[bind(X_204,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_2906,plain,
    ( greatest_lower_bound(least_upper_bound(a,c),identity) != greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))
    | greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) = greatest_lower_bound(least_upper_bound(a,c),identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(a,c),identity))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))))]]) ).

cnf(refute_0_2907,plain,
    greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) = greatest_lower_bound(least_upper_bound(a,c),identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),identity),greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))) )],[refute_0_2905,refute_0_2906]) ).

cnf(refute_0_2908,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))) != greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))
    | greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) != greatest_lower_bound(least_upper_bound(a,c),identity)
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) = greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))),greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))) ),[0,1],$fot(greatest_lower_bound(least_upper_bound(a,c),identity))]]) ).

cnf(refute_0_2909,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))) != greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) = greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity))),greatest_lower_bound(least_upper_bound(a,c),identity)) )],[refute_0_2907,refute_0_2908]) ).

cnf(refute_0_2910,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) = greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))),greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))) )],[refute_0_2904,refute_0_2909]) ).

cnf(refute_0_2911,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b),
    inference(subst,[],[refute_0_794:[bind(Y,$fot(b)),bind(X_23,$fot(greatest_lower_bound(least_upper_bound(a,c),X_39)))]]) ).

cnf(refute_0_2912,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39)) = greatest_lower_bound(b,X_39),
    inference(subst,[],[refute_0_2903:[bind(X_38,$fot(X_39))]]) ).

cnf(refute_0_2913,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39)) != greatest_lower_bound(b,X_39)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)) ),[0,1],$fot(greatest_lower_bound(b,X_39))]]) ).

cnf(refute_0_2914,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39)),greatest_lower_bound(b,X_39)) )],[refute_0_2912,refute_0_2913]) ).

cnf(refute_0_2915,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)) )],[refute_0_2911,refute_0_2914]) ).

cnf(refute_0_2916,plain,
    greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)) = greatest_lower_bound(X_39,least_upper_bound(a,c)),
    inference(subst,[],[refute_0_794:[bind(Y,$fot(least_upper_bound(a,c))),bind(X_23,$fot(X_39))]]) ).

cnf(refute_0_2917,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))) = greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))))]]) ).

cnf(refute_0_2918,plain,
    ( greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)) != greatest_lower_bound(X_39,least_upper_bound(a,c))
    | greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))) != greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)))
    | greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))) = greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))),greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)))) ),[1,1],$fot(greatest_lower_bound(X_39,least_upper_bound(a,c)))]]) ).

cnf(refute_0_2919,plain,
    ( greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)) != greatest_lower_bound(X_39,least_upper_bound(a,c))
    | greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))) = greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))),greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)))) )],[refute_0_2917,refute_0_2918]) ).

cnf(refute_0_2920,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))) = greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)),greatest_lower_bound(X_39,least_upper_bound(a,c))) )],[refute_0_2916,refute_0_2919]) ).

cnf(refute_0_2921,plain,
    greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),X_39)) = greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))),
    inference(subst,[],[refute_0_1452:[bind(X_36,$fot(b)),bind(X_37,$fot(greatest_lower_bound(least_upper_bound(a,c),X_39))),bind(X_38,$fot(X_39))]]) ).

cnf(refute_0_2922,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) = greatest_lower_bound(greatest_lower_bound(X_36,greatest_lower_bound(Y,X_36)),X_38),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(greatest_lower_bound(Y,X_36))),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_2923,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(Y,X_36)) = greatest_lower_bound(X_36,Y),
    inference(subst,[],[refute_0_794:[bind(X_23,$fot(X_36))]]) ).

cnf(refute_0_2924,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(Y,X_36)) != greatest_lower_bound(X_36,Y)
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,greatest_lower_bound(Y,X_36)),X_38)
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) = greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)),greatest_lower_bound(greatest_lower_bound(X_36,greatest_lower_bound(Y,X_36)),X_38)) ),[1,0],$fot(greatest_lower_bound(X_36,Y))]]) ).

cnf(refute_0_2925,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,greatest_lower_bound(Y,X_36)),X_38)
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) = greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(Y,X_36)),greatest_lower_bound(X_36,Y)) )],[refute_0_2923,refute_0_2924]) ).

cnf(refute_0_2926,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) = greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)),greatest_lower_bound(greatest_lower_bound(X_36,greatest_lower_bound(Y,X_36)),X_38)) )],[refute_0_2922,refute_0_2925]) ).

cnf(refute_0_2927,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))) = greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)),
    inference(subst,[],[refute_0_895:[bind(Y,$fot(X_38)),bind(X_36,$fot(Y)),bind(X_37,$fot(X_36))]]) ).

cnf(refute_0_2928,plain,
    greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38) = greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(Y)),bind(Y,$fot(X_36)),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_2929,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) = greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)))]]) ).

cnf(refute_0_2930,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) != greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38))
    | greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38) != greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) = greatest_lower_bound(X_36,greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)),greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)))]]) ).

cnf(refute_0_2931,plain,
    ( greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38) != greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) = greatest_lower_bound(X_36,greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)),greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38))) )],[refute_0_2929,refute_0_2930]) ).

cnf(refute_0_2932,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) = greatest_lower_bound(X_36,greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38),greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))) )],[refute_0_2928,refute_0_2931]) ).

cnf(refute_0_2933,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))) != greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) != greatest_lower_bound(X_36,greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)))
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) = greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)))),bind(Y0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))))]]) ).

cnf(refute_0_2934,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))) != greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) = greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)),greatest_lower_bound(X_36,greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)))) )],[refute_0_2932,refute_0_2933]) ).

cnf(refute_0_2935,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) = greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))),greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))) )],[refute_0_2927,refute_0_2934]) ).

cnf(refute_0_2936,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) != greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))
    | greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38)
    | greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) = greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)),greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38)) ),[0],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)))]]) ).

cnf(refute_0_2937,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38)
    | greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) = greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)),greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38))) )],[refute_0_2935,refute_0_2936]) ).

cnf(refute_0_2938,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38) = greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_36)),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_2939,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38)
    | greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38) != greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38))
    | greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) = greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)),greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38))]]) ).

cnf(refute_0_2940,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38)
    | greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) = greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38),greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38))) )],[refute_0_2938,refute_0_2939]) ).

cnf(refute_0_2941,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38)
    | greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) = greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)),greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38)) )],[refute_0_2937,refute_0_2940]) ).

cnf(refute_0_2942,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) = greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(greatest_lower_bound(Y,X_36),X_38)),greatest_lower_bound(greatest_lower_bound(X_36,Y),X_38)) )],[refute_0_2926,refute_0_2941]) ).

cnf(refute_0_2943,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) != greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38))
    | greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38)) = greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)))),bind(Y0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38))))]]) ).

cnf(refute_0_2944,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38)) = greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_36,X_38)),greatest_lower_bound(X_36,greatest_lower_bound(Y,X_38))) )],[refute_0_2942,refute_0_2943]) ).

cnf(refute_0_2945,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) = greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),X_39)),
    inference(subst,[],[refute_0_2944:[bind(Y,$fot(b)),bind(X_36,$fot(greatest_lower_bound(least_upper_bound(a,c),X_39))),bind(X_38,$fot(X_39))]]) ).

cnf(refute_0_2946,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),X_39)) != greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) != greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),X_39))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) = greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),X_39)))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)))))]]) ).

cnf(refute_0_2947,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),X_39)) != greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) = greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)),greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),X_39))) )],[refute_0_2945,refute_0_2946]) ).

cnf(refute_0_2948,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) = greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),X_39)),greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)))) )],[refute_0_2921,refute_0_2947]) ).

cnf(refute_0_2949,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))) != greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) != greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) = greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))))),bind(Z0,$fot(greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c)))))]]) ).

cnf(refute_0_2950,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))) != greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) = greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)),greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39)))) )],[refute_0_2948,refute_0_2949]) ).

cnf(refute_0_2951,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) = greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_39,greatest_lower_bound(least_upper_bound(a,c),X_39))),greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c)))) )],[refute_0_2920,refute_0_2950]) ).

cnf(refute_0_2952,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) != greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c)))
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)) ),[0],$fot(greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))))]]) ).

cnf(refute_0_2953,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)),greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c)))) )],[refute_0_2951,refute_0_2952]) ).

cnf(refute_0_2954,plain,
    greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39)),
    inference(subst,[],[refute_0_886:[bind(X,$fot(b)),bind(X_36,$fot(least_upper_bound(a,c))),bind(X_37,$fot(X_39))]]) ).

cnf(refute_0_2955,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39)) != greatest_lower_bound(b,X_39)
    | greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)) != greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39))
    | greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)) = greatest_lower_bound(b,X_39) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39)))),bind(Z0,$fot(greatest_lower_bound(b,X_39)))]]) ).

cnf(refute_0_2956,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39)) != greatest_lower_bound(b,X_39)
    | greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)) = greatest_lower_bound(b,X_39) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)),greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39))) )],[refute_0_2954,refute_0_2955]) ).

cnf(refute_0_2957,plain,
    greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)) = greatest_lower_bound(b,X_39),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X_39)),greatest_lower_bound(b,X_39)) )],[refute_0_2912,refute_0_2956]) ).

cnf(refute_0_2958,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(least_upper_bound(a,c))),bind(Y,$fot(X_39)),bind(Z,$fot(b))]]) ).

cnf(refute_0_2959,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b) != greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b))
    | greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)) != greatest_lower_bound(b,X_39)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b) = greatest_lower_bound(b,X_39) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)))),bind(Z0,$fot(greatest_lower_bound(b,X_39)))]]) ).

cnf(refute_0_2960,plain,
    ( greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)) != greatest_lower_bound(b,X_39)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b) = greatest_lower_bound(b,X_39) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b),greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b))) )],[refute_0_2958,refute_0_2959]) ).

cnf(refute_0_2961,plain,
    greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b) = greatest_lower_bound(b,X_39),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X_39,b)),greatest_lower_bound(b,X_39)) )],[refute_0_2957,refute_0_2960]) ).

cnf(refute_0_2962,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)
    | greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b) != greatest_lower_bound(b,X_39)
    | greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) = greatest_lower_bound(b,X_39) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))),greatest_lower_bound(b,X_39)) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b))]]) ).

cnf(refute_0_2963,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) = greatest_lower_bound(b,X_39) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b),greatest_lower_bound(b,X_39)) )],[refute_0_2961,refute_0_2962]) ).

cnf(refute_0_2964,plain,
    ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)) != greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)
    | greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) = greatest_lower_bound(b,X_39) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)) )],[refute_0_2953,refute_0_2963]) ).

cnf(refute_0_2965,plain,
    greatest_lower_bound(b,greatest_lower_bound(X_39,least_upper_bound(a,c))) = greatest_lower_bound(b,X_39),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),greatest_lower_bound(b,X_39)),greatest_lower_bound(greatest_lower_bound(least_upper_bound(a,c),X_39),b)) )],[refute_0_2915,refute_0_2964]) ).

cnf(refute_0_2966,plain,
    greatest_lower_bound(b,greatest_lower_bound(identity,least_upper_bound(a,c))) = greatest_lower_bound(b,identity),
    inference(subst,[],[refute_0_2965:[bind(X_39,$fot(identity))]]) ).

cnf(refute_0_2967,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) = greatest_lower_bound(b,greatest_lower_bound(identity,least_upper_bound(a,c))),
    inference(subst,[],[refute_0_1493:[bind(Y,$fot(identity)),bind(X_75,$fot(least_upper_bound(a,c))),bind(X_77,$fot(b))]]) ).

cnf(refute_0_2968,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(identity,least_upper_bound(a,c))) != greatest_lower_bound(b,identity)
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) != greatest_lower_bound(b,greatest_lower_bound(identity,least_upper_bound(a,c)))
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) = greatest_lower_bound(b,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)))),bind(Y0,$fot(greatest_lower_bound(b,greatest_lower_bound(identity,least_upper_bound(a,c))))),bind(Z0,$fot(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2969,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(identity,least_upper_bound(a,c))) != greatest_lower_bound(b,identity)
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) = greatest_lower_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)),greatest_lower_bound(b,greatest_lower_bound(identity,least_upper_bound(a,c)))) )],[refute_0_2967,refute_0_2968]) ).

cnf(refute_0_2970,plain,
    greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) = greatest_lower_bound(b,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,least_upper_bound(a,c))),greatest_lower_bound(b,identity)) )],[refute_0_2966,refute_0_2969]) ).

cnf(refute_0_2971,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) != greatest_lower_bound(b,identity)
    | greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) != greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)),greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).

cnf(refute_0_2972,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) != greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)),greatest_lower_bound(b,identity)) )],[refute_0_2970,refute_0_2971]) ).

cnf(refute_0_2973,plain,
    inverse(greatest_lower_bound(least_upper_bound(a,c),identity)) = inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),
    inference(subst,[],[refute_0_1990:[bind(X_168,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_2974,plain,
    greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) = greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))))]]) ).

cnf(refute_0_2975,plain,
    ( greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) != greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))
    | inverse(greatest_lower_bound(least_upper_bound(a,c),identity)) != inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))
    | greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) = greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))),greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).

cnf(refute_0_2976,plain,
    ( inverse(greatest_lower_bound(least_upper_bound(a,c),identity)) != inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))
    | greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) = greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))),greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))) )],[refute_0_2974,refute_0_2975]) ).

cnf(refute_0_2977,plain,
    greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) = greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(a,c),identity)),inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) )],[refute_0_2973,refute_0_2976]) ).

cnf(refute_0_2978,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))
    | greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))) != greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,identity),greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))) ),[0],$fot(greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))))]]) ).

cnf(refute_0_2979,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity))),greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))) )],[refute_0_2977,refute_0_2978]) ).

cnf(refute_0_2980,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)) != greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))) )],[refute_0_2972,refute_0_2979]) ).

cnf(refute_0_2981,plain,
    greatest_lower_bound(b,identity) = greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),identity)),greatest_lower_bound(b,inverse(greatest_lower_bound(least_upper_bound(a,c),identity)))) )],[refute_0_2910,refute_0_2980]) ).

cnf(refute_0_2982,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))
    | greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) = greatest_lower_bound(b,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(b,identity))),bind(Y0,$fot(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))))]]) ).

cnf(refute_0_2983,plain,
    greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) = greatest_lower_bound(b,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))) )],[refute_0_2981,refute_0_2982]) ).

cnf(refute_0_2984,plain,
    ( greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))) != greatest_lower_bound(b,identity)
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) != inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) = inverse(greatest_lower_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)),inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))))) ),[1,0],$fot(greatest_lower_bound(b,identity))]]) ).

cnf(refute_0_2985,plain,
    ( inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) != inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) = inverse(greatest_lower_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))),greatest_lower_bound(b,identity)) )],[refute_0_2983,refute_0_2984]) ).

cnf(refute_0_2986,plain,
    inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) = inverse(greatest_lower_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)),inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))))) )],[refute_0_2895,refute_0_2985]) ).

cnf(refute_0_2987,plain,
    inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))) = least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))),
    inference(subst,[],[refute_0_1559:[bind(X,$fot(b)),bind(X_89,$fot(greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).

cnf(refute_0_2988,plain,
    ( inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))) != least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c)))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) != inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) = least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)))),bind(Y0,$fot(inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))))),bind(Z0,$fot(least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c)))))]]) ).

cnf(refute_0_2989,plain,
    ( inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))) != least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c)))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) = least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)),inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c)))))) )],[refute_0_2895,refute_0_2988]) ).

cnf(refute_0_2990,plain,
    inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) = least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(identity,least_upper_bound(a,c))))),least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c)))) )],[refute_0_2987,refute_0_2989]) ).

cnf(refute_0_2991,plain,
    ( inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) != inverse(greatest_lower_bound(b,identity))
    | inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) != least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c)))
    | least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))) = inverse(greatest_lower_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)),inverse(greatest_lower_bound(b,identity))) ),[0],$fot(least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))))]]) ).

cnf(refute_0_2992,plain,
    ( inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)) != inverse(greatest_lower_bound(b,identity))
    | least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))) = inverse(greatest_lower_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)),least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c)))) )],[refute_0_2990,refute_0_2991]) ).

cnf(refute_0_2993,plain,
    least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))) = inverse(greatest_lower_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(a,c))),b)),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2986,refute_0_2992]) ).

cnf(refute_0_2994,plain,
    ( multiply(least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))),b) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))
    | least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))) != inverse(greatest_lower_bound(b,identity))
    | multiply(inverse(greatest_lower_bound(b,identity)),b) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))),b),least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) ),[0,0],$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_2995,plain,
    ( multiply(least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))),b) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))
    | multiply(inverse(greatest_lower_bound(b,identity)),b) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2993,refute_0_2994]) ).

cnf(refute_0_2996,plain,
    multiply(inverse(greatest_lower_bound(b,identity)),b) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(b),greatest_lower_bound(identity,least_upper_bound(a,c))),b),least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) )],[refute_0_2894,refute_0_2995]) ).

cnf(refute_0_2997,plain,
    multiply(inverse(greatest_lower_bound(b,identity)),b) = least_upper_bound(b,identity),
    inference(subst,[],[refute_0_2750:[bind(X_117,$fot(b))]]) ).

cnf(refute_0_2998,plain,
    ( multiply(inverse(greatest_lower_bound(b,identity)),b) != least_upper_bound(b,identity)
    | multiply(inverse(greatest_lower_bound(b,identity)),b) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))
    | least_upper_bound(b,identity) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(b,identity)),b),least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) ),[0],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_2999,plain,
    ( multiply(inverse(greatest_lower_bound(b,identity)),b) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))
    | least_upper_bound(b,identity) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(b,identity)),b),least_upper_bound(b,identity)) )],[refute_0_2997,refute_0_2998]) ).

cnf(refute_0_3000,plain,
    least_upper_bound(b,identity) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(b,identity)),b),least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) )],[refute_0_2996,refute_0_2999]) ).

cnf(refute_0_3001,plain,
    ( least_upper_bound(b,identity) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))
    | least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)) = least_upper_bound(b,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(b,identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))))]]) ).

cnf(refute_0_3002,plain,
    least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) )],[refute_0_3000,refute_0_3001]) ).

cnf(refute_0_3003,plain,
    ( least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) != least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))))
    | least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)) != least_upper_bound(b,identity)
    | least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) = least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))),least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))))) ),[1,1,1],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_3004,plain,
    ( least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) != least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))))
    | least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) = least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)),least_upper_bound(b,identity)) )],[refute_0_3002,refute_0_3003]) ).

cnf(refute_0_3005,plain,
    least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) = least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))),least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))))) )],[refute_0_2893,refute_0_3004]) ).

cnf(refute_0_3006,plain,
    least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) = least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))))]]) ).

cnf(refute_0_3007,plain,
    ( least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) != least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)))
    | least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)) != least_upper_bound(b,identity)
    | least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) = least_upper_bound(X_43,least_upper_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))),least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)))) ),[1,1],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_3008,plain,
    ( least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)) != least_upper_bound(b,identity)
    | least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) = least_upper_bound(X_43,least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))),least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)))) )],[refute_0_3006,refute_0_3007]) ).

cnf(refute_0_3009,plain,
    least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) = least_upper_bound(X_43,least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b)),least_upper_bound(b,identity)) )],[refute_0_3002,refute_0_3008]) ).

cnf(refute_0_3010,plain,
    ( least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) != least_upper_bound(X_43,least_upper_bound(b,identity))
    | least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) != least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity)))
    | least_upper_bound(X_43,least_upper_bound(b,identity)) = least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))),least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity)))) ),[0],$fot(least_upper_bound(X_43,least_upper_bound(b,identity)))]]) ).

cnf(refute_0_3011,plain,
    ( least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) != least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity)))
    | least_upper_bound(X_43,least_upper_bound(b,identity)) = least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))),least_upper_bound(X_43,least_upper_bound(b,identity))) )],[refute_0_3009,refute_0_3010]) ).

cnf(refute_0_3012,plain,
    least_upper_bound(identity,least_upper_bound(X_43,identity)) = least_upper_bound(identity,X_43),
    inference(subst,[],[refute_0_426:[bind(Y,$fot(X_43)),bind(X_21,$fot(identity))]]) ).

cnf(refute_0_3013,plain,
    least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))) = least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))),
    introduced(tautology,[refl,[$fot(least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))))]]) ).

cnf(refute_0_3014,plain,
    ( least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))) != least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity)))
    | least_upper_bound(identity,least_upper_bound(X_43,identity)) != least_upper_bound(identity,X_43)
    | least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))) = least_upper_bound(b,least_upper_bound(identity,X_43)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))),least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_43))]]) ).

cnf(refute_0_3015,plain,
    ( least_upper_bound(identity,least_upper_bound(X_43,identity)) != least_upper_bound(identity,X_43)
    | least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))) = least_upper_bound(b,least_upper_bound(identity,X_43)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))),least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity)))) )],[refute_0_3013,refute_0_3014]) ).

cnf(refute_0_3016,plain,
    least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))) = least_upper_bound(b,least_upper_bound(identity,X_43)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_43,identity)),least_upper_bound(identity,X_43)) )],[refute_0_3012,refute_0_3015]) ).

cnf(refute_0_3017,plain,
    least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)) = least_upper_bound(identity,least_upper_bound(X_194,least_upper_bound(Y,X_45))),
    inference(subst,[],[refute_0_1707:[bind(X_192,$fot(X_194)),bind(X_193,$fot(least_upper_bound(Y,X_45)))]]) ).

cnf(refute_0_3018,plain,
    least_upper_bound(Y,least_upper_bound(X_194,X_45)) = least_upper_bound(X_194,least_upper_bound(Y,X_45)),
    inference(subst,[],[refute_0_1102:[bind(X_43,$fot(X_194))]]) ).

cnf(refute_0_3019,plain,
    ( least_upper_bound(Y,least_upper_bound(X_194,X_45)) != least_upper_bound(X_194,least_upper_bound(Y,X_45))
    | least_upper_bound(X_194,least_upper_bound(Y,X_45)) = least_upper_bound(Y,least_upper_bound(X_194,X_45)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_194,X_45)))),bind(Y0,$fot(least_upper_bound(X_194,least_upper_bound(Y,X_45))))]]) ).

cnf(refute_0_3020,plain,
    least_upper_bound(X_194,least_upper_bound(Y,X_45)) = least_upper_bound(Y,least_upper_bound(X_194,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_194,X_45)),least_upper_bound(X_194,least_upper_bound(Y,X_45))) )],[refute_0_3018,refute_0_3019]) ).

cnf(refute_0_3021,plain,
    ( least_upper_bound(X_194,least_upper_bound(Y,X_45)) != least_upper_bound(Y,least_upper_bound(X_194,X_45))
    | least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)) != least_upper_bound(identity,least_upper_bound(X_194,least_upper_bound(Y,X_45)))
    | least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)) = least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)),least_upper_bound(identity,least_upper_bound(X_194,least_upper_bound(Y,X_45)))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_194,X_45)))]]) ).

cnf(refute_0_3022,plain,
    ( least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)) != least_upper_bound(identity,least_upper_bound(X_194,least_upper_bound(Y,X_45)))
    | least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)) = least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_194,least_upper_bound(Y,X_45)),least_upper_bound(Y,least_upper_bound(X_194,X_45))) )],[refute_0_3020,refute_0_3021]) ).

cnf(refute_0_3023,plain,
    least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)) = least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)),least_upper_bound(identity,least_upper_bound(X_194,least_upper_bound(Y,X_45)))) )],[refute_0_3017,refute_0_3022]) ).

cnf(refute_0_3024,plain,
    least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)) = least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45))),
    inference(subst,[],[refute_0_2464:[bind(X_195,$fot(least_upper_bound(Y,X_45)))]]) ).

cnf(refute_0_3025,plain,
    ( least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)) != least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45)))
    | least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)) != least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45)))
    | least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45))) = least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)),least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45)))) ),[0],$fot(least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45))))]]) ).

cnf(refute_0_3026,plain,
    ( least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)) != least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45)))
    | least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45))) = least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)),least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45)))) )],[refute_0_3024,refute_0_3025]) ).

cnf(refute_0_3027,plain,
    least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45))) = least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_194,least_upper_bound(least_upper_bound(Y,X_45),identity)),least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45)))) )],[refute_0_3023,refute_0_3026]) ).

cnf(refute_0_3028,plain,
    ( least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45))) != least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45)))
    | least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45))) = least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45)))))]]) ).

cnf(refute_0_3029,plain,
    least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45))) = least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_194,least_upper_bound(identity,least_upper_bound(Y,X_45))),least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_194,X_45)))) )],[refute_0_3027,refute_0_3028]) ).

cnf(refute_0_3030,plain,
    least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))) = least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))),
    inference(subst,[],[refute_0_3029:[bind(Y,$fot(X_43)),bind(X_194,$fot(b)),bind(X_45,$fot(identity))]]) ).

cnf(refute_0_3031,plain,
    ( least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))) != least_upper_bound(b,least_upper_bound(identity,X_43))
    | least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))) != least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity)))
    | least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))) = least_upper_bound(b,least_upper_bound(identity,X_43)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(identity,X_43))))]]) ).

cnf(refute_0_3032,plain,
    ( least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))) != least_upper_bound(b,least_upper_bound(identity,X_43))
    | least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))) = least_upper_bound(b,least_upper_bound(identity,X_43)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))),least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity)))) )],[refute_0_3030,refute_0_3031]) ).

cnf(refute_0_3033,plain,
    least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))) = least_upper_bound(b,least_upper_bound(identity,X_43)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,least_upper_bound(X_43,identity))),least_upper_bound(b,least_upper_bound(identity,X_43))) )],[refute_0_3016,refute_0_3032]) ).

cnf(refute_0_3034,plain,
    ( least_upper_bound(X_43,least_upper_bound(b,identity)) != least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity)))
    | least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))) != least_upper_bound(b,least_upper_bound(identity,X_43))
    | least_upper_bound(X_43,least_upper_bound(b,identity)) = least_upper_bound(b,least_upper_bound(identity,X_43)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_43,least_upper_bound(b,identity)),least_upper_bound(b,least_upper_bound(identity,X_43))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_3035,plain,
    ( least_upper_bound(X_43,least_upper_bound(b,identity)) != least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity)))
    | least_upper_bound(X_43,least_upper_bound(b,identity)) = least_upper_bound(b,least_upper_bound(identity,X_43)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity))),least_upper_bound(b,least_upper_bound(identity,X_43))) )],[refute_0_3033,refute_0_3034]) ).

cnf(refute_0_3036,plain,
    ( least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))) != least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity)))
    | least_upper_bound(X_43,least_upper_bound(b,identity)) = least_upper_bound(b,least_upper_bound(identity,X_43)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(b,identity)),least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity)))) )],[refute_0_3011,refute_0_3035]) ).

cnf(refute_0_3037,plain,
    least_upper_bound(X_43,least_upper_bound(b,identity)) = least_upper_bound(b,least_upper_bound(identity,X_43)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(identity,multiply(greatest_lower_bound(identity,least_upper_bound(a,c)),b))),least_upper_bound(identity,least_upper_bound(X_43,least_upper_bound(b,identity)))) )],[refute_0_3005,refute_0_3036]) ).

cnf(refute_0_3038,plain,
    least_upper_bound(inverse(X_36),least_upper_bound(b,identity)) = least_upper_bound(b,least_upper_bound(identity,inverse(X_36))),
    inference(subst,[],[refute_0_3037:[bind(X_43,$fot(inverse(X_36)))]]) ).

cnf(refute_0_3039,plain,
    inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) = least_upper_bound(inverse(X_36),least_upper_bound(b,identity)),
    inference(subst,[],[refute_0_1559:[bind(X,$fot(X_36)),bind(X_89,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_3040,plain,
    ( inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) != least_upper_bound(inverse(X_36),least_upper_bound(b,identity))
    | least_upper_bound(inverse(X_36),least_upper_bound(b,identity)) != least_upper_bound(b,least_upper_bound(identity,inverse(X_36)))
    | inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,least_upper_bound(identity,inverse(X_36))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))))),bind(Y0,$fot(least_upper_bound(inverse(X_36),least_upper_bound(b,identity)))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(identity,inverse(X_36)))))]]) ).

cnf(refute_0_3041,plain,
    ( least_upper_bound(inverse(X_36),least_upper_bound(b,identity)) != least_upper_bound(b,least_upper_bound(identity,inverse(X_36)))
    | inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,least_upper_bound(identity,inverse(X_36))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))),least_upper_bound(inverse(X_36),least_upper_bound(b,identity))) )],[refute_0_3039,refute_0_3040]) ).

cnf(refute_0_3042,plain,
    inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,least_upper_bound(identity,inverse(X_36))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_36),least_upper_bound(b,identity)),least_upper_bound(b,least_upper_bound(identity,inverse(X_36)))) )],[refute_0_3038,refute_0_3041]) ).

cnf(refute_0_3043,plain,
    ( inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) != least_upper_bound(b,least_upper_bound(identity,inverse(X_36)))
    | least_upper_bound(b,least_upper_bound(identity,inverse(X_36))) != least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36)))
    | inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(identity,inverse(X_36))))),bind(Z0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36)))))]]) ).

cnf(refute_0_3044,plain,
    ( least_upper_bound(b,least_upper_bound(identity,inverse(X_36))) != least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36)))
    | inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))),least_upper_bound(b,least_upper_bound(identity,inverse(X_36)))) )],[refute_0_3042,refute_0_3043]) ).

cnf(refute_0_3045,plain,
    inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(X_36))),least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36)))) )],[refute_0_2892,refute_0_3044]) ).

cnf(refute_0_3046,plain,
    ( inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))) != least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36)))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) != inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))),inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) ),[1],$fot(least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))))]]) ).

cnf(refute_0_3047,plain,
    ( least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) != inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity)))),least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36)))) )],[refute_0_3045,refute_0_3046]) ).

cnf(refute_0_3048,plain,
    ( inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))),inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) )],[refute_0_2887,refute_0_3047]) ).

cnf(refute_0_3049,plain,
    least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(a,c)),greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))),inverse(greatest_lower_bound(X_36,inverse(least_upper_bound(b,identity))))) )],[refute_0_2843,refute_0_3048]) ).

cnf(refute_0_3050,plain,
    ( least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) != least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36)))
    | least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))) = least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))))),bind(Y0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36)))))]]) ).

cnf(refute_0_3051,plain,
    least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36))) = least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(X_36,identity))),least_upper_bound(b,inverse(greatest_lower_bound(identity,X_36)))) )],[refute_0_3049,refute_0_3050]) ).

cnf(refute_0_3052,plain,
    least_upper_bound(b,inverse(greatest_lower_bound(identity,b))) = least_upper_bound(b,inverse(greatest_lower_bound(b,identity))),
    inference(subst,[],[refute_0_3051:[bind(X_36,$fot(b))]]) ).

cnf(refute_0_3053,plain,
    least_upper_bound(identity,least_upper_bound(b,inverse(b))) = least_upper_bound(b,inverse(greatest_lower_bound(identity,b))),
    inference(subst,[],[refute_0_1784:[bind(X_166,$fot(b)),bind(X_272,$fot(b))]]) ).

cnf(refute_0_3054,plain,
    ( least_upper_bound(b,inverse(greatest_lower_bound(identity,b))) != least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))
    | least_upper_bound(identity,least_upper_bound(b,inverse(b))) != least_upper_bound(b,inverse(greatest_lower_bound(identity,b)))
    | least_upper_bound(identity,least_upper_bound(b,inverse(b))) = least_upper_bound(b,inverse(greatest_lower_bound(b,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(b,inverse(b))))),bind(Y0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(identity,b))))),bind(Z0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))]]) ).

cnf(refute_0_3055,plain,
    ( least_upper_bound(b,inverse(greatest_lower_bound(identity,b))) != least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))
    | least_upper_bound(identity,least_upper_bound(b,inverse(b))) = least_upper_bound(b,inverse(greatest_lower_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(b,inverse(b))),least_upper_bound(b,inverse(greatest_lower_bound(identity,b)))) )],[refute_0_3053,refute_0_3054]) ).

cnf(refute_0_3056,plain,
    least_upper_bound(identity,least_upper_bound(b,inverse(b))) = least_upper_bound(b,inverse(greatest_lower_bound(b,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(identity,b))),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) )],[refute_0_3052,refute_0_3055]) ).

cnf(refute_0_3057,plain,
    multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),multiply(inverse(greatest_lower_bound(X_165,identity)),X_165)),
    inference(subst,[],[refute_0_480:[bind(X_93,$fot(inverse(greatest_lower_bound(X_165,identity)))),bind(X_94,$fot(X_165))]]) ).

cnf(refute_0_3058,plain,
    multiply(inverse(greatest_lower_bound(X_165,identity)),X_165) = least_upper_bound(X_165,identity),
    inference(subst,[],[refute_0_2750:[bind(X_117,$fot(X_165))]]) ).

cnf(refute_0_3059,plain,
    ( multiply(inverse(greatest_lower_bound(X_165,identity)),X_165) != least_upper_bound(X_165,identity)
    | multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) != least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),multiply(inverse(greatest_lower_bound(X_165,identity)),X_165))
    | multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),multiply(inverse(greatest_lower_bound(X_165,identity)),X_165))) ),[1,1],$fot(least_upper_bound(X_165,identity))]]) ).

cnf(refute_0_3060,plain,
    ( multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) != least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),multiply(inverse(greatest_lower_bound(X_165,identity)),X_165))
    | multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_165,identity)),X_165),least_upper_bound(X_165,identity)) )],[refute_0_3058,refute_0_3059]) ).

cnf(refute_0_3061,plain,
    multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),multiply(inverse(greatest_lower_bound(X_165,identity)),X_165))) )],[refute_0_3057,refute_0_3060]) ).

cnf(refute_0_3062,plain,
    inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) = inverse(inverse(least_upper_bound(Y,least_upper_bound(X_83,X_84)))),
    inference(subst,[],[refute_0_603:[bind(X,$fot(least_upper_bound(X_83,X_84)))]]) ).

cnf(refute_0_3063,plain,
    least_upper_bound(Y,least_upper_bound(X_83,X_84)) = least_upper_bound(X_83,least_upper_bound(Y,X_84)),
    inference(subst,[],[refute_0_1102:[bind(X_43,$fot(X_83)),bind(X_45,$fot(X_84))]]) ).

cnf(refute_0_3064,plain,
    ( inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) != inverse(inverse(least_upper_bound(Y,least_upper_bound(X_83,X_84))))
    | least_upper_bound(Y,least_upper_bound(X_83,X_84)) != least_upper_bound(X_83,least_upper_bound(Y,X_84))
    | inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) = inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))),inverse(inverse(least_upper_bound(Y,least_upper_bound(X_83,X_84))))) ),[1,0,0],$fot(least_upper_bound(X_83,least_upper_bound(Y,X_84)))]]) ).

cnf(refute_0_3065,plain,
    ( inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) != inverse(inverse(least_upper_bound(Y,least_upper_bound(X_83,X_84))))
    | inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) = inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_83,X_84)),least_upper_bound(X_83,least_upper_bound(Y,X_84))) )],[refute_0_3063,refute_0_3064]) ).

cnf(refute_0_3066,plain,
    inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) = inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))),inverse(inverse(least_upper_bound(Y,least_upper_bound(X_83,X_84))))) )],[refute_0_3062,refute_0_3065]) ).

cnf(refute_0_3067,plain,
    least_upper_bound(least_upper_bound(X_83,X_84),Y) = least_upper_bound(X_83,least_upper_bound(X_84,Y)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(X_83)),bind(Y,$fot(X_84)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_3068,plain,
    inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)) = inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)))]]) ).

cnf(refute_0_3069,plain,
    ( inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)) != inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))
    | least_upper_bound(least_upper_bound(X_83,X_84),Y) != least_upper_bound(X_83,least_upper_bound(X_84,Y))
    | inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)) = inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)),inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) ),[1,0],$fot(least_upper_bound(X_83,least_upper_bound(X_84,Y)))]]) ).

cnf(refute_0_3070,plain,
    ( least_upper_bound(least_upper_bound(X_83,X_84),Y) != least_upper_bound(X_83,least_upper_bound(X_84,Y))
    | inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)) = inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)),inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) )],[refute_0_3068,refute_0_3069]) ).

cnf(refute_0_3071,plain,
    inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)) = inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_83,X_84),Y),least_upper_bound(X_83,least_upper_bound(X_84,Y))) )],[refute_0_3067,refute_0_3070]) ).

cnf(refute_0_3072,plain,
    inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) = inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))),
    introduced(tautology,[refl,[$fot(inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))))]]) ).

cnf(refute_0_3073,plain,
    ( inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) != inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)))
    | inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)) != inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))
    | inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) = inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))),inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)))) ),[1,0],$fot(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y))))]]) ).

cnf(refute_0_3074,plain,
    ( inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)) != inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))
    | inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) = inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))),inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)))) )],[refute_0_3072,refute_0_3073]) ).

cnf(refute_0_3075,plain,
    inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) = inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y)),inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))) )],[refute_0_3071,refute_0_3074]) ).

cnf(refute_0_3076,plain,
    ( inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) != inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))
    | inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) != inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y))))
    | inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))) = inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))),inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))) ),[0],$fot(inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))))]]) ).

cnf(refute_0_3077,plain,
    ( inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))) != inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))
    | inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))) = inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84)))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))),inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y))))) )],[refute_0_3075,refute_0_3076]) ).

cnf(refute_0_3078,plain,
    inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))) = inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(least_upper_bound(X_83,X_84),Y))),inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))) )],[refute_0_3066,refute_0_3077]) ).

cnf(refute_0_3079,plain,
    inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))) = least_upper_bound(X_83,least_upper_bound(X_84,Y)),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(least_upper_bound(X_83,least_upper_bound(X_84,Y))))]]) ).

cnf(refute_0_3080,plain,
    ( inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))) != inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))
    | inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))) != least_upper_bound(X_83,least_upper_bound(X_84,Y))
    | least_upper_bound(X_83,least_upper_bound(X_84,Y)) = inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))),inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))) ),[0],$fot(least_upper_bound(X_83,least_upper_bound(X_84,Y)))]]) ).

cnf(refute_0_3081,plain,
    ( inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))) != inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))
    | least_upper_bound(X_83,least_upper_bound(X_84,Y)) = inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84)))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))),least_upper_bound(X_83,least_upper_bound(X_84,Y))) )],[refute_0_3079,refute_0_3080]) ).

cnf(refute_0_3082,plain,
    inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84)))) = least_upper_bound(X_83,least_upper_bound(Y,X_84)),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(least_upper_bound(X_83,least_upper_bound(Y,X_84))))]]) ).

cnf(refute_0_3083,plain,
    ( inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84)))) != least_upper_bound(X_83,least_upper_bound(Y,X_84))
    | least_upper_bound(X_83,least_upper_bound(X_84,Y)) != inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))
    | least_upper_bound(X_83,least_upper_bound(X_84,Y)) = least_upper_bound(X_83,least_upper_bound(Y,X_84)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_83,least_upper_bound(X_84,Y)),inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))) ),[1],$fot(least_upper_bound(X_83,least_upper_bound(Y,X_84)))]]) ).

cnf(refute_0_3084,plain,
    ( least_upper_bound(X_83,least_upper_bound(X_84,Y)) != inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))
    | least_upper_bound(X_83,least_upper_bound(X_84,Y)) = least_upper_bound(X_83,least_upper_bound(Y,X_84)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84)))),least_upper_bound(X_83,least_upper_bound(Y,X_84))) )],[refute_0_3082,refute_0_3083]) ).

cnf(refute_0_3085,plain,
    ( inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))) != inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))
    | least_upper_bound(X_83,least_upper_bound(X_84,Y)) = least_upper_bound(X_83,least_upper_bound(Y,X_84)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_83,least_upper_bound(X_84,Y)),inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))) )],[refute_0_3081,refute_0_3084]) ).

cnf(refute_0_3086,plain,
    least_upper_bound(X_83,least_upper_bound(X_84,Y)) = least_upper_bound(X_83,least_upper_bound(Y,X_84)),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_83,least_upper_bound(X_84,Y)))),inverse(inverse(least_upper_bound(X_83,least_upper_bound(Y,X_84))))) )],[refute_0_3078,refute_0_3085]) ).

cnf(refute_0_3087,plain,
    ( least_upper_bound(X_83,least_upper_bound(X_84,Y)) != least_upper_bound(X_83,least_upper_bound(Y,X_84))
    | least_upper_bound(X_83,least_upper_bound(Y,X_84)) = least_upper_bound(X_83,least_upper_bound(X_84,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_83,least_upper_bound(X_84,Y)))),bind(Y0,$fot(least_upper_bound(X_83,least_upper_bound(Y,X_84))))]]) ).

cnf(refute_0_3088,plain,
    least_upper_bound(X_83,least_upper_bound(Y,X_84)) = least_upper_bound(X_83,least_upper_bound(X_84,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_83,least_upper_bound(X_84,Y)),least_upper_bound(X_83,least_upper_bound(Y,X_84))) )],[refute_0_3086,refute_0_3087]) ).

cnf(refute_0_3089,plain,
    least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),X_165)) = least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))),
    inference(subst,[],[refute_0_3088:[bind(Y,$fot(inverse(greatest_lower_bound(X_165,identity)))),bind(X_83,$fot(identity)),bind(X_84,$fot(X_165))]]) ).

cnf(refute_0_3090,plain,
    least_upper_bound(X,least_upper_bound(Y,least_upper_bound(Y,X_145))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)),
    inference(subst,[],[associativity_of_lub:[bind(Z,$fot(least_upper_bound(Y,X_145)))]]) ).

cnf(refute_0_3091,plain,
    least_upper_bound(Y,least_upper_bound(Y,X_145)) = least_upper_bound(Y,X_145),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(X_145)),bind(X_31,$fot(Y))]]) ).

cnf(refute_0_3092,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(Y,X_145))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145))
    | least_upper_bound(Y,least_upper_bound(Y,X_145)) != least_upper_bound(Y,X_145)
    | least_upper_bound(X,least_upper_bound(Y,X_145)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(Y,X_145))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145))) ),[0,1],$fot(least_upper_bound(Y,X_145))]]) ).

cnf(refute_0_3093,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(Y,X_145))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145))
    | least_upper_bound(X,least_upper_bound(Y,X_145)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(Y,X_145)),least_upper_bound(Y,X_145)) )],[refute_0_3091,refute_0_3092]) ).

cnf(refute_0_3094,plain,
    least_upper_bound(X,least_upper_bound(Y,X_145)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(Y,X_145))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145))) )],[refute_0_3090,refute_0_3093]) ).

cnf(refute_0_3095,plain,
    least_upper_bound(Y,least_upper_bound(X_145,least_upper_bound(X,Y))) = least_upper_bound(Y,least_upper_bound(X_145,X)),
    inference(subst,[],[refute_0_1695:[bind(X_21,$fot(Y)),bind(X_43,$fot(X_145)),bind(X_44,$fot(X))]]) ).

cnf(refute_0_3096,plain,
    least_upper_bound(X_82,least_upper_bound(X_83,X_84)) = least_upper_bound(X_83,least_upper_bound(X_82,X_84)),
    inference(subst,[],[refute_0_1102:[bind(Y,$fot(X_82)),bind(X_43,$fot(X_83)),bind(X_45,$fot(X_84))]]) ).

cnf(refute_0_3097,plain,
    least_upper_bound(X_84,X_83) = least_upper_bound(X_83,X_84),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_84)),bind(Y,$fot(X_83))]]) ).

cnf(refute_0_3098,plain,
    ( least_upper_bound(X_84,X_83) != least_upper_bound(X_83,X_84)
    | least_upper_bound(X_83,X_84) = least_upper_bound(X_84,X_83) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_84,X_83))),bind(Y0,$fot(least_upper_bound(X_83,X_84)))]]) ).

cnf(refute_0_3099,plain,
    least_upper_bound(X_83,X_84) = least_upper_bound(X_84,X_83),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_84,X_83),least_upper_bound(X_83,X_84)) )],[refute_0_3097,refute_0_3098]) ).

cnf(refute_0_3100,plain,
    ( least_upper_bound(X_82,least_upper_bound(X_83,X_84)) != least_upper_bound(X_83,least_upper_bound(X_82,X_84))
    | least_upper_bound(X_83,X_84) != least_upper_bound(X_84,X_83)
    | least_upper_bound(X_82,least_upper_bound(X_84,X_83)) = least_upper_bound(X_83,least_upper_bound(X_82,X_84)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_82,least_upper_bound(X_83,X_84)),least_upper_bound(X_83,least_upper_bound(X_82,X_84))) ),[0,1],$fot(least_upper_bound(X_84,X_83))]]) ).

cnf(refute_0_3101,plain,
    ( least_upper_bound(X_82,least_upper_bound(X_83,X_84)) != least_upper_bound(X_83,least_upper_bound(X_82,X_84))
    | least_upper_bound(X_82,least_upper_bound(X_84,X_83)) = least_upper_bound(X_83,least_upper_bound(X_82,X_84)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_83,X_84),least_upper_bound(X_84,X_83)) )],[refute_0_3099,refute_0_3100]) ).

cnf(refute_0_3102,plain,
    least_upper_bound(X_82,least_upper_bound(X_84,X_83)) = least_upper_bound(X_83,least_upper_bound(X_82,X_84)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_82,least_upper_bound(X_83,X_84)),least_upper_bound(X_83,least_upper_bound(X_82,X_84))) )],[refute_0_3096,refute_0_3101]) ).

cnf(refute_0_3103,plain,
    ( least_upper_bound(X_82,least_upper_bound(X_84,X_83)) != least_upper_bound(X_83,least_upper_bound(X_82,X_84))
    | least_upper_bound(X_83,least_upper_bound(X_82,X_84)) = least_upper_bound(X_82,least_upper_bound(X_84,X_83)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_82,least_upper_bound(X_84,X_83)))),bind(Y0,$fot(least_upper_bound(X_83,least_upper_bound(X_82,X_84))))]]) ).

cnf(refute_0_3104,plain,
    least_upper_bound(X_83,least_upper_bound(X_82,X_84)) = least_upper_bound(X_82,least_upper_bound(X_84,X_83)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_82,least_upper_bound(X_84,X_83)),least_upper_bound(X_83,least_upper_bound(X_82,X_84))) )],[refute_0_3102,refute_0_3103]) ).

cnf(refute_0_3105,plain,
    least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)) = least_upper_bound(Y,least_upper_bound(X_145,least_upper_bound(X,Y))),
    inference(subst,[],[refute_0_3104:[bind(X_82,$fot(Y)),bind(X_83,$fot(least_upper_bound(X,Y))),bind(X_84,$fot(X_145))]]) ).

cnf(refute_0_3106,plain,
    ( least_upper_bound(Y,least_upper_bound(X_145,least_upper_bound(X,Y))) != least_upper_bound(Y,least_upper_bound(X_145,X))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)) != least_upper_bound(Y,least_upper_bound(X_145,least_upper_bound(X,Y)))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)) = least_upper_bound(Y,least_upper_bound(X_145,X)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_145,least_upper_bound(X,Y))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_145,X))))]]) ).

cnf(refute_0_3107,plain,
    ( least_upper_bound(Y,least_upper_bound(X_145,least_upper_bound(X,Y))) != least_upper_bound(Y,least_upper_bound(X_145,X))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)) = least_upper_bound(Y,least_upper_bound(X_145,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)),least_upper_bound(Y,least_upper_bound(X_145,least_upper_bound(X,Y)))) )],[refute_0_3105,refute_0_3106]) ).

cnf(refute_0_3108,plain,
    least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)) = least_upper_bound(Y,least_upper_bound(X_145,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_145,least_upper_bound(X,Y))),least_upper_bound(Y,least_upper_bound(X_145,X))) )],[refute_0_3095,refute_0_3107]) ).

cnf(refute_0_3109,plain,
    ( least_upper_bound(X,least_upper_bound(Y,X_145)) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)) != least_upper_bound(Y,least_upper_bound(X_145,X))
    | least_upper_bound(X,least_upper_bound(Y,X_145)) = least_upper_bound(Y,least_upper_bound(X_145,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(Y,X_145)),least_upper_bound(Y,least_upper_bound(X_145,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)))]]) ).

cnf(refute_0_3110,plain,
    ( least_upper_bound(X,least_upper_bound(Y,X_145)) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145))
    | least_upper_bound(X,least_upper_bound(Y,X_145)) = least_upper_bound(Y,least_upper_bound(X_145,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145)),least_upper_bound(Y,least_upper_bound(X_145,X))) )],[refute_0_3108,refute_0_3109]) ).

cnf(refute_0_3111,plain,
    least_upper_bound(X,least_upper_bound(Y,X_145)) = least_upper_bound(Y,least_upper_bound(X_145,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_145)),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_145))) )],[refute_0_3094,refute_0_3110]) ).

cnf(refute_0_3112,plain,
    ( least_upper_bound(X,least_upper_bound(Y,X_145)) != least_upper_bound(Y,least_upper_bound(X_145,X))
    | least_upper_bound(Y,least_upper_bound(X_145,X)) = least_upper_bound(X,least_upper_bound(Y,X_145)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,X_145)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_145,X))))]]) ).

cnf(refute_0_3113,plain,
    least_upper_bound(Y,least_upper_bound(X_145,X)) = least_upper_bound(X,least_upper_bound(Y,X_145)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_145)),least_upper_bound(Y,least_upper_bound(X_145,X))) )],[refute_0_3111,refute_0_3112]) ).

cnf(refute_0_3114,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),X_165)),
    inference(subst,[],[refute_0_3113:[bind(X,$fot(identity)),bind(Y,$fot(inverse(greatest_lower_bound(X_165,identity)))),bind(X_145,$fot(X_165))]]) ).

cnf(refute_0_3115,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),X_165)) != least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))
    | least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),X_165))
    | least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),X_165)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))))]]) ).

cnf(refute_0_3116,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),X_165)) != least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))
    | least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),X_165))) )],[refute_0_3114,refute_0_3115]) ).

cnf(refute_0_3117,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),X_165)),least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))) )],[refute_0_3089,refute_0_3116]) ).

cnf(refute_0_3118,plain,
    ( multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) != least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity))
    | least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) != least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))
    | multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)))]]) ).

cnf(refute_0_3119,plain,
    ( multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) != least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity))
    | multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))) )],[refute_0_3117,refute_0_3118]) ).

cnf(refute_0_3120,plain,
    multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),least_upper_bound(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity))) )],[refute_0_3061,refute_0_3119]) ).

cnf(refute_0_3121,plain,
    multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) = least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),multiply(X_230,inverse(greatest_lower_bound(X_230,identity)))),
    inference(subst,[],[refute_0_728:[bind(X_110,$fot(inverse(greatest_lower_bound(X_230,identity)))),bind(X_111,$fot(X_230))]]) ).

cnf(refute_0_3122,plain,
    multiply(X_96,least_upper_bound(identity,inverse(X_96))) = least_upper_bound(identity,multiply(X_96,identity)),
    inference(subst,[],[refute_0_251:[bind(X_93,$fot(X_96)),bind(X_94,$fot(identity))]]) ).

cnf(refute_0_3123,plain,
    inverse(greatest_lower_bound(identity,X_96)) = least_upper_bound(identity,inverse(X_96)),
    inference(subst,[],[refute_0_486:[bind(Y,$fot(X_96))]]) ).

cnf(refute_0_3124,plain,
    ( inverse(greatest_lower_bound(identity,X_96)) != least_upper_bound(identity,inverse(X_96))
    | least_upper_bound(identity,inverse(X_96)) = inverse(greatest_lower_bound(identity,X_96)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_96)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_96))))]]) ).

cnf(refute_0_3125,plain,
    least_upper_bound(identity,inverse(X_96)) = inverse(greatest_lower_bound(identity,X_96)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_96)),least_upper_bound(identity,inverse(X_96))) )],[refute_0_3123,refute_0_3124]) ).

cnf(refute_0_3126,plain,
    ( multiply(X_96,least_upper_bound(identity,inverse(X_96))) != least_upper_bound(identity,multiply(X_96,identity))
    | least_upper_bound(identity,inverse(X_96)) != inverse(greatest_lower_bound(identity,X_96))
    | multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) = least_upper_bound(identity,multiply(X_96,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_96,least_upper_bound(identity,inverse(X_96))),least_upper_bound(identity,multiply(X_96,identity))) ),[0,1],$fot(inverse(greatest_lower_bound(identity,X_96)))]]) ).

cnf(refute_0_3127,plain,
    ( multiply(X_96,least_upper_bound(identity,inverse(X_96))) != least_upper_bound(identity,multiply(X_96,identity))
    | multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) = least_upper_bound(identity,multiply(X_96,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_96)),inverse(greatest_lower_bound(identity,X_96))) )],[refute_0_3125,refute_0_3126]) ).

cnf(refute_0_3128,plain,
    multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) = least_upper_bound(identity,multiply(X_96,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_96,least_upper_bound(identity,inverse(X_96))),least_upper_bound(identity,multiply(X_96,identity))) )],[refute_0_3122,refute_0_3127]) ).

cnf(refute_0_3129,plain,
    multiply(X_96,identity) = X_96,
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(X_96))]]) ).

cnf(refute_0_3130,plain,
    least_upper_bound(identity,multiply(X_96,identity)) = least_upper_bound(identity,multiply(X_96,identity)),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_96,identity)))]]) ).

cnf(refute_0_3131,plain,
    ( multiply(X_96,identity) != X_96
    | least_upper_bound(identity,multiply(X_96,identity)) != least_upper_bound(identity,multiply(X_96,identity))
    | least_upper_bound(identity,multiply(X_96,identity)) = least_upper_bound(identity,X_96) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_96,identity)),least_upper_bound(identity,multiply(X_96,identity))) ),[1,1],$fot(X_96)]]) ).

cnf(refute_0_3132,plain,
    ( multiply(X_96,identity) != X_96
    | least_upper_bound(identity,multiply(X_96,identity)) = least_upper_bound(identity,X_96) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_96,identity)),least_upper_bound(identity,multiply(X_96,identity))) )],[refute_0_3130,refute_0_3131]) ).

cnf(refute_0_3133,plain,
    least_upper_bound(identity,multiply(X_96,identity)) = least_upper_bound(identity,X_96),
    inference(resolve,[$cnf( $equal(multiply(X_96,identity),X_96) )],[refute_0_3129,refute_0_3132]) ).

cnf(refute_0_3134,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) != least_upper_bound(identity,multiply(X_96,identity))
    | least_upper_bound(identity,multiply(X_96,identity)) != least_upper_bound(identity,X_96)
    | multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) = least_upper_bound(identity,X_96) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_96,inverse(greatest_lower_bound(identity,X_96))),least_upper_bound(identity,X_96)) ),[0],$fot(least_upper_bound(identity,multiply(X_96,identity)))]]) ).

cnf(refute_0_3135,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) != least_upper_bound(identity,multiply(X_96,identity))
    | multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) = least_upper_bound(identity,X_96) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_96,identity)),least_upper_bound(identity,X_96)) )],[refute_0_3133,refute_0_3134]) ).

cnf(refute_0_3136,plain,
    multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) = least_upper_bound(identity,X_96),
    inference(resolve,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(identity,X_96))),least_upper_bound(identity,multiply(X_96,identity))) )],[refute_0_3128,refute_0_3135]) ).

cnf(refute_0_3137,plain,
    multiply(X_98,inverse(greatest_lower_bound(identity,X_98))) = least_upper_bound(identity,X_98),
    inference(subst,[],[refute_0_3136:[bind(X_96,$fot(X_98))]]) ).

cnf(refute_0_3138,plain,
    greatest_lower_bound(X_98,identity) = greatest_lower_bound(identity,X_98),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_98)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_3139,plain,
    ( greatest_lower_bound(X_98,identity) != greatest_lower_bound(identity,X_98)
    | greatest_lower_bound(identity,X_98) = greatest_lower_bound(X_98,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_98,identity))),bind(Y0,$fot(greatest_lower_bound(identity,X_98)))]]) ).

cnf(refute_0_3140,plain,
    greatest_lower_bound(identity,X_98) = greatest_lower_bound(X_98,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_98,identity),greatest_lower_bound(identity,X_98)) )],[refute_0_3138,refute_0_3139]) ).

cnf(refute_0_3141,plain,
    ( multiply(X_98,inverse(greatest_lower_bound(identity,X_98))) != least_upper_bound(identity,X_98)
    | greatest_lower_bound(identity,X_98) != greatest_lower_bound(X_98,identity)
    | multiply(X_98,inverse(greatest_lower_bound(X_98,identity))) = least_upper_bound(identity,X_98) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_98,inverse(greatest_lower_bound(identity,X_98))),least_upper_bound(identity,X_98)) ),[0,1,0],$fot(greatest_lower_bound(X_98,identity))]]) ).

cnf(refute_0_3142,plain,
    ( multiply(X_98,inverse(greatest_lower_bound(identity,X_98))) != least_upper_bound(identity,X_98)
    | multiply(X_98,inverse(greatest_lower_bound(X_98,identity))) = least_upper_bound(identity,X_98) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_98),greatest_lower_bound(X_98,identity)) )],[refute_0_3140,refute_0_3141]) ).

cnf(refute_0_3143,plain,
    multiply(X_98,inverse(greatest_lower_bound(X_98,identity))) = least_upper_bound(identity,X_98),
    inference(resolve,[$cnf( $equal(multiply(X_98,inverse(greatest_lower_bound(identity,X_98))),least_upper_bound(identity,X_98)) )],[refute_0_3137,refute_0_3142]) ).

cnf(refute_0_3144,plain,
    multiply(X_230,inverse(greatest_lower_bound(X_230,identity))) = least_upper_bound(identity,X_230),
    inference(subst,[],[refute_0_3143:[bind(X_98,$fot(X_230))]]) ).

cnf(refute_0_3145,plain,
    ( multiply(X_230,inverse(greatest_lower_bound(X_230,identity))) != least_upper_bound(identity,X_230)
    | multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) != least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),multiply(X_230,inverse(greatest_lower_bound(X_230,identity))))
    | multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) = least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))),least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),multiply(X_230,inverse(greatest_lower_bound(X_230,identity))))) ),[1,1],$fot(least_upper_bound(identity,X_230))]]) ).

cnf(refute_0_3146,plain,
    ( multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) != least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),multiply(X_230,inverse(greatest_lower_bound(X_230,identity))))
    | multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) = least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)) ),
    inference(resolve,[$cnf( $equal(multiply(X_230,inverse(greatest_lower_bound(X_230,identity))),least_upper_bound(identity,X_230)) )],[refute_0_3144,refute_0_3145]) ).

cnf(refute_0_3147,plain,
    multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) = least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))),least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),multiply(X_230,inverse(greatest_lower_bound(X_230,identity))))) )],[refute_0_3121,refute_0_3146]) ).

cnf(refute_0_3148,plain,
    ( multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) != least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))
    | least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) = multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))))]]) ).

cnf(refute_0_3149,plain,
    least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) = multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))) )],[refute_0_3120,refute_0_3148]) ).

cnf(refute_0_3150,plain,
    least_upper_bound(identity,least_upper_bound(X_230,inverse(greatest_lower_bound(X_230,identity)))) = multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity)),
    inference(subst,[],[refute_0_3149:[bind(X_165,$fot(X_230))]]) ).

cnf(refute_0_3151,plain,
    X_60 = multiply(inverse(least_upper_bound(X_114,inverse(X_60))),multiply(least_upper_bound(X_114,inverse(X_60)),X_60)),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(least_upper_bound(X_114,inverse(X_60))))]]) ).

cnf(refute_0_3152,plain,
    multiply(least_upper_bound(X_114,inverse(X_60)),X_60) = least_upper_bound(identity,multiply(X_114,X_60)),
    inference(subst,[],[refute_0_92:[bind(X_110,$fot(X_60)),bind(X_111,$fot(X_114))]]) ).

cnf(refute_0_3153,plain,
    ( X_60 != multiply(inverse(least_upper_bound(X_114,inverse(X_60))),multiply(least_upper_bound(X_114,inverse(X_60)),X_60))
    | multiply(least_upper_bound(X_114,inverse(X_60)),X_60) != least_upper_bound(identity,multiply(X_114,X_60))
    | X_60 = multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))) ),
    introduced(tautology,[equality,[$cnf( $equal(X_60,multiply(inverse(least_upper_bound(X_114,inverse(X_60))),multiply(least_upper_bound(X_114,inverse(X_60)),X_60))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_114,X_60)))]]) ).

cnf(refute_0_3154,plain,
    ( X_60 != multiply(inverse(least_upper_bound(X_114,inverse(X_60))),multiply(least_upper_bound(X_114,inverse(X_60)),X_60))
    | X_60 = multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_114,inverse(X_60)),X_60),least_upper_bound(identity,multiply(X_114,X_60))) )],[refute_0_3152,refute_0_3153]) ).

cnf(refute_0_3155,plain,
    X_60 = multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))),
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(least_upper_bound(X_114,inverse(X_60))),multiply(least_upper_bound(X_114,inverse(X_60)),X_60))) )],[refute_0_3151,refute_0_3154]) ).

cnf(refute_0_3156,plain,
    inverse(least_upper_bound(X_114,inverse(X_60))) = greatest_lower_bound(inverse(X_114),X_60),
    inference(subst,[],[refute_0_582:[bind(X,$fot(X_114)),bind(X_89,$fot(X_60))]]) ).

cnf(refute_0_3157,plain,
    multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))) = multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))),
    introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))))]]) ).

cnf(refute_0_3158,plain,
    ( multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))) != multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60)))
    | inverse(least_upper_bound(X_114,inverse(X_60))) != greatest_lower_bound(inverse(X_114),X_60)
    | multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))) = multiply(greatest_lower_bound(inverse(X_114),X_60),least_upper_bound(identity,multiply(X_114,X_60))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))),multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60)))) ),[1,0],$fot(greatest_lower_bound(inverse(X_114),X_60))]]) ).

cnf(refute_0_3159,plain,
    ( inverse(least_upper_bound(X_114,inverse(X_60))) != greatest_lower_bound(inverse(X_114),X_60)
    | multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))) = multiply(greatest_lower_bound(inverse(X_114),X_60),least_upper_bound(identity,multiply(X_114,X_60))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))),multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60)))) )],[refute_0_3157,refute_0_3158]) ).

cnf(refute_0_3160,plain,
    multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))) = multiply(greatest_lower_bound(inverse(X_114),X_60),least_upper_bound(identity,multiply(X_114,X_60))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_114,inverse(X_60))),greatest_lower_bound(inverse(X_114),X_60)) )],[refute_0_3156,refute_0_3159]) ).

cnf(refute_0_3161,plain,
    ( X_60 != multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60)))
    | multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))) != multiply(greatest_lower_bound(inverse(X_114),X_60),least_upper_bound(identity,multiply(X_114,X_60)))
    | X_60 = multiply(greatest_lower_bound(inverse(X_114),X_60),least_upper_bound(identity,multiply(X_114,X_60))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_60,multiply(greatest_lower_bound(inverse(X_114),X_60),least_upper_bound(identity,multiply(X_114,X_60)))) ),[0],$fot(multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))))]]) ).

cnf(refute_0_3162,plain,
    ( X_60 != multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60)))
    | X_60 = multiply(greatest_lower_bound(inverse(X_114),X_60),least_upper_bound(identity,multiply(X_114,X_60))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60))),multiply(greatest_lower_bound(inverse(X_114),X_60),least_upper_bound(identity,multiply(X_114,X_60)))) )],[refute_0_3160,refute_0_3161]) ).

cnf(refute_0_3163,plain,
    X_60 = multiply(greatest_lower_bound(inverse(X_114),X_60),least_upper_bound(identity,multiply(X_114,X_60))),
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(least_upper_bound(X_114,inverse(X_60))),least_upper_bound(identity,multiply(X_114,X_60)))) )],[refute_0_3155,refute_0_3162]) ).

cnf(refute_0_3164,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) = multiply(greatest_lower_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))),
    inference(subst,[],[refute_0_3163:[bind(X_114,$fot(X_221)),bind(X_60,$fot(least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))]]) ).

cnf(refute_0_3165,plain,
    greatest_lower_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) = inverse(X_221),
    inference(subst,[],[refute_0_1684:[bind(X_10,$fot(inverse(X_221)))]]) ).

cnf(refute_0_3166,plain,
    ( greatest_lower_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) != inverse(X_221)
    | least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) != multiply(greatest_lower_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))))
    | least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) = multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))),multiply(greatest_lower_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))))) ),[1,0],$fot(inverse(X_221))]]) ).

cnf(refute_0_3167,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) != multiply(greatest_lower_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))))
    | least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) = multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),inverse(X_221)) )],[refute_0_3165,refute_0_3166]) ).

cnf(refute_0_3168,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) = multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))),multiply(greatest_lower_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))))) )],[refute_0_3164,refute_0_3167]) ).

cnf(refute_0_3169,plain,
    least_upper_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)),
    inference(subst,[],[refute_0_1695:[bind(X_21,$fot(inverse(X_221)))]]) ).

cnf(refute_0_3170,plain,
    multiply(inverse(X_221),identity) = inverse(X_221),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(inverse(X_221)))]]) ).

cnf(refute_0_3171,plain,
    least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) = least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))]]) ).

cnf(refute_0_3172,plain,
    ( multiply(inverse(X_221),identity) != inverse(X_221)
    | least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) != least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))
    | least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))) ),[1,0],$fot(inverse(X_221))]]) ).

cnf(refute_0_3173,plain,
    ( multiply(inverse(X_221),identity) != inverse(X_221)
    | least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))) )],[refute_0_3171,refute_0_3172]) ).

cnf(refute_0_3174,plain,
    least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_221),identity),inverse(X_221)) )],[refute_0_3170,refute_0_3173]) ).

cnf(refute_0_3175,plain,
    ( least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) != least_upper_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))
    | least_upper_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) != least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))
    | least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))),bind(Y0,$fot(least_upper_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))),bind(Z0,$fot(least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))))]]) ).

cnf(refute_0_3176,plain,
    ( least_upper_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) != least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))
    | least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),least_upper_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))) )],[refute_0_3174,refute_0_3175]) ).

cnf(refute_0_3177,plain,
    least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_221),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))) )],[refute_0_3169,refute_0_3176]) ).

cnf(refute_0_3178,plain,
    multiply(inverse(X_59),least_upper_bound(X_94,multiply(X_59,X_60))) = least_upper_bound(multiply(inverse(X_59),X_94),multiply(inverse(X_59),multiply(X_59,X_60))),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_59))),bind(Y,$fot(X_94)),bind(Z,$fot(multiply(X_59,X_60)))]]) ).

cnf(refute_0_3179,plain,
    ( multiply(inverse(X_59),multiply(X_59,X_60)) != X_60
    | multiply(inverse(X_59),least_upper_bound(X_94,multiply(X_59,X_60))) != least_upper_bound(multiply(inverse(X_59),X_94),multiply(inverse(X_59),multiply(X_59,X_60)))
    | multiply(inverse(X_59),least_upper_bound(X_94,multiply(X_59,X_60))) = least_upper_bound(multiply(inverse(X_59),X_94),X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(X_94,multiply(X_59,X_60))),least_upper_bound(multiply(inverse(X_59),X_94),multiply(inverse(X_59),multiply(X_59,X_60)))) ),[1,1],$fot(X_60)]]) ).

cnf(refute_0_3180,plain,
    ( multiply(inverse(X_59),least_upper_bound(X_94,multiply(X_59,X_60))) != least_upper_bound(multiply(inverse(X_59),X_94),multiply(inverse(X_59),multiply(X_59,X_60)))
    | multiply(inverse(X_59),least_upper_bound(X_94,multiply(X_59,X_60))) = least_upper_bound(multiply(inverse(X_59),X_94),X_60) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_59),multiply(X_59,X_60)),X_60) )],[refute_0_1308,refute_0_3179]) ).

cnf(refute_0_3181,plain,
    multiply(inverse(X_59),least_upper_bound(X_94,multiply(X_59,X_60))) = least_upper_bound(multiply(inverse(X_59),X_94),X_60),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(X_94,multiply(X_59,X_60))),least_upper_bound(multiply(inverse(X_59),X_94),multiply(inverse(X_59),multiply(X_59,X_60)))) )],[refute_0_3178,refute_0_3180]) ).

cnf(refute_0_3182,plain,
    multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))) = least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),
    inference(subst,[],[refute_0_3181:[bind(X_59,$fot(X_221)),bind(X_60,$fot(least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))),bind(X_94,$fot(identity))]]) ).

cnf(refute_0_3183,plain,
    ( multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))) != least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))
    | least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) != least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))
    | multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))))),bind(Y0,$fot(least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))),bind(Z0,$fot(least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))))]]) ).

cnf(refute_0_3184,plain,
    ( least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))) != least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))
    | multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))),least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))) )],[refute_0_3182,refute_0_3183]) ).

cnf(refute_0_3185,plain,
    multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_221),identity),least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))),least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))) )],[refute_0_3177,refute_0_3184]) ).

cnf(refute_0_3186,plain,
    ( multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))) != least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))
    | least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) != multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))))
    | least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))),multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))))) ),[1],$fot(least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)))]]) ).

cnf(refute_0_3187,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) != multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))))
    | least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221)))))),least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))) )],[refute_0_3185,refute_0_3186]) ).

cnf(refute_0_3188,plain,
    least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) = least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))),multiply(inverse(X_221),least_upper_bound(identity,multiply(X_221,least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))))) )],[refute_0_3168,refute_0_3187]) ).

cnf(refute_0_3189,plain,
    ( least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) != least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))
    | least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))))),bind(Y0,$fot(least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))))]]) ).

cnf(refute_0_3190,plain,
    least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_44,inverse(X_221))),least_upper_bound(inverse(X_221),least_upper_bound(X_43,X_44))) )],[refute_0_3188,refute_0_3189]) ).

cnf(refute_0_3191,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)) = least_upper_bound(identity,least_upper_bound(X_230,inverse(greatest_lower_bound(X_230,identity)))),
    inference(subst,[],[refute_0_3190:[bind(X_221,$fot(greatest_lower_bound(X_230,identity))),bind(X_43,$fot(identity)),bind(X_44,$fot(X_230))]]) ).

cnf(refute_0_3192,plain,
    ( least_upper_bound(identity,least_upper_bound(X_230,inverse(greatest_lower_bound(X_230,identity)))) != multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity))
    | least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)) != least_upper_bound(identity,least_upper_bound(X_230,inverse(greatest_lower_bound(X_230,identity))))
    | least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)) = multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_230,inverse(greatest_lower_bound(X_230,identity)))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity))))]]) ).

cnf(refute_0_3193,plain,
    ( least_upper_bound(identity,least_upper_bound(X_230,inverse(greatest_lower_bound(X_230,identity)))) != multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity))
    | least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)) = multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)),least_upper_bound(identity,least_upper_bound(X_230,inverse(greatest_lower_bound(X_230,identity))))) )],[refute_0_3191,refute_0_3192]) ).

cnf(refute_0_3194,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)) = multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_230,inverse(greatest_lower_bound(X_230,identity)))),multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity))) )],[refute_0_3150,refute_0_3193]) ).

cnf(refute_0_3195,plain,
    ( multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) != least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230))
    | least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)) != multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity))
    | multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) = multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))),multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)))]]) ).

cnf(refute_0_3196,plain,
    ( multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) != least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230))
    | multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) = multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230)),multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity))) )],[refute_0_3194,refute_0_3195]) ).

cnf(refute_0_3197,plain,
    multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) = multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))),least_upper_bound(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(identity,X_230))) )],[refute_0_3147,refute_0_3196]) ).

cnf(refute_0_3198,plain,
    ( multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) != multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity))
    | multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity)) = multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity))))]]) ).

cnf(refute_0_3199,plain,
    multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity)) = multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_230,identity),inverse(greatest_lower_bound(X_230,identity))),multiply(inverse(greatest_lower_bound(X_230,identity)),least_upper_bound(X_230,identity))) )],[refute_0_3197,refute_0_3198]) ).

cnf(refute_0_3200,plain,
    multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) = multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))),
    inference(subst,[],[refute_0_3199:[bind(X_230,$fot(X_165))]]) ).

cnf(refute_0_3201,plain,
    ( multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) != multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity)))
    | multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) != least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))
    | multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))) = least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))) ),[0],$fot(multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))))]]) ).

cnf(refute_0_3202,plain,
    ( multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)) != least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))
    | multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))) = least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity)))) )],[refute_0_3200,refute_0_3201]) ).

cnf(refute_0_3203,plain,
    multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))) = least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_165,identity)),least_upper_bound(X_165,identity)),least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))) )],[refute_0_3120,refute_0_3202]) ).

cnf(refute_0_3204,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30),
    inference(subst,[],[refute_0_433:[bind(X_31,$fot(inverse(greatest_lower_bound(identity,X_272))))]]) ).

cnf(refute_0_3205,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)),
    inference(subst,[],[refute_0_1641:[bind(Z,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))),bind(X_64,$fot(X_272))]]) ).

cnf(refute_0_3206,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) = least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))))]]) ).

cnf(refute_0_3207,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) = least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) )],[refute_0_3205,refute_0_3206]) ).

cnf(refute_0_3208,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) != least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))))]]) ).

cnf(refute_0_3209,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)),least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)))) )],[refute_0_3207,refute_0_3208]) ).

cnf(refute_0_3210,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) )],[refute_0_3204,refute_0_3209]) ).

cnf(refute_0_3211,plain,
    least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(least_upper_bound(X_30,inverse(X_272)))),bind(X_31,$fot(identity))]]) ).

cnf(refute_0_3212,plain,
    least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)) = least_upper_bound(least_upper_bound(inverse(X),inverse(Y)),X_45),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(inverse(X))),bind(Y,$fot(inverse(Y))),bind(Z,$fot(X_45))]]) ).

cnf(refute_0_3213,plain,
    ( least_upper_bound(inverse(X),inverse(Y)) != inverse(greatest_lower_bound(X,Y))
    | least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)) != least_upper_bound(least_upper_bound(inverse(X),inverse(Y)),X_45)
    | least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)) = least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)),least_upper_bound(least_upper_bound(inverse(X),inverse(Y)),X_45)) ),[1,0],$fot(inverse(greatest_lower_bound(X,Y)))]]) ).

cnf(refute_0_3214,plain,
    ( least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)) != least_upper_bound(least_upper_bound(inverse(X),inverse(Y)),X_45)
    | least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)) = least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(Y)),inverse(greatest_lower_bound(X,Y))) )],[refute_0_136,refute_0_3213]) ).

cnf(refute_0_3215,plain,
    least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)) = least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)),least_upper_bound(least_upper_bound(inverse(X),inverse(Y)),X_45)) )],[refute_0_3212,refute_0_3214]) ).

cnf(refute_0_3216,plain,
    least_upper_bound(inverse(X_249),least_upper_bound(inverse(identity),X_251)) = least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251),
    inference(subst,[],[refute_0_3215:[bind(X,$fot(X_249)),bind(Y,$fot(identity)),bind(X_45,$fot(X_251))]]) ).

cnf(refute_0_3217,plain,
    ( inverse(identity) != identity
    | least_upper_bound(inverse(X_249),least_upper_bound(inverse(identity),X_251)) != least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251)
    | least_upper_bound(inverse(X_249),least_upper_bound(identity,X_251)) = least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X_249),least_upper_bound(inverse(identity),X_251)),least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251)) ),[0,1,0],$fot(identity)]]) ).

cnf(refute_0_3218,plain,
    ( least_upper_bound(inverse(X_249),least_upper_bound(inverse(identity),X_251)) != least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251)
    | least_upper_bound(inverse(X_249),least_upper_bound(identity,X_251)) = least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251) ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_3217]) ).

cnf(refute_0_3219,plain,
    least_upper_bound(inverse(X_249),least_upper_bound(identity,X_251)) = least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_249),least_upper_bound(inverse(identity),X_251)),least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251)) )],[refute_0_3216,refute_0_3218]) ).

cnf(refute_0_3220,plain,
    least_upper_bound(inverse(X_249),least_upper_bound(identity,X_251)) = least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249))),
    inference(subst,[],[refute_0_1776:[bind(X_246,$fot(inverse(X_249))),bind(X_247,$fot(identity)),bind(X_248,$fot(X_251))]]) ).

cnf(refute_0_3221,plain,
    ( least_upper_bound(inverse(X_249),least_upper_bound(identity,X_251)) != least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249)))
    | least_upper_bound(inverse(X_249),least_upper_bound(identity,X_251)) != least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251)
    | least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249))) = least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X_249),least_upper_bound(identity,X_251)),least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249))))]]) ).

cnf(refute_0_3222,plain,
    ( least_upper_bound(inverse(X_249),least_upper_bound(identity,X_251)) != least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251)
    | least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249))) = least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_249),least_upper_bound(identity,X_251)),least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249)))) )],[refute_0_3220,refute_0_3221]) ).

cnf(refute_0_3223,plain,
    least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249))) = least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_249),least_upper_bound(identity,X_251)),least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251)) )],[refute_0_3219,refute_0_3222]) ).

cnf(refute_0_3224,plain,
    ( least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249))) != least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251)
    | least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251) = least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249))))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251)))]]) ).

cnf(refute_0_3225,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251) = least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_251,inverse(X_249))),least_upper_bound(inverse(greatest_lower_bound(X_249,identity)),X_251)) )],[refute_0_3223,refute_0_3224]) ).

cnf(refute_0_3226,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_272,identity)),X_30) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))),
    inference(subst,[],[refute_0_3225:[bind(X_249,$fot(X_272)),bind(X_251,$fot(X_30))]]) ).

cnf(refute_0_3227,plain,
    greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)) = greatest_lower_bound(X_272,identity),
    inference(subst,[],[refute_0_794:[bind(Y,$fot(identity)),bind(X_23,$fot(X_272))]]) ).

cnf(refute_0_3228,plain,
    inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))) = inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))))]]) ).

cnf(refute_0_3229,plain,
    ( greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)) != greatest_lower_bound(X_272,identity)
    | inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))) != inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))
    | inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))) = inverse(greatest_lower_bound(X_272,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))) ),[1,0],$fot(greatest_lower_bound(X_272,identity))]]) ).

cnf(refute_0_3230,plain,
    ( greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)) != greatest_lower_bound(X_272,identity)
    | inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))) = inverse(greatest_lower_bound(X_272,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))) )],[refute_0_3228,refute_0_3229]) ).

cnf(refute_0_3231,plain,
    inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))) = inverse(greatest_lower_bound(X_272,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)),greatest_lower_bound(X_272,identity)) )],[refute_0_3227,refute_0_3230]) ).

cnf(refute_0_3232,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30) = least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30),
    introduced(tautology,[refl,[$fot(least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30))]]) ).

cnf(refute_0_3233,plain,
    ( inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))) != inverse(greatest_lower_bound(X_272,identity))
    | least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30) != least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30)
    | least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30) = least_upper_bound(inverse(greatest_lower_bound(X_272,identity)),X_30) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30),least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30)) ),[1,0],$fot(inverse(greatest_lower_bound(X_272,identity)))]]) ).

cnf(refute_0_3234,plain,
    ( inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))) != inverse(greatest_lower_bound(X_272,identity))
    | least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30) = least_upper_bound(inverse(greatest_lower_bound(X_272,identity)),X_30) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30),least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30)) )],[refute_0_3232,refute_0_3233]) ).

cnf(refute_0_3235,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30) = least_upper_bound(inverse(greatest_lower_bound(X_272,identity)),X_30),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),inverse(greatest_lower_bound(X_272,identity))) )],[refute_0_3231,refute_0_3234]) ).

cnf(refute_0_3236,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30) != least_upper_bound(inverse(greatest_lower_bound(X_272,identity)),X_30)
    | least_upper_bound(inverse(greatest_lower_bound(X_272,identity)),X_30) != least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))
    | least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_272,identity)),X_30))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))))]]) ).

cnf(refute_0_3237,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(X_272,identity)),X_30) != least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))
    | least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30),least_upper_bound(inverse(greatest_lower_bound(X_272,identity)),X_30)) )],[refute_0_3235,refute_0_3236]) ).

cnf(refute_0_3238,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_272,identity)),X_30),least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))) )],[refute_0_3226,refute_0_3237]) ).

cnf(refute_0_3239,plain,
    least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) = least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30),
    inference(subst,[],[refute_0_3215:[bind(X,$fot(X_272)),bind(Y,$fot(greatest_lower_bound(identity,X_272))),bind(X_45,$fot(X_30))]]) ).

cnf(refute_0_3240,plain,
    ( least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) != least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30)
    | least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30) != least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))
    | least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))))]]) ).

cnf(refute_0_3241,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30) != least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))
    | least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)),least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30)) )],[refute_0_3239,refute_0_3240]) ).

cnf(refute_0_3242,plain,
    least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),X_30),least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))) )],[refute_0_3238,refute_0_3241]) ).

cnf(refute_0_3243,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))))]]) ).

cnf(refute_0_3244,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) != least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)))
    | least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) != least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) = least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))),least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)))) ),[1,1],$fot(least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))))]]) ).

cnf(refute_0_3245,plain,
    ( least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) != least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) = least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))),least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)))) )],[refute_0_3243,refute_0_3244]) ).

cnf(refute_0_3246,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) = least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)),least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))) )],[refute_0_3242,refute_0_3245]) ).

cnf(refute_0_3247,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))) != least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) != least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))))
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))))]]) ).

cnf(refute_0_3248,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))) != least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))))) )],[refute_0_3246,refute_0_3247]) ).

cnf(refute_0_3249,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))),least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))) )],[refute_0_3211,refute_0_3248]) ).

cnf(refute_0_3250,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) != least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)
    | least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))))]]) ).

cnf(refute_0_3251,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)
    | least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))),least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272)))) )],[refute_0_3249,refute_0_3250]) ).

cnf(refute_0_3252,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30) = least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30)),
    inference(subst,[],[refute_0_2549:[bind(Z,$fot(X_30)),bind(X_64,$fot(X_272))]]) ).

cnf(refute_0_3253,plain,
    ( least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30) != least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30))
    | least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))),least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))]]) ).

cnf(refute_0_3254,plain,
    ( least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)
    | least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30),least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30))) )],[refute_0_3252,refute_0_3253]) ).

cnf(refute_0_3255,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)
    | least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) )],[refute_0_3251,refute_0_3254]) ).

cnf(refute_0_3256,plain,
    least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),X_30)) )],[refute_0_3210,refute_0_3255]) ).

cnf(refute_0_3257,plain,
    ( least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) != least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30))
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30)) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30))))]]) ).

cnf(refute_0_3258,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30)) = least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_30,inverse(X_272))),least_upper_bound(identity,least_upper_bound(inverse(X_272),X_30))) )],[refute_0_3256,refute_0_3257]) ).

cnf(refute_0_3259,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_165),X_165)) = least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))),
    inference(subst,[],[refute_0_3258:[bind(X_272,$fot(X_165)),bind(X_30,$fot(X_165))]]) ).

cnf(refute_0_3260,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y),
    inference(subst,[],[refute_0_426:[bind(X_21,$fot(inverse(greatest_lower_bound(identity,X_272))))]]) ).

cnf(refute_0_3261,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))),
    inference(subst,[],[refute_0_1641:[bind(Z,$fot(least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))),bind(X_64,$fot(X_272))]]) ).

cnf(refute_0_3262,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))))]]) ).

cnf(refute_0_3263,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) )],[refute_0_3261,refute_0_3262]) ).

cnf(refute_0_3264,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) != least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))))
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))))]]) ).

cnf(refute_0_3265,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))),least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))))) )],[refute_0_3263,refute_0_3264]) ).

cnf(refute_0_3266,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) )],[refute_0_3260,refute_0_3265]) ).

cnf(refute_0_3267,plain,
    least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))) = least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))))]]) ).

cnf(refute_0_3268,plain,
    ( inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))) != inverse(greatest_lower_bound(X_272,identity))
    | least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))) != least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))))
    | least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))) = least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))),least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))))) ),[1,1],$fot(inverse(greatest_lower_bound(X_272,identity)))]]) ).

cnf(refute_0_3269,plain,
    ( inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))) != inverse(greatest_lower_bound(X_272,identity))
    | least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))) = least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))),least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))))) )],[refute_0_3267,refute_0_3268]) ).

cnf(refute_0_3270,plain,
    least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))) = least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))),inverse(greatest_lower_bound(X_272,identity))) )],[refute_0_3231,refute_0_3269]) ).

cnf(refute_0_3271,plain,
    least_upper_bound(X_82,least_upper_bound(inverse(X),inverse(Y))) = least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y))),
    inference(subst,[],[refute_0_1102:[bind(Y,$fot(X_82)),bind(X_43,$fot(inverse(X))),bind(X_45,$fot(inverse(Y)))]]) ).

cnf(refute_0_3272,plain,
    ( least_upper_bound(X_82,least_upper_bound(inverse(X),inverse(Y))) != least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y)))
    | least_upper_bound(inverse(X),inverse(Y)) != inverse(greatest_lower_bound(X,Y))
    | least_upper_bound(X_82,inverse(greatest_lower_bound(X,Y))) = least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_82,least_upper_bound(inverse(X),inverse(Y))),least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y)))) ),[0,1],$fot(inverse(greatest_lower_bound(X,Y)))]]) ).

cnf(refute_0_3273,plain,
    ( least_upper_bound(X_82,least_upper_bound(inverse(X),inverse(Y))) != least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y)))
    | least_upper_bound(X_82,inverse(greatest_lower_bound(X,Y))) = least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(Y)),inverse(greatest_lower_bound(X,Y))) )],[refute_0_136,refute_0_3272]) ).

cnf(refute_0_3274,plain,
    least_upper_bound(X_82,inverse(greatest_lower_bound(X,Y))) = least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_82,least_upper_bound(inverse(X),inverse(Y))),least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y)))) )],[refute_0_3271,refute_0_3273]) ).

cnf(refute_0_3275,plain,
    ( least_upper_bound(X_82,inverse(greatest_lower_bound(X,Y))) != least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y)))
    | least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y))) = least_upper_bound(X_82,inverse(greatest_lower_bound(X,Y))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_82,inverse(greatest_lower_bound(X,Y))))),bind(Y0,$fot(least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y)))))]]) ).

cnf(refute_0_3276,plain,
    least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y))) = least_upper_bound(X_82,inverse(greatest_lower_bound(X,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_82,inverse(greatest_lower_bound(X,Y))),least_upper_bound(inverse(X),least_upper_bound(X_82,inverse(Y)))) )],[refute_0_3274,refute_0_3275]) ).

cnf(refute_0_3277,plain,
    least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) = least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))),
    inference(subst,[],[refute_0_3276:[bind(X,$fot(X_272)),bind(Y,$fot(greatest_lower_bound(identity,X_272))),bind(X_82,$fot(Y))]]) ).

cnf(refute_0_3278,plain,
    ( least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))) != least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))
    | least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) != least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))))
    | least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) = least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))))),bind(Y0,$fot(least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))))),bind(Z0,$fot(least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))))]]) ).

cnf(refute_0_3279,plain,
    ( least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))) != least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))
    | least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) = least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))),least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272))))) )],[refute_0_3277,refute_0_3278]) ).

cnf(refute_0_3280,plain,
    least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) = least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,inverse(greatest_lower_bound(X_272,greatest_lower_bound(identity,X_272)))),least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) )],[refute_0_3270,refute_0_3279]) ).

cnf(refute_0_3281,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))))]]) ).

cnf(refute_0_3282,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) != least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))))
    | least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) != least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) = least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))),least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))))) ),[1,1],$fot(least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity))))]]) ).

cnf(refute_0_3283,plain,
    ( least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))) != least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) = least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))),least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))))) )],[refute_0_3281,refute_0_3282]) ).

cnf(refute_0_3284,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) = least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272)))),least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) )],[refute_0_3280,refute_0_3283]) ).

cnf(refute_0_3285,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) != least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity))))
    | least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)
    | least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))))]]) ).

cnf(refute_0_3286,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)
    | least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) = least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))),least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity))))) )],[refute_0_3284,refute_0_3285]) ).

cnf(refute_0_3287,plain,
    ( least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)
    | least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y) != least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))
    | least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),Y)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))),least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y))]]) ).

cnf(refute_0_3288,plain,
    ( least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)
    | least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y),least_upper_bound(identity,least_upper_bound(inverse(X_272),Y))) )],[refute_0_2128,refute_0_3287]) ).

cnf(refute_0_3289,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))) != least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)
    | least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) )],[refute_0_3286,refute_0_3288]) ).

cnf(refute_0_3290,plain,
    least_upper_bound(identity,least_upper_bound(Y,inverse(greatest_lower_bound(X_272,identity)))) = least_upper_bound(identity,least_upper_bound(inverse(X_272),Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_272),least_upper_bound(Y,inverse(greatest_lower_bound(identity,X_272))))),least_upper_bound(inverse(greatest_lower_bound(identity,X_272)),Y)) )],[refute_0_3266,refute_0_3289]) ).

cnf(refute_0_3291,plain,
    least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) = least_upper_bound(identity,least_upper_bound(inverse(X_165),X_165)),
    inference(subst,[],[refute_0_3290:[bind(Y,$fot(X_165)),bind(X_272,$fot(X_165))]]) ).

cnf(refute_0_3292,plain,
    ( least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) != least_upper_bound(identity,least_upper_bound(inverse(X_165),X_165))
    | least_upper_bound(identity,least_upper_bound(inverse(X_165),X_165)) != least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))
    | least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) = least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_165),X_165)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))))]]) ).

cnf(refute_0_3293,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_165),X_165)) != least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))
    | least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) = least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))),least_upper_bound(identity,least_upper_bound(inverse(X_165),X_165))) )],[refute_0_3291,refute_0_3292]) ).

cnf(refute_0_3294,plain,
    least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) = least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_165),X_165)),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) )],[refute_0_3259,refute_0_3293]) ).

cnf(refute_0_3295,plain,
    ( multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))) != least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))
    | least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))) != least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))
    | multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))) = least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))))]]) ).

cnf(refute_0_3296,plain,
    ( multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))) != least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))
    | multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))) = least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity)))),least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165)))) )],[refute_0_3294,refute_0_3295]) ).

cnf(refute_0_3297,plain,
    multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))) = least_upper_bound(identity,least_upper_bound(X_165,inverse(X_165))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_165,identity),inverse(greatest_lower_bound(X_165,identity))),least_upper_bound(identity,least_upper_bound(X_165,inverse(greatest_lower_bound(X_165,identity))))) )],[refute_0_3203,refute_0_3296]) ).

cnf(refute_0_3298,plain,
    multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))) = least_upper_bound(identity,least_upper_bound(b,inverse(b))),
    inference(subst,[],[refute_0_3297:[bind(X_165,$fot(b))]]) ).

cnf(refute_0_3299,plain,
    ( multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))) != least_upper_bound(identity,least_upper_bound(b,inverse(b)))
    | least_upper_bound(identity,least_upper_bound(b,inverse(b))) != least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))
    | multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(b,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(b,inverse(b))))),bind(Z0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))]]) ).

cnf(refute_0_3300,plain,
    ( least_upper_bound(identity,least_upper_bound(b,inverse(b))) != least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))
    | multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))),least_upper_bound(identity,least_upper_bound(b,inverse(b)))) )],[refute_0_3298,refute_0_3299]) ).

cnf(refute_0_3301,plain,
    multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(b,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(b,inverse(b))),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) )],[refute_0_3056,refute_0_3300]) ).

cnf(refute_0_3302,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))))]]) ).

cnf(refute_0_3303,plain,
    ( multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))) != least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))))) ),[1,1],$fot(least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_3304,plain,
    ( multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))) != least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))))) )],[refute_0_3302,refute_0_3303]) ).

cnf(refute_0_3305,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) )],[refute_0_3301,refute_0_3304]) ).

cnf(refute_0_3306,plain,
    multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))),
    inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))),bind(Y,$fot(least_upper_bound(b,identity))),bind(Z,$fot(inverse(greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_3307,plain,
    ( multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))
    | multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))))),bind(Y0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))))),bind(Z0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))))]]) ).

cnf(refute_0_3308,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))
    | multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity))))) )],[refute_0_3306,refute_0_3307]) ).

cnf(refute_0_3309,plain,
    multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(b,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) )],[refute_0_3305,refute_0_3308]) ).

cnf(refute_0_3310,plain,
    multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))) = multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))))]]) ).

cnf(refute_0_3311,plain,
    ( multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))) != multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))),multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))))) ),[1,1],$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))]]) ).

cnf(refute_0_3312,plain,
    ( multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))),multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))))) )],[refute_0_3310,refute_0_3311]) ).

cnf(refute_0_3313,plain,
    multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) )],[refute_0_3309,refute_0_3312]) ).

cnf(refute_0_3314,plain,
    multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) = multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))),
    inference(subst,[],[associativity:[bind(X,$fot(b)),bind(Y,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),bind(Z,$fot(inverse(greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_3315,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) != multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))))),bind(Y0,$fot(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))))),bind(Z0,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))))]]) ).

cnf(refute_0_3316,plain,
    ( multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))),multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity))))) )],[refute_0_3314,refute_0_3315]) ).

cnf(refute_0_3317,plain,
    multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(b,identity)))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))) )],[refute_0_3313,refute_0_3316]) ).

cnf(refute_0_3318,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))) ),[0],$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))))]]) ).

cnf(refute_0_3319,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))) )],[refute_0_3317,refute_0_3318]) ).

cnf(refute_0_3320,plain,
    multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_3321,plain,
    multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)) = multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)),
    introduced(tautology,[refl,[$fot(multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))]]) ).

cnf(refute_0_3322,plain,
    ( multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)) != multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))
    | inverse(identity) != identity
    | multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)) = multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)),multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_3323,plain,
    ( inverse(identity) != identity
    | multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)) = multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)),multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) )],[refute_0_3321,refute_0_3322]) ).

cnf(refute_0_3324,plain,
    multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)) = multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_3323]) ).

cnf(refute_0_3325,plain,
    multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_92:[bind(X_110,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),bind(X_111,$fot(b))]]) ).

cnf(refute_0_3326,plain,
    ( multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != least_upper_bound(b,identity)
    | multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) ),[0,0],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_3327,plain,
    ( multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),least_upper_bound(b,identity)) )],[refute_0_2660,refute_0_3326]) ).

cnf(refute_0_3328,plain,
    multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_3325,refute_0_3327]) ).

cnf(refute_0_3329,plain,
    ( multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))
    | least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),bind(Y0,$fot(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_3330,plain,
    least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) )],[refute_0_3328,refute_0_3329]) ).

cnf(refute_0_3331,plain,
    multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) = multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)))]]) ).

cnf(refute_0_3332,plain,
    ( multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) != multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity))
    | least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) = multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)),multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity))) ),[1,0],$fot(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))]]) ).

cnf(refute_0_3333,plain,
    ( least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) = multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)),multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity))) )],[refute_0_3331,refute_0_3332]) ).

cnf(refute_0_3334,plain,
    multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) = multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) )],[refute_0_3330,refute_0_3333]) ).

cnf(refute_0_3335,plain,
    ( multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)) != multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity)
    | multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) != multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))
    | multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) = multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)))),bind(Y0,$fot(multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))),bind(Z0,$fot(multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity)))]]) ).

cnf(refute_0_3336,plain,
    ( multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)) != multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity)
    | multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) = multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)),multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) )],[refute_0_3334,refute_0_3335]) ).

cnf(refute_0_3337,plain,
    multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) = multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)),multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity)) )],[refute_0_3324,refute_0_3336]) ).

cnf(refute_0_3338,plain,
    ( multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) != multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity)
    | multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)))),bind(Y0,$fot(multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity))),bind(Z0,$fot(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_3339,plain,
    ( multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)),multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity)) )],[refute_0_3337,refute_0_3338]) ).

cnf(refute_0_3340,plain,
    multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) )],[refute_0_3320,refute_0_3339]) ).

cnf(refute_0_3341,plain,
    multiply(least_upper_bound(X_112,X_111),inverse(X_112)) = least_upper_bound(identity,multiply(X_111,inverse(X_112))),
    inference(subst,[],[refute_0_170:[bind(X_116,$fot(X_111)),bind(X_87,$fot(X_112))]]) ).

cnf(refute_0_3342,plain,
    ( multiply(least_upper_bound(X_112,X_111),inverse(X_112)) != least_upper_bound(identity,multiply(X_111,inverse(X_112)))
    | least_upper_bound(identity,multiply(X_111,inverse(X_112))) = multiply(least_upper_bound(X_112,X_111),inverse(X_112)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_112,X_111),inverse(X_112)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_111,inverse(X_112)))))]]) ).

cnf(refute_0_3343,plain,
    least_upper_bound(identity,multiply(X_111,inverse(X_112))) = multiply(least_upper_bound(X_112,X_111),inverse(X_112)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_112,X_111),inverse(X_112)),least_upper_bound(identity,multiply(X_111,inverse(X_112)))) )],[refute_0_3341,refute_0_3342]) ).

cnf(refute_0_3344,plain,
    ( multiply(least_upper_bound(X_111,X_112),inverse(X_112)) != least_upper_bound(identity,multiply(X_111,inverse(X_112)))
    | least_upper_bound(identity,multiply(X_111,inverse(X_112))) != multiply(least_upper_bound(X_112,X_111),inverse(X_112))
    | multiply(least_upper_bound(X_111,X_112),inverse(X_112)) = multiply(least_upper_bound(X_112,X_111),inverse(X_112)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),multiply(least_upper_bound(X_112,X_111),inverse(X_112))) ),[0],$fot(least_upper_bound(identity,multiply(X_111,inverse(X_112))))]]) ).

cnf(refute_0_3345,plain,
    ( multiply(least_upper_bound(X_111,X_112),inverse(X_112)) != least_upper_bound(identity,multiply(X_111,inverse(X_112)))
    | multiply(least_upper_bound(X_111,X_112),inverse(X_112)) = multiply(least_upper_bound(X_112,X_111),inverse(X_112)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_111,inverse(X_112))),multiply(least_upper_bound(X_112,X_111),inverse(X_112))) )],[refute_0_3343,refute_0_3344]) ).

cnf(refute_0_3346,plain,
    multiply(least_upper_bound(X_111,X_112),inverse(X_112)) = multiply(least_upper_bound(X_112,X_111),inverse(X_112)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),least_upper_bound(identity,multiply(X_111,inverse(X_112)))) )],[refute_0_363,refute_0_3345]) ).

cnf(refute_0_3347,plain,
    multiply(least_upper_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),inverse(identity)) = multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)),
    inference(subst,[],[refute_0_3346:[bind(X_111,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),bind(X_112,$fot(identity))]]) ).

cnf(refute_0_3348,plain,
    multiply(least_upper_bound(identity,multiply(X_277,inverse(X_278))),inverse(multiply(X_277,inverse(X_278)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))),
    inference(subst,[],[refute_0_363:[bind(X_111,$fot(identity)),bind(X_112,$fot(multiply(X_277,inverse(X_278))))]]) ).

cnf(refute_0_3349,plain,
    ( multiply(least_upper_bound(X_278,X_277),inverse(X_278)) != least_upper_bound(identity,multiply(X_277,inverse(X_278)))
    | least_upper_bound(identity,multiply(X_277,inverse(X_278))) = multiply(least_upper_bound(X_278,X_277),inverse(X_278)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_278,X_277),inverse(X_278)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_277,inverse(X_278)))))]]) ).

cnf(refute_0_3350,plain,
    least_upper_bound(identity,multiply(X_277,inverse(X_278))) = multiply(least_upper_bound(X_278,X_277),inverse(X_278)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))) )],[refute_0_944,refute_0_3349]) ).

cnf(refute_0_3351,plain,
    ( multiply(least_upper_bound(identity,multiply(X_277,inverse(X_278))),inverse(multiply(X_277,inverse(X_278)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))
    | least_upper_bound(identity,multiply(X_277,inverse(X_278))) != multiply(least_upper_bound(X_278,X_277),inverse(X_278))
    | multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_277,inverse(X_278))),inverse(multiply(X_277,inverse(X_278)))),least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))) ),[0,0],$fot(multiply(least_upper_bound(X_278,X_277),inverse(X_278)))]]) ).

cnf(refute_0_3352,plain,
    ( multiply(least_upper_bound(identity,multiply(X_277,inverse(X_278))),inverse(multiply(X_277,inverse(X_278)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))
    | multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_277,inverse(X_278))),multiply(least_upper_bound(X_278,X_277),inverse(X_278))) )],[refute_0_3350,refute_0_3351]) ).

cnf(refute_0_3353,plain,
    multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_277,inverse(X_278))),inverse(multiply(X_277,inverse(X_278)))),least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))) )],[refute_0_3348,refute_0_3352]) ).

cnf(refute_0_3354,plain,
    multiply(X_277,identity) = X_277,
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(X_277))]]) ).

cnf(refute_0_3355,plain,
    multiply(inverse(X_278),X_278) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_278))]]) ).

cnf(refute_0_3356,plain,
    multiply(X_277,multiply(inverse(X_278),X_278)) = multiply(X_277,multiply(inverse(X_278),X_278)),
    introduced(tautology,[refl,[$fot(multiply(X_277,multiply(inverse(X_278),X_278)))]]) ).

cnf(refute_0_3357,plain,
    ( multiply(X_277,multiply(inverse(X_278),X_278)) != multiply(X_277,multiply(inverse(X_278),X_278))
    | multiply(inverse(X_278),X_278) != identity
    | multiply(X_277,multiply(inverse(X_278),X_278)) = multiply(X_277,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_277,multiply(inverse(X_278),X_278)),multiply(X_277,multiply(inverse(X_278),X_278))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_3358,plain,
    ( multiply(inverse(X_278),X_278) != identity
    | multiply(X_277,multiply(inverse(X_278),X_278)) = multiply(X_277,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_277,multiply(inverse(X_278),X_278)),multiply(X_277,multiply(inverse(X_278),X_278))) )],[refute_0_3356,refute_0_3357]) ).

cnf(refute_0_3359,plain,
    multiply(X_277,multiply(inverse(X_278),X_278)) = multiply(X_277,identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_278),X_278),identity) )],[refute_0_3355,refute_0_3358]) ).

cnf(refute_0_3360,plain,
    ( multiply(X_277,multiply(inverse(X_278),X_278)) != multiply(X_277,identity)
    | multiply(X_277,identity) != X_277
    | multiply(X_277,multiply(inverse(X_278),X_278)) = X_277 ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(X_277,multiply(inverse(X_278),X_278)))),bind(Y0,$fot(multiply(X_277,identity))),bind(Z0,$fot(X_277))]]) ).

cnf(refute_0_3361,plain,
    ( multiply(X_277,identity) != X_277
    | multiply(X_277,multiply(inverse(X_278),X_278)) = X_277 ),
    inference(resolve,[$cnf( $equal(multiply(X_277,multiply(inverse(X_278),X_278)),multiply(X_277,identity)) )],[refute_0_3359,refute_0_3360]) ).

cnf(refute_0_3362,plain,
    multiply(X_277,multiply(inverse(X_278),X_278)) = X_277,
    inference(resolve,[$cnf( $equal(multiply(X_277,identity),X_277) )],[refute_0_3354,refute_0_3361]) ).

cnf(refute_0_3363,plain,
    multiply(multiply(X_277,inverse(X_278)),X_278) = multiply(X_277,multiply(inverse(X_278),X_278)),
    inference(subst,[],[associativity:[bind(X,$fot(X_277)),bind(Y,$fot(inverse(X_278))),bind(Z,$fot(X_278))]]) ).

cnf(refute_0_3364,plain,
    ( multiply(X_277,multiply(inverse(X_278),X_278)) != X_277
    | multiply(multiply(X_277,inverse(X_278)),X_278) != multiply(X_277,multiply(inverse(X_278),X_278))
    | multiply(multiply(X_277,inverse(X_278)),X_278) = X_277 ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(X_277,inverse(X_278)),X_278))),bind(Y0,$fot(multiply(X_277,multiply(inverse(X_278),X_278)))),bind(Z0,$fot(X_277))]]) ).

cnf(refute_0_3365,plain,
    ( multiply(X_277,multiply(inverse(X_278),X_278)) != X_277
    | multiply(multiply(X_277,inverse(X_278)),X_278) = X_277 ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_277,inverse(X_278)),X_278),multiply(X_277,multiply(inverse(X_278),X_278))) )],[refute_0_3363,refute_0_3364]) ).

cnf(refute_0_3366,plain,
    multiply(multiply(X_277,inverse(X_278)),X_278) = X_277,
    inference(resolve,[$cnf( $equal(multiply(X_277,multiply(inverse(X_278),X_278)),X_277) )],[refute_0_3362,refute_0_3365]) ).

cnf(refute_0_3367,plain,
    inverse(multiply(multiply(X_277,inverse(X_278)),X_278)) = inverse(multiply(multiply(X_277,inverse(X_278)),X_278)),
    introduced(tautology,[refl,[$fot(inverse(multiply(multiply(X_277,inverse(X_278)),X_278)))]]) ).

cnf(refute_0_3368,plain,
    ( multiply(multiply(X_277,inverse(X_278)),X_278) != X_277
    | inverse(multiply(multiply(X_277,inverse(X_278)),X_278)) != inverse(multiply(multiply(X_277,inverse(X_278)),X_278))
    | inverse(multiply(multiply(X_277,inverse(X_278)),X_278)) = inverse(X_277) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(X_277,inverse(X_278)),X_278)),inverse(multiply(multiply(X_277,inverse(X_278)),X_278))) ),[1,0],$fot(X_277)]]) ).

cnf(refute_0_3369,plain,
    ( multiply(multiply(X_277,inverse(X_278)),X_278) != X_277
    | inverse(multiply(multiply(X_277,inverse(X_278)),X_278)) = inverse(X_277) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_277,inverse(X_278)),X_278)),inverse(multiply(multiply(X_277,inverse(X_278)),X_278))) )],[refute_0_3367,refute_0_3368]) ).

cnf(refute_0_3370,plain,
    inverse(multiply(multiply(X_277,inverse(X_278)),X_278)) = inverse(X_277),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_277,inverse(X_278)),X_278),X_277) )],[refute_0_3366,refute_0_3369]) ).

cnf(refute_0_3371,plain,
    multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))) = inverse(multiply(multiply(X_277,inverse(X_278)),X_278)),
    inference(subst,[],[refute_0_667:[bind(X_198,$fot(multiply(X_277,inverse(X_278)))),bind(X_59,$fot(X_278))]]) ).

cnf(refute_0_3372,plain,
    ( multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))) != inverse(multiply(multiply(X_277,inverse(X_278)),X_278))
    | inverse(multiply(multiply(X_277,inverse(X_278)),X_278)) != inverse(X_277)
    | multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))) = inverse(X_277) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))))),bind(Y0,$fot(inverse(multiply(multiply(X_277,inverse(X_278)),X_278)))),bind(Z0,$fot(inverse(X_277)))]]) ).

cnf(refute_0_3373,plain,
    ( inverse(multiply(multiply(X_277,inverse(X_278)),X_278)) != inverse(X_277)
    | multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))) = inverse(X_277) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))),inverse(multiply(multiply(X_277,inverse(X_278)),X_278))) )],[refute_0_3371,refute_0_3372]) ).

cnf(refute_0_3374,plain,
    multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))) = inverse(X_277),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_277,inverse(X_278)),X_278)),inverse(X_277)) )],[refute_0_3370,refute_0_3373]) ).

cnf(refute_0_3375,plain,
    multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))) = multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))))]]) ).

cnf(refute_0_3376,plain,
    ( multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))) != inverse(X_277)
    | multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))) != multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))))
    | multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))) = multiply(least_upper_bound(X_278,X_277),inverse(X_277)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))),multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))))) ),[1,1],$fot(inverse(X_277))]]) ).

cnf(refute_0_3377,plain,
    ( multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))) != inverse(X_277)
    | multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))) = multiply(least_upper_bound(X_278,X_277),inverse(X_277)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))),multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))))) )],[refute_0_3375,refute_0_3376]) ).

cnf(refute_0_3378,plain,
    multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))) = multiply(least_upper_bound(X_278,X_277),inverse(X_277)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))),inverse(X_277)) )],[refute_0_3374,refute_0_3377]) ).

cnf(refute_0_3379,plain,
    multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) = multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))),
    inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(X_278,X_277))),bind(Y,$fot(inverse(X_278))),bind(Z,$fot(inverse(multiply(X_277,inverse(X_278)))))]]) ).

cnf(refute_0_3380,plain,
    ( multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) != multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))))
    | multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))) != multiply(least_upper_bound(X_278,X_277),inverse(X_277))
    | multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) = multiply(least_upper_bound(X_278,X_277),inverse(X_277)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))))),bind(Y0,$fot(multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))))),bind(Z0,$fot(multiply(least_upper_bound(X_278,X_277),inverse(X_277))))]]) ).

cnf(refute_0_3381,plain,
    ( multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))) != multiply(least_upper_bound(X_278,X_277),inverse(X_277))
    | multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) = multiply(least_upper_bound(X_278,X_277),inverse(X_277)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))),multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278)))))) )],[refute_0_3379,refute_0_3380]) ).

cnf(refute_0_3382,plain,
    multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) = multiply(least_upper_bound(X_278,X_277),inverse(X_277)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),multiply(inverse(X_278),inverse(multiply(X_277,inverse(X_278))))),multiply(least_upper_bound(X_278,X_277),inverse(X_277))) )],[refute_0_3378,refute_0_3381]) ).

cnf(refute_0_3383,plain,
    ( multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) != multiply(least_upper_bound(X_278,X_277),inverse(X_277))
    | multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))
    | multiply(least_upper_bound(X_278,X_277),inverse(X_277)) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))),least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))) ),[0],$fot(multiply(least_upper_bound(X_278,X_277),inverse(X_277)))]]) ).

cnf(refute_0_3384,plain,
    ( multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))
    | multiply(least_upper_bound(X_278,X_277),inverse(X_277)) = least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))),multiply(least_upper_bound(X_278,X_277),inverse(X_277))) )],[refute_0_3382,refute_0_3383]) ).

cnf(refute_0_3385,plain,
    multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))) = inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))),
    inference(subst,[],[left_identity:[bind(X,$fot(inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))))]]) ).

cnf(refute_0_3386,plain,
    multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))) = multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))),
    inference(subst,[],[refute_0_1032:[bind(Y,$fot(multiply(X_277,inverse(X_278)))),bind(X_99,$fot(identity))]]) ).

cnf(refute_0_3387,plain,
    ( multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))) != multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))))
    | multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))) != inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))
    | multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))) = inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))))),bind(Y0,$fot(multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))))]]) ).

cnf(refute_0_3388,plain,
    ( multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))) != inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))
    | multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))) = inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))) ),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))),multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))))) )],[refute_0_3386,refute_0_3387]) ).

cnf(refute_0_3389,plain,
    multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))) = inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))),inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))) )],[refute_0_3385,refute_0_3388]) ).

cnf(refute_0_3390,plain,
    multiply(X_220,inverse(greatest_lower_bound(X_220,X_219))) = least_upper_bound(identity,multiply(X_220,inverse(X_219))),
    inference(subst,[],[refute_0_243:[bind(Y,$fot(X_219)),bind(X_99,$fot(X_220))]]) ).

cnf(refute_0_3391,plain,
    greatest_lower_bound(X_219,X_220) = greatest_lower_bound(X_220,X_219),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_219)),bind(Y,$fot(X_220))]]) ).

cnf(refute_0_3392,plain,
    ( greatest_lower_bound(X_219,X_220) != greatest_lower_bound(X_220,X_219)
    | greatest_lower_bound(X_220,X_219) = greatest_lower_bound(X_219,X_220) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_219,X_220))),bind(Y0,$fot(greatest_lower_bound(X_220,X_219)))]]) ).

cnf(refute_0_3393,plain,
    greatest_lower_bound(X_220,X_219) = greatest_lower_bound(X_219,X_220),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_219,X_220),greatest_lower_bound(X_220,X_219)) )],[refute_0_3391,refute_0_3392]) ).

cnf(refute_0_3394,plain,
    ( multiply(X_220,inverse(greatest_lower_bound(X_220,X_219))) != least_upper_bound(identity,multiply(X_220,inverse(X_219)))
    | greatest_lower_bound(X_220,X_219) != greatest_lower_bound(X_219,X_220)
    | multiply(X_220,inverse(greatest_lower_bound(X_219,X_220))) = least_upper_bound(identity,multiply(X_220,inverse(X_219))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_220,inverse(greatest_lower_bound(X_220,X_219))),least_upper_bound(identity,multiply(X_220,inverse(X_219)))) ),[0,1,0],$fot(greatest_lower_bound(X_219,X_220))]]) ).

cnf(refute_0_3395,plain,
    ( multiply(X_220,inverse(greatest_lower_bound(X_220,X_219))) != least_upper_bound(identity,multiply(X_220,inverse(X_219)))
    | multiply(X_220,inverse(greatest_lower_bound(X_219,X_220))) = least_upper_bound(identity,multiply(X_220,inverse(X_219))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_220,X_219),greatest_lower_bound(X_219,X_220)) )],[refute_0_3393,refute_0_3394]) ).

cnf(refute_0_3396,plain,
    multiply(X_220,inverse(greatest_lower_bound(X_219,X_220))) = least_upper_bound(identity,multiply(X_220,inverse(X_219))),
    inference(resolve,[$cnf( $equal(multiply(X_220,inverse(greatest_lower_bound(X_220,X_219))),least_upper_bound(identity,multiply(X_220,inverse(X_219)))) )],[refute_0_3390,refute_0_3395]) ).

cnf(refute_0_3397,plain,
    ( multiply(X_220,inverse(greatest_lower_bound(X_219,X_220))) != least_upper_bound(identity,multiply(X_220,inverse(X_219)))
    | least_upper_bound(identity,multiply(X_220,inverse(X_219))) = multiply(X_220,inverse(greatest_lower_bound(X_219,X_220))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_220,inverse(greatest_lower_bound(X_219,X_220))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_220,inverse(X_219)))))]]) ).

cnf(refute_0_3398,plain,
    least_upper_bound(identity,multiply(X_220,inverse(X_219))) = multiply(X_220,inverse(greatest_lower_bound(X_219,X_220))),
    inference(resolve,[$cnf( $equal(multiply(X_220,inverse(greatest_lower_bound(X_219,X_220))),least_upper_bound(identity,multiply(X_220,inverse(X_219)))) )],[refute_0_3396,refute_0_3397]) ).

cnf(refute_0_3399,plain,
    least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))) = multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))),
    inference(subst,[],[refute_0_3398:[bind(X_219,$fot(multiply(X_277,inverse(X_278)))),bind(X_220,$fot(identity))]]) ).

cnf(refute_0_3400,plain,
    ( multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))) != inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))
    | least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))) != multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity)))
    | least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))) = inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))))),bind(Y0,$fot(multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))))]]) ).

cnf(refute_0_3401,plain,
    ( multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))) != inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))
    | least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))) = inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))),multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity)))) )],[refute_0_3399,refute_0_3400]) ).

cnf(refute_0_3402,plain,
    least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))) = inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(greatest_lower_bound(multiply(X_277,inverse(X_278)),identity))),inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))) )],[refute_0_3389,refute_0_3401]) ).

cnf(refute_0_3403,plain,
    ( multiply(least_upper_bound(X_278,X_277),inverse(X_277)) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))
    | least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))) != inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))
    | multiply(least_upper_bound(X_278,X_277),inverse(X_277)) = inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_278,X_277),inverse(X_277)),inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))) ),[0],$fot(least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))))]]) ).

cnf(refute_0_3404,plain,
    ( multiply(least_upper_bound(X_278,X_277),inverse(X_277)) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))
    | multiply(least_upper_bound(X_278,X_277),inverse(X_277)) = inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278))))),inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))) )],[refute_0_3402,refute_0_3403]) ).

cnf(refute_0_3405,plain,
    ( multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))) != least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))
    | multiply(least_upper_bound(X_278,X_277),inverse(X_277)) = inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),inverse(X_277)),least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))) )],[refute_0_3384,refute_0_3404]) ).

cnf(refute_0_3406,plain,
    multiply(least_upper_bound(X_278,X_277),inverse(X_277)) = inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),inverse(multiply(X_277,inverse(X_278)))),least_upper_bound(identity,multiply(identity,inverse(multiply(X_277,inverse(X_278)))))) )],[refute_0_3353,refute_0_3405]) ).

cnf(refute_0_3407,plain,
    multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) = least_upper_bound(identity,multiply(X_277,inverse(greatest_lower_bound(X,X_277)))),
    inference(subst,[],[refute_0_170:[bind(X_116,$fot(X_277)),bind(X_87,$fot(greatest_lower_bound(X,X_277)))]]) ).

cnf(refute_0_3408,plain,
    multiply(X_277,inverse(greatest_lower_bound(X,X_277))) = least_upper_bound(identity,multiply(X_277,inverse(X))),
    inference(subst,[],[refute_0_258:[bind(X_96,$fot(X_277))]]) ).

cnf(refute_0_3409,plain,
    ( multiply(X_277,inverse(greatest_lower_bound(X,X_277))) != least_upper_bound(identity,multiply(X_277,inverse(X)))
    | multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) != least_upper_bound(identity,multiply(X_277,inverse(greatest_lower_bound(X,X_277))))
    | multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))),least_upper_bound(identity,multiply(X_277,inverse(greatest_lower_bound(X,X_277))))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_277,inverse(X))))]]) ).

cnf(refute_0_3410,plain,
    ( multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) != least_upper_bound(identity,multiply(X_277,inverse(greatest_lower_bound(X,X_277))))
    | multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_277,inverse(greatest_lower_bound(X,X_277))),least_upper_bound(identity,multiply(X_277,inverse(X)))) )],[refute_0_3408,refute_0_3409]) ).

cnf(refute_0_3411,plain,
    multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))),least_upper_bound(identity,multiply(X_277,inverse(greatest_lower_bound(X,X_277))))) )],[refute_0_3407,refute_0_3410]) ).

cnf(refute_0_3412,plain,
    multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))),
    inference(subst,[],[refute_0_1305:[bind(X_121,$fot(inverse(X_131))),bind(X_123,$fot(greatest_lower_bound(X_130,X_131)))]]) ).

cnf(refute_0_3413,plain,
    multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) = greatest_lower_bound(multiply(X_122,inverse(X_123)),multiply(X_123,inverse(X_123))),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(inverse(X_123))),bind(Y,$fot(X_122)),bind(Z,$fot(X_123))]]) ).

cnf(refute_0_3414,plain,
    multiply(X_123,inverse(X_123)) = identity,
    inference(subst,[],[refute_0_232:[bind(X_66,$fot(X_123))]]) ).

cnf(refute_0_3415,plain,
    ( multiply(X_123,inverse(X_123)) != identity
    | multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) != greatest_lower_bound(multiply(X_122,inverse(X_123)),multiply(X_123,inverse(X_123)))
    | multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) = greatest_lower_bound(multiply(X_122,inverse(X_123)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),greatest_lower_bound(multiply(X_122,inverse(X_123)),multiply(X_123,inverse(X_123)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_3416,plain,
    ( multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) != greatest_lower_bound(multiply(X_122,inverse(X_123)),multiply(X_123,inverse(X_123)))
    | multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) = greatest_lower_bound(multiply(X_122,inverse(X_123)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_123,inverse(X_123)),identity) )],[refute_0_3414,refute_0_3415]) ).

cnf(refute_0_3417,plain,
    multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) = greatest_lower_bound(multiply(X_122,inverse(X_123)),identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),greatest_lower_bound(multiply(X_122,inverse(X_123)),multiply(X_123,inverse(X_123)))) )],[refute_0_3413,refute_0_3416]) ).

cnf(refute_0_3418,plain,
    greatest_lower_bound(multiply(X_122,inverse(X_123)),identity) = greatest_lower_bound(identity,multiply(X_122,inverse(X_123))),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(multiply(X_122,inverse(X_123)))),bind(X_25,$fot(identity))]]) ).

cnf(refute_0_3419,plain,
    ( multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) != greatest_lower_bound(multiply(X_122,inverse(X_123)),identity)
    | greatest_lower_bound(multiply(X_122,inverse(X_123)),identity) != greatest_lower_bound(identity,multiply(X_122,inverse(X_123)))
    | multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) = greatest_lower_bound(identity,multiply(X_122,inverse(X_123))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),greatest_lower_bound(identity,multiply(X_122,inverse(X_123)))) ),[0],$fot(greatest_lower_bound(multiply(X_122,inverse(X_123)),identity))]]) ).

cnf(refute_0_3420,plain,
    ( multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) != greatest_lower_bound(multiply(X_122,inverse(X_123)),identity)
    | multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) = greatest_lower_bound(identity,multiply(X_122,inverse(X_123))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,inverse(X_123)),identity),greatest_lower_bound(identity,multiply(X_122,inverse(X_123)))) )],[refute_0_3418,refute_0_3419]) ).

cnf(refute_0_3421,plain,
    multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) = greatest_lower_bound(identity,multiply(X_122,inverse(X_123))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),greatest_lower_bound(multiply(X_122,inverse(X_123)),identity)) )],[refute_0_3417,refute_0_3420]) ).

cnf(refute_0_3422,plain,
    multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)) = greatest_lower_bound(identity,multiply(X_130,inverse(X_131))),
    inference(subst,[],[refute_0_3421:[bind(X_122,$fot(X_130)),bind(X_123,$fot(X_131))]]) ).

cnf(refute_0_3423,plain,
    ( multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)) != greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))
    | multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)))
    | multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(X_130,inverse(X_131))))]]) ).

cnf(refute_0_3424,plain,
    ( multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)))
    | multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)),greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))) )],[refute_0_3422,refute_0_3423]) ).

cnf(refute_0_3425,plain,
    multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)))) )],[refute_0_3412,refute_0_3424]) ).

cnf(refute_0_3426,plain,
    ( multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)))
    | multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131))))
    | greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131))))) ),[0],$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))))]]) ).

cnf(refute_0_3427,plain,
    ( multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131))))
    | greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))) = greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)))) )],[refute_0_3412,refute_0_3426]) ).

cnf(refute_0_3428,plain,
    greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))) = greatest_lower_bound(identity,multiply(X_130,inverse(X_131))),
    inference(subst,[],[refute_0_801:[bind(X_32,$fot(multiply(X_130,inverse(X_131)))),bind(X_33,$fot(identity))]]) ).

cnf(refute_0_3429,plain,
    ( greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131))))
    | greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))) != greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))
    | greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))) = greatest_lower_bound(identity,multiply(X_130,inverse(X_131))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))),greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))))]]) ).

cnf(refute_0_3430,plain,
    ( greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131))))
    | greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))) = greatest_lower_bound(identity,multiply(X_130,inverse(X_131))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))),greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))) )],[refute_0_3428,refute_0_3429]) ).

cnf(refute_0_3431,plain,
    ( multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)) != greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131))))
    | greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))) = greatest_lower_bound(identity,multiply(X_130,inverse(X_131))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131))))) )],[refute_0_3427,refute_0_3430]) ).

cnf(refute_0_3432,plain,
    greatest_lower_bound(identity,multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))) = greatest_lower_bound(identity,multiply(X_130,inverse(X_131))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(inverse(X_131)),greatest_lower_bound(X_130,X_131)),inverse(X_131)),greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(X_130,inverse(X_131))))) )],[refute_0_3425,refute_0_3431]) ).

cnf(refute_0_3433,plain,
    greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))) = greatest_lower_bound(identity,multiply(X,inverse(X_277))),
    inference(subst,[],[refute_0_3432:[bind(X_130,$fot(X)),bind(X_131,$fot(X_277))]]) ).

cnf(refute_0_3434,plain,
    inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))) = inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))))]]) ).

cnf(refute_0_3435,plain,
    ( greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))) != greatest_lower_bound(identity,multiply(X,inverse(X_277)))
    | inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))) != inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))))
    | inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))) = inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X,inverse(X_277))))]]) ).

cnf(refute_0_3436,plain,
    ( greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))) != greatest_lower_bound(identity,multiply(X,inverse(X_277)))
    | inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))) = inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))))) )],[refute_0_3434,refute_0_3435]) ).

cnf(refute_0_3437,plain,
    inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))) = inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))),greatest_lower_bound(identity,multiply(X,inverse(X_277)))) )],[refute_0_3433,refute_0_3436]) ).

cnf(refute_0_3438,plain,
    multiply(least_upper_bound(X_277,greatest_lower_bound(X,X_277)),inverse(greatest_lower_bound(X,X_277))) = inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))),
    inference(subst,[],[refute_0_3406:[bind(X_277,$fot(greatest_lower_bound(X,X_277))),bind(X_278,$fot(X_277))]]) ).

cnf(refute_0_3439,plain,
    ( multiply(least_upper_bound(X_111,X_112),inverse(X_112)) != multiply(least_upper_bound(X_112,X_111),inverse(X_112))
    | multiply(least_upper_bound(X_112,X_111),inverse(X_112)) = multiply(least_upper_bound(X_111,X_112),inverse(X_112)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_111,X_112),inverse(X_112)))),bind(Y0,$fot(multiply(least_upper_bound(X_112,X_111),inverse(X_112))))]]) ).

cnf(refute_0_3440,plain,
    multiply(least_upper_bound(X_112,X_111),inverse(X_112)) = multiply(least_upper_bound(X_111,X_112),inverse(X_112)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),multiply(least_upper_bound(X_112,X_111),inverse(X_112))) )],[refute_0_3346,refute_0_3439]) ).

cnf(refute_0_3441,plain,
    multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) = multiply(least_upper_bound(X_277,greatest_lower_bound(X,X_277)),inverse(greatest_lower_bound(X,X_277))),
    inference(subst,[],[refute_0_3440:[bind(X_111,$fot(X_277)),bind(X_112,$fot(greatest_lower_bound(X,X_277)))]]) ).

cnf(refute_0_3442,plain,
    ( multiply(least_upper_bound(X_277,greatest_lower_bound(X,X_277)),inverse(greatest_lower_bound(X,X_277))) != inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))))
    | multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) != multiply(least_upper_bound(X_277,greatest_lower_bound(X,X_277)),inverse(greatest_lower_bound(X,X_277)))
    | multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) = inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))))),bind(Y0,$fot(multiply(least_upper_bound(X_277,greatest_lower_bound(X,X_277)),inverse(greatest_lower_bound(X,X_277))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))))))]]) ).

cnf(refute_0_3443,plain,
    ( multiply(least_upper_bound(X_277,greatest_lower_bound(X,X_277)),inverse(greatest_lower_bound(X,X_277))) != inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))))
    | multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) = inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))),multiply(least_upper_bound(X_277,greatest_lower_bound(X,X_277)),inverse(greatest_lower_bound(X,X_277)))) )],[refute_0_3441,refute_0_3442]) ).

cnf(refute_0_3444,plain,
    multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) = inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_277,greatest_lower_bound(X,X_277)),inverse(greatest_lower_bound(X,X_277))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))))) )],[refute_0_3438,refute_0_3443]) ).

cnf(refute_0_3445,plain,
    ( multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) != inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))))
    | inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))) != inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277))))
    | multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) = inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277))))))]]) ).

cnf(refute_0_3446,plain,
    ( inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))) != inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277))))
    | multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) = inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))),inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277))))) )],[refute_0_3444,refute_0_3445]) ).

cnf(refute_0_3447,plain,
    multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) = inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(X,X_277),inverse(X_277)))),inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277))))) )],[refute_0_3437,refute_0_3446]) ).

cnf(refute_0_3448,plain,
    ( multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) != inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277))))
    | multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X))))
    | inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X))))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))))]]) ).

cnf(refute_0_3449,plain,
    ( multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X))))
    | inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) = least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))),inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277))))) )],[refute_0_3447,refute_0_3448]) ).

cnf(refute_0_3450,plain,
    least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X)))) = least_upper_bound(identity,multiply(X_277,inverse(X))),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(multiply(X_277,inverse(X)))),bind(X_31,$fot(identity))]]) ).

cnf(refute_0_3451,plain,
    ( inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X))))
    | least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X)))) != least_upper_bound(identity,multiply(X_277,inverse(X)))
    | inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) = least_upper_bound(identity,multiply(X_277,inverse(X))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))),least_upper_bound(identity,multiply(X_277,inverse(X)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X)))))]]) ).

cnf(refute_0_3452,plain,
    ( inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X))))
    | inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) = least_upper_bound(identity,multiply(X_277,inverse(X))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X)))),least_upper_bound(identity,multiply(X_277,inverse(X)))) )],[refute_0_3450,refute_0_3451]) ).

cnf(refute_0_3453,plain,
    ( multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))) != least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X))))
    | inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) = least_upper_bound(identity,multiply(X_277,inverse(X))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X))))) )],[refute_0_3449,refute_0_3452]) ).

cnf(refute_0_3454,plain,
    inverse(greatest_lower_bound(identity,multiply(X,inverse(X_277)))) = least_upper_bound(identity,multiply(X_277,inverse(X))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X,X_277),X_277),inverse(greatest_lower_bound(X,X_277))),least_upper_bound(identity,least_upper_bound(identity,multiply(X_277,inverse(X))))) )],[refute_0_3411,refute_0_3453]) ).

cnf(refute_0_3455,plain,
    inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))) = least_upper_bound(identity,multiply(X_278,inverse(X_277))),
    inference(subst,[],[refute_0_3454:[bind(X,$fot(X_277)),bind(X_277,$fot(X_278))]]) ).

cnf(refute_0_3456,plain,
    ( multiply(least_upper_bound(X_278,X_277),inverse(X_277)) != inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))
    | inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))) != least_upper_bound(identity,multiply(X_278,inverse(X_277)))
    | multiply(least_upper_bound(X_278,X_277),inverse(X_277)) = least_upper_bound(identity,multiply(X_278,inverse(X_277))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_278,X_277),inverse(X_277)),least_upper_bound(identity,multiply(X_278,inverse(X_277)))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))))]]) ).

cnf(refute_0_3457,plain,
    ( multiply(least_upper_bound(X_278,X_277),inverse(X_277)) != inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))
    | multiply(least_upper_bound(X_278,X_277),inverse(X_277)) = least_upper_bound(identity,multiply(X_278,inverse(X_277))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278)))),least_upper_bound(identity,multiply(X_278,inverse(X_277)))) )],[refute_0_3455,refute_0_3456]) ).

cnf(refute_0_3458,plain,
    multiply(least_upper_bound(X_278,X_277),inverse(X_277)) = least_upper_bound(identity,multiply(X_278,inverse(X_277))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),inverse(X_277)),inverse(greatest_lower_bound(identity,multiply(X_277,inverse(X_278))))) )],[refute_0_3406,refute_0_3457]) ).

cnf(refute_0_3459,plain,
    ( multiply(least_upper_bound(X_278,X_277),inverse(X_277)) != least_upper_bound(identity,multiply(X_278,inverse(X_277)))
    | least_upper_bound(identity,multiply(X_278,inverse(X_277))) = multiply(least_upper_bound(X_278,X_277),inverse(X_277)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_278,X_277),inverse(X_277)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_278,inverse(X_277)))))]]) ).

cnf(refute_0_3460,plain,
    least_upper_bound(identity,multiply(X_278,inverse(X_277))) = multiply(least_upper_bound(X_278,X_277),inverse(X_277)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),inverse(X_277)),least_upper_bound(identity,multiply(X_278,inverse(X_277)))) )],[refute_0_3458,refute_0_3459]) ).

cnf(refute_0_3461,plain,
    least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) = multiply(least_upper_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),inverse(identity)),
    inference(subst,[],[refute_0_3460:[bind(X_277,$fot(identity)),bind(X_278,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_3462,plain,
    ( multiply(least_upper_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),inverse(identity)) != multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity))
    | least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) != multiply(least_upper_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),inverse(identity))
    | least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) = multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))))),bind(Y0,$fot(multiply(least_upper_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),inverse(identity)))),bind(Z0,$fot(multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity))))]]) ).

cnf(refute_0_3463,plain,
    ( multiply(least_upper_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),inverse(identity)) != multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity))
    | least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) = multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))),multiply(least_upper_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),inverse(identity))) )],[refute_0_3461,refute_0_3462]) ).

cnf(refute_0_3464,plain,
    least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) = multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),identity),inverse(identity)),multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity))) )],[refute_0_3347,refute_0_3463]) ).

cnf(refute_0_3465,plain,
    ( multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) != multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity))
    | least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)))),bind(Z0,$fot(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_3466,plain,
    ( multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))),multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity))) )],[refute_0_3464,refute_0_3465]) ).

cnf(refute_0_3467,plain,
    least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),inverse(identity)),multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) )],[refute_0_3340,refute_0_3466]) ).

cnf(refute_0_3468,plain,
    ( multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))
    | least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))),multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),[0],$fot(least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))))]]) ).

cnf(refute_0_3469,plain,
    ( multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity))),multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) )],[refute_0_3467,refute_0_3468]) ).

cnf(refute_0_3470,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))) )],[refute_0_3319,refute_0_3469]) ).

cnf(refute_0_3471,plain,
    multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(b,identity))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(identity)))) )],[refute_0_2817,refute_0_3470]) ).

cnf(refute_0_3472,plain,
    least_upper_bound(b,inverse(greatest_lower_bound(b,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(b,identity))),
    introduced(tautology,[refl,[$fot(least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_3473,plain,
    ( inverse(greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(b,inverse(greatest_lower_bound(b,identity))) != least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))
    | least_upper_bound(b,inverse(greatest_lower_bound(b,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(b,identity))),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) ),[1,1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3474,plain,
    ( inverse(greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(b,inverse(greatest_lower_bound(b,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(b,identity))),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) )],[refute_0_3472,refute_0_3473]) ).

cnf(refute_0_3475,plain,
    least_upper_bound(b,inverse(greatest_lower_bound(b,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2216,refute_0_3474]) ).

cnf(refute_0_3476,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))]]) ).

cnf(refute_0_3477,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))
    | least_upper_bound(b,inverse(greatest_lower_bound(b,identity))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) ),[1,1],$fot(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3478,plain,
    ( least_upper_bound(b,inverse(greatest_lower_bound(b,identity))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) )],[refute_0_3476,refute_0_3477]) ).

cnf(refute_0_3479,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(b,identity))),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_3475,refute_0_3478]) ).

cnf(refute_0_3480,plain,
    multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))),
    introduced(tautology,[refl,[$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))))]]) ).

cnf(refute_0_3481,plain,
    ( multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))) ),[1,1],$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3482,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))))) )],[refute_0_3480,refute_0_3481]) ).

cnf(refute_0_3483,plain,
    multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3479,refute_0_3482]) ).

cnf(refute_0_3484,plain,
    ( multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))),multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) ),[0],$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_3485,plain,
    ( multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_3483,refute_0_3484]) ).

cnf(refute_0_3486,plain,
    multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(b,identity))))),multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) )],[refute_0_3471,refute_0_3485]) ).

cnf(refute_0_3487,plain,
    multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,inverse(greatest_lower_bound(a,identity)))),
    inference(subst,[],[refute_0_728:[bind(X_110,$fot(inverse(greatest_lower_bound(a,identity)))),bind(X_111,$fot(b))]]) ).

cnf(refute_0_3488,plain,
    multiply(b,least_upper_bound(inverse(b),greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))),
    inference(subst,[],[refute_0_236:[bind(X_93,$fot(b)),bind(X_95,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3489,plain,
    ( multiply(b,least_upper_bound(inverse(b),greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))
    | least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) != inverse(greatest_lower_bound(a,identity))
    | multiply(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(b,least_upper_bound(inverse(b),greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))) ),[0,1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3490,plain,
    ( multiply(b,least_upper_bound(inverse(b),greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))
    | multiply(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2104,refute_0_3489]) ).

cnf(refute_0_3491,plain,
    multiply(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(b,least_upper_bound(inverse(b),greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))) )],[refute_0_3488,refute_0_3490]) ).

cnf(refute_0_3492,plain,
    multiply(inverse(inverse(b)),least_upper_bound(inverse(b),greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))),
    inference(subst,[],[refute_0_1801:[bind(X_94,$fot(inverse(b))),bind(X_95,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3493,plain,
    ( multiply(inverse(inverse(b)),least_upper_bound(inverse(b),greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))
    | least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) != inverse(greatest_lower_bound(a,identity))
    | multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(b)),least_upper_bound(inverse(b),greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))) ),[0,1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3494,plain,
    ( multiply(inverse(inverse(b)),least_upper_bound(inverse(b),greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))
    | multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2104,refute_0_3493]) ).

cnf(refute_0_3495,plain,
    multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(b)),least_upper_bound(inverse(b),greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))) )],[refute_0_3492,refute_0_3494]) ).

cnf(refute_0_3496,plain,
    inverse(inverse(least_upper_bound(b,identity))) = least_upper_bound(b,identity),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_3497,plain,
    multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_508:[bind(Y,$fot(greatest_lower_bound(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_3498,plain,
    ( multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | inverse(greatest_lower_bound(a,least_upper_bound(b,identity))) != inverse(b)
    | multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) ),[0,1],$fot(inverse(b))]]) ).

cnf(refute_0_3499,plain,
    ( multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) )],[refute_0_1268,refute_0_3498]) ).

cnf(refute_0_3500,plain,
    multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,least_upper_bound(b,identity)))),inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_3497,refute_0_3499]) ).

cnf(refute_0_3501,plain,
    multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)) = multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)))]]) ).

cnf(refute_0_3502,plain,
    ( multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)) != multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b))
    | greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)) != greatest_lower_bound(a,identity)
    | multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)) = multiply(greatest_lower_bound(a,identity),inverse(b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)),multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b))) ),[1,0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_3503,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)) != greatest_lower_bound(a,identity)
    | multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)) = multiply(greatest_lower_bound(a,identity),inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)),multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b))) )],[refute_0_3501,refute_0_3502]) ).

cnf(refute_0_3504,plain,
    multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)) = multiply(greatest_lower_bound(a,identity),inverse(b)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),greatest_lower_bound(a,identity)) )],[refute_0_1497,refute_0_3503]) ).

cnf(refute_0_3505,plain,
    multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121) = greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_121)),bind(Y,$fot(X_122)),bind(Z,$fot(greatest_lower_bound(X_37,X)))]]) ).

cnf(refute_0_3506,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)) = greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),
    inference(subst,[],[refute_0_839:[bind(X_36,$fot(X_122))]]) ).

cnf(refute_0_3507,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)) != greatest_lower_bound(X_122,greatest_lower_bound(X_37,X))
    | greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)) = greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)))),bind(Y0,$fot(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X))))]]) ).

cnf(refute_0_3508,plain,
    greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)) = greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),greatest_lower_bound(X_122,greatest_lower_bound(X_37,X))) )],[refute_0_3506,refute_0_3507]) ).

cnf(refute_0_3509,plain,
    ( multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121) != greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121))
    | greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)) != greatest_lower_bound(X,greatest_lower_bound(X_122,X_37))
    | multiply(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),X_121) = greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121))) ),[0,0],$fot(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)))]]) ).

cnf(refute_0_3510,plain,
    ( multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121) != greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121))
    | multiply(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),X_121) = greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),greatest_lower_bound(X,greatest_lower_bound(X_122,X_37))) )],[refute_0_3508,refute_0_3509]) ).

cnf(refute_0_3511,plain,
    multiply(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),X_121) = greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121))) )],[refute_0_3505,refute_0_3510]) ).

cnf(refute_0_3512,plain,
    greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121)) = multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121),
    inference(subst,[],[refute_0_1238:[bind(X,$fot(X_121)),bind(Y,$fot(X_122)),bind(Z,$fot(greatest_lower_bound(X_37,X)))]]) ).

cnf(refute_0_3513,plain,
    ( multiply(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),X_121) != greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121))
    | greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121)) != multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121)
    | multiply(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),X_121) = multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),X_121),multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121)) ),[0],$fot(greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121)))]]) ).

cnf(refute_0_3514,plain,
    ( multiply(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),X_121) != greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121))
    | multiply(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),X_121) = multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121)),multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121)) )],[refute_0_3512,refute_0_3513]) ).

cnf(refute_0_3515,plain,
    multiply(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),X_121) = multiply(greatest_lower_bound(X_122,greatest_lower_bound(X_37,X)),X_121),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X,greatest_lower_bound(X_122,X_37)),X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(greatest_lower_bound(X_37,X),X_121))) )],[refute_0_3511,refute_0_3514]) ).

cnf(refute_0_3516,plain,
    multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) = multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)),
    inference(subst,[],[refute_0_3515:[bind(X,$fot(identity)),bind(X_121,$fot(inverse(b))),bind(X_122,$fot(a)),bind(X_37,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_3517,plain,
    ( multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)) != multiply(greatest_lower_bound(a,identity),inverse(b))
    | multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) != multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b))
    | multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) = multiply(greatest_lower_bound(a,identity),inverse(b)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)))),bind(Y0,$fot(multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)))),bind(Z0,$fot(multiply(greatest_lower_bound(a,identity),inverse(b))))]]) ).

cnf(refute_0_3518,plain,
    ( multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)) != multiply(greatest_lower_bound(a,identity),inverse(b))
    | multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) = multiply(greatest_lower_bound(a,identity),inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)),multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b))) )],[refute_0_3516,refute_0_3517]) ).

cnf(refute_0_3519,plain,
    multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) = multiply(greatest_lower_bound(a,identity),inverse(b)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(b,identity),identity)),inverse(b)),multiply(greatest_lower_bound(a,identity),inverse(b))) )],[refute_0_3504,refute_0_3518]) ).

cnf(refute_0_3520,plain,
    ( multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) != multiply(greatest_lower_bound(a,identity),inverse(b))
    | multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | multiply(greatest_lower_bound(a,identity),inverse(b)) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)),inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) ),[0],$fot(multiply(greatest_lower_bound(a,identity),inverse(b)))]]) ).

cnf(refute_0_3521,plain,
    ( multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | multiply(greatest_lower_bound(a,identity),inverse(b)) = inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)),multiply(greatest_lower_bound(a,identity),inverse(b))) )],[refute_0_3519,refute_0_3520]) ).

cnf(refute_0_3522,plain,
    ( multiply(greatest_lower_bound(a,identity),inverse(b)) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))) != multiply(inverse(b),greatest_lower_bound(a,identity))
    | multiply(greatest_lower_bound(a,identity),inverse(b)) = multiply(inverse(b),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(a,identity),inverse(b)),multiply(inverse(b),greatest_lower_bound(a,identity))) ),[0],$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_3523,plain,
    ( multiply(greatest_lower_bound(a,identity),inverse(b)) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | multiply(greatest_lower_bound(a,identity),inverse(b)) = multiply(inverse(b),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity)))),multiply(inverse(b),greatest_lower_bound(a,identity))) )],[refute_0_1527,refute_0_3522]) ).

cnf(refute_0_3524,plain,
    ( multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)) != inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))
    | multiply(greatest_lower_bound(a,identity),inverse(b)) = multiply(inverse(b),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),inverse(b)),inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_3521,refute_0_3523]) ).

cnf(refute_0_3525,plain,
    multiply(greatest_lower_bound(a,identity),inverse(b)) = multiply(inverse(b),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))),inverse(b)),inverse(least_upper_bound(identity,greatest_lower_bound(a,least_upper_bound(b,identity))))) )],[refute_0_3500,refute_0_3524]) ).

cnf(refute_0_3526,plain,
    ( multiply(greatest_lower_bound(a,identity),inverse(b)) != multiply(inverse(b),greatest_lower_bound(a,identity))
    | multiply(inverse(b),greatest_lower_bound(a,identity)) != inverse(least_upper_bound(b,identity))
    | multiply(greatest_lower_bound(a,identity),inverse(b)) = inverse(least_upper_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(a,identity),inverse(b)),inverse(least_upper_bound(b,identity))) ),[0],$fot(multiply(inverse(b),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3527,plain,
    ( multiply(greatest_lower_bound(a,identity),inverse(b)) != multiply(inverse(b),greatest_lower_bound(a,identity))
    | multiply(greatest_lower_bound(a,identity),inverse(b)) = inverse(least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(b),greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))) )],[refute_0_1533,refute_0_3526]) ).

cnf(refute_0_3528,plain,
    multiply(greatest_lower_bound(a,identity),inverse(b)) = inverse(least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),inverse(b)),multiply(inverse(b),greatest_lower_bound(a,identity))) )],[refute_0_3525,refute_0_3527]) ).

cnf(refute_0_3529,plain,
    inverse(multiply(greatest_lower_bound(a,identity),inverse(b))) = inverse(multiply(greatest_lower_bound(a,identity),inverse(b))),
    introduced(tautology,[refl,[$fot(inverse(multiply(greatest_lower_bound(a,identity),inverse(b))))]]) ).

cnf(refute_0_3530,plain,
    ( multiply(greatest_lower_bound(a,identity),inverse(b)) != inverse(least_upper_bound(b,identity))
    | inverse(multiply(greatest_lower_bound(a,identity),inverse(b))) != inverse(multiply(greatest_lower_bound(a,identity),inverse(b)))
    | inverse(multiply(greatest_lower_bound(a,identity),inverse(b))) = inverse(inverse(least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(greatest_lower_bound(a,identity),inverse(b))),inverse(multiply(greatest_lower_bound(a,identity),inverse(b)))) ),[1,0],$fot(inverse(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_3531,plain,
    ( multiply(greatest_lower_bound(a,identity),inverse(b)) != inverse(least_upper_bound(b,identity))
    | inverse(multiply(greatest_lower_bound(a,identity),inverse(b))) = inverse(inverse(least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(a,identity),inverse(b))),inverse(multiply(greatest_lower_bound(a,identity),inverse(b)))) )],[refute_0_3529,refute_0_3530]) ).

cnf(refute_0_3532,plain,
    inverse(multiply(greatest_lower_bound(a,identity),inverse(b))) = inverse(inverse(least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),inverse(b)),inverse(least_upper_bound(b,identity))) )],[refute_0_3528,refute_0_3531]) ).

cnf(refute_0_3533,plain,
    ( inverse(multiply(greatest_lower_bound(a,identity),inverse(b))) != inverse(inverse(least_upper_bound(b,identity)))
    | inverse(inverse(least_upper_bound(b,identity))) != least_upper_bound(b,identity)
    | inverse(multiply(greatest_lower_bound(a,identity),inverse(b))) = least_upper_bound(b,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(multiply(greatest_lower_bound(a,identity),inverse(b))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(b,identity))))),bind(Z0,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_3534,plain,
    ( inverse(inverse(least_upper_bound(b,identity))) != least_upper_bound(b,identity)
    | inverse(multiply(greatest_lower_bound(a,identity),inverse(b))) = least_upper_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(a,identity),inverse(b))),inverse(inverse(least_upper_bound(b,identity)))) )],[refute_0_3532,refute_0_3533]) ).

cnf(refute_0_3535,plain,
    inverse(multiply(greatest_lower_bound(a,identity),inverse(b))) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(b,identity))),least_upper_bound(b,identity)) )],[refute_0_3496,refute_0_3534]) ).

cnf(refute_0_3536,plain,
    multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) = inverse(multiply(greatest_lower_bound(a,identity),inverse(b))),
    inference(subst,[],[refute_0_667:[bind(X_198,$fot(greatest_lower_bound(a,identity))),bind(X_59,$fot(inverse(b)))]]) ).

cnf(refute_0_3537,plain,
    ( multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) != inverse(multiply(greatest_lower_bound(a,identity),inverse(b)))
    | inverse(multiply(greatest_lower_bound(a,identity),inverse(b))) != least_upper_bound(b,identity)
    | multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))))),bind(Y0,$fot(inverse(multiply(greatest_lower_bound(a,identity),inverse(b))))),bind(Z0,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_3538,plain,
    ( inverse(multiply(greatest_lower_bound(a,identity),inverse(b))) != least_upper_bound(b,identity)
    | multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))),inverse(multiply(greatest_lower_bound(a,identity),inverse(b)))) )],[refute_0_3536,refute_0_3537]) ).

cnf(refute_0_3539,plain,
    multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(inverse(multiply(greatest_lower_bound(a,identity),inverse(b))),least_upper_bound(b,identity)) )],[refute_0_3535,refute_0_3538]) ).

cnf(refute_0_3540,plain,
    ( multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(b,identity)
    | multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))
    | least_upper_bound(b,identity) = least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))) ),[0],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_3541,plain,
    ( multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))
    | least_upper_bound(b,identity) = least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))),least_upper_bound(b,identity)) )],[refute_0_3539,refute_0_3540]) ).

cnf(refute_0_3542,plain,
    multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)) = multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)),
    introduced(tautology,[refl,[$fot(multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3543,plain,
    ( multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)) != multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))
    | inverse(inverse(b)) != b
    | multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)) = multiply(b,greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)),multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) ),[1,0],$fot(b)]]) ).

cnf(refute_0_3544,plain,
    ( inverse(inverse(b)) != b
    | multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)) = multiply(b,greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)),multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) )],[refute_0_3542,refute_0_3543]) ).

cnf(refute_0_3545,plain,
    multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)) = multiply(b,greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),b) )],[refute_0_1272,refute_0_3544]) ).

cnf(refute_0_3546,plain,
    least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3547,plain,
    ( multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)) != multiply(b,greatest_lower_bound(a,identity))
    | least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))
    | least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))) ),[1,1],$fot(multiply(b,greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3548,plain,
    ( multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)) != multiply(b,greatest_lower_bound(a,identity))
    | least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))) )],[refute_0_3546,refute_0_3547]) ).

cnf(refute_0_3549,plain,
    least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)),multiply(b,greatest_lower_bound(a,identity))) )],[refute_0_3545,refute_0_3548]) ).

cnf(refute_0_3550,plain,
    ( least_upper_bound(b,identity) != least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))
    | least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))
    | least_upper_bound(b,identity) = least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(b,identity),least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3551,plain,
    ( least_upper_bound(b,identity) != least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))
    | least_upper_bound(b,identity) = least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))) )],[refute_0_3549,refute_0_3550]) ).

cnf(refute_0_3552,plain,
    ( multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))
    | least_upper_bound(b,identity) = least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))) )],[refute_0_3541,refute_0_3551]) ).

cnf(refute_0_3553,plain,
    least_upper_bound(b,identity) = least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(b)),inverse(greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(inverse(inverse(b)),greatest_lower_bound(a,identity)))) )],[refute_0_3495,refute_0_3552]) ).

cnf(refute_0_3554,plain,
    ( least_upper_bound(b,identity) != least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))
    | least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))) = least_upper_bound(b,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(b,identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3555,plain,
    least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))) )],[refute_0_3553,refute_0_3554]) ).

cnf(refute_0_3556,plain,
    ( multiply(b,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))
    | least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))) != least_upper_bound(b,identity)
    | multiply(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,identity) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(b,inverse(greatest_lower_bound(a,identity))),least_upper_bound(b,identity)) ),[0],$fot(least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3557,plain,
    ( multiply(b,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))
    | multiply(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity))),least_upper_bound(b,identity)) )],[refute_0_3555,refute_0_3556]) ).

cnf(refute_0_3558,plain,
    multiply(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(b,greatest_lower_bound(a,identity)))) )],[refute_0_3491,refute_0_3557]) ).

cnf(refute_0_3559,plain,
    ( multiply(b,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(b,identity)
    | multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,inverse(greatest_lower_bound(a,identity))))
    | multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))),least_upper_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,inverse(greatest_lower_bound(a,identity))))) ),[1,1],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_3560,plain,
    ( multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,inverse(greatest_lower_bound(a,identity))))
    | multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(a,identity))),least_upper_bound(b,identity)) )],[refute_0_3558,refute_0_3559]) ).

cnf(refute_0_3561,plain,
    multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))),least_upper_bound(inverse(greatest_lower_bound(a,identity)),multiply(b,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3487,refute_0_3560]) ).

cnf(refute_0_3562,plain,
    greatest_lower_bound(identity,identity) = identity,
    inference(subst,[],[idempotence_of_gld:[bind(X,$fot(identity))]]) ).

cnf(refute_0_3563,plain,
    greatest_lower_bound(b,greatest_lower_bound(identity,identity)) = greatest_lower_bound(b,greatest_lower_bound(identity,identity)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(b,greatest_lower_bound(identity,identity)))]]) ).

cnf(refute_0_3564,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(identity,identity)) != greatest_lower_bound(b,greatest_lower_bound(identity,identity))
    | greatest_lower_bound(identity,identity) != identity
    | greatest_lower_bound(b,greatest_lower_bound(identity,identity)) = greatest_lower_bound(b,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,identity)),greatest_lower_bound(b,greatest_lower_bound(identity,identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_3565,plain,
    ( greatest_lower_bound(identity,identity) != identity
    | greatest_lower_bound(b,greatest_lower_bound(identity,identity)) = greatest_lower_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,identity)),greatest_lower_bound(b,greatest_lower_bound(identity,identity))) )],[refute_0_3563,refute_0_3564]) ).

cnf(refute_0_3566,plain,
    greatest_lower_bound(b,greatest_lower_bound(identity,identity)) = greatest_lower_bound(b,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,identity),identity) )],[refute_0_3562,refute_0_3565]) ).

cnf(refute_0_3567,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(identity,identity)) != greatest_lower_bound(b,identity)
    | greatest_lower_bound(b,identity) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(b,greatest_lower_bound(identity,identity)) = greatest_lower_bound(a,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(b,greatest_lower_bound(identity,identity)))),bind(Y0,$fot(greatest_lower_bound(b,identity))),bind(Z0,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3568,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(b,greatest_lower_bound(identity,identity)) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,identity)),greatest_lower_bound(b,identity)) )],[refute_0_3566,refute_0_3567]) ).

cnf(refute_0_3569,plain,
    greatest_lower_bound(b,greatest_lower_bound(identity,identity)) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(a,identity)) )],[refute_0_2212,refute_0_3568]) ).

cnf(refute_0_3570,plain,
    inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))))]]) ).

cnf(refute_0_3571,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(identity,identity)) != greatest_lower_bound(a,identity)
    | inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity)))
    | inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))) = inverse(greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))),inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity)))) ),[1,0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_3572,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(identity,identity)) != greatest_lower_bound(a,identity)
    | inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))),inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity)))) )],[refute_0_3570,refute_0_3571]) ).

cnf(refute_0_3573,plain,
    inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(identity,identity)),greatest_lower_bound(a,identity)) )],[refute_0_3569,refute_0_3572]) ).

cnf(refute_0_3574,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) = least_upper_bound(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),inverse(Y)),
    inference(subst,[],[p12x_3:[bind(X,$fot(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_3575,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) != least_upper_bound(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),inverse(Y))
    | inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(b,identity))
    | inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) = least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)),least_upper_bound(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),inverse(Y))) ),[1,0],$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_3576,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) != least_upper_bound(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),inverse(Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) = least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2739,refute_0_3575]) ).

cnf(refute_0_3577,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) = least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)),least_upper_bound(inverse(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),inverse(Y))) )],[refute_0_3574,refute_0_3576]) ).

cnf(refute_0_3578,plain,
    greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(identity)),bind(Y,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),bind(Z,$fot(Y))]]) ).

cnf(refute_0_3579,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) = inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)))]]) ).

cnf(refute_0_3580,plain,
    ( greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y) != greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) != inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) = inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)),inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y))) ),[1,0],$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y)))]]) ).

cnf(refute_0_3581,plain,
    ( greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y) != greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) = inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)),inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y))) )],[refute_0_3579,refute_0_3580]) ).

cnf(refute_0_3582,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) = inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y),greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) )],[refute_0_3578,refute_0_3581]) ).

cnf(refute_0_3583,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) != inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y)))
    | inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) != least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) = least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)),least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y))) ),[0],$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))))]]) ).

cnf(refute_0_3584,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) != least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) = least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)),inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y)))) )],[refute_0_3582,refute_0_3583]) ).

cnf(refute_0_3585,plain,
    multiply(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),X_60) = multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(greatest_lower_bound(X_24,X_25)))),bind(Y,$fot(greatest_lower_bound(X_25,X_24))),bind(Z,$fot(X_60))]]) ).

cnf(refute_0_3586,plain,
    ( multiply(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),X_60) != multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)) != identity
    | multiply(identity,X_60) = multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),X_60),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_3587,plain,
    ( multiply(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),X_60) != multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))
    | multiply(identity,X_60) = multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),identity) )],[refute_0_144,refute_0_3586]) ).

cnf(refute_0_3588,plain,
    multiply(identity,X_60) = multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_25,X_24)),X_60),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))) )],[refute_0_3585,refute_0_3587]) ).

cnf(refute_0_3589,plain,
    ( multiply(identity,X_60) != X_60
    | multiply(identity,X_60) != multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))
    | X_60 = multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_60),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))) ),[0],$fot(X_60)]]) ).

cnf(refute_0_3590,plain,
    ( multiply(identity,X_60) != multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))
    | X_60 = multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_60),X_60) )],[refute_0_5,refute_0_3589]) ).

cnf(refute_0_3591,plain,
    X_60 = multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_60),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))) )],[refute_0_3588,refute_0_3590]) ).

cnf(refute_0_3592,plain,
    inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) = multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))))),
    inference(subst,[],[refute_0_3591:[bind(X_60,$fot(inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24)))))]]) ).

cnf(refute_0_3593,plain,
    multiply(greatest_lower_bound(X_25,X_24),inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24)))) = least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234))),
    inference(subst,[],[refute_0_258:[bind(X,$fot(X_234)),bind(X_96,$fot(greatest_lower_bound(X_25,X_24)))]]) ).

cnf(refute_0_3594,plain,
    ( multiply(greatest_lower_bound(X_25,X_24),inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24)))) != least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))
    | inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) != multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24)))))
    | inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) = multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24)))))) ),[1,1],$fot(least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234))))]]) ).

cnf(refute_0_3595,plain,
    ( inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) != multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24)))))
    | inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) = multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_25,X_24),inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24)))),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))) )],[refute_0_3593,refute_0_3594]) ).

cnf(refute_0_3596,plain,
    inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) = multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24)))))) )],[refute_0_3592,refute_0_3595]) ).

cnf(refute_0_3597,plain,
    greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234) = greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(X_234))]]) ).

cnf(refute_0_3598,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)) = inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)))]]) ).

cnf(refute_0_3599,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234) != greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)) != inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)),inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234))) ),[1,0],$fot(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))]]) ).

cnf(refute_0_3600,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234) != greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)),inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234))) )],[refute_0_3598,refute_0_3599]) ).

cnf(refute_0_3601,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234),greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) )],[refute_0_3597,refute_0_3600]) ).

cnf(refute_0_3602,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)) = inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)),
    inference(subst,[],[refute_0_136:[bind(X,$fot(greatest_lower_bound(X_24,X_25))),bind(Y,$fot(X_234))]]) ).

cnf(refute_0_3603,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))
    | least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)) != inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234))
    | least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)))),bind(Y0,$fot(inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)))),bind(Z0,$fot(inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))))]]) ).

cnf(refute_0_3604,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))
    | least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)),inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234))) )],[refute_0_3602,refute_0_3603]) ).

cnf(refute_0_3605,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_24,X_25),X_234)),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))) )],[refute_0_3601,refute_0_3604]) ).

cnf(refute_0_3606,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),identity) = inverse(greatest_lower_bound(X_24,X_25)),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(inverse(greatest_lower_bound(X_24,X_25))))]]) ).

cnf(refute_0_3607,plain,
    least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)) = least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)),
    introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)))]]) ).

cnf(refute_0_3608,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),identity) != inverse(greatest_lower_bound(X_24,X_25))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)) != least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)) = least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)),least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234))) ),[1,0],$fot(inverse(greatest_lower_bound(X_24,X_25)))]]) ).

cnf(refute_0_3609,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),identity) != inverse(greatest_lower_bound(X_24,X_25))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)) = least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)),least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234))) )],[refute_0_3607,refute_0_3608]) ).

cnf(refute_0_3610,plain,
    least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)) = least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(greatest_lower_bound(X_24,X_25))) )],[refute_0_3606,refute_0_3609]) ).

cnf(refute_0_3611,plain,
    ( least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)) != least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234))
    | least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)))),bind(Z0,$fot(inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))))]]) ).

cnf(refute_0_3612,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)),least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234))) )],[refute_0_3610,refute_0_3611]) ).

cnf(refute_0_3613,plain,
    least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_24,X_25)),inverse(X_234)),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))) )],[refute_0_3605,refute_0_3612]) ).

cnf(refute_0_3614,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(X_94,multiply(greatest_lower_bound(X_25,X_24),X_60))) = least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_94),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(greatest_lower_bound(X_24,X_25)))),bind(Y,$fot(X_94)),bind(Z,$fot(multiply(greatest_lower_bound(X_25,X_24),X_60)))]]) ).

cnf(refute_0_3615,plain,
    ( X_60 != multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)) = X_60 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_60)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))))]]) ).

cnf(refute_0_3616,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)) = X_60,
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))) )],[refute_0_3591,refute_0_3615]) ).

cnf(refute_0_3617,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)) != X_60
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(X_94,multiply(greatest_lower_bound(X_25,X_24),X_60))) != least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_94),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(X_94,multiply(greatest_lower_bound(X_25,X_24),X_60))) = least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_94),X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(X_94,multiply(greatest_lower_bound(X_25,X_24),X_60))),least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_94),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)))) ),[1,1],$fot(X_60)]]) ).

cnf(refute_0_3618,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(X_94,multiply(greatest_lower_bound(X_25,X_24),X_60))) != least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_94),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(X_94,multiply(greatest_lower_bound(X_25,X_24),X_60))) = least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_94),X_60) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)),X_60) )],[refute_0_3616,refute_0_3617]) ).

cnf(refute_0_3619,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(X_94,multiply(greatest_lower_bound(X_25,X_24),X_60))) = least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_94),X_60),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(X_94,multiply(greatest_lower_bound(X_25,X_24),X_60))),least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_94),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)))) )],[refute_0_3614,refute_0_3618]) ).

cnf(refute_0_3620,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))) = least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)),
    inference(subst,[],[refute_0_3619:[bind(X_60,$fot(inverse(X_234))),bind(X_94,$fot(identity))]]) ).

cnf(refute_0_3621,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))) != least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))))),bind(Y0,$fot(least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)))),bind(Z0,$fot(inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))))]]) ).

cnf(refute_0_3622,plain,
    ( least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))),least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234))) )],[refute_0_3620,refute_0_3621]) ).

cnf(refute_0_3623,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(X_234)),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))) )],[refute_0_3613,refute_0_3622]) ).

cnf(refute_0_3624,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))
    | inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) != multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234))))
    | inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))),multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234))))) ),[1],$fot(inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))))]]) ).

cnf(refute_0_3625,plain,
    ( inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) != multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234))))
    | inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234)))),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))) )],[refute_0_3623,refute_0_3624]) ).

cnf(refute_0_3626,plain,
    inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) = inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))),multiply(inverse(greatest_lower_bound(X_24,X_25)),least_upper_bound(identity,multiply(greatest_lower_bound(X_25,X_24),inverse(X_234))))) )],[refute_0_3596,refute_0_3625]) ).

cnf(refute_0_3627,plain,
    ( inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))
    | inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) = inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))))),bind(Y0,$fot(inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))))]]) ).

cnf(refute_0_3628,plain,
    inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234))) = inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_234,greatest_lower_bound(X_25,X_24))),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,X_234)))) )],[refute_0_3626,refute_0_3627]) ).

cnf(refute_0_3629,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(Y,b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))),
    inference(subst,[],[refute_0_3628:[bind(X_234,$fot(b)),bind(X_24,$fot(identity)),bind(X_25,$fot(Y))]]) ).

cnf(refute_0_3630,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(Y,b))),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(greatest_lower_bound(Y,b)))]]) ).

cnf(refute_0_3631,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(Y,b))) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))
    | least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(Y,b)))
    | least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(Y,b))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))))]]) ).

cnf(refute_0_3632,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(Y,b))) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))
    | least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))),inverse(greatest_lower_bound(identity,greatest_lower_bound(Y,b)))) )],[refute_0_3630,refute_0_3631]) ).

cnf(refute_0_3633,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(Y,b))),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))) )],[refute_0_3629,refute_0_3632]) ).

cnf(refute_0_3634,plain,
    least_upper_bound(inverse(Y),inverse(b)) = inverse(greatest_lower_bound(Y,b)),
    inference(subst,[],[refute_0_136:[bind(X,$fot(Y)),bind(Y,$fot(b))]]) ).

cnf(refute_0_3635,plain,
    least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))) = least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))))]]) ).

cnf(refute_0_3636,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))) != least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b)))
    | least_upper_bound(inverse(Y),inverse(b)) != inverse(greatest_lower_bound(Y,b))
    | least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))) = least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))),least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b)))) ),[1,1],$fot(inverse(greatest_lower_bound(Y,b)))]]) ).

cnf(refute_0_3637,plain,
    ( least_upper_bound(inverse(Y),inverse(b)) != inverse(greatest_lower_bound(Y,b))
    | least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))) = least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))),least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b)))) )],[refute_0_3635,refute_0_3636]) ).

cnf(refute_0_3638,plain,
    least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))) = least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(Y),inverse(b)),inverse(greatest_lower_bound(Y,b))) )],[refute_0_3634,refute_0_3637]) ).

cnf(refute_0_3639,plain,
    ( least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))
    | least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))) != least_upper_bound(identity,inverse(greatest_lower_bound(Y,b)))
    | least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))))]]) ).

cnf(refute_0_3640,plain,
    ( least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))
    | least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))),least_upper_bound(identity,inverse(greatest_lower_bound(Y,b)))) )],[refute_0_3638,refute_0_3639]) ).

cnf(refute_0_3641,plain,
    least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(Y,b))),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))) )],[refute_0_3633,refute_0_3640]) ).

cnf(refute_0_3642,plain,
    least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)) = least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))),
    inference(subst,[],[refute_0_3225:[bind(X_249,$fot(b)),bind(X_251,$fot(inverse(Y)))]]) ).

cnf(refute_0_3643,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))
    | least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)) != least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b)))
    | least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))))]]) ).

cnf(refute_0_3644,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))
    | least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)),least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b)))) )],[refute_0_3642,refute_0_3643]) ).

cnf(refute_0_3645,plain,
    least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(Y),inverse(b))),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))) )],[refute_0_3641,refute_0_3644]) ).

cnf(refute_0_3646,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) != least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y))
    | least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)))]]) ).

cnf(refute_0_3647,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) != least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y)),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))) )],[refute_0_3645,refute_0_3646]) ).

cnf(refute_0_3648,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)) != least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))),least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y))) )],[refute_0_3584,refute_0_3647]) ).

cnf(refute_0_3649,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),Y)),least_upper_bound(inverse(greatest_lower_bound(b,identity)),inverse(Y))) )],[refute_0_3577,refute_0_3648]) ).

cnf(refute_0_3650,plain,
    greatest_lower_bound(X,greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)),
    inference(subst,[],[refute_0_839:[bind(X_36,$fot(identity)),bind(X_37,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_3651,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))
    | greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) != greatest_lower_bound(b,identity)
    | greatest_lower_bound(X,greatest_lower_bound(b,identity)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))) ),[0,1],$fot(greatest_lower_bound(b,identity))]]) ).

cnf(refute_0_3652,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))
    | greatest_lower_bound(X,greatest_lower_bound(b,identity)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),greatest_lower_bound(b,identity)) )],[refute_0_2787,refute_0_3651]) ).

cnf(refute_0_3653,plain,
    greatest_lower_bound(X,greatest_lower_bound(b,identity)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))),greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))) )],[refute_0_3650,refute_0_3652]) ).

cnf(refute_0_3654,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(b,identity)) != greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) = greatest_lower_bound(X,greatest_lower_bound(b,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(b,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))))]]) ).

cnf(refute_0_3655,plain,
    greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) = greatest_lower_bound(X,greatest_lower_bound(b,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(b,identity)),greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))) )],[refute_0_3653,refute_0_3654]) ).

cnf(refute_0_3656,plain,
    greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y)) = greatest_lower_bound(Y,greatest_lower_bound(b,identity)),
    inference(subst,[],[refute_0_3655:[bind(X,$fot(Y))]]) ).

cnf(refute_0_3657,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))))]]) ).

cnf(refute_0_3658,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y)) != greatest_lower_bound(Y,greatest_lower_bound(b,identity))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y)))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))),inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y)))) ),[1,0],$fot(greatest_lower_bound(Y,greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_3659,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y)) != greatest_lower_bound(Y,greatest_lower_bound(b,identity))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))),inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y)))) )],[refute_0_3657,refute_0_3658]) ).

cnf(refute_0_3660,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y)),greatest_lower_bound(Y,greatest_lower_bound(b,identity))) )],[refute_0_3656,refute_0_3659]) ).

cnf(refute_0_3661,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) != inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity)))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))
    | inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))) ),[0],$fot(inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_3662,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))
    | inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))),inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity)))) )],[refute_0_3660,refute_0_3661]) ).

cnf(refute_0_3663,plain,
    inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),Y))),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))) )],[refute_0_3649,refute_0_3662]) ).

cnf(refute_0_3664,plain,
    greatest_lower_bound(Y,greatest_lower_bound(b,identity)) = greatest_lower_bound(Y,greatest_lower_bound(b,identity)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(Y,greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_3665,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(b,identity)) != greatest_lower_bound(Y,greatest_lower_bound(b,identity))
    | greatest_lower_bound(b,identity) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(Y,greatest_lower_bound(b,identity)) = greatest_lower_bound(Y,greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(b,identity)),greatest_lower_bound(Y,greatest_lower_bound(b,identity))) ),[1,1],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_3666,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(Y,greatest_lower_bound(b,identity)) = greatest_lower_bound(Y,greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(b,identity)),greatest_lower_bound(Y,greatest_lower_bound(b,identity))) )],[refute_0_3664,refute_0_3665]) ).

cnf(refute_0_3667,plain,
    greatest_lower_bound(Y,greatest_lower_bound(b,identity)) = greatest_lower_bound(Y,greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(a,identity)) )],[refute_0_2212,refute_0_3666]) ).

cnf(refute_0_3668,plain,
    inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_3669,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(b,identity)) != greatest_lower_bound(Y,greatest_lower_bound(a,identity))
    | inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) != inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity)))
    | inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))),inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity)))) ),[1,0],$fot(greatest_lower_bound(Y,greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3670,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(b,identity)) != greatest_lower_bound(Y,greatest_lower_bound(a,identity))
    | inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))),inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity)))) )],[refute_0_3668,refute_0_3669]) ).

cnf(refute_0_3671,plain,
    inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) = inverse(greatest_lower_bound(Y,greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(b,identity)),greatest_lower_bound(Y,greatest_lower_bound(a,identity))) )],[refute_0_3667,refute_0_3670]) ).

cnf(refute_0_3672,plain,
    ( inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) != inverse(greatest_lower_bound(Y,greatest_lower_bound(a,identity)))
    | inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))
    | inverse(greatest_lower_bound(Y,greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))) ),[0],$fot(inverse(greatest_lower_bound(Y,greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3673,plain,
    ( inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))) != inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))
    | inverse(greatest_lower_bound(Y,greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))),inverse(greatest_lower_bound(Y,greatest_lower_bound(a,identity)))) )],[refute_0_3671,refute_0_3672]) ).

cnf(refute_0_3674,plain,
    inverse(greatest_lower_bound(Y,greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(Y,greatest_lower_bound(b,identity))),inverse(greatest_lower_bound(b,greatest_lower_bound(Y,identity)))) )],[refute_0_3663,refute_0_3673]) ).

cnf(refute_0_3675,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))),
    inference(subst,[],[refute_0_3674:[bind(Y,$fot(identity))]]) ).

cnf(refute_0_3676,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(a,identity))),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3677,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(a,identity))) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity)))
    | least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(a,identity)))
    | least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,identity))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity)))))]]) ).

cnf(refute_0_3678,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(a,identity))) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity)))
    | least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,identity)))) )],[refute_0_3676,refute_0_3677]) ).

cnf(refute_0_3679,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity)))) )],[refute_0_3675,refute_0_3678]) ).

cnf(refute_0_3680,plain,
    ( inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))) != inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity)))
    | least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(a,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))),bind(Y0,$fot(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))))),bind(Z0,$fot(inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3681,plain,
    ( inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity)))) )],[refute_0_3679,refute_0_3680]) ).

cnf(refute_0_3682,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,greatest_lower_bound(identity,identity))),inverse(greatest_lower_bound(a,identity))) )],[refute_0_3573,refute_0_3681]) ).

cnf(refute_0_3683,plain,
    least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3684,plain,
    ( least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))),least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))) ),[1,1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3685,plain,
    ( least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))),least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3683,refute_0_3684]) ).

cnf(refute_0_3686,plain,
    least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))) )],[refute_0_3682,refute_0_3685]) ).

cnf(refute_0_3687,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_192,X_193)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))),
    inference(subst,[],[refute_0_170:[bind(X_116,$fot(least_upper_bound(X_192,X_193))),bind(X_87,$fot(identity))]]) ).

cnf(refute_0_3688,plain,
    ( least_upper_bound(X_192,least_upper_bound(X_193,identity)) != least_upper_bound(identity,least_upper_bound(X_192,X_193))
    | least_upper_bound(identity,least_upper_bound(X_192,X_193)) = least_upper_bound(X_192,least_upper_bound(X_193,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_192,least_upper_bound(X_193,identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_192,X_193))))]]) ).

cnf(refute_0_3689,plain,
    least_upper_bound(identity,least_upper_bound(X_192,X_193)) = least_upper_bound(X_192,least_upper_bound(X_193,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_192,least_upper_bound(X_193,identity)),least_upper_bound(identity,least_upper_bound(X_192,X_193))) )],[refute_0_1707,refute_0_3688]) ).

cnf(refute_0_3690,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_192,X_193)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))
    | least_upper_bound(identity,least_upper_bound(X_192,X_193)) != least_upper_bound(X_192,least_upper_bound(X_193,identity))
    | multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_192,X_193)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))) ),[0,0],$fot(least_upper_bound(X_192,least_upper_bound(X_193,identity)))]]) ).

cnf(refute_0_3691,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_192,X_193)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))
    | multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_192,X_193)),least_upper_bound(X_192,least_upper_bound(X_193,identity))) )],[refute_0_3689,refute_0_3690]) ).

cnf(refute_0_3692,plain,
    multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_192,X_193)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))) )],[refute_0_3687,refute_0_3691]) ).

cnf(refute_0_3693,plain,
    multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity) = least_upper_bound(X_192,least_upper_bound(X_193,identity)),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(least_upper_bound(X_192,least_upper_bound(X_193,identity))))]]) ).

cnf(refute_0_3694,plain,
    multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) = multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)))]]) ).

cnf(refute_0_3695,plain,
    ( multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) != multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity))
    | inverse(identity) != identity
    | multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) = multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)),multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_3696,plain,
    ( inverse(identity) != identity
    | multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) = multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)),multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity))) )],[refute_0_3694,refute_0_3695]) ).

cnf(refute_0_3697,plain,
    multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) = multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_3696]) ).

cnf(refute_0_3698,plain,
    ( multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity) != least_upper_bound(X_192,least_upper_bound(X_193,identity))
    | multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) != multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)
    | multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) = least_upper_bound(X_192,least_upper_bound(X_193,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity))),bind(Z0,$fot(least_upper_bound(X_192,least_upper_bound(X_193,identity))))]]) ).

cnf(refute_0_3699,plain,
    ( multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity) != least_upper_bound(X_192,least_upper_bound(X_193,identity))
    | multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) = least_upper_bound(X_192,least_upper_bound(X_193,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)),multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity)) )],[refute_0_3697,refute_0_3698]) ).

cnf(refute_0_3700,plain,
    multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) = least_upper_bound(X_192,least_upper_bound(X_193,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),identity),least_upper_bound(X_192,least_upper_bound(X_193,identity))) )],[refute_0_3693,refute_0_3699]) ).

cnf(refute_0_3701,plain,
    ( multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) != least_upper_bound(X_192,least_upper_bound(X_193,identity))
    | multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))
    | least_upper_bound(X_192,least_upper_bound(X_193,identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))) ),[0],$fot(least_upper_bound(X_192,least_upper_bound(X_193,identity)))]]) ).

cnf(refute_0_3702,plain,
    ( multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))
    | least_upper_bound(X_192,least_upper_bound(X_193,identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)),least_upper_bound(X_192,least_upper_bound(X_193,identity))) )],[refute_0_3700,refute_0_3701]) ).

cnf(refute_0_3703,plain,
    multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),identity) = least_upper_bound(X_193,least_upper_bound(identity,X_192)),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(least_upper_bound(X_193,least_upper_bound(identity,X_192))))]]) ).

cnf(refute_0_3704,plain,
    multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)) = multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)))]]) ).

cnf(refute_0_3705,plain,
    ( multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)) != multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity))
    | inverse(identity) != identity
    | multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)) = multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)),multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_3706,plain,
    ( inverse(identity) != identity
    | multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)) = multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)),multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity))) )],[refute_0_3704,refute_0_3705]) ).

cnf(refute_0_3707,plain,
    multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)) = multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),identity),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_3706]) ).

cnf(refute_0_3708,plain,
    ( multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),identity) != least_upper_bound(X_193,least_upper_bound(identity,X_192))
    | multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)) != multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),identity)
    | multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)) = least_upper_bound(X_193,least_upper_bound(identity,X_192)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),identity))),bind(Z0,$fot(least_upper_bound(X_193,least_upper_bound(identity,X_192))))]]) ).

cnf(refute_0_3709,plain,
    ( multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),identity) != least_upper_bound(X_193,least_upper_bound(identity,X_192))
    | multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)) = least_upper_bound(X_193,least_upper_bound(identity,X_192)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)),multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),identity)) )],[refute_0_3707,refute_0_3708]) ).

cnf(refute_0_3710,plain,
    multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)) = least_upper_bound(X_193,least_upper_bound(identity,X_192)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),identity),least_upper_bound(X_193,least_upper_bound(identity,X_192))) )],[refute_0_3703,refute_0_3709]) ).

cnf(refute_0_3711,plain,
    multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) = least_upper_bound(multiply(Y,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),inverse(X_278))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_278))),bind(Z,$fot(least_upper_bound(X_278,X_277)))]]) ).

cnf(refute_0_3712,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) != least_upper_bound(multiply(Y,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),inverse(X_278)))
    | multiply(least_upper_bound(X_278,X_277),inverse(X_278)) != least_upper_bound(identity,multiply(X_277,inverse(X_278)))
    | multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) = least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)),least_upper_bound(multiply(Y,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),inverse(X_278)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_277,inverse(X_278))))]]) ).

cnf(refute_0_3713,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) != least_upper_bound(multiply(Y,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),inverse(X_278)))
    | multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) = least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_278,X_277),inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))) )],[refute_0_944,refute_0_3712]) ).

cnf(refute_0_3714,plain,
    multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) = least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)),least_upper_bound(multiply(Y,inverse(X_278)),multiply(least_upper_bound(X_278,X_277),inverse(X_278)))) )],[refute_0_3711,refute_0_3713]) ).

cnf(refute_0_3715,plain,
    least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278))) = multiply(least_upper_bound(X_277,Y),inverse(X_278)),
    inference(subst,[],[refute_0_384:[bind(X,$fot(inverse(X_278))),bind(Y,$fot(X_277)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_3716,plain,
    least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))) = least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))))]]) ).

cnf(refute_0_3717,plain,
    ( least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278))) != multiply(least_upper_bound(X_277,Y),inverse(X_278))
    | least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))) != least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278))))
    | least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))),least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278))))) ),[1,1],$fot(multiply(least_upper_bound(X_277,Y),inverse(X_278)))]]) ).

cnf(refute_0_3718,plain,
    ( least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278))) != multiply(least_upper_bound(X_277,Y),inverse(X_278))
    | least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))),least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278))))) )],[refute_0_3716,refute_0_3717]) ).

cnf(refute_0_3719,plain,
    least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278))),multiply(least_upper_bound(X_277,Y),inverse(X_278))) )],[refute_0_3715,refute_0_3718]) ).

cnf(refute_0_3720,plain,
    least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))) = least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))),
    inference(subst,[],[refute_0_1776:[bind(X_246,$fot(multiply(Y,inverse(X_278)))),bind(X_247,$fot(identity)),bind(X_248,$fot(multiply(X_277,inverse(X_278))))]]) ).

cnf(refute_0_3721,plain,
    ( least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))) != least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278))))
    | least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))) != least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278)))
    | least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278)))))]]) ).

cnf(refute_0_3722,plain,
    ( least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))) != least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278)))
    | least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))),least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278))))) )],[refute_0_3720,refute_0_3721]) ).

cnf(refute_0_3723,plain,
    least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))) = least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_277,inverse(X_278)),multiply(Y,inverse(X_278)))),least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278)))) )],[refute_0_3719,refute_0_3722]) ).

cnf(refute_0_3724,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) != least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278))))
    | least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))) != least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278)))
    | multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) = least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)),least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278)))) ),[0],$fot(least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))))]]) ).

cnf(refute_0_3725,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) != least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278))))
    | multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) = least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278)))),least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278)))) )],[refute_0_3723,refute_0_3724]) ).

cnf(refute_0_3726,plain,
    multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) = least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)),least_upper_bound(multiply(Y,inverse(X_278)),least_upper_bound(identity,multiply(X_277,inverse(X_278))))) )],[refute_0_3714,refute_0_3725]) ).

cnf(refute_0_3727,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) != least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278)))
    | least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278))) = multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)))),bind(Y0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278)))))]]) ).

cnf(refute_0_3728,plain,
    least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278))) = multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_278,X_277)),inverse(X_278)),least_upper_bound(identity,multiply(least_upper_bound(X_277,Y),inverse(X_278)))) )],[refute_0_3726,refute_0_3727]) ).

cnf(refute_0_3729,plain,
    least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))) = multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)),
    inference(subst,[],[refute_0_3728:[bind(Y,$fot(X_193)),bind(X_277,$fot(X_192)),bind(X_278,$fot(identity))]]) ).

cnf(refute_0_3730,plain,
    ( multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)) != least_upper_bound(X_193,least_upper_bound(identity,X_192))
    | least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))) != multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity))
    | least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))) = least_upper_bound(X_193,least_upper_bound(identity,X_192)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))))),bind(Y0,$fot(multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)))),bind(Z0,$fot(least_upper_bound(X_193,least_upper_bound(identity,X_192))))]]) ).

cnf(refute_0_3731,plain,
    ( multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)) != least_upper_bound(X_193,least_upper_bound(identity,X_192))
    | least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))) = least_upper_bound(X_193,least_upper_bound(identity,X_192)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))),multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity))) )],[refute_0_3729,refute_0_3730]) ).

cnf(refute_0_3732,plain,
    least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))) = least_upper_bound(X_193,least_upper_bound(identity,X_192)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_193,least_upper_bound(identity,X_192)),inverse(identity)),least_upper_bound(X_193,least_upper_bound(identity,X_192))) )],[refute_0_3710,refute_0_3731]) ).

cnf(refute_0_3733,plain,
    ( least_upper_bound(X_192,least_upper_bound(X_193,identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))
    | least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))) != least_upper_bound(X_193,least_upper_bound(identity,X_192))
    | least_upper_bound(X_192,least_upper_bound(X_193,identity)) = least_upper_bound(X_193,least_upper_bound(identity,X_192)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_192,least_upper_bound(X_193,identity)),least_upper_bound(X_193,least_upper_bound(identity,X_192))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))))]]) ).

cnf(refute_0_3734,plain,
    ( least_upper_bound(X_192,least_upper_bound(X_193,identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))
    | least_upper_bound(X_192,least_upper_bound(X_193,identity)) = least_upper_bound(X_193,least_upper_bound(identity,X_192)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity))),least_upper_bound(X_193,least_upper_bound(identity,X_192))) )],[refute_0_3732,refute_0_3733]) ).

cnf(refute_0_3735,plain,
    ( multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))
    | least_upper_bound(X_192,least_upper_bound(X_193,identity)) = least_upper_bound(X_193,least_upper_bound(identity,X_192)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_192,least_upper_bound(X_193,identity)),least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))) )],[refute_0_3702,refute_0_3734]) ).

cnf(refute_0_3736,plain,
    least_upper_bound(X_192,least_upper_bound(X_193,identity)) = least_upper_bound(X_193,least_upper_bound(identity,X_192)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_192,least_upper_bound(X_193,identity)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_192,X_193),inverse(identity)))) )],[refute_0_3692,refute_0_3735]) ).

cnf(refute_0_3737,plain,
    least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)) = least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))),
    inference(subst,[],[refute_0_3736:[bind(X_192,$fot(inverse(greatest_lower_bound(a,identity)))),bind(X_193,$fot(b))]]) ).

cnf(refute_0_3738,plain,
    ( least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)) != least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))
    | least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))))),bind(Z0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3739,plain,
    ( least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)),least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3737,refute_0_3738]) ).

cnf(refute_0_3740,plain,
    least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(greatest_lower_bound(a,identity)))),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_3686,refute_0_3739]) ).

cnf(refute_0_3741,plain,
    ( multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity))
    | least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)))]]) ).

cnf(refute_0_3742,plain,
    ( multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity))
    | multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_3740,refute_0_3741]) ).

cnf(refute_0_3743,plain,
    multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))),least_upper_bound(inverse(greatest_lower_bound(a,identity)),least_upper_bound(b,identity))) )],[refute_0_3561,refute_0_3742]) ).

cnf(refute_0_3744,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3745,plain,
    ( multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))))) ),[1,1],$fot(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3746,plain,
    ( multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3744,refute_0_3745]) ).

cnf(refute_0_3747,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_3743,refute_0_3746]) ).

cnf(refute_0_3748,plain,
    multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))),
    inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))),bind(Y,$fot(least_upper_bound(b,identity))),bind(Z,$fot(inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3749,plain,
    ( multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))
    | multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))))),bind(Y0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))))),bind(Z0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_3750,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))
    | multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3748,refute_0_3749]) ).

cnf(refute_0_3751,plain,
    multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3747,refute_0_3750]) ).

cnf(refute_0_3752,plain,
    multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) = multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))),
    introduced(tautology,[refl,[$fot(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3753,plain,
    ( multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) != multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))),multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))))) ),[1,1],$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3754,plain,
    ( multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))),multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3752,refute_0_3753]) ).

cnf(refute_0_3755,plain,
    multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3751,refute_0_3754]) ).

cnf(refute_0_3756,plain,
    ( multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))))),bind(Y0,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))))),bind(Z0,$fot(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_3757,plain,
    ( multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_3755,refute_0_3756]) ).

cnf(refute_0_3758,plain,
    multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))),multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) )],[refute_0_3486,refute_0_3757]) ).

cnf(refute_0_3759,plain,
    multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) = multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))),
    inference(subst,[],[associativity:[bind(X,$fot(b)),bind(Y,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),bind(Z,$fot(inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3760,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) != multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))))),bind(Y0,$fot(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))))),bind(Z0,$fot(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_3761,plain,
    ( multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))),multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3759,refute_0_3760]) ).

cnf(refute_0_3762,plain,
    multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) = multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) )],[refute_0_3758,refute_0_3761]) ).

cnf(refute_0_3763,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) != multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))) ),[0],$fot(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))))]]) ).

cnf(refute_0_3764,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))),multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))) )],[refute_0_3762,refute_0_3763]) ).

cnf(refute_0_3765,plain,
    inverse(inverse(greatest_lower_bound(a,identity))) = greatest_lower_bound(a,identity),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3766,plain,
    multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3767,plain,
    ( multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))
    | inverse(inverse(greatest_lower_bound(a,identity))) != greatest_lower_bound(a,identity)
    | multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) ),[1,1],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_3768,plain,
    ( inverse(inverse(greatest_lower_bound(a,identity))) != greatest_lower_bound(a,identity)
    | multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3766,refute_0_3767]) ).

cnf(refute_0_3769,plain,
    multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(a,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3765,refute_0_3768]) ).

cnf(refute_0_3770,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_3771,plain,
    ( multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))) ),[1,1],$fot(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3772,plain,
    ( multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_3770,refute_0_3771]) ).

cnf(refute_0_3773,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) )],[refute_0_3769,refute_0_3772]) ).

cnf(refute_0_3774,plain,
    multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))),
    inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))),bind(Y,$fot(least_upper_bound(b,identity))),bind(Z,$fot(inverse(inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3775,plain,
    ( multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))
    | multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))),bind(Y0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))))),bind(Z0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3776,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))
    | multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_3774,refute_0_3775]) ).

cnf(refute_0_3777,plain,
    multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) )],[refute_0_3773,refute_0_3776]) ).

cnf(refute_0_3778,plain,
    multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))),
    introduced(tautology,[refl,[$fot(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_3779,plain,
    ( multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) != multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))),multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))) ),[1,1],$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3780,plain,
    ( multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))),multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_3778,refute_0_3779]) ).

cnf(refute_0_3781,plain,
    multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) )],[refute_0_3777,refute_0_3780]) ).

cnf(refute_0_3782,plain,
    multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))),
    inference(subst,[],[associativity:[bind(X,$fot(b)),bind(Y,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)))),bind(Z,$fot(inverse(inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3783,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))),bind(Y0,$fot(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))))),bind(Z0,$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_3784,plain,
    ( multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))
    | multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_3782,refute_0_3783]) ).

cnf(refute_0_3785,plain,
    multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) )],[refute_0_3781,refute_0_3784]) ).

cnf(refute_0_3786,plain,
    least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))) = least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_3787,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))
    | least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))
    | least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))) ),[1,1],$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3788,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))
    | least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_3786,refute_0_3787]) ).

cnf(refute_0_3789,plain,
    least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) )],[refute_0_3785,refute_0_3788]) ).

cnf(refute_0_3790,plain,
    ( multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))
    | least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))) != least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))) ),[0],$fot(least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_3791,plain,
    ( multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity))))),least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))) )],[refute_0_3789,refute_0_3790]) ).

cnf(refute_0_3792,plain,
    ( multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_3764,refute_0_3791]) ).

cnf(refute_0_3793,plain,
    multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))),
    inference(resolve,[$cnf( $equal(multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_2813,refute_0_3792]) ).

cnf(refute_0_3794,plain,
    inverse(inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3795,plain,
    multiply(inverse(greatest_lower_bound(a,identity)),inverse(multiply(b,inverse(greatest_lower_bound(a,identity))))) = inverse(b),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(inverse(greatest_lower_bound(a,identity)))),bind(X_59,$fot(b))]]) ).

cnf(refute_0_3796,plain,
    ( multiply(b,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(b,identity)
    | multiply(inverse(greatest_lower_bound(a,identity)),inverse(multiply(b,inverse(greatest_lower_bound(a,identity))))) != inverse(b)
    | multiply(inverse(greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))) = inverse(b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,identity)),inverse(multiply(b,inverse(greatest_lower_bound(a,identity))))),inverse(b)) ),[0,1,0],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_3797,plain,
    ( multiply(inverse(greatest_lower_bound(a,identity)),inverse(multiply(b,inverse(greatest_lower_bound(a,identity))))) != inverse(b)
    | multiply(inverse(greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))) = inverse(b) ),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(a,identity))),least_upper_bound(b,identity)) )],[refute_0_3558,refute_0_3796]) ).

cnf(refute_0_3798,plain,
    multiply(inverse(greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))) = inverse(b),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,identity)),inverse(multiply(b,inverse(greatest_lower_bound(a,identity))))),inverse(b)) )],[refute_0_3795,refute_0_3797]) ).

cnf(refute_0_3799,plain,
    multiply(inverse(greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))) = inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),
    inference(subst,[],[refute_0_667:[bind(X_198,$fot(least_upper_bound(b,identity))),bind(X_59,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3800,plain,
    ( multiply(inverse(greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))) != inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))
    | multiply(inverse(greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))) != inverse(b)
    | inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) = inverse(b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))),inverse(b)) ),[0],$fot(inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3801,plain,
    ( multiply(inverse(greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))) != inverse(b)
    | inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) = inverse(b) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))),inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) )],[refute_0_3799,refute_0_3800]) ).

cnf(refute_0_3802,plain,
    inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) = inverse(b),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,identity)),inverse(least_upper_bound(b,identity))),inverse(b)) )],[refute_0_3798,refute_0_3801]) ).

cnf(refute_0_3803,plain,
    ( inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) != inverse(b)
    | inverse(inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))
    | inverse(inverse(b)) = multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) ),[0,0],$fot(inverse(b))]]) ).

cnf(refute_0_3804,plain,
    ( inverse(inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))
    | inverse(inverse(b)) = multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),inverse(b)) )],[refute_0_3802,refute_0_3803]) ).

cnf(refute_0_3805,plain,
    inverse(inverse(b)) = multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) )],[refute_0_3794,refute_0_3804]) ).

cnf(refute_0_3806,plain,
    ( inverse(inverse(b)) != multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))
    | inverse(inverse(b)) != b
    | b = multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(b)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) ),[0],$fot(b)]]) ).

cnf(refute_0_3807,plain,
    ( inverse(inverse(b)) != multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))
    | b = multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),b) )],[refute_0_1272,refute_0_3806]) ).

cnf(refute_0_3808,plain,
    b = multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(b)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) )],[refute_0_3805,refute_0_3807]) ).

cnf(refute_0_3809,plain,
    ( b != multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) = b ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(b)),bind(Y0,$fot(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3810,plain,
    multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) = b,
    inference(resolve,[$cnf( $equal(b,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) )],[refute_0_3808,refute_0_3809]) ).

cnf(refute_0_3811,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3812,plain,
    ( multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) != b
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) ),[1,1],$fot(b)]]) ).

cnf(refute_0_3813,plain,
    ( multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) != b
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) )],[refute_0_3811,refute_0_3812]) ).

cnf(refute_0_3814,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)),b) )],[refute_0_3810,refute_0_3813]) ).

cnf(refute_0_3815,plain,
    multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))),
    introduced(tautology,[refl,[$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3816,plain,
    ( multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) ),[1,1],$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))]]) ).

cnf(refute_0_3817,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)
    | multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) ),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) )],[refute_0_3815,refute_0_3816]) ).

cnf(refute_0_3818,plain,
    multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) = multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)) )],[refute_0_3814,refute_0_3817]) ).

cnf(refute_0_3819,plain,
    least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_3820,plain,
    ( multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))
    | least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) != least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))
    | least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))),least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))) ),[1,1],$fot(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))]]) ).

cnf(refute_0_3821,plain,
    ( multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) != multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))
    | least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))),least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))) )],[refute_0_3819,refute_0_3820]) ).

cnf(refute_0_3822,plain,
    least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),
    inference(resolve,[$cnf( $equal(multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))),multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) )],[refute_0_3818,refute_0_3821]) ).

cnf(refute_0_3823,plain,
    ( multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))
    | least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))) != least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))
    | multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) ),[0],$fot(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_3824,plain,
    ( multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))),least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) )],[refute_0_3822,refute_0_3823]) ).

cnf(refute_0_3825,plain,
    multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))))) )],[refute_0_3793,refute_0_3824]) ).

cnf(refute_0_3826,plain,
    greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X) = greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))]]) ).

cnf(refute_0_3827,plain,
    ( multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))
    | greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X) != greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)
    | greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X) = greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X),greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) ),[1,0],$fot(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))))]]) ).

cnf(refute_0_3828,plain,
    ( multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))
    | greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X) = greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X),greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) )],[refute_0_3826,refute_0_3827]) ).

cnf(refute_0_3829,plain,
    greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X) = greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b)))) )],[refute_0_3825,refute_0_3828]) ).

cnf(refute_0_3830,plain,
    greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)))]]) ).

cnf(refute_0_3831,plain,
    ( greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X) != greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X)
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) != greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)),greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))) ),[1,1],$fot(greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X))]]) ).

cnf(refute_0_3832,plain,
    ( greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X) != greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X)
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)),greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))) )],[refute_0_3830,refute_0_3831]) ).

cnf(refute_0_3833,plain,
    greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X),greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X)) )],[refute_0_3829,refute_0_3832]) ).

cnf(refute_0_3834,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) != greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X))
    | greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X)) != greatest_lower_bound(identity,X)
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) = greatest_lower_bound(identity,X) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X)))),bind(Z0,$fot(greatest_lower_bound(identity,X)))]]) ).

cnf(refute_0_3835,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X)) != greatest_lower_bound(identity,X)
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) = greatest_lower_bound(identity,X) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)),greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X))) )],[refute_0_3833,refute_0_3834]) ).

cnf(refute_0_3836,plain,
    greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) = greatest_lower_bound(identity,X),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,multiply(b,multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),b))),X)),greatest_lower_bound(identity,X)) )],[refute_0_2773,refute_0_3835]) ).

cnf(refute_0_3837,plain,
    ( greatest_lower_bound(X,identity) != greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)) != greatest_lower_bound(identity,X)
    | greatest_lower_bound(X,identity) = greatest_lower_bound(identity,X) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,identity),greatest_lower_bound(identity,X)) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)))]]) ).

cnf(refute_0_3838,plain,
    ( greatest_lower_bound(X,identity) != greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))
    | greatest_lower_bound(X,identity) = greatest_lower_bound(identity,X) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X)),greatest_lower_bound(identity,X)) )],[refute_0_3836,refute_0_3837]) ).

cnf(refute_0_3839,plain,
    greatest_lower_bound(X,identity) = greatest_lower_bound(identity,X),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,identity),greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(b,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),least_upper_bound(b,identity))),X))) )],[refute_0_2767,refute_0_3838]) ).

cnf(refute_0_3840,plain,
    ( greatest_lower_bound(X,identity) != greatest_lower_bound(identity,X)
    | greatest_lower_bound(identity,X) = greatest_lower_bound(X,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,identity))),bind(Y0,$fot(greatest_lower_bound(identity,X)))]]) ).

cnf(refute_0_3841,plain,
    greatest_lower_bound(identity,X) = greatest_lower_bound(X,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,identity),greatest_lower_bound(identity,X)) )],[refute_0_3839,refute_0_3840]) ).

cnf(refute_0_3842,plain,
    greatest_lower_bound(identity,a) = greatest_lower_bound(a,identity),
    inference(subst,[],[refute_0_3841:[bind(X,$fot(a))]]) ).

cnf(refute_0_3843,plain,
    multiply(X_197,inverse(multiply(inverse(greatest_lower_bound(identity,X_197)),X_197))) = inverse(inverse(greatest_lower_bound(identity,X_197))),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(X_197)),bind(X_59,$fot(inverse(greatest_lower_bound(identity,X_197))))]]) ).

cnf(refute_0_3844,plain,
    multiply(inverse(greatest_lower_bound(identity,X_197)),X_197) = least_upper_bound(X_197,identity),
    inference(subst,[],[refute_0_1664:[bind(X_113,$fot(X_197))]]) ).

cnf(refute_0_3845,plain,
    ( multiply(X_197,inverse(multiply(inverse(greatest_lower_bound(identity,X_197)),X_197))) != inverse(inverse(greatest_lower_bound(identity,X_197)))
    | multiply(inverse(greatest_lower_bound(identity,X_197)),X_197) != least_upper_bound(X_197,identity)
    | multiply(X_197,inverse(least_upper_bound(X_197,identity))) = inverse(inverse(greatest_lower_bound(identity,X_197))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_197,inverse(multiply(inverse(greatest_lower_bound(identity,X_197)),X_197))),inverse(inverse(greatest_lower_bound(identity,X_197)))) ),[0,1,0],$fot(least_upper_bound(X_197,identity))]]) ).

cnf(refute_0_3846,plain,
    ( multiply(X_197,inverse(multiply(inverse(greatest_lower_bound(identity,X_197)),X_197))) != inverse(inverse(greatest_lower_bound(identity,X_197)))
    | multiply(X_197,inverse(least_upper_bound(X_197,identity))) = inverse(inverse(greatest_lower_bound(identity,X_197))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_197)),X_197),least_upper_bound(X_197,identity)) )],[refute_0_3844,refute_0_3845]) ).

cnf(refute_0_3847,plain,
    multiply(X_197,inverse(least_upper_bound(X_197,identity))) = inverse(inverse(greatest_lower_bound(identity,X_197))),
    inference(resolve,[$cnf( $equal(multiply(X_197,inverse(multiply(inverse(greatest_lower_bound(identity,X_197)),X_197))),inverse(inverse(greatest_lower_bound(identity,X_197)))) )],[refute_0_3843,refute_0_3846]) ).

cnf(refute_0_3848,plain,
    inverse(inverse(greatest_lower_bound(identity,X_197))) = greatest_lower_bound(identity,X_197),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(identity,X_197)))]]) ).

cnf(refute_0_3849,plain,
    ( multiply(X_197,inverse(least_upper_bound(X_197,identity))) != inverse(inverse(greatest_lower_bound(identity,X_197)))
    | inverse(inverse(greatest_lower_bound(identity,X_197))) != greatest_lower_bound(identity,X_197)
    | multiply(X_197,inverse(least_upper_bound(X_197,identity))) = greatest_lower_bound(identity,X_197) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_197,inverse(least_upper_bound(X_197,identity))),greatest_lower_bound(identity,X_197)) ),[0],$fot(inverse(inverse(greatest_lower_bound(identity,X_197))))]]) ).

cnf(refute_0_3850,plain,
    ( multiply(X_197,inverse(least_upper_bound(X_197,identity))) != inverse(inverse(greatest_lower_bound(identity,X_197)))
    | multiply(X_197,inverse(least_upper_bound(X_197,identity))) = greatest_lower_bound(identity,X_197) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,X_197))),greatest_lower_bound(identity,X_197)) )],[refute_0_3848,refute_0_3849]) ).

cnf(refute_0_3851,plain,
    multiply(X_197,inverse(least_upper_bound(X_197,identity))) = greatest_lower_bound(identity,X_197),
    inference(resolve,[$cnf( $equal(multiply(X_197,inverse(least_upper_bound(X_197,identity))),inverse(inverse(greatest_lower_bound(identity,X_197)))) )],[refute_0_3847,refute_0_3850]) ).

cnf(refute_0_3852,plain,
    multiply(a,inverse(least_upper_bound(a,identity))) = greatest_lower_bound(identity,a),
    inference(subst,[],[refute_0_3851:[bind(X_197,$fot(a))]]) ).

cnf(refute_0_3853,plain,
    ( multiply(a,inverse(least_upper_bound(a,identity))) != greatest_lower_bound(identity,a)
    | greatest_lower_bound(identity,a) != greatest_lower_bound(a,identity)
    | multiply(a,inverse(least_upper_bound(a,identity))) = greatest_lower_bound(a,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(a,inverse(least_upper_bound(a,identity))))),bind(Y0,$fot(greatest_lower_bound(identity,a))),bind(Z0,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3854,plain,
    ( greatest_lower_bound(identity,a) != greatest_lower_bound(a,identity)
    | multiply(a,inverse(least_upper_bound(a,identity))) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(least_upper_bound(a,identity))),greatest_lower_bound(identity,a)) )],[refute_0_3852,refute_0_3853]) ).

cnf(refute_0_3855,plain,
    multiply(a,inverse(least_upper_bound(a,identity))) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,a),greatest_lower_bound(a,identity)) )],[refute_0_3842,refute_0_3854]) ).

cnf(refute_0_3856,plain,
    ( multiply(a,inverse(least_upper_bound(a,identity))) != greatest_lower_bound(a,identity)
    | multiply(a,inverse(least_upper_bound(a,identity))) != greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(a,identity) = greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,inverse(least_upper_bound(a,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) ),[0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_3857,plain,
    ( multiply(a,inverse(least_upper_bound(a,identity))) != greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(a,identity) = greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(least_upper_bound(a,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3855,refute_0_3856]) ).

cnf(refute_0_3858,plain,
    greatest_lower_bound(a,identity) = greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(least_upper_bound(a,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) )],[refute_0_2318,refute_0_3857]) ).

cnf(refute_0_3859,plain,
    ( greatest_lower_bound(a,identity) != greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) = greatest_lower_bound(a,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(a,identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_3860,plain,
    greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) )],[refute_0_3858,refute_0_3859]) ).

cnf(refute_0_3861,plain,
    ( multiply(a,least_upper_bound(b,identity)) != multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))
    | greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | multiply(a,least_upper_bound(b,identity)) = multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,least_upper_bound(b,identity)),multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))) ),[1,1],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_3862,plain,
    ( multiply(a,least_upper_bound(b,identity)) != multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))
    | multiply(a,least_upper_bound(b,identity)) = multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3860,refute_0_3861]) ).

cnf(refute_0_3863,plain,
    multiply(a,least_upper_bound(b,identity)) = multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,identity)),multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))) )],[refute_0_1281,refute_0_3862]) ).

cnf(refute_0_3864,plain,
    least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))),
    inference(subst,[],[refute_0_764:[bind(X_93,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_3865,plain,
    ( greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))) ),[1,1,1],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_3866,plain,
    ( least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3860,refute_0_3865]) ).

cnf(refute_0_3867,plain,
    least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))) )],[refute_0_3864,refute_0_3866]) ).

cnf(refute_0_3868,plain,
    multiply(least_upper_bound(a,inverse(least_upper_bound(b,identity))),inverse(inverse(least_upper_bound(b,identity)))) = least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))),
    inference(subst,[],[refute_0_363:[bind(X_111,$fot(a)),bind(X_112,$fot(inverse(least_upper_bound(b,identity))))]]) ).

cnf(refute_0_3869,plain,
    ( multiply(least_upper_bound(a,inverse(least_upper_bound(b,identity))),inverse(inverse(least_upper_bound(b,identity)))) != least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))
    | least_upper_bound(a,inverse(least_upper_bound(b,identity))) != least_upper_bound(a,identity)
    | multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) = least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,inverse(least_upper_bound(b,identity))),inverse(inverse(least_upper_bound(b,identity)))),least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))) ),[0,0],$fot(least_upper_bound(a,identity))]]) ).

cnf(refute_0_3870,plain,
    ( multiply(least_upper_bound(a,inverse(least_upper_bound(b,identity))),inverse(inverse(least_upper_bound(b,identity)))) != least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))
    | multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) = least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,inverse(least_upper_bound(b,identity))),least_upper_bound(a,identity)) )],[refute_0_2305,refute_0_3869]) ).

cnf(refute_0_3871,plain,
    multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) = least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,inverse(least_upper_bound(b,identity))),inverse(inverse(least_upper_bound(b,identity)))),least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))) )],[refute_0_3868,refute_0_3870]) ).

cnf(refute_0_3872,plain,
    multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_3873,plain,
    ( multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity))))
    | inverse(inverse(least_upper_bound(b,identity))) != least_upper_bound(b,identity)
    | multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity))))) ),[1,1],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_3874,plain,
    ( inverse(inverse(least_upper_bound(b,identity))) != least_upper_bound(b,identity)
    | multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity))))) )],[refute_0_3872,refute_0_3873]) ).

cnf(refute_0_3875,plain,
    multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(b,identity))),least_upper_bound(b,identity)) )],[refute_0_3496,refute_0_3874]) ).

cnf(refute_0_3876,plain,
    ( multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))
    | multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) != least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))
    | multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))),least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))) ),[0],$fot(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))]]) ).

cnf(refute_0_3877,plain,
    ( multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) != least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))
    | multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) )],[refute_0_3875,refute_0_3876]) ).

cnf(refute_0_3878,plain,
    least_upper_bound(X_211,least_upper_bound(identity,multiply(X_230,identity))) = least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)),
    inference(subst,[],[refute_0_1726:[bind(X_166,$fot(multiply(X_230,identity)))]]) ).

cnf(refute_0_3879,plain,
    multiply(least_upper_bound(X_230,identity),identity) = least_upper_bound(identity,multiply(X_230,identity)),
    inference(subst,[],[refute_0_728:[bind(X_110,$fot(identity)),bind(X_111,$fot(X_230))]]) ).

cnf(refute_0_3880,plain,
    ( multiply(least_upper_bound(X_230,identity),identity) != least_upper_bound(identity,multiply(X_230,identity))
    | least_upper_bound(identity,multiply(X_230,identity)) = multiply(least_upper_bound(X_230,identity),identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_230,identity),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_230,identity))))]]) ).

cnf(refute_0_3881,plain,
    least_upper_bound(identity,multiply(X_230,identity)) = multiply(least_upper_bound(X_230,identity),identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_230,identity),identity),least_upper_bound(identity,multiply(X_230,identity))) )],[refute_0_3879,refute_0_3880]) ).

cnf(refute_0_3882,plain,
    ( least_upper_bound(X_211,least_upper_bound(identity,multiply(X_230,identity))) != least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))
    | least_upper_bound(identity,multiply(X_230,identity)) != multiply(least_upper_bound(X_230,identity),identity)
    | least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) = least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_211,least_upper_bound(identity,multiply(X_230,identity))),least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))) ),[0,1],$fot(multiply(least_upper_bound(X_230,identity),identity))]]) ).

cnf(refute_0_3883,plain,
    ( least_upper_bound(X_211,least_upper_bound(identity,multiply(X_230,identity))) != least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))
    | least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) = least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_230,identity)),multiply(least_upper_bound(X_230,identity),identity)) )],[refute_0_3881,refute_0_3882]) ).

cnf(refute_0_3884,plain,
    least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) = least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_211,least_upper_bound(identity,multiply(X_230,identity))),least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))) )],[refute_0_3878,refute_0_3883]) ).

cnf(refute_0_3885,plain,
    multiply(least_upper_bound(X_230,identity),identity) = least_upper_bound(X_230,identity),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(least_upper_bound(X_230,identity)))]]) ).

cnf(refute_0_3886,plain,
    least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) = least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)))]]) ).

cnf(refute_0_3887,plain,
    ( multiply(least_upper_bound(X_230,identity),identity) != least_upper_bound(X_230,identity)
    | least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) != least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity))
    | least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) = least_upper_bound(X_211,least_upper_bound(X_230,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)),least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity))) ),[1,1],$fot(least_upper_bound(X_230,identity))]]) ).

cnf(refute_0_3888,plain,
    ( multiply(least_upper_bound(X_230,identity),identity) != least_upper_bound(X_230,identity)
    | least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) = least_upper_bound(X_211,least_upper_bound(X_230,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)),least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity))) )],[refute_0_3886,refute_0_3887]) ).

cnf(refute_0_3889,plain,
    least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) = least_upper_bound(X_211,least_upper_bound(X_230,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_230,identity),identity),least_upper_bound(X_230,identity)) )],[refute_0_3885,refute_0_3888]) ).

cnf(refute_0_3890,plain,
    ( least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) != least_upper_bound(X_211,least_upper_bound(X_230,identity))
    | least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) != least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))
    | least_upper_bound(X_211,least_upper_bound(X_230,identity)) = least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)),least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))) ),[0],$fot(least_upper_bound(X_211,least_upper_bound(X_230,identity)))]]) ).

cnf(refute_0_3891,plain,
    ( least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) != least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))
    | least_upper_bound(X_211,least_upper_bound(X_230,identity)) = least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)),least_upper_bound(X_211,least_upper_bound(X_230,identity))) )],[refute_0_3889,refute_0_3890]) ).

cnf(refute_0_3892,plain,
    multiply(X_230,identity) = X_230,
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(X_230))]]) ).

cnf(refute_0_3893,plain,
    least_upper_bound(multiply(X_230,identity),X_211) = least_upper_bound(multiply(X_230,identity),X_211),
    introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_230,identity),X_211))]]) ).

cnf(refute_0_3894,plain,
    ( multiply(X_230,identity) != X_230
    | least_upper_bound(multiply(X_230,identity),X_211) != least_upper_bound(multiply(X_230,identity),X_211)
    | least_upper_bound(multiply(X_230,identity),X_211) = least_upper_bound(X_230,X_211) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_230,identity),X_211),least_upper_bound(multiply(X_230,identity),X_211)) ),[1,0],$fot(X_230)]]) ).

cnf(refute_0_3895,plain,
    ( multiply(X_230,identity) != X_230
    | least_upper_bound(multiply(X_230,identity),X_211) = least_upper_bound(X_230,X_211) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_230,identity),X_211),least_upper_bound(multiply(X_230,identity),X_211)) )],[refute_0_3893,refute_0_3894]) ).

cnf(refute_0_3896,plain,
    least_upper_bound(multiply(X_230,identity),X_211) = least_upper_bound(X_230,X_211),
    inference(resolve,[$cnf( $equal(multiply(X_230,identity),X_230) )],[refute_0_3892,refute_0_3895]) ).

cnf(refute_0_3897,plain,
    least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)) = least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)))]]) ).

cnf(refute_0_3898,plain,
    ( least_upper_bound(multiply(X_230,identity),X_211) != least_upper_bound(X_230,X_211)
    | least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)) != least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))
    | least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)) = least_upper_bound(identity,least_upper_bound(X_230,X_211)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)),least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))) ),[1,1],$fot(least_upper_bound(X_230,X_211))]]) ).

cnf(refute_0_3899,plain,
    ( least_upper_bound(multiply(X_230,identity),X_211) != least_upper_bound(X_230,X_211)
    | least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)) = least_upper_bound(identity,least_upper_bound(X_230,X_211)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)),least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))) )],[refute_0_3897,refute_0_3898]) ).

cnf(refute_0_3900,plain,
    least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)) = least_upper_bound(identity,least_upper_bound(X_230,X_211)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_230,identity),X_211),least_upper_bound(X_230,X_211)) )],[refute_0_3896,refute_0_3899]) ).

cnf(refute_0_3901,plain,
    ( least_upper_bound(X_211,least_upper_bound(X_230,identity)) != least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))
    | least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)) != least_upper_bound(identity,least_upper_bound(X_230,X_211))
    | least_upper_bound(X_211,least_upper_bound(X_230,identity)) = least_upper_bound(identity,least_upper_bound(X_230,X_211)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_211,least_upper_bound(X_230,identity)),least_upper_bound(identity,least_upper_bound(X_230,X_211))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)))]]) ).

cnf(refute_0_3902,plain,
    ( least_upper_bound(X_211,least_upper_bound(X_230,identity)) != least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))
    | least_upper_bound(X_211,least_upper_bound(X_230,identity)) = least_upper_bound(identity,least_upper_bound(X_230,X_211)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211)),least_upper_bound(identity,least_upper_bound(X_230,X_211))) )],[refute_0_3900,refute_0_3901]) ).

cnf(refute_0_3903,plain,
    ( least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)) != least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))
    | least_upper_bound(X_211,least_upper_bound(X_230,identity)) = least_upper_bound(identity,least_upper_bound(X_230,X_211)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_211,least_upper_bound(X_230,identity)),least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))) )],[refute_0_3891,refute_0_3902]) ).

cnf(refute_0_3904,plain,
    least_upper_bound(X_211,least_upper_bound(X_230,identity)) = least_upper_bound(identity,least_upper_bound(X_230,X_211)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_211,multiply(least_upper_bound(X_230,identity),identity)),least_upper_bound(identity,least_upper_bound(multiply(X_230,identity),X_211))) )],[refute_0_3884,refute_0_3903]) ).

cnf(refute_0_3905,plain,
    least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)) = least_upper_bound(identity,least_upper_bound(X_265,multiply(X_265,X_94))),
    inference(subst,[],[refute_0_3904:[bind(X_211,$fot(multiply(X_265,X_94))),bind(X_230,$fot(X_265))]]) ).

cnf(refute_0_3906,plain,
    multiply(X_265,least_upper_bound(X_94,identity)) = least_upper_bound(X_265,multiply(X_265,X_94)),
    inference(subst,[],[refute_0_480:[bind(X_93,$fot(X_265))]]) ).

cnf(refute_0_3907,plain,
    ( multiply(X_265,least_upper_bound(X_94,identity)) != least_upper_bound(X_265,multiply(X_265,X_94))
    | least_upper_bound(X_265,multiply(X_265,X_94)) = multiply(X_265,least_upper_bound(X_94,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_265,least_upper_bound(X_94,identity)))),bind(Y0,$fot(least_upper_bound(X_265,multiply(X_265,X_94))))]]) ).

cnf(refute_0_3908,plain,
    least_upper_bound(X_265,multiply(X_265,X_94)) = multiply(X_265,least_upper_bound(X_94,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_265,least_upper_bound(X_94,identity)),least_upper_bound(X_265,multiply(X_265,X_94))) )],[refute_0_3906,refute_0_3907]) ).

cnf(refute_0_3909,plain,
    ( least_upper_bound(X_265,multiply(X_265,X_94)) != multiply(X_265,least_upper_bound(X_94,identity))
    | least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)) != least_upper_bound(identity,least_upper_bound(X_265,multiply(X_265,X_94)))
    | least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)) = least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)),least_upper_bound(identity,least_upper_bound(X_265,multiply(X_265,X_94)))) ),[1,1],$fot(multiply(X_265,least_upper_bound(X_94,identity)))]]) ).

cnf(refute_0_3910,plain,
    ( least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)) != least_upper_bound(identity,least_upper_bound(X_265,multiply(X_265,X_94)))
    | least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)) = least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_265,multiply(X_265,X_94)),multiply(X_265,least_upper_bound(X_94,identity))) )],[refute_0_3908,refute_0_3909]) ).

cnf(refute_0_3911,plain,
    least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)) = least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)),least_upper_bound(identity,least_upper_bound(X_265,multiply(X_265,X_94)))) )],[refute_0_3905,refute_0_3910]) ).

cnf(refute_0_3912,plain,
    multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_265,X_264))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))),
    inference(subst,[],[refute_0_1801:[bind(X_94,$fot(identity)),bind(X_95,$fot(least_upper_bound(X_265,X_264)))]]) ).

cnf(refute_0_3913,plain,
    least_upper_bound(X_264,least_upper_bound(X_265,identity)) = least_upper_bound(identity,least_upper_bound(X_265,X_264)),
    inference(subst,[],[refute_0_3904:[bind(X_211,$fot(X_264)),bind(X_230,$fot(X_265))]]) ).

cnf(refute_0_3914,plain,
    ( least_upper_bound(X_264,least_upper_bound(X_265,identity)) != least_upper_bound(identity,least_upper_bound(X_265,X_264))
    | least_upper_bound(identity,least_upper_bound(X_265,X_264)) = least_upper_bound(X_264,least_upper_bound(X_265,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_264,least_upper_bound(X_265,identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_265,X_264))))]]) ).

cnf(refute_0_3915,plain,
    least_upper_bound(identity,least_upper_bound(X_265,X_264)) = least_upper_bound(X_264,least_upper_bound(X_265,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_264,least_upper_bound(X_265,identity)),least_upper_bound(identity,least_upper_bound(X_265,X_264))) )],[refute_0_3913,refute_0_3914]) ).

cnf(refute_0_3916,plain,
    ( multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_265,X_264))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))
    | least_upper_bound(identity,least_upper_bound(X_265,X_264)) != least_upper_bound(X_264,least_upper_bound(X_265,identity))
    | multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_265,X_264))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))) ),[0,1],$fot(least_upper_bound(X_264,least_upper_bound(X_265,identity)))]]) ).

cnf(refute_0_3917,plain,
    ( multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_265,X_264))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))
    | multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_265,X_264)),least_upper_bound(X_264,least_upper_bound(X_265,identity))) )],[refute_0_3915,refute_0_3916]) ).

cnf(refute_0_3918,plain,
    multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(identity,least_upper_bound(X_265,X_264))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))) )],[refute_0_3912,refute_0_3917]) ).

cnf(refute_0_3919,plain,
    multiply(identity,least_upper_bound(X_264,least_upper_bound(X_265,identity))) = least_upper_bound(X_264,least_upper_bound(X_265,identity)),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_264,least_upper_bound(X_265,identity))))]]) ).

cnf(refute_0_3920,plain,
    multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) = multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))),
    introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))))]]) ).

cnf(refute_0_3921,plain,
    ( multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) != multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity)))
    | inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) = multiply(identity,least_upper_bound(X_264,least_upper_bound(X_265,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))),multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_3922,plain,
    ( inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) = multiply(identity,least_upper_bound(X_264,least_upper_bound(X_265,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))),multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity)))) )],[refute_0_3920,refute_0_3921]) ).

cnf(refute_0_3923,plain,
    multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) = multiply(identity,least_upper_bound(X_264,least_upper_bound(X_265,identity))),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_3922]) ).

cnf(refute_0_3924,plain,
    ( multiply(identity,least_upper_bound(X_264,least_upper_bound(X_265,identity))) != least_upper_bound(X_264,least_upper_bound(X_265,identity))
    | multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) != multiply(identity,least_upper_bound(X_264,least_upper_bound(X_265,identity)))
    | multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) = least_upper_bound(X_264,least_upper_bound(X_265,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_264,least_upper_bound(X_265,identity))))),bind(Z0,$fot(least_upper_bound(X_264,least_upper_bound(X_265,identity))))]]) ).

cnf(refute_0_3925,plain,
    ( multiply(identity,least_upper_bound(X_264,least_upper_bound(X_265,identity))) != least_upper_bound(X_264,least_upper_bound(X_265,identity))
    | multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) = least_upper_bound(X_264,least_upper_bound(X_265,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))),multiply(identity,least_upper_bound(X_264,least_upper_bound(X_265,identity)))) )],[refute_0_3923,refute_0_3924]) ).

cnf(refute_0_3926,plain,
    multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) = least_upper_bound(X_264,least_upper_bound(X_265,identity)),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_264,least_upper_bound(X_265,identity))),least_upper_bound(X_264,least_upper_bound(X_265,identity))) )],[refute_0_3919,refute_0_3925]) ).

cnf(refute_0_3927,plain,
    ( multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) != least_upper_bound(X_264,least_upper_bound(X_265,identity))
    | multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))
    | least_upper_bound(X_264,least_upper_bound(X_265,identity)) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))) ),[0],$fot(least_upper_bound(X_264,least_upper_bound(X_265,identity)))]]) ).

cnf(refute_0_3928,plain,
    ( multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))
    | least_upper_bound(X_264,least_upper_bound(X_265,identity)) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))),least_upper_bound(X_264,least_upper_bound(X_265,identity))) )],[refute_0_3926,refute_0_3927]) ).

cnf(refute_0_3929,plain,
    multiply(identity,least_upper_bound(X_265,least_upper_bound(identity,X_264))) = least_upper_bound(X_265,least_upper_bound(identity,X_264)),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_265,least_upper_bound(identity,X_264))))]]) ).

cnf(refute_0_3930,plain,
    multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))) = multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))),
    introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))))]]) ).

cnf(refute_0_3931,plain,
    ( multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))) != multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264)))
    | inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))) = multiply(identity,least_upper_bound(X_265,least_upper_bound(identity,X_264))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))),multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_3932,plain,
    ( inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))) = multiply(identity,least_upper_bound(X_265,least_upper_bound(identity,X_264))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))),multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264)))) )],[refute_0_3930,refute_0_3931]) ).

cnf(refute_0_3933,plain,
    multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))) = multiply(identity,least_upper_bound(X_265,least_upper_bound(identity,X_264))),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_3932]) ).

cnf(refute_0_3934,plain,
    ( multiply(identity,least_upper_bound(X_265,least_upper_bound(identity,X_264))) != least_upper_bound(X_265,least_upper_bound(identity,X_264))
    | multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))) != multiply(identity,least_upper_bound(X_265,least_upper_bound(identity,X_264)))
    | multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))) = least_upper_bound(X_265,least_upper_bound(identity,X_264)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_265,least_upper_bound(identity,X_264))))),bind(Z0,$fot(least_upper_bound(X_265,least_upper_bound(identity,X_264))))]]) ).

cnf(refute_0_3935,plain,
    ( multiply(identity,least_upper_bound(X_265,least_upper_bound(identity,X_264))) != least_upper_bound(X_265,least_upper_bound(identity,X_264))
    | multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))) = least_upper_bound(X_265,least_upper_bound(identity,X_264)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))),multiply(identity,least_upper_bound(X_265,least_upper_bound(identity,X_264)))) )],[refute_0_3933,refute_0_3934]) ).

cnf(refute_0_3936,plain,
    multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))) = least_upper_bound(X_265,least_upper_bound(identity,X_264)),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_265,least_upper_bound(identity,X_264))),least_upper_bound(X_265,least_upper_bound(identity,X_264))) )],[refute_0_3929,refute_0_3935]) ).

cnf(refute_0_3937,plain,
    least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))) = multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))),
    inference(subst,[],[refute_0_2456:[bind(Y,$fot(X_265)),bind(X_103,$fot(identity)),bind(X_104,$fot(X_264))]]) ).

cnf(refute_0_3938,plain,
    ( multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))) != least_upper_bound(X_265,least_upper_bound(identity,X_264))
    | least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))) != multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264)))
    | least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))) = least_upper_bound(X_265,least_upper_bound(identity,X_264)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))))),bind(Y0,$fot(multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))))),bind(Z0,$fot(least_upper_bound(X_265,least_upper_bound(identity,X_264))))]]) ).

cnf(refute_0_3939,plain,
    ( multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))) != least_upper_bound(X_265,least_upper_bound(identity,X_264))
    | least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))) = least_upper_bound(X_265,least_upper_bound(identity,X_264)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))),multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264)))) )],[refute_0_3937,refute_0_3938]) ).

cnf(refute_0_3940,plain,
    least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))) = least_upper_bound(X_265,least_upper_bound(identity,X_264)),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_265,least_upper_bound(identity,X_264))),least_upper_bound(X_265,least_upper_bound(identity,X_264))) )],[refute_0_3936,refute_0_3939]) ).

cnf(refute_0_3941,plain,
    ( least_upper_bound(X_264,least_upper_bound(X_265,identity)) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))
    | least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))) != least_upper_bound(X_265,least_upper_bound(identity,X_264))
    | least_upper_bound(X_264,least_upper_bound(X_265,identity)) = least_upper_bound(X_265,least_upper_bound(identity,X_264)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_264,least_upper_bound(X_265,identity)),least_upper_bound(X_265,least_upper_bound(identity,X_264))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))))]]) ).

cnf(refute_0_3942,plain,
    ( least_upper_bound(X_264,least_upper_bound(X_265,identity)) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))
    | least_upper_bound(X_264,least_upper_bound(X_265,identity)) = least_upper_bound(X_265,least_upper_bound(identity,X_264)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264))),least_upper_bound(X_265,least_upper_bound(identity,X_264))) )],[refute_0_3940,refute_0_3941]) ).

cnf(refute_0_3943,plain,
    ( multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))
    | least_upper_bound(X_264,least_upper_bound(X_265,identity)) = least_upper_bound(X_265,least_upper_bound(identity,X_264)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_264,least_upper_bound(X_265,identity)),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))) )],[refute_0_3928,refute_0_3942]) ).

cnf(refute_0_3944,plain,
    least_upper_bound(X_264,least_upper_bound(X_265,identity)) = least_upper_bound(X_265,least_upper_bound(identity,X_264)),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_264,least_upper_bound(X_265,identity))),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(X_265,X_264)))) )],[refute_0_3918,refute_0_3943]) ).

cnf(refute_0_3945,plain,
    least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)) = least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94))),
    inference(subst,[],[refute_0_3944:[bind(X_264,$fot(multiply(X_265,X_94)))]]) ).

cnf(refute_0_3946,plain,
    ( least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)) != least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94)))
    | least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)) != least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity)))
    | least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94))) = least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)),least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity)))) ),[0],$fot(least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94))))]]) ).

cnf(refute_0_3947,plain,
    ( least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)) != least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity)))
    | least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94))) = least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)),least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94)))) )],[refute_0_3945,refute_0_3946]) ).

cnf(refute_0_3948,plain,
    least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94))) = least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_265,X_94),least_upper_bound(X_265,identity)),least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity)))) )],[refute_0_3911,refute_0_3947]) ).

cnf(refute_0_3949,plain,
    ( least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94))) != least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity)))
    | least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity))) = least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity)))))]]) ).

cnf(refute_0_3950,plain,
    least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity))) = least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_265,least_upper_bound(identity,multiply(X_265,X_94))),least_upper_bound(identity,multiply(X_265,least_upper_bound(X_94,identity)))) )],[refute_0_3948,refute_0_3949]) ).

cnf(refute_0_3951,plain,
    least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))),
    inference(subst,[],[refute_0_3950:[bind(X_265,$fot(a)),bind(X_94,$fot(b))]]) ).

cnf(refute_0_3952,plain,
    multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))) = least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X,identity)))),
    inference(subst,[],[monotony_lub1:[bind(Z,$fot(inverse(greatest_lower_bound(X,identity))))]]) ).

cnf(refute_0_3953,plain,
    multiply(X,inverse(greatest_lower_bound(X,identity))) = least_upper_bound(identity,X),
    inference(subst,[],[refute_0_3143:[bind(X_98,$fot(X))]]) ).

cnf(refute_0_3954,plain,
    ( multiply(X,inverse(greatest_lower_bound(X,identity))) != least_upper_bound(identity,X)
    | multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))) != least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X,identity))))
    | multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))) = least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))),least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X,identity))))) ),[1,1],$fot(least_upper_bound(identity,X))]]) ).

cnf(refute_0_3955,plain,
    ( multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))) != least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X,identity))))
    | multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))) = least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)) ),
    inference(resolve,[$cnf( $equal(multiply(X,inverse(greatest_lower_bound(X,identity))),least_upper_bound(identity,X)) )],[refute_0_3953,refute_0_3954]) ).

cnf(refute_0_3956,plain,
    multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))) = least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))),least_upper_bound(multiply(X,Y),multiply(X,inverse(greatest_lower_bound(X,identity))))) )],[refute_0_3952,refute_0_3955]) ).

cnf(refute_0_3957,plain,
    least_upper_bound(X,multiply(X,Y)) = multiply(X,least_upper_bound(Y,identity)),
    inference(subst,[],[refute_0_549:[bind(X_93,$fot(X)),bind(X_94,$fot(Y))]]) ).

cnf(refute_0_3958,plain,
    least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))) = least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))))]]) ).

cnf(refute_0_3959,plain,
    ( least_upper_bound(X,multiply(X,Y)) != multiply(X,least_upper_bound(Y,identity))
    | least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))) != least_upper_bound(identity,least_upper_bound(X,multiply(X,Y)))
    | least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))),least_upper_bound(identity,least_upper_bound(X,multiply(X,Y)))) ),[1,1],$fot(multiply(X,least_upper_bound(Y,identity)))]]) ).

cnf(refute_0_3960,plain,
    ( least_upper_bound(X,multiply(X,Y)) != multiply(X,least_upper_bound(Y,identity))
    | least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))),least_upper_bound(identity,least_upper_bound(X,multiply(X,Y)))) )],[refute_0_3958,refute_0_3959]) ).

cnf(refute_0_3961,plain,
    least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(X,Y)),multiply(X,least_upper_bound(Y,identity))) )],[refute_0_3957,refute_0_3960]) ).

cnf(refute_0_3962,plain,
    least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)) = least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))),
    inference(subst,[],[refute_0_3104:[bind(X_82,$fot(identity)),bind(X_83,$fot(multiply(X,Y))),bind(X_84,$fot(X))]]) ).

cnf(refute_0_3963,plain,
    ( least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)) != least_upper_bound(identity,least_upper_bound(X,multiply(X,Y)))
    | least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))) != least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity)))
    | least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))))),bind(Z0,$fot(least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity)))))]]) ).

cnf(refute_0_3964,plain,
    ( least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))) != least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity)))
    | least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)),least_upper_bound(identity,least_upper_bound(X,multiply(X,Y)))) )],[refute_0_3962,refute_0_3963]) ).

cnf(refute_0_3965,plain,
    least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X,multiply(X,Y))),least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity)))) )],[refute_0_3961,refute_0_3964]) ).

cnf(refute_0_3966,plain,
    ( multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))) != least_upper_bound(multiply(X,Y),least_upper_bound(identity,X))
    | least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)) != least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity)))
    | multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))),least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity)))) ),[0],$fot(least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)))]]) ).

cnf(refute_0_3967,plain,
    ( multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))) != least_upper_bound(multiply(X,Y),least_upper_bound(identity,X))
    | multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),least_upper_bound(identity,X)),least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity)))) )],[refute_0_3965,refute_0_3966]) ).

cnf(refute_0_3968,plain,
    multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))) = least_upper_bound(identity,multiply(X,least_upper_bound(Y,identity))),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,inverse(greatest_lower_bound(X,identity)))),least_upper_bound(multiply(X,Y),least_upper_bound(identity,X))) )],[refute_0_3956,refute_0_3967]) ).

cnf(refute_0_3969,plain,
    multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_3968:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_3970,plain,
    ( multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(identity,multiply(a,least_upper_bound(b,identity)))
    | least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) != least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))
    | multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))))]]) ).

cnf(refute_0_3971,plain,
    ( least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) != least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))
    | multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) ),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))),least_upper_bound(identity,multiply(a,least_upper_bound(b,identity)))) )],[refute_0_3969,refute_0_3970]) ).

cnf(refute_0_3972,plain,
    multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))) )],[refute_0_3951,refute_0_3971]) ).

cnf(refute_0_3973,plain,
    inverse(greatest_lower_bound(identity,a)) = inverse(greatest_lower_bound(a,identity)),
    inference(subst,[],[refute_0_2091:[bind(X_94,$fot(a))]]) ).

cnf(refute_0_3974,plain,
    least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(identity,a)),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(a))]]) ).

cnf(refute_0_3975,plain,
    ( inverse(greatest_lower_bound(identity,a)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(identity,a))
    | least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,inverse(a)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,a)))),bind(Z0,$fot(inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3976,plain,
    ( inverse(greatest_lower_bound(identity,a)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),inverse(greatest_lower_bound(identity,a))) )],[refute_0_3974,refute_0_3975]) ).

cnf(refute_0_3977,plain,
    least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,a)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_3973,refute_0_3976]) ).

cnf(refute_0_3978,plain,
    least_upper_bound(b,least_upper_bound(identity,inverse(a))) = least_upper_bound(b,least_upper_bound(identity,inverse(a))),
    introduced(tautology,[refl,[$fot(least_upper_bound(b,least_upper_bound(identity,inverse(a))))]]) ).

cnf(refute_0_3979,plain,
    ( least_upper_bound(b,least_upper_bound(identity,inverse(a))) != least_upper_bound(b,least_upper_bound(identity,inverse(a)))
    | least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(b,least_upper_bound(identity,inverse(a))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(a))),least_upper_bound(b,least_upper_bound(identity,inverse(a)))) ),[1,1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_3980,plain,
    ( least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(b,least_upper_bound(identity,inverse(a))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(a))),least_upper_bound(b,least_upper_bound(identity,inverse(a)))) )],[refute_0_3978,refute_0_3979]) ).

cnf(refute_0_3981,plain,
    least_upper_bound(b,least_upper_bound(identity,inverse(a))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_3977,refute_0_3980]) ).

cnf(refute_0_3982,plain,
    least_upper_bound(inverse(a),least_upper_bound(b,identity)) = least_upper_bound(b,least_upper_bound(identity,inverse(a))),
    inference(subst,[],[refute_0_3736:[bind(X_192,$fot(inverse(a))),bind(X_193,$fot(b))]]) ).

cnf(refute_0_3983,plain,
    inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))) = least_upper_bound(inverse(a),least_upper_bound(b,identity)),
    inference(subst,[],[refute_0_1559:[bind(X,$fot(a)),bind(X_89,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_3984,plain,
    ( inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))) != least_upper_bound(inverse(a),least_upper_bound(b,identity))
    | least_upper_bound(inverse(a),least_upper_bound(b,identity)) != least_upper_bound(b,least_upper_bound(identity,inverse(a)))
    | inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,least_upper_bound(identity,inverse(a))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))))),bind(Y0,$fot(least_upper_bound(inverse(a),least_upper_bound(b,identity)))),bind(Z0,$fot(least_upper_bound(b,least_upper_bound(identity,inverse(a)))))]]) ).

cnf(refute_0_3985,plain,
    ( least_upper_bound(inverse(a),least_upper_bound(b,identity)) != least_upper_bound(b,least_upper_bound(identity,inverse(a)))
    | inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,least_upper_bound(identity,inverse(a))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))),least_upper_bound(inverse(a),least_upper_bound(b,identity))) )],[refute_0_3983,refute_0_3984]) ).

cnf(refute_0_3986,plain,
    inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,least_upper_bound(identity,inverse(a))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),least_upper_bound(b,identity)),least_upper_bound(b,least_upper_bound(identity,inverse(a)))) )],[refute_0_3982,refute_0_3985]) ).

cnf(refute_0_3987,plain,
    ( inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))) != least_upper_bound(b,least_upper_bound(identity,inverse(a)))
    | least_upper_bound(b,least_upper_bound(identity,inverse(a))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(identity,inverse(a))))),bind(Z0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_3988,plain,
    ( least_upper_bound(b,least_upper_bound(identity,inverse(a))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))),least_upper_bound(b,least_upper_bound(identity,inverse(a)))) )],[refute_0_3986,refute_0_3987]) ).

cnf(refute_0_3989,plain,
    inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(identity,inverse(a))),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_3981,refute_0_3988]) ).

cnf(refute_0_3990,plain,
    multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) = multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))),
    introduced(tautology,[refl,[$fot(multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_3991,plain,
    ( multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) != multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))))
    | inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) = multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))),multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))))) ),[1,1],$fot(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_3992,plain,
    ( inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) = multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))),multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))))) )],[refute_0_3990,refute_0_3991]) ).

cnf(refute_0_3993,plain,
    multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) = multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_3989,refute_0_3992]) ).

cnf(refute_0_3994,plain,
    ( multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) != multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))
    | multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))
    | multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))))),bind(Y0,$fot(multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))))]]) ).

cnf(refute_0_3995,plain,
    ( multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))
    | multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) ),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))),multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_3993,refute_0_3994]) ).

cnf(refute_0_3996,plain,
    multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))),least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))) )],[refute_0_3972,refute_0_3995]) ).

cnf(refute_0_3997,plain,
    multiply(a,inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),a))) = multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))),
    inference(subst,[],[refute_0_1032:[bind(Y,$fot(inverse(least_upper_bound(b,identity)))),bind(X_99,$fot(a))]]) ).

cnf(refute_0_3998,plain,
    least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) = multiply(a,inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),a))),
    inference(subst,[],[refute_0_3398:[bind(X_219,$fot(inverse(least_upper_bound(b,identity)))),bind(X_220,$fot(a))]]) ).

cnf(refute_0_3999,plain,
    ( multiply(a,inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),a))) != multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))))
    | least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) != multiply(a,inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),a)))
    | least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) = multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))))),bind(Y0,$fot(multiply(a,inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),a))))),bind(Z0,$fot(multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))))))]]) ).

cnf(refute_0_4000,plain,
    ( multiply(a,inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),a))) != multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))))
    | least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) = multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))),multiply(a,inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),a)))) )],[refute_0_3998,refute_0_3999]) ).

cnf(refute_0_4001,plain,
    least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) = multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(inverse(least_upper_bound(b,identity)),a))),multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))))) )],[refute_0_3997,refute_0_4000]) ).

cnf(refute_0_4002,plain,
    ( multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) != least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))
    | least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) != multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))))
    | least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))))),bind(Y0,$fot(multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))))]]) ).

cnf(refute_0_4003,plain,
    ( multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))) != least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))
    | least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))),multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity)))))) )],[refute_0_4001,refute_0_4002]) ).

cnf(refute_0_4004,plain,
    least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(a,inverse(least_upper_bound(b,identity))))),least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))) )],[refute_0_3996,refute_0_4003]) ).

cnf(refute_0_4005,plain,
    ( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))
    | least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))) != least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))
    | multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))) ),[0],$fot(least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_4006,plain,
    ( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))
    | multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity))))),least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))) )],[refute_0_4004,refute_0_4005]) ).

cnf(refute_0_4007,plain,
    ( multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))) != least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))
    | multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))) )],[refute_0_3877,refute_0_4006]) ).

cnf(refute_0_4008,plain,
    multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(a,least_upper_bound(identity,multiply(a,b))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(inverse(least_upper_bound(b,identity)))),least_upper_bound(identity,multiply(a,inverse(inverse(least_upper_bound(b,identity)))))) )],[refute_0_3871,refute_0_4007]) ).

cnf(refute_0_4009,plain,
    ( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))
    | least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))))]]) ).

cnf(refute_0_4010,plain,
    least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))) )],[refute_0_4008,refute_0_4009]) ).

cnf(refute_0_4011,plain,
    ( least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))
    | least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) != least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))
    | least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(identity,multiply(a,b))))),bind(Z0,$fot(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))))]]) ).

cnf(refute_0_4012,plain,
    ( least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))
    | least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))) )],[refute_0_3951,refute_0_4011]) ).

cnf(refute_0_4013,plain,
    least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,multiply(a,b))),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) )],[refute_0_4010,refute_0_4012]) ).

cnf(refute_0_4014,plain,
    multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) = least_upper_bound(identity,multiply(X_96,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))),
    inference(subst,[],[refute_0_258:[bind(X,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))]]) ).

cnf(refute_0_4015,plain,
    multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,least_upper_bound(X_94,X_145))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94)),
    inference(subst,[],[refute_0_2530:[bind(X_95,$fot(least_upper_bound(X_94,X_145)))]]) ).

cnf(refute_0_4016,plain,
    least_upper_bound(X_94,least_upper_bound(X_94,X_145)) = least_upper_bound(X_94,X_145),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(X_145)),bind(X_31,$fot(X_94))]]) ).

cnf(refute_0_4017,plain,
    ( multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,least_upper_bound(X_94,X_145))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94))
    | least_upper_bound(X_94,least_upper_bound(X_94,X_145)) != least_upper_bound(X_94,X_145)
    | multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,X_145)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,least_upper_bound(X_94,X_145))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94))) ),[0,1],$fot(least_upper_bound(X_94,X_145))]]) ).

cnf(refute_0_4018,plain,
    ( multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,least_upper_bound(X_94,X_145))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94))
    | multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,X_145)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_94,least_upper_bound(X_94,X_145)),least_upper_bound(X_94,X_145)) )],[refute_0_4016,refute_0_4017]) ).

cnf(refute_0_4019,plain,
    multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,X_145)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94)),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,least_upper_bound(X_94,X_145))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94))) )],[refute_0_4015,refute_0_4018]) ).

cnf(refute_0_4020,plain,
    multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,X_145)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(X_94,X_145)))]]) ).

cnf(refute_0_4021,plain,
    ( multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,X_145)) != identity
    | multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,X_145)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94))
    | identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,X_145)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94))) ),[0],$fot(identity)]]) ).

cnf(refute_0_4022,plain,
    ( multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,X_145)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94))
    | identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,X_145)),identity) )],[refute_0_4020,refute_0_4021]) ).

cnf(refute_0_4023,plain,
    identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94)),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_94,X_145)),least_upper_bound(X_94,X_145)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_94,X_145)),X_94))) )],[refute_0_4019,refute_0_4022]) ).

cnf(refute_0_4024,plain,
    identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_150,least_upper_bound(a,c))),X_150)),
    inference(subst,[],[refute_0_4023:[bind(X_145,$fot(least_upper_bound(a,c))),bind(X_94,$fot(X_150))]]) ).

cnf(refute_0_4025,plain,
    least_upper_bound(a,least_upper_bound(c,X_150)) = least_upper_bound(X_150,least_upper_bound(a,c)),
    inference(subst,[],[refute_0_1140:[bind(X_79,$fot(X_150))]]) ).

cnf(refute_0_4026,plain,
    ( least_upper_bound(a,least_upper_bound(c,X_150)) != least_upper_bound(X_150,least_upper_bound(a,c))
    | least_upper_bound(X_150,least_upper_bound(a,c)) = least_upper_bound(a,least_upper_bound(c,X_150)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(c,X_150)))),bind(Y0,$fot(least_upper_bound(X_150,least_upper_bound(a,c))))]]) ).

cnf(refute_0_4027,plain,
    least_upper_bound(X_150,least_upper_bound(a,c)) = least_upper_bound(a,least_upper_bound(c,X_150)),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(c,X_150)),least_upper_bound(X_150,least_upper_bound(a,c))) )],[refute_0_4025,refute_0_4026]) ).

cnf(refute_0_4028,plain,
    ( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_150,least_upper_bound(a,c))),X_150))
    | least_upper_bound(X_150,least_upper_bound(a,c)) != least_upper_bound(a,least_upper_bound(c,X_150))
    | identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,X_150))),X_150)) ),
    introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_150,least_upper_bound(a,c))),X_150))) ),[1,1,0,0],$fot(least_upper_bound(a,least_upper_bound(c,X_150)))]]) ).

cnf(refute_0_4029,plain,
    ( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_150,least_upper_bound(a,c))),X_150))
    | identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,X_150))),X_150)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_150,least_upper_bound(a,c)),least_upper_bound(a,least_upper_bound(c,X_150))) )],[refute_0_4027,refute_0_4028]) ).

cnf(refute_0_4030,plain,
    identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,X_150))),X_150)),
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_150,least_upper_bound(a,c))),X_150))) )],[refute_0_4024,refute_0_4029]) ).

cnf(refute_0_4031,plain,
    identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,inverse(least_upper_bound(identity,c))))),inverse(least_upper_bound(identity,c)))),
    inference(subst,[],[refute_0_4030:[bind(X_150,$fot(inverse(least_upper_bound(identity,c))))]]) ).

cnf(refute_0_4032,plain,
    least_upper_bound(c,identity) = least_upper_bound(c,inverse(least_upper_bound(identity,c))),
    inference(subst,[],[refute_0_712:[bind(X_210,$fot(c))]]) ).

cnf(refute_0_4033,plain,
    ( least_upper_bound(c,identity) != least_upper_bound(c,inverse(least_upper_bound(identity,c)))
    | least_upper_bound(c,inverse(least_upper_bound(identity,c))) = least_upper_bound(c,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(c,identity))),bind(Y0,$fot(least_upper_bound(c,inverse(least_upper_bound(identity,c)))))]]) ).

cnf(refute_0_4034,plain,
    least_upper_bound(c,inverse(least_upper_bound(identity,c))) = least_upper_bound(c,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(c,identity),least_upper_bound(c,inverse(least_upper_bound(identity,c)))) )],[refute_0_4032,refute_0_4033]) ).

cnf(refute_0_4035,plain,
    ( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,inverse(least_upper_bound(identity,c))))),inverse(least_upper_bound(identity,c))))
    | least_upper_bound(c,inverse(least_upper_bound(identity,c))) != least_upper_bound(c,identity)
    | identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,inverse(least_upper_bound(identity,c))))),inverse(least_upper_bound(identity,c))))) ),[1,1,0,0,1],$fot(least_upper_bound(c,identity))]]) ).

cnf(refute_0_4036,plain,
    ( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,inverse(least_upper_bound(identity,c))))),inverse(least_upper_bound(identity,c))))
    | identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(c,inverse(least_upper_bound(identity,c))),least_upper_bound(c,identity)) )],[refute_0_4034,refute_0_4035]) ).

cnf(refute_0_4037,plain,
    identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))),
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,inverse(least_upper_bound(identity,c))))),inverse(least_upper_bound(identity,c))))) )],[refute_0_4031,refute_0_4036]) ).

cnf(refute_0_4038,plain,
    least_upper_bound(identity,inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))]]) ).

cnf(refute_0_4039,plain,
    multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity))) = inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),
    inference(subst,[],[refute_0_667:[bind(X_198,$fot(least_upper_bound(c,identity))),bind(X_59,$fot(least_upper_bound(a,least_upper_bound(c,identity))))]]) ).

cnf(refute_0_4040,plain,
    least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))))]]) ).

cnf(refute_0_4041,plain,
    ( multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity))) != inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity))))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))) = least_upper_bound(identity,inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity))))) ),[1,1],$fot(inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))]]) ).

cnf(refute_0_4042,plain,
    ( multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity))) != inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))) = least_upper_bound(identity,inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity))))) )],[refute_0_4040,refute_0_4041]) ).

cnf(refute_0_4043,plain,
    least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))) = least_upper_bound(identity,inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity))),inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) )],[refute_0_4039,refute_0_4042]) ).

cnf(refute_0_4044,plain,
    ( least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))) != least_upper_bound(identity,inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))
    | least_upper_bound(identity,inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))))),bind(Y0,$fot(least_upper_bound(identity,inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))]]) ).

cnf(refute_0_4045,plain,
    ( least_upper_bound(identity,inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))),least_upper_bound(identity,inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) )],[refute_0_4043,refute_0_4044]) ).

cnf(refute_0_4046,plain,
    least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) )],[refute_0_4038,refute_0_4045]) ).

cnf(refute_0_4047,plain,
    multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))) = least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15)))),
    inference(subst,[],[refute_0_363:[bind(X_111,$fot(X_118)),bind(X_112,$fot(least_upper_bound(X_14,X_15)))]]) ).

cnf(refute_0_4048,plain,
    ( multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))) != least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15))))
    | inverse(least_upper_bound(X_14,X_15)) != inverse(least_upper_bound(X_15,X_14))
    | multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))) = least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))),least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15))))) ),[1,1,1],$fot(inverse(least_upper_bound(X_15,X_14)))]]) ).

cnf(refute_0_4049,plain,
    ( multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))) != least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15))))
    | multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))) = least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14)))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_15,X_14))) )],[refute_0_1540,refute_0_4048]) ).

cnf(refute_0_4050,plain,
    multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))) = least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))),least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15))))) )],[refute_0_4047,refute_0_4049]) ).

cnf(refute_0_4051,plain,
    ( multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))) != least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15))))
    | multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))) != least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14))))
    | least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15)))) = least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))),least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14))))) ),[0],$fot(least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15)))))]]) ).

cnf(refute_0_4052,plain,
    ( multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))) != least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14))))
    | least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15)))) = least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))),least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15))))) )],[refute_0_4047,refute_0_4051]) ).

cnf(refute_0_4053,plain,
    least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15)))) = least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_118,least_upper_bound(X_14,X_15)),inverse(least_upper_bound(X_14,X_15))),least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14))))) )],[refute_0_4050,refute_0_4052]) ).

cnf(refute_0_4054,plain,
    ( least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15)))) != least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14))))
    | least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14)))) = least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15)))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14))))))]]) ).

cnf(refute_0_4055,plain,
    least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14)))) = least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_14,X_15)))),least_upper_bound(identity,multiply(X_118,inverse(least_upper_bound(X_15,X_14))))) )],[refute_0_4053,refute_0_4054]) ).

cnf(refute_0_4056,plain,
    least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))),
    inference(subst,[],[refute_0_4055:[bind(X_118,$fot(inverse(least_upper_bound(a,least_upper_bound(c,identity))))),bind(X_14,$fot(c)),bind(X_15,$fot(identity))]]) ).

cnf(refute_0_4057,plain,
    ( least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity))))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))]]) ).

cnf(refute_0_4058,plain,
    ( least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity))))) )],[refute_0_4056,refute_0_4057]) ).

cnf(refute_0_4059,plain,
    least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))) = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(c,identity)))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) )],[refute_0_4046,refute_0_4058]) ).

cnf(refute_0_4060,plain,
    ( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c))))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))) != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))
    | identity = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(identity,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))))]]) ).

cnf(refute_0_4061,plain,
    ( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c))))
    | identity = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c)))),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) )],[refute_0_4059,refute_0_4060]) ).

cnf(refute_0_4062,plain,
    identity = inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))),
    inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(c,identity))),inverse(least_upper_bound(identity,c))))) )],[refute_0_4037,refute_0_4061]) ).

cnf(refute_0_4063,plain,
    ( identity != inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))
    | inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))]]) ).

cnf(refute_0_4064,plain,
    inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) = identity,
    inference(resolve,[$cnf( $equal(identity,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) )],[refute_0_4062,refute_0_4063]) ).

cnf(refute_0_4065,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) != least_upper_bound(identity,multiply(X_96,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))
    | inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) != identity
    | multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) = least_upper_bound(identity,multiply(X_96,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))),least_upper_bound(identity,multiply(X_96,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))) ),[1,1,1],$fot(identity)]]) ).

cnf(refute_0_4066,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) != least_upper_bound(identity,multiply(X_96,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))
    | multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) = least_upper_bound(identity,multiply(X_96,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))),identity) )],[refute_0_4064,refute_0_4065]) ).

cnf(refute_0_4067,plain,
    multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) = least_upper_bound(identity,multiply(X_96,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))),least_upper_bound(identity,multiply(X_96,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))) )],[refute_0_4014,refute_0_4066]) ).

cnf(refute_0_4068,plain,
    greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96) = greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(identity)),bind(Y,$fot(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))),bind(Z,$fot(X_96))]]) ).

cnf(refute_0_4069,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)) = inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)))]]) ).

cnf(refute_0_4070,plain,
    ( greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96) != greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))
    | inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)) != inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))
    | inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)) = inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)),inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) ),[1,0],$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))]]) ).

cnf(refute_0_4071,plain,
    ( greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96) != greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))
    | inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)) = inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)),inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) )],[refute_0_4069,refute_0_4070]) ).

cnf(refute_0_4072,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)) = inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96),greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))) )],[refute_0_4068,refute_0_4071]) ).

cnf(refute_0_4073,plain,
    multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) = multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))),
    introduced(tautology,[refl,[$fot(multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))))]]) ).

cnf(refute_0_4074,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) != multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)))
    | inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)) != inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))
    | multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) = multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))),multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))))]]) ).

cnf(refute_0_4075,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)) != inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))
    | multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) = multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))),multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)))) )],[refute_0_4073,refute_0_4074]) ).

cnf(refute_0_4076,plain,
    multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) = multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96)),inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) )],[refute_0_4072,refute_0_4075]) ).

cnf(refute_0_4077,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) != multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))))
    | multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) != least_upper_bound(identity,multiply(X_96,identity))
    | multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = least_upper_bound(identity,multiply(X_96,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))),least_upper_bound(identity,multiply(X_96,identity))) ),[0],$fot(multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))))]]) ).

cnf(refute_0_4078,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) != least_upper_bound(identity,multiply(X_96,identity))
    | multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = least_upper_bound(identity,multiply(X_96,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))),multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))))) )],[refute_0_4076,refute_0_4077]) ).

cnf(refute_0_4079,plain,
    multiply(least_upper_bound(X_96,identity),identity) = least_upper_bound(X_96,identity),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(least_upper_bound(X_96,identity)))]]) ).

cnf(refute_0_4080,plain,
    least_upper_bound(identity,multiply(X_96,identity)) = multiply(least_upper_bound(X_96,identity),identity),
    inference(subst,[],[refute_0_730:[bind(X_110,$fot(identity)),bind(X_111,$fot(X_96))]]) ).

cnf(refute_0_4081,plain,
    ( multiply(least_upper_bound(X_96,identity),identity) != least_upper_bound(X_96,identity)
    | least_upper_bound(identity,multiply(X_96,identity)) != multiply(least_upper_bound(X_96,identity),identity)
    | least_upper_bound(identity,multiply(X_96,identity)) = least_upper_bound(X_96,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(X_96,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_96,identity),identity))),bind(Z0,$fot(least_upper_bound(X_96,identity)))]]) ).

cnf(refute_0_4082,plain,
    ( multiply(least_upper_bound(X_96,identity),identity) != least_upper_bound(X_96,identity)
    | least_upper_bound(identity,multiply(X_96,identity)) = least_upper_bound(X_96,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_96,identity)),multiply(least_upper_bound(X_96,identity),identity)) )],[refute_0_4080,refute_0_4081]) ).

cnf(refute_0_4083,plain,
    least_upper_bound(identity,multiply(X_96,identity)) = least_upper_bound(X_96,identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_96,identity),identity),least_upper_bound(X_96,identity)) )],[refute_0_4079,refute_0_4082]) ).

cnf(refute_0_4084,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) != least_upper_bound(identity,multiply(X_96,identity))
    | least_upper_bound(identity,multiply(X_96,identity)) != least_upper_bound(X_96,identity)
    | multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = least_upper_bound(X_96,identity) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))),least_upper_bound(X_96,identity)) ),[0],$fot(least_upper_bound(identity,multiply(X_96,identity)))]]) ).

cnf(refute_0_4085,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) != least_upper_bound(identity,multiply(X_96,identity))
    | multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = least_upper_bound(X_96,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_96,identity)),least_upper_bound(X_96,identity)) )],[refute_0_4083,refute_0_4084]) ).

cnf(refute_0_4086,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))) != least_upper_bound(identity,multiply(X_96,identity))
    | multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = least_upper_bound(X_96,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))),least_upper_bound(identity,multiply(X_96,identity))) )],[refute_0_4078,refute_0_4085]) ).

cnf(refute_0_4087,plain,
    multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = least_upper_bound(X_96,identity),
    inference(resolve,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_96))),least_upper_bound(identity,multiply(X_96,identity))) )],[refute_0_4067,refute_0_4086]) ).

cnf(refute_0_4088,plain,
    multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) = greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))),
    inference(subst,[],[refute_0_340:[bind(X_122,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))]]) ).

cnf(refute_0_4089,plain,
    ( multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) != greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))
    | inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) != identity
    | multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) = greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))),greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_4090,plain,
    ( multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) != greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))
    | multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) = greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))),identity) )],[refute_0_4064,refute_0_4089]) ).

cnf(refute_0_4091,plain,
    multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) = greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))),greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))) )],[refute_0_4088,refute_0_4090]) ).

cnf(refute_0_4092,plain,
    greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123) = greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(identity)),bind(Y,$fot(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))),bind(Z,$fot(X_123))]]) ).

cnf(refute_0_4093,plain,
    multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) = greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123)))]]) ).

cnf(refute_0_4094,plain,
    ( multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) != greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123)
    | greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123) != greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123))
    | multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) = greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123))))]]) ).

cnf(refute_0_4095,plain,
    ( greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123) != greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123))
    | multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) = greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity),greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123)) )],[refute_0_4093,refute_0_4094]) ).

cnf(refute_0_4096,plain,
    multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) = greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123))) )],[refute_0_4092,refute_0_4095]) ).

cnf(refute_0_4097,plain,
    ( multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) != greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))
    | multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) != greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)) = greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity),greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)))]]) ).

cnf(refute_0_4098,plain,
    ( multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) != greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)) = greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity),greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123))) )],[refute_0_4096,refute_0_4097]) ).

cnf(refute_0_4099,plain,
    multiply(X_123,identity) = X_123,
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(X_123))]]) ).

cnf(refute_0_4100,plain,
    multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) = multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))),
    introduced(tautology,[refl,[$fot(multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))]]) ).

cnf(refute_0_4101,plain,
    ( multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) != multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))
    | inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) != identity
    | multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) = multiply(X_123,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))),multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_4102,plain,
    ( inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))) != identity
    | multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) = multiply(X_123,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))),multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) )],[refute_0_4100,refute_0_4101]) ).

cnf(refute_0_4103,plain,
    multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) = multiply(X_123,identity),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))),identity) )],[refute_0_4064,refute_0_4102]) ).

cnf(refute_0_4104,plain,
    ( multiply(X_123,identity) != X_123
    | multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) != multiply(X_123,identity)
    | multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) = X_123 ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))),bind(Y0,$fot(multiply(X_123,identity))),bind(Z0,$fot(X_123))]]) ).

cnf(refute_0_4105,plain,
    ( multiply(X_123,identity) != X_123
    | multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) = X_123 ),
    inference(resolve,[$cnf( $equal(multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))),multiply(X_123,identity)) )],[refute_0_4103,refute_0_4104]) ).

cnf(refute_0_4106,plain,
    multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) = X_123,
    inference(resolve,[$cnf( $equal(multiply(X_123,identity),X_123) )],[refute_0_4099,refute_0_4105]) ).

cnf(refute_0_4107,plain,
    greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) = greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))))]]) ).

cnf(refute_0_4108,plain,
    ( multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) != X_123
    | greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) != greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))
    | greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) = greatest_lower_bound(identity,X_123) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))),greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))) ),[1,1],$fot(X_123)]]) ).

cnf(refute_0_4109,plain,
    ( multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))) != X_123
    | greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) = greatest_lower_bound(identity,X_123) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))),greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))) )],[refute_0_4107,refute_0_4108]) ).

cnf(refute_0_4110,plain,
    greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) = greatest_lower_bound(identity,X_123),
    inference(resolve,[$cnf( $equal(multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))),X_123) )],[refute_0_4106,refute_0_4109]) ).

cnf(refute_0_4111,plain,
    ( greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))) != greatest_lower_bound(identity,X_123)
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)) != greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)) = greatest_lower_bound(identity,X_123) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)),greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))) ),[1],$fot(greatest_lower_bound(identity,X_123))]]) ).

cnf(refute_0_4112,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)) != greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)) = greatest_lower_bound(identity,X_123) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))))))),greatest_lower_bound(identity,X_123)) )],[refute_0_4110,refute_0_4111]) ).

cnf(refute_0_4113,plain,
    ( multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity) != greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)) = greatest_lower_bound(identity,X_123) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)),greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))) )],[refute_0_4098,refute_0_4112]) ).

cnf(refute_0_4114,plain,
    greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_123)) = greatest_lower_bound(identity,X_123),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))),X_123),identity),greatest_lower_bound(identity,multiply(X_123,inverse(greatest_lower_bound(identity,multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity)))))))) )],[refute_0_4091,refute_0_4113]) ).

cnf(refute_0_4115,plain,
    greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)) = greatest_lower_bound(identity,X_96),
    inference(subst,[],[refute_0_4114:[bind(X_123,$fot(X_96))]]) ).

cnf(refute_0_4116,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))))]]) ).

cnf(refute_0_4117,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)) != greatest_lower_bound(identity,X_96)
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))) = inverse(greatest_lower_bound(identity,X_96)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))),inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) ),[1,0],$fot(greatest_lower_bound(identity,X_96))]]) ).

cnf(refute_0_4118,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)) != greatest_lower_bound(identity,X_96)
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))) = inverse(greatest_lower_bound(identity,X_96)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))),inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) )],[refute_0_4116,refute_0_4117]) ).

cnf(refute_0_4119,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))) = inverse(greatest_lower_bound(identity,X_96)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)),greatest_lower_bound(identity,X_96)) )],[refute_0_4115,refute_0_4118]) ).

cnf(refute_0_4120,plain,
    multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))),
    introduced(tautology,[refl,[$fot(multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))))]]) ).

cnf(refute_0_4121,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) != multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))) != inverse(greatest_lower_bound(identity,X_96))
    | multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))),multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,X_96)))]]) ).

cnf(refute_0_4122,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))) != inverse(greatest_lower_bound(identity,X_96))
    | multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) ),
    inference(resolve,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))),multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))))) )],[refute_0_4120,refute_0_4121]) ).

cnf(refute_0_4123,plain,
    multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = multiply(X_96,inverse(greatest_lower_bound(identity,X_96))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96))),inverse(greatest_lower_bound(identity,X_96))) )],[refute_0_4119,refute_0_4122]) ).

cnf(refute_0_4124,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) != least_upper_bound(identity,X_96)
    | multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) != multiply(X_96,inverse(greatest_lower_bound(identity,X_96)))
    | multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = least_upper_bound(identity,X_96) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))))),bind(Y0,$fot(multiply(X_96,inverse(greatest_lower_bound(identity,X_96))))),bind(Z0,$fot(least_upper_bound(identity,X_96)))]]) ).

cnf(refute_0_4125,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(identity,X_96))) != least_upper_bound(identity,X_96)
    | multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = least_upper_bound(identity,X_96) ),
    inference(resolve,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))),multiply(X_96,inverse(greatest_lower_bound(identity,X_96)))) )],[refute_0_4123,refute_0_4124]) ).

cnf(refute_0_4126,plain,
    multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) = least_upper_bound(identity,X_96),
    inference(resolve,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(identity,X_96))),least_upper_bound(identity,X_96)) )],[refute_0_3136,refute_0_4125]) ).

cnf(refute_0_4127,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) != least_upper_bound(X_96,identity)
    | multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) != least_upper_bound(identity,X_96)
    | least_upper_bound(identity,X_96) = least_upper_bound(X_96,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))),least_upper_bound(X_96,identity)) ),[0],$fot(least_upper_bound(identity,X_96))]]) ).

cnf(refute_0_4128,plain,
    ( multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))) != least_upper_bound(X_96,identity)
    | least_upper_bound(identity,X_96) = least_upper_bound(X_96,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))),least_upper_bound(identity,X_96)) )],[refute_0_4126,refute_0_4127]) ).

cnf(refute_0_4129,plain,
    least_upper_bound(identity,X_96) = least_upper_bound(X_96,identity),
    inference(resolve,[$cnf( $equal(multiply(X_96,inverse(greatest_lower_bound(identity,greatest_lower_bound(multiply(least_upper_bound(c,identity),least_upper_bound(a,least_upper_bound(c,identity))),X_96)))),least_upper_bound(X_96,identity)) )],[refute_0_4087,refute_0_4128]) ).

cnf(refute_0_4130,plain,
    ( least_upper_bound(identity,X_96) != least_upper_bound(X_96,identity)
    | least_upper_bound(X_96,identity) = least_upper_bound(identity,X_96) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,X_96))),bind(Y0,$fot(least_upper_bound(X_96,identity)))]]) ).

cnf(refute_0_4131,plain,
    least_upper_bound(X_96,identity) = least_upper_bound(identity,X_96),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_96),least_upper_bound(X_96,identity)) )],[refute_0_4129,refute_0_4130]) ).

cnf(refute_0_4132,plain,
    least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_4131:[bind(X_96,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_4133,plain,
    ( least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(a,least_upper_bound(b,identity)))
    | least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))))),bind(Z0,$fot(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))))]]) ).

cnf(refute_0_4134,plain,
    ( least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),least_upper_bound(identity,multiply(a,least_upper_bound(b,identity)))) )],[refute_0_4132,refute_0_4133]) ).

cnf(refute_0_4135,plain,
    least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) )],[refute_0_4013,refute_0_4134]) ).

cnf(refute_0_4136,plain,
    ( least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))) ),[0],$fot(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))]]) ).

cnf(refute_0_4137,plain,
    ( least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) )],[refute_0_4135,refute_0_4136]) ).

cnf(refute_0_4138,plain,
    multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) = multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),
    introduced(tautology,[refl,[$fot(multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_4139,plain,
    ( multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) != multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) != b
    | multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) = multiply(a,b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) ),[1,1],$fot(b)]]) ).

cnf(refute_0_4140,plain,
    ( multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) != b
    | multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) = multiply(a,b) ),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) )],[refute_0_4138,refute_0_4139]) ).

cnf(refute_0_4141,plain,
    multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) = multiply(a,b),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)),b) )],[refute_0_3810,refute_0_4140]) ).

cnf(refute_0_4142,plain,
    multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)) = multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),
    inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(least_upper_bound(b,identity))),bind(Z,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_4143,plain,
    ( multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)) != multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))
    | multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) != multiply(a,b)
    | multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)) = multiply(a,b) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))),bind(Y0,$fot(multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))))),bind(Z0,$fot(multiply(a,b)))]]) ).

cnf(refute_0_4144,plain,
    ( multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) != multiply(a,b)
    | multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)) = multiply(a,b) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)),multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))) )],[refute_0_4142,refute_0_4143]) ).

cnf(refute_0_4145,plain,
    multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)) = multiply(a,b),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))),multiply(a,b)) )],[refute_0_4141,refute_0_4144]) ).

cnf(refute_0_4146,plain,
    least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_4147,plain,
    ( multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)) != multiply(a,b)
    | least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))
    | least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(a,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))) ),[1,1],$fot(multiply(a,b))]]) ).

cnf(refute_0_4148,plain,
    ( multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)) != multiply(a,b)
    | least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))) )],[refute_0_4146,refute_0_4147]) ).

cnf(refute_0_4149,plain,
    least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))) = least_upper_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)),multiply(a,b)) )],[refute_0_4145,refute_0_4148]) ).

cnf(refute_0_4150,plain,
    ( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))
    | least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))) != least_upper_bound(identity,multiply(a,b))
    | multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(a,b)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),least_upper_bound(identity,multiply(a,b))) ),[0],$fot(least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_4151,plain,
    ( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_4149,refute_0_4150]) ).

cnf(refute_0_4152,plain,
    ( least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))) )],[refute_0_4137,refute_0_4151]) ).

cnf(refute_0_4153,plain,
    multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),least_upper_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(a,identity)))) )],[refute_0_3867,refute_0_4152]) ).

cnf(refute_0_4154,plain,
    ( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_bound(identity,multiply(a,b))
    | least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))
    | least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) = least_upper_bound(identity,multiply(a,b)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(a,least_upper_bound(identity,multiply(a,b))))),bind(Y0,$fot(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))),bind(Z0,$fot(least_upper_bound(identity,multiply(a,b))))]]) ).

cnf(refute_0_4155,plain,
    ( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_bound(identity,multiply(a,b))
    | least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) = least_upper_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,multiply(a,b))),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) )],[refute_0_4010,refute_0_4154]) ).

cnf(refute_0_4156,plain,
    least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) = least_upper_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),least_upper_bound(identity,multiply(a,b))) )],[refute_0_4153,refute_0_4155]) ).

cnf(refute_0_4157,plain,
    ( least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) != least_upper_bound(identity,multiply(a,b))
    | least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) != least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))
    | least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(a,b)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(identity,multiply(a,b))))),bind(Z0,$fot(least_upper_bound(identity,multiply(a,b))))]]) ).

cnf(refute_0_4158,plain,
    ( least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) != least_upper_bound(identity,multiply(a,b))
    | least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))) )],[refute_0_3951,refute_0_4157]) ).

cnf(refute_0_4159,plain,
    least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) = least_upper_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,multiply(a,b))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_4156,refute_0_4158]) ).

cnf(refute_0_4160,plain,
    multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) = multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_4161,plain,
    ( multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) != multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity))
    | least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(a,b))
    | multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)),multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity))) ),[1,0],$fot(least_upper_bound(identity,multiply(a,b)))]]) ).

cnf(refute_0_4162,plain,
    ( least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(a,b))
    | multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)),multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity))) )],[refute_0_4160,refute_0_4161]) ).

cnf(refute_0_4163,plain,
    multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_4159,refute_0_4162]) ).

cnf(refute_0_4164,plain,
    ( multiply(a,least_upper_bound(b,identity)) != multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) != multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity))
    | multiply(a,least_upper_bound(b,identity)) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,least_upper_bound(b,identity)),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity))) ),[0],$fot(multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_4165,plain,
    ( multiply(a,least_upper_bound(b,identity)) != multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity))
    | multiply(a,least_upper_bound(b,identity)) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity))) )],[refute_0_4163,refute_0_4164]) ).

cnf(refute_0_4166,plain,
    multiply(a,least_upper_bound(b,identity)) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,identity)),multiply(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity))) )],[refute_0_3863,refute_0_4165]) ).

cnf(refute_0_4167,plain,
    ( multiply(a,least_upper_bound(b,identity)) != multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)) = multiply(a,least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(a,least_upper_bound(b,identity)))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_4168,plain,
    multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)) = multiply(a,least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,identity)),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity))) )],[refute_0_4166,refute_0_4167]) ).

cnf(refute_0_4169,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)) != multiply(a,least_upper_bound(b,identity))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) != greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)))) ),[1,1],$fot(multiply(a,least_upper_bound(b,identity)))]]) ).

cnf(refute_0_4170,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) != greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))) )],[refute_0_4168,refute_0_4169]) ).

cnf(refute_0_4171,plain,
    multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)))) )],[refute_0_1280,refute_0_4170]) ).

cnf(refute_0_4172,plain,
    greatest_lower_bound(a,greatest_lower_bound(identity,identity)) = greatest_lower_bound(a,greatest_lower_bound(identity,identity)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(identity,identity)))]]) ).

cnf(refute_0_4173,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,identity)) != greatest_lower_bound(a,greatest_lower_bound(identity,identity))
    | greatest_lower_bound(identity,identity) != identity
    | greatest_lower_bound(a,greatest_lower_bound(identity,identity)) = greatest_lower_bound(a,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,identity)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_4174,plain,
    ( greatest_lower_bound(identity,identity) != identity
    | greatest_lower_bound(a,greatest_lower_bound(identity,identity)) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,identity)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) )],[refute_0_4172,refute_0_4173]) ).

cnf(refute_0_4175,plain,
    greatest_lower_bound(a,greatest_lower_bound(identity,identity)) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,identity),identity) )],[refute_0_3562,refute_0_4174]) ).

cnf(refute_0_4176,plain,
    multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))))]]) ).

cnf(refute_0_4177,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) != multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity)))
    | greatest_lower_bound(a,greatest_lower_bound(identity,identity)) != greatest_lower_bound(a,identity)
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity)))) ),[1,1],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_4178,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,identity)) != greatest_lower_bound(a,identity)
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity)))) )],[refute_0_4176,refute_0_4177]) ).

cnf(refute_0_4179,plain,
    multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,identity)),greatest_lower_bound(a,identity)) )],[refute_0_4175,refute_0_4178]) ).

cnf(refute_0_4180,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) != multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)) != multiply(a,least_upper_bound(b,identity))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) = multiply(a,least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)))),bind(Z0,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_4181,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)) != multiply(a,least_upper_bound(b,identity))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) = multiply(a,least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity))) )],[refute_0_4179,refute_0_4180]) ).

cnf(refute_0_4182,plain,
    multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) = multiply(a,least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))) )],[refute_0_4168,refute_0_4181]) ).

cnf(refute_0_4183,plain,
    multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,greatest_lower_bound(a,identity))) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))),
    inference(subst,[],[refute_0_1518:[bind(X,$fot(a)),bind(Y,$fot(identity)),bind(X_231,$fot(least_upper_bound(identity,multiply(a,b))))]]) ).

cnf(refute_0_4184,plain,
    least_upper_bound(greatest_lower_bound(X_32,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_32,X_9))) = greatest_lower_bound(X_32,X_9),
    inference(subst,[],[refute_0_117:[bind(X_8,$fot(greatest_lower_bound(X_32,X_9)))]]) ).

cnf(refute_0_4185,plain,
    greatest_lower_bound(X_9,greatest_lower_bound(X_32,X_9)) = greatest_lower_bound(X_9,X_32),
    inference(subst,[],[refute_0_794:[bind(Y,$fot(X_32)),bind(X_23,$fot(X_9))]]) ).

cnf(refute_0_4186,plain,
    ( greatest_lower_bound(X_9,greatest_lower_bound(X_32,X_9)) != greatest_lower_bound(X_9,X_32)
    | least_upper_bound(greatest_lower_bound(X_32,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_32,X_9))) != greatest_lower_bound(X_32,X_9)
    | least_upper_bound(greatest_lower_bound(X_32,X_9),greatest_lower_bound(X_9,X_32)) = greatest_lower_bound(X_32,X_9) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_32,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_32,X_9))),greatest_lower_bound(X_32,X_9)) ),[0,1],$fot(greatest_lower_bound(X_9,X_32))]]) ).

cnf(refute_0_4187,plain,
    ( least_upper_bound(greatest_lower_bound(X_32,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_32,X_9))) != greatest_lower_bound(X_32,X_9)
    | least_upper_bound(greatest_lower_bound(X_32,X_9),greatest_lower_bound(X_9,X_32)) = greatest_lower_bound(X_32,X_9) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,greatest_lower_bound(X_32,X_9)),greatest_lower_bound(X_9,X_32)) )],[refute_0_4185,refute_0_4186]) ).

cnf(refute_0_4188,plain,
    least_upper_bound(greatest_lower_bound(X_32,X_9),greatest_lower_bound(X_9,X_32)) = greatest_lower_bound(X_32,X_9),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_32,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_32,X_9))),greatest_lower_bound(X_32,X_9)) )],[refute_0_4184,refute_0_4187]) ).

cnf(refute_0_4189,plain,
    least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)),
    inference(subst,[],[refute_0_4188:[bind(X_32,$fot(multiply(X,Z))),bind(X_9,$fot(multiply(X,Y)))]]) ).

cnf(refute_0_4190,plain,
    ( greatest_lower_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,greatest_lower_bound(Y,Z))
    | least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
    | least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).

cnf(refute_0_4191,plain,
    ( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
    | least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_831,refute_0_4190]) ).

cnf(refute_0_4192,plain,
    least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_4189,refute_0_4191]) ).

cnf(refute_0_4193,plain,
    least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) = greatest_lower_bound(Y,Z),
    inference(subst,[],[refute_0_4188:[bind(X_32,$fot(Y)),bind(X_9,$fot(Z))]]) ).

cnf(refute_0_4194,plain,
    multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),
    introduced(tautology,[refl,[$fot(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))]]) ).

cnf(refute_0_4195,plain,
    ( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))
    | least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
    | multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) ),[1,1],$fot(greatest_lower_bound(Y,Z))]]) ).

cnf(refute_0_4196,plain,
    ( least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
    | multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) )],[refute_0_4194,refute_0_4195]) ).

cnf(refute_0_4197,plain,
    multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),greatest_lower_bound(Y,Z)) )],[refute_0_4193,refute_0_4196]) ).

cnf(refute_0_4198,plain,
    least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),
    inference(subst,[],[refute_0_540:[bind(Y,$fot(greatest_lower_bound(Y,Z))),bind(Z,$fot(greatest_lower_bound(Z,Y)))]]) ).

cnf(refute_0_4199,plain,
    ( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
    | least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))
    | least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))))),bind(Y0,$fot(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).

cnf(refute_0_4200,plain,
    ( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
    | least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) )],[refute_0_4198,refute_0_4199]) ).

cnf(refute_0_4201,plain,
    least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_4197,refute_0_4200]) ).

cnf(refute_0_4202,plain,
    greatest_lower_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,greatest_lower_bound(Z,Y)),
    inference(subst,[],[refute_0_831:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_4203,plain,
    least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),
    introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))]]) ).

cnf(refute_0_4204,plain,
    ( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
    | least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))
    | least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,greatest_lower_bound(Z,Y)))]]) ).

cnf(refute_0_4205,plain,
    ( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
    | least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_4203,refute_0_4204]) ).

cnf(refute_0_4206,plain,
    least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_4202,refute_0_4205]) ).

cnf(refute_0_4207,plain,
    ( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
    | least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y)))
    | least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).

cnf(refute_0_4208,plain,
    ( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
    | least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y)))) )],[refute_0_4206,refute_0_4207]) ).

cnf(refute_0_4209,plain,
    least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_4201,refute_0_4208]) ).

cnf(refute_0_4210,plain,
    least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(greatest_lower_bound(multiply(X,Z),multiply(X,Y)))),bind(X_17,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).

cnf(refute_0_4211,plain,
    ( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,greatest_lower_bound(Y,Z))
    | least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))
    | least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))))),bind(Y0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).

cnf(refute_0_4212,plain,
    ( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,greatest_lower_bound(Y,Z))
    | least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_4210,refute_0_4211]) ).

cnf(refute_0_4213,plain,
    least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_4209,refute_0_4212]) ).

cnf(refute_0_4214,plain,
    ( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != multiply(X,greatest_lower_bound(Y,Z))
    | least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).

cnf(refute_0_4215,plain,
    ( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_4213,refute_0_4214]) ).

cnf(refute_0_4216,plain,
    ( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
    | greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
    | multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),[0],$fot(greatest_lower_bound(multiply(X,Z),multiply(X,Y)))]]) ).

cnf(refute_0_4217,plain,
    ( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_4202,refute_0_4216]) ).

cnf(refute_0_4218,plain,
    ( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
    inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_4215,refute_0_4217]) ).

cnf(refute_0_4219,plain,
    multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_4192,refute_0_4218]) ).

cnf(refute_0_4220,plain,
    ( multiply(X,greatest_lower_bound(Y,Z)) != multiply(X,greatest_lower_bound(Z,Y))
    | multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(multiply(X,greatest_lower_bound(Z,Y))))]]) ).

cnf(refute_0_4221,plain,
    multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_4219,refute_0_4220]) ).

cnf(refute_0_4222,plain,
    multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,greatest_lower_bound(a,identity))),
    inference(subst,[],[refute_0_4221:[bind(X,$fot(least_upper_bound(identity,multiply(a,b)))),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_4223,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) != multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,greatest_lower_bound(a,identity))) != multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity)))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,greatest_lower_bound(a,identity))))),bind(Z0,$fot(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity)))))]]) ).

cnf(refute_0_4224,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,greatest_lower_bound(a,identity))) != multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity)))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,greatest_lower_bound(a,identity)))) )],[refute_0_4222,refute_0_4223]) ).

cnf(refute_0_4225,plain,
    multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,greatest_lower_bound(a,identity))),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity)))) )],[refute_0_4183,refute_0_4224]) ).

cnf(refute_0_4226,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) != multiply(a,least_upper_bound(b,identity))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) != multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity)))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) = multiply(a,least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))))),bind(Z0,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_4227,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))) != multiply(a,least_upper_bound(b,identity))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) = multiply(a,least_upper_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity)))) )],[refute_0_4225,refute_0_4226]) ).

cnf(refute_0_4228,plain,
    multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) = multiply(a,least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(a,greatest_lower_bound(identity,identity))),multiply(a,least_upper_bound(b,identity))) )],[refute_0_4182,refute_0_4227]) ).

cnf(refute_0_4229,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) != multiply(a,least_upper_bound(b,identity))
    | multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) != greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity)))
    | multiply(a,least_upper_bound(b,identity)) = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity)))) ),[0],$fot(multiply(a,least_upper_bound(b,identity)))]]) ).

cnf(refute_0_4230,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) != greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity)))
    | multiply(a,least_upper_bound(b,identity)) = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)),multiply(a,least_upper_bound(b,identity))) )],[refute_0_4228,refute_0_4229]) ).

cnf(refute_0_4231,plain,
    multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) = greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,least_upper_bound(X_94,inverse(X_107)))),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_107)),bind(Y,$fot(X_108)),bind(Z,$fot(least_upper_bound(X_94,inverse(X_107))))]]) ).

cnf(refute_0_4232,plain,
    multiply(X_107,least_upper_bound(X_94,inverse(X_107))) = least_upper_bound(identity,multiply(X_107,X_94)),
    inference(subst,[],[refute_0_251:[bind(X_93,$fot(X_107))]]) ).

cnf(refute_0_4233,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) != greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,least_upper_bound(X_94,inverse(X_107))))
    | multiply(X_107,least_upper_bound(X_94,inverse(X_107))) != least_upper_bound(identity,multiply(X_107,X_94))
    | multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) = greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_94))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,least_upper_bound(X_94,inverse(X_107))))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_107,X_94)))]]) ).

cnf(refute_0_4234,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) != greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,least_upper_bound(X_94,inverse(X_107))))
    | multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) = greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_94))) ),
    inference(resolve,[$cnf( $equal(multiply(X_107,least_upper_bound(X_94,inverse(X_107))),least_upper_bound(identity,multiply(X_107,X_94))) )],[refute_0_4232,refute_0_4233]) ).

cnf(refute_0_4235,plain,
    multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) = greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_94))),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,least_upper_bound(X_94,inverse(X_107))))) )],[refute_0_4231,refute_0_4234]) ).

cnf(refute_0_4236,plain,
    multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))) = greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,least_upper_bound(inverse(X_107),X_95))),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_107)),bind(Y,$fot(X_108)),bind(Z,$fot(least_upper_bound(inverse(X_107),X_95)))]]) ).

cnf(refute_0_4237,plain,
    multiply(X_107,least_upper_bound(inverse(X_107),X_95)) = least_upper_bound(identity,multiply(X_107,X_95)),
    inference(subst,[],[refute_0_236:[bind(X_93,$fot(X_107))]]) ).

cnf(refute_0_4238,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))) != greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,least_upper_bound(inverse(X_107),X_95)))
    | multiply(X_107,least_upper_bound(inverse(X_107),X_95)) != least_upper_bound(identity,multiply(X_107,X_95))
    | multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))) = greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_95))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,least_upper_bound(inverse(X_107),X_95)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_107,X_95)))]]) ).

cnf(refute_0_4239,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))) != greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,least_upper_bound(inverse(X_107),X_95)))
    | multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))) = greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_95))) ),
    inference(resolve,[$cnf( $equal(multiply(X_107,least_upper_bound(inverse(X_107),X_95)),least_upper_bound(identity,multiply(X_107,X_95))) )],[refute_0_4237,refute_0_4238]) ).

cnf(refute_0_4240,plain,
    multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))) = greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_95))),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,least_upper_bound(inverse(X_107),X_95)))) )],[refute_0_4236,refute_0_4239]) ).

cnf(refute_0_4241,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))) != greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_95)))
    | greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_95))) = multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))))),bind(Y0,$fot(greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_95)))))]]) ).

cnf(refute_0_4242,plain,
    greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_95))) = multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_95))),greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_95)))) )],[refute_0_4240,refute_0_4241]) ).

cnf(refute_0_4243,plain,
    greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_94))) = multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94))),
    inference(subst,[],[refute_0_4242:[bind(X_95,$fot(X_94))]]) ).

cnf(refute_0_4244,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) != greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_94)))
    | greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_94))) != multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94)))
    | multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) = multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))),multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94)))) ),[0],$fot(greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_94))))]]) ).

cnf(refute_0_4245,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) != greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_94)))
    | multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) = multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_94))),multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94)))) )],[refute_0_4243,refute_0_4244]) ).

cnf(refute_0_4246,plain,
    multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) = multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94))),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))),greatest_lower_bound(multiply(X_107,X_108),least_upper_bound(identity,multiply(X_107,X_94)))) )],[refute_0_4235,refute_0_4245]) ).

cnf(refute_0_4247,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) != multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94)))
    | multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94))) = multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))))),bind(Y0,$fot(multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94)))))]]) ).

cnf(refute_0_4248,plain,
    multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94))) = multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(X_94,inverse(X_107)))),multiply(X_107,greatest_lower_bound(X_108,least_upper_bound(inverse(X_107),X_94)))) )],[refute_0_4246,refute_0_4247]) ).

cnf(refute_0_4249,plain,
    multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(inverse(a),b))) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))),
    inference(subst,[],[refute_0_4248:[bind(X_107,$fot(a)),bind(X_108,$fot(least_upper_bound(b,identity))),bind(X_94,$fot(b))]]) ).

cnf(refute_0_4250,plain,
    multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(inverse(a),b))),
    inference(subst,[],[refute_0_4221:[bind(X,$fot(a)),bind(Y,$fot(least_upper_bound(b,identity))),bind(Z,$fot(least_upper_bound(inverse(a),b)))]]) ).

cnf(refute_0_4251,plain,
    ( multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(inverse(a),b))) != multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))
    | multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))) != multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(inverse(a),b)))
    | multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))))),bind(Y0,$fot(multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(inverse(a),b))))),bind(Z0,$fot(multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))))]]) ).

cnf(refute_0_4252,plain,
    ( multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(inverse(a),b))) != multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))
    | multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) ),
    inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))),multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(inverse(a),b)))) )],[refute_0_4250,refute_0_4251]) ).

cnf(refute_0_4253,plain,
    multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))),
    inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(inverse(a),b))),multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))) )],[refute_0_4249,refute_0_4252]) ).

cnf(refute_0_4254,plain,
    multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)) = greatest_lower_bound(multiply(X_107,least_upper_bound(inverse(X_107),X_95)),multiply(X_107,X_109)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_107)),bind(Y,$fot(least_upper_bound(inverse(X_107),X_95))),bind(Z,$fot(X_109))]]) ).

cnf(refute_0_4255,plain,
    ( multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)) != greatest_lower_bound(multiply(X_107,least_upper_bound(inverse(X_107),X_95)),multiply(X_107,X_109))
    | multiply(X_107,least_upper_bound(inverse(X_107),X_95)) != least_upper_bound(identity,multiply(X_107,X_95))
    | multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)) = greatest_lower_bound(least_upper_bound(identity,multiply(X_107,X_95)),multiply(X_107,X_109)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)),greatest_lower_bound(multiply(X_107,least_upper_bound(inverse(X_107),X_95)),multiply(X_107,X_109))) ),[1,0],$fot(least_upper_bound(identity,multiply(X_107,X_95)))]]) ).

cnf(refute_0_4256,plain,
    ( multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)) != greatest_lower_bound(multiply(X_107,least_upper_bound(inverse(X_107),X_95)),multiply(X_107,X_109))
    | multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)) = greatest_lower_bound(least_upper_bound(identity,multiply(X_107,X_95)),multiply(X_107,X_109)) ),
    inference(resolve,[$cnf( $equal(multiply(X_107,least_upper_bound(inverse(X_107),X_95)),least_upper_bound(identity,multiply(X_107,X_95))) )],[refute_0_4237,refute_0_4255]) ).

cnf(refute_0_4257,plain,
    multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)) = greatest_lower_bound(least_upper_bound(identity,multiply(X_107,X_95)),multiply(X_107,X_109)),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)),greatest_lower_bound(multiply(X_107,least_upper_bound(inverse(X_107),X_95)),multiply(X_107,X_109))) )],[refute_0_4254,refute_0_4256]) ).

cnf(refute_0_4258,plain,
    ( multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)) != greatest_lower_bound(least_upper_bound(identity,multiply(X_107,X_95)),multiply(X_107,X_109))
    | greatest_lower_bound(least_upper_bound(identity,multiply(X_107,X_95)),multiply(X_107,X_109)) = multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,multiply(X_107,X_95)),multiply(X_107,X_109))))]]) ).

cnf(refute_0_4259,plain,
    greatest_lower_bound(least_upper_bound(identity,multiply(X_107,X_95)),multiply(X_107,X_109)) = multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(least_upper_bound(inverse(X_107),X_95),X_109)),greatest_lower_bound(least_upper_bound(identity,multiply(X_107,X_95)),multiply(X_107,X_109))) )],[refute_0_4257,refute_0_4258]) ).

cnf(refute_0_4260,plain,
    greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))) = multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_4259:[bind(X_107,$fot(a)),bind(X_109,$fot(least_upper_bound(b,identity))),bind(X_95,$fot(b))]]) ).

cnf(refute_0_4261,plain,
    ( multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))) != multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))
    | greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))) != multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity)))
    | greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))))),bind(Y0,$fot(multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))))),bind(Z0,$fot(multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))))]]) ).

cnf(refute_0_4262,plain,
    ( multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))) != multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))
    | greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))),multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity)))) )],[refute_0_4260,refute_0_4261]) ).

cnf(refute_0_4263,plain,
    greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))),
    inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(least_upper_bound(inverse(a),b),least_upper_bound(b,identity))),multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))) )],[refute_0_4253,refute_0_4262]) ).

cnf(refute_0_4264,plain,
    ( multiply(a,least_upper_bound(b,identity)) != greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))) != multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))
    | multiply(a,least_upper_bound(b,identity)) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,least_upper_bound(b,identity)),multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_4265,plain,
    ( multiply(a,least_upper_bound(b,identity)) != greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity)))
    | multiply(a,least_upper_bound(b,identity)) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity))),multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))) )],[refute_0_4263,refute_0_4264]) ).

cnf(refute_0_4266,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)) != greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity)))
    | multiply(a,least_upper_bound(b,identity)) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) ),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,identity)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity)))) )],[refute_0_4230,refute_0_4265]) ).

cnf(refute_0_4267,plain,
    multiply(a,least_upper_bound(b,identity)) = multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(greatest_lower_bound(a,identity),identity)),greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,least_upper_bound(b,identity)))) )],[refute_0_4171,refute_0_4266]) ).

cnf(refute_0_4268,plain,
    ( multiply(a,least_upper_bound(b,identity)) != multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))
    | multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) = multiply(a,least_upper_bound(b,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(a,least_upper_bound(b,identity)))),bind(Y0,$fot(multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))))]]) ).

cnf(refute_0_4269,plain,
    multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) = multiply(a,least_upper_bound(b,identity)),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(b,identity)),multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))))) )],[refute_0_4267,refute_0_4268]) ).

cnf(refute_0_4270,plain,
    ( multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) != multiply(a,least_upper_bound(b,identity))
    | greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) != multiply(inverse(a),multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))))
    | greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) = multiply(inverse(a),multiply(a,least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))),multiply(inverse(a),multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))))) ),[1,1],$fot(multiply(a,least_upper_bound(b,identity)))]]) ).

cnf(refute_0_4271,plain,
    ( greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) != multiply(inverse(a),multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))))
    | greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) = multiply(inverse(a),multiply(a,least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))),multiply(a,least_upper_bound(b,identity))) )],[refute_0_4269,refute_0_4270]) ).

cnf(refute_0_4272,plain,
    greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) = multiply(inverse(a),multiply(a,least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))),multiply(inverse(a),multiply(a,greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))))) )],[refute_0_1279,refute_0_4271]) ).

cnf(refute_0_4273,plain,
    multiply(inverse(a),multiply(a,least_upper_bound(b,identity))) = least_upper_bound(b,identity),
    inference(subst,[],[refute_0_1308:[bind(X_59,$fot(a)),bind(X_60,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_4274,plain,
    ( multiply(inverse(a),multiply(a,least_upper_bound(b,identity))) != least_upper_bound(b,identity)
    | greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) != multiply(inverse(a),multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) = least_upper_bound(b,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))),multiply(inverse(a),multiply(a,least_upper_bound(b,identity)))) ),[1],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_4275,plain,
    ( greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) != multiply(inverse(a),multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) = least_upper_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(a,least_upper_bound(b,identity))),least_upper_bound(b,identity)) )],[refute_0_4273,refute_0_4274]) ).

cnf(refute_0_4276,plain,
    greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))),multiply(inverse(a),multiply(a,least_upper_bound(b,identity)))) )],[refute_0_4272,refute_0_4275]) ).

cnf(refute_0_4277,plain,
    ( greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))) != least_upper_bound(b,identity)
    | least_upper_bound(least_upper_bound(b,inverse(a)),greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) != least_upper_bound(b,inverse(a))
    | least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)) = least_upper_bound(b,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(b,inverse(a)),greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))),least_upper_bound(b,inverse(a))) ),[0,1],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_4278,plain,
    ( least_upper_bound(least_upper_bound(b,inverse(a)),greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))) != least_upper_bound(b,inverse(a))
    | least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)) = least_upper_bound(b,inverse(a)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a))),least_upper_bound(b,identity)) )],[refute_0_4276,refute_0_4277]) ).

cnf(refute_0_4279,plain,
    least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)) = least_upper_bound(b,inverse(a)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,inverse(a)),greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(a)))),least_upper_bound(b,inverse(a))) )],[refute_0_1278,refute_0_4278]) ).

cnf(refute_0_4280,plain,
    least_upper_bound(b,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(inverse(greatest_lower_bound(a,identity)))),bind(X_31,$fot(b))]]) ).

cnf(refute_0_4281,plain,
    least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)) = least_upper_bound(Y,least_upper_bound(identity,least_upper_bound(X_320,inverse(a)))),
    inference(subst,[],[refute_0_3111:[bind(X,$fot(least_upper_bound(X_320,inverse(a)))),bind(X_145,$fot(identity))]]) ).

cnf(refute_0_4282,plain,
    least_upper_bound(X_317,least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) = least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317)),
    inference(subst,[],[refute_0_3111:[bind(X,$fot(X_317)),bind(Y,$fot(greatest_lower_bound(a,identity))),bind(X_145,$fot(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4283,plain,
    least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)),
    inference(subst,[],[refute_0_1566:[bind(X_12,$fot(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_4284,plain,
    inverse(inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) = greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4285,plain,
    multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))),
    inference(subst,[],[refute_0_170:[bind(X_116,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),bind(X_87,$fot(b))]]) ).

cnf(refute_0_4286,plain,
    ( multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))
    | least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) != least_upper_bound(b,identity)
    | multiply(least_upper_bound(b,identity),inverse(b)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b)),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))) ),[0,0],$fot(least_upper_bound(b,identity))]]) ).

cnf(refute_0_4287,plain,
    ( multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))
    | multiply(least_upper_bound(b,identity),inverse(b)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),least_upper_bound(b,identity)) )],[refute_0_2473,refute_0_4286]) ).

cnf(refute_0_4288,plain,
    multiply(least_upper_bound(b,identity),inverse(b)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b)),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))) )],[refute_0_4285,refute_0_4287]) ).

cnf(refute_0_4289,plain,
    ( multiply(least_upper_bound(b,identity),inverse(b)) != inverse(greatest_lower_bound(b,identity))
    | multiply(least_upper_bound(b,identity),inverse(b)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))
    | inverse(greatest_lower_bound(b,identity)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(b)),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))) ),[0],$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_4290,plain,
    ( multiply(least_upper_bound(b,identity),inverse(b)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))
    | inverse(greatest_lower_bound(b,identity)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(b)),inverse(greatest_lower_bound(b,identity))) )],[refute_0_2672,refute_0_4289]) ).

cnf(refute_0_4291,plain,
    multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b)) = inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_2728:[bind(X_278,$fot(b)),bind(X_94,$fot(least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_4292,plain,
    least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))) = multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b)),
    inference(subst,[],[refute_0_448:[bind(Y,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),bind(X_132,$fot(b))]]) ).

cnf(refute_0_4293,plain,
    ( multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b)) != inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))) != multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))) = inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))))),bind(Y0,$fot(multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b)))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_4294,plain,
    ( multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b)) != inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))) = inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))),multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b))) )],[refute_0_4292,refute_0_4293]) ).

cnf(refute_0_4295,plain,
    least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))) = inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(b)),inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4291,refute_0_4294]) ).

cnf(refute_0_4296,plain,
    ( inverse(greatest_lower_bound(b,identity)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))) != inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))))]]) ).

cnf(refute_0_4297,plain,
    ( inverse(greatest_lower_bound(b,identity)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))
    | inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b))),inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4295,refute_0_4296]) ).

cnf(refute_0_4298,plain,
    ( multiply(least_upper_bound(b,identity),inverse(b)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))
    | inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,identity)),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))) )],[refute_0_4290,refute_0_4297]) ).

cnf(refute_0_4299,plain,
    inverse(greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(b)),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(b)))) )],[refute_0_4288,refute_0_4298]) ).

cnf(refute_0_4300,plain,
    ( inverse(greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(b,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(b,identity)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_4301,plain,
    inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4299,refute_0_4300]) ).

cnf(refute_0_4302,plain,
    ( inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(b,identity))
    | inverse(inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) != greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))
    | inverse(inverse(greatest_lower_bound(b,identity))) = greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) ),[0,0],$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_4303,plain,
    ( inverse(inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) != greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))
    | inverse(inverse(greatest_lower_bound(b,identity))) = greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(b,identity))) )],[refute_0_4301,refute_0_4302]) ).

cnf(refute_0_4304,plain,
    inverse(inverse(greatest_lower_bound(b,identity))) = greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) )],[refute_0_4284,refute_0_4303]) ).

cnf(refute_0_4305,plain,
    ( inverse(inverse(greatest_lower_bound(b,identity))) != greatest_lower_bound(b,identity)
    | inverse(inverse(greatest_lower_bound(b,identity))) != greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(b,identity))),greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).

cnf(refute_0_4306,plain,
    ( inverse(inverse(greatest_lower_bound(b,identity))) != greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))
    | greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(b,identity))),greatest_lower_bound(b,identity)) )],[refute_0_2487,refute_0_4305]) ).

cnf(refute_0_4307,plain,
    greatest_lower_bound(b,identity) = greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(b,identity))),greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) )],[refute_0_4304,refute_0_4306]) ).

cnf(refute_0_4308,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))
    | greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))) = greatest_lower_bound(b,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(b,identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4309,plain,
    greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))) = greatest_lower_bound(b,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) )],[refute_0_4307,refute_0_4308]) ).

cnf(refute_0_4310,plain,
    ( greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))) != greatest_lower_bound(b,identity)
    | least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))
    | least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))) ),[0,1],$fot(greatest_lower_bound(b,identity))]]) ).

cnf(refute_0_4311,plain,
    ( least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))
    | least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)) )],[refute_0_4309,refute_0_4310]) ).

cnf(refute_0_4312,plain,
    least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)) = inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))) )],[refute_0_4283,refute_0_4311]) ).

cnf(refute_0_4313,plain,
    least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)) = least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))),bind(X_17,$fot(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_4314,plain,
    ( least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))
    | least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)) != least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))) ),[0],$fot(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4315,plain,
    ( least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)),least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4313,refute_0_4314]) ).

cnf(refute_0_4316,plain,
    inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)) = inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_2093:[bind(X_94,$fot(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_4317,plain,
    ( inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)) != inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(b,identity))
    | inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)) = inverse(greatest_lower_bound(b,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Z0,$fot(inverse(greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_4318,plain,
    ( inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(b,identity))
    | inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)) = inverse(greatest_lower_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)),inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4316,refute_0_4317]) ).

cnf(refute_0_4319,plain,
    inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)) = inverse(greatest_lower_bound(b,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(b,identity))) )],[refute_0_4301,refute_0_4318]) ).

cnf(refute_0_4320,plain,
    ( inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)) != inverse(greatest_lower_bound(b,identity))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(b,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))) ),[1],$fot(inverse(greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_4321,plain,
    ( least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity)),inverse(greatest_lower_bound(b,identity))) )],[refute_0_4319,refute_0_4320]) ).

cnf(refute_0_4322,plain,
    ( least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(b,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))) )],[refute_0_4315,refute_0_4321]) ).

cnf(refute_0_4323,plain,
    least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(b,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))),identity))) )],[refute_0_4312,refute_0_4322]) ).

cnf(refute_0_4324,plain,
    ( inverse(greatest_lower_bound(b,identity)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(b,identity))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(b,identity))) ),[1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_4325,plain,
    ( least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(b,identity))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2216,refute_0_4324]) ).

cnf(refute_0_4326,plain,
    least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(b,identity))) )],[refute_0_4323,refute_0_4325]) ).

cnf(refute_0_4327,plain,
    least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4328,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(a,identity)
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),[1,0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_4329,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(a,identity)
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4327,refute_0_4328]) ).

cnf(refute_0_4330,plain,
    least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(a,identity)) )],[refute_0_2212,refute_0_4329]) ).

cnf(refute_0_4331,plain,
    ( least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(a,identity))) ),[0],$fot(least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4332,plain,
    ( least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4330,refute_0_4331]) ).

cnf(refute_0_4333,plain,
    least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(b,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(a,identity))) )],[refute_0_4326,refute_0_4332]) ).

cnf(refute_0_4334,plain,
    ( least_upper_bound(X_317,least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) != least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317))
    | least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(X_317,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_317,least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317))) ),[0,1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_4335,plain,
    ( least_upper_bound(X_317,least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))) != least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317))
    | least_upper_bound(X_317,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(a,identity))) )],[refute_0_4333,refute_0_4334]) ).

cnf(refute_0_4336,plain,
    least_upper_bound(X_317,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_317,least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317))) )],[refute_0_4282,refute_0_4335]) ).

cnf(refute_0_4337,plain,
    least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)) = least_upper_bound(least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),Z),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(greatest_lower_bound(a,identity))),bind(Y,$fot(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4338,plain,
    ( least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)) != least_upper_bound(least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),Z)
    | least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)) = least_upper_bound(inverse(greatest_lower_bound(a,identity)),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)),least_upper_bound(least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),Z)) ),[1,0],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_4339,plain,
    ( least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)) != least_upper_bound(least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),Z)
    | least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)) = least_upper_bound(inverse(greatest_lower_bound(a,identity)),Z) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(greatest_lower_bound(a,identity))) )],[refute_0_4333,refute_0_4338]) ).

cnf(refute_0_4340,plain,
    least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)) = least_upper_bound(inverse(greatest_lower_bound(a,identity)),Z),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)),least_upper_bound(least_upper_bound(greatest_lower_bound(a,identity),inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c))))),Z)) )],[refute_0_4337,refute_0_4339]) ).

cnf(refute_0_4341,plain,
    least_upper_bound(inverse(greatest_lower_bound(a,identity)),Z) = least_upper_bound(identity,least_upper_bound(Z,inverse(a))),
    inference(subst,[],[refute_0_3225:[bind(X_249,$fot(a)),bind(X_251,$fot(Z))]]) ).

cnf(refute_0_4342,plain,
    ( least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)) != least_upper_bound(inverse(greatest_lower_bound(a,identity)),Z)
    | least_upper_bound(inverse(greatest_lower_bound(a,identity)),Z) != least_upper_bound(identity,least_upper_bound(Z,inverse(a)))
    | least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)) = least_upper_bound(identity,least_upper_bound(Z,inverse(a))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)),least_upper_bound(identity,least_upper_bound(Z,inverse(a)))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(a,identity)),Z))]]) ).

cnf(refute_0_4343,plain,
    ( least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)) != least_upper_bound(inverse(greatest_lower_bound(a,identity)),Z)
    | least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)) = least_upper_bound(identity,least_upper_bound(Z,inverse(a))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,identity)),Z),least_upper_bound(identity,least_upper_bound(Z,inverse(a)))) )],[refute_0_4341,refute_0_4342]) ).

cnf(refute_0_4344,plain,
    least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)) = least_upper_bound(identity,least_upper_bound(Z,inverse(a))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),Z)),least_upper_bound(inverse(greatest_lower_bound(a,identity)),Z)) )],[refute_0_4340,refute_0_4343]) ).

cnf(refute_0_4345,plain,
    least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317)) = least_upper_bound(identity,least_upper_bound(X_317,inverse(a))),
    inference(subst,[],[refute_0_4344:[bind(Z,$fot(X_317))]]) ).

cnf(refute_0_4346,plain,
    ( least_upper_bound(X_317,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317))
    | least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317)) != least_upper_bound(identity,least_upper_bound(X_317,inverse(a)))
    | least_upper_bound(X_317,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,least_upper_bound(X_317,inverse(a))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_317,inverse(greatest_lower_bound(a,identity))),least_upper_bound(identity,least_upper_bound(X_317,inverse(a)))) ),[0],$fot(least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317)))]]) ).

cnf(refute_0_4347,plain,
    ( least_upper_bound(X_317,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317))
    | least_upper_bound(X_317,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,least_upper_bound(X_317,inverse(a))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317)),least_upper_bound(identity,least_upper_bound(X_317,inverse(a)))) )],[refute_0_4345,refute_0_4346]) ).

cnf(refute_0_4348,plain,
    least_upper_bound(X_317,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,least_upper_bound(X_317,inverse(a))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_317,inverse(greatest_lower_bound(a,identity))),least_upper_bound(greatest_lower_bound(a,identity),least_upper_bound(inverse(multiply(b,least_upper_bound(identity,greatest_lower_bound(a,c)))),X_317))) )],[refute_0_4336,refute_0_4347]) ).

cnf(refute_0_4349,plain,
    least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,least_upper_bound(X_320,inverse(a))),
    inference(subst,[],[refute_0_4348:[bind(X_317,$fot(X_320))]]) ).

cnf(refute_0_4350,plain,
    ( least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(identity,least_upper_bound(X_320,inverse(a)))
    | least_upper_bound(identity,least_upper_bound(X_320,inverse(a))) = least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_320,inverse(a)))))]]) ).

cnf(refute_0_4351,plain,
    least_upper_bound(identity,least_upper_bound(X_320,inverse(a))) = least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity))),least_upper_bound(identity,least_upper_bound(X_320,inverse(a)))) )],[refute_0_4349,refute_0_4350]) ).

cnf(refute_0_4352,plain,
    ( least_upper_bound(identity,least_upper_bound(X_320,inverse(a))) != least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)) != least_upper_bound(Y,least_upper_bound(identity,least_upper_bound(X_320,inverse(a))))
    | least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)) = least_upper_bound(Y,least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)),least_upper_bound(Y,least_upper_bound(identity,least_upper_bound(X_320,inverse(a))))) ),[1,1],$fot(least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_4353,plain,
    ( least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)) != least_upper_bound(Y,least_upper_bound(identity,least_upper_bound(X_320,inverse(a))))
    | least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)) = least_upper_bound(Y,least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_320,inverse(a))),least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_4351,refute_0_4352]) ).

cnf(refute_0_4354,plain,
    least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)) = least_upper_bound(Y,least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)),least_upper_bound(Y,least_upper_bound(identity,least_upper_bound(X_320,inverse(a))))) )],[refute_0_4281,refute_0_4353]) ).

cnf(refute_0_4355,plain,
    least_upper_bound(X_45,least_upper_bound(X_43,Y)) = least_upper_bound(X_43,least_upper_bound(Y,X_45)),
    inference(subst,[],[refute_0_3111:[bind(X,$fot(X_45)),bind(Y,$fot(X_43)),bind(X_145,$fot(Y))]]) ).

cnf(refute_0_4356,plain,
    ( least_upper_bound(X_45,least_upper_bound(X_43,Y)) != least_upper_bound(X_43,least_upper_bound(Y,X_45))
    | least_upper_bound(X_43,least_upper_bound(Y,X_45)) = least_upper_bound(X_45,least_upper_bound(X_43,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_45,least_upper_bound(X_43,Y)))),bind(Y0,$fot(least_upper_bound(X_43,least_upper_bound(Y,X_45))))]]) ).

cnf(refute_0_4357,plain,
    least_upper_bound(X_43,least_upper_bound(Y,X_45)) = least_upper_bound(X_45,least_upper_bound(X_43,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(X_43,Y)),least_upper_bound(X_43,least_upper_bound(Y,X_45))) )],[refute_0_4355,refute_0_4356]) ).

cnf(refute_0_4358,plain,
    ( least_upper_bound(Y,least_upper_bound(X_43,X_45)) != least_upper_bound(X_43,least_upper_bound(Y,X_45))
    | least_upper_bound(X_43,least_upper_bound(Y,X_45)) != least_upper_bound(X_45,least_upper_bound(X_43,Y))
    | least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(X_45,least_upper_bound(X_43,Y)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_43,X_45)),least_upper_bound(X_45,least_upper_bound(X_43,Y))) ),[0],$fot(least_upper_bound(X_43,least_upper_bound(Y,X_45)))]]) ).

cnf(refute_0_4359,plain,
    ( least_upper_bound(Y,least_upper_bound(X_43,X_45)) != least_upper_bound(X_43,least_upper_bound(Y,X_45))
    | least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(X_45,least_upper_bound(X_43,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(Y,X_45)),least_upper_bound(X_45,least_upper_bound(X_43,Y))) )],[refute_0_4357,refute_0_4358]) ).

cnf(refute_0_4360,plain,
    least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(X_45,least_upper_bound(X_43,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_43,X_45)),least_upper_bound(X_43,least_upper_bound(Y,X_45))) )],[refute_0_1102,refute_0_4359]) ).

cnf(refute_0_4361,plain,
    ( least_upper_bound(Y,least_upper_bound(X_43,X_45)) != least_upper_bound(X_45,least_upper_bound(X_43,Y))
    | least_upper_bound(X_45,least_upper_bound(X_43,Y)) = least_upper_bound(Y,least_upper_bound(X_43,X_45)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_43,X_45)))),bind(Y0,$fot(least_upper_bound(X_45,least_upper_bound(X_43,Y))))]]) ).

cnf(refute_0_4362,plain,
    least_upper_bound(X_45,least_upper_bound(X_43,Y)) = least_upper_bound(Y,least_upper_bound(X_43,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_43,X_45)),least_upper_bound(X_45,least_upper_bound(X_43,Y))) )],[refute_0_4360,refute_0_4361]) ).

cnf(refute_0_4363,plain,
    least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)) = least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_320,inverse(a)))),
    inference(subst,[],[refute_0_4362:[bind(Y,$fot(identity)),bind(X_43,$fot(Y)),bind(X_45,$fot(least_upper_bound(X_320,inverse(a))))]]) ).

cnf(refute_0_4364,plain,
    ( least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)) != least_upper_bound(Y,least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity))))
    | least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)) != least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_320,inverse(a))))
    | least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_320,inverse(a)))) = least_upper_bound(Y,least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)),least_upper_bound(Y,least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity))))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_320,inverse(a)))))]]) ).

cnf(refute_0_4365,plain,
    ( least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)) != least_upper_bound(Y,least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity))))
    | least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_320,inverse(a)))) = least_upper_bound(Y,least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)),least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_320,inverse(a))))) )],[refute_0_4363,refute_0_4364]) ).

cnf(refute_0_4366,plain,
    least_upper_bound(identity,least_upper_bound(Y,least_upper_bound(X_320,inverse(a)))) = least_upper_bound(Y,least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_320,inverse(a)),least_upper_bound(Y,identity)),least_upper_bound(Y,least_upper_bound(X_320,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_4354,refute_0_4365]) ).

cnf(refute_0_4367,plain,
    least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))) = least_upper_bound(b,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))),
    inference(subst,[],[refute_0_4366:[bind(Y,$fot(b)),bind(X_320,$fot(b))]]) ).

cnf(refute_0_4368,plain,
    ( least_upper_bound(b,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))) != least_upper_bound(b,least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))
    | least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))))),bind(Y0,$fot(least_upper_bound(b,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))),bind(Z0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_4369,plain,
    ( least_upper_bound(b,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))),least_upper_bound(b,least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))) )],[refute_0_4367,refute_0_4368]) ).

cnf(refute_0_4370,plain,
    least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_4280,refute_0_4369]) ).

cnf(refute_0_4371,plain,
    least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)) = least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))),
    inference(subst,[],[refute_0_4362:[bind(Y,$fot(identity)),bind(X_43,$fot(b)),bind(X_45,$fot(least_upper_bound(b,inverse(a))))]]) ).

cnf(refute_0_4372,plain,
    ( least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)) != least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a))))
    | least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))))),bind(Z0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_4373,plain,
    ( least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)),least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a))))) )],[refute_0_4371,refute_0_4372]) ).

cnf(refute_0_4374,plain,
    least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)) = least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(b,least_upper_bound(b,inverse(a)))),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_4370,refute_0_4373]) ).

cnf(refute_0_4375,plain,
    ( least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)) != least_upper_bound(b,inverse(a))
    | least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)) != least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)),least_upper_bound(b,inverse(a))) ),[0],$fot(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_4376,plain,
    ( least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)) != least_upper_bound(b,inverse(a))
    | least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,inverse(a)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)),least_upper_bound(b,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_4374,refute_0_4375]) ).

cnf(refute_0_4377,plain,
    least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(b,inverse(a)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(b,inverse(a)),least_upper_bound(b,identity)),least_upper_bound(b,inverse(a))) )],[refute_0_4279,refute_0_4376]) ).

cnf(refute_0_4378,plain,
    ( multiply(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))
    | least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(b,inverse(a))
    | multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),inverse(inverse(greatest_lower_bound(a,identity)))),least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))) ),[0,0],$fot(least_upper_bound(b,inverse(a)))]]) ).

cnf(refute_0_4379,plain,
    ( multiply(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),least_upper_bound(b,inverse(a))) )],[refute_0_4377,refute_0_4378]) ).

cnf(refute_0_4380,plain,
    multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),inverse(inverse(greatest_lower_bound(a,identity)))),least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_1277,refute_0_4379]) ).

cnf(refute_0_4381,plain,
    multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_4382,plain,
    ( multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity))))
    | inverse(inverse(greatest_lower_bound(a,identity))) != greatest_lower_bound(a,identity)
    | multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity))))) ),[1,1],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_4383,plain,
    ( inverse(inverse(greatest_lower_bound(a,identity))) != greatest_lower_bound(a,identity)
    | multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity))))) )],[refute_0_4381,refute_0_4382]) ).

cnf(refute_0_4384,plain,
    multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(a,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3765,refute_0_4383]) ).

cnf(refute_0_4385,plain,
    ( multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))),least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))) ),[0],$fot(multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_4386,plain,
    ( multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity))) )],[refute_0_4384,refute_0_4385]) ).

cnf(refute_0_4387,plain,
    inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))) = least_upper_bound(inverse(b),greatest_lower_bound(a,identity)),
    inference(subst,[],[refute_0_1559:[bind(X,$fot(b)),bind(X_89,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_4388,plain,
    ( inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(inverse(b),greatest_lower_bound(a,identity))
    | least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) != inverse(greatest_lower_bound(a,identity))
    | inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))))),bind(Y0,$fot(least_upper_bound(inverse(b),greatest_lower_bound(a,identity)))),bind(Z0,$fot(inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_4389,plain,
    ( least_upper_bound(inverse(b),greatest_lower_bound(a,identity)) != inverse(greatest_lower_bound(a,identity))
    | inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))),least_upper_bound(inverse(b),greatest_lower_bound(a,identity))) )],[refute_0_4387,refute_0_4388]) ).

cnf(refute_0_4390,plain,
    inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_2104,refute_0_4389]) ).

cnf(refute_0_4391,plain,
    multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) = multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))),
    introduced(tautology,[refl,[$fot(multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_4392,plain,
    ( multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) != multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))))
    | inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))) != inverse(greatest_lower_bound(a,identity))
    | multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) = multiply(b,inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))),multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))))) ),[1,1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_4393,plain,
    ( inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))) != inverse(greatest_lower_bound(a,identity))
    | multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) = multiply(b,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))),multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_4391,refute_0_4392]) ).

cnf(refute_0_4394,plain,
    multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) = multiply(b,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))),inverse(greatest_lower_bound(a,identity))) )],[refute_0_4390,refute_0_4393]) ).

cnf(refute_0_4395,plain,
    ( multiply(b,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(b,identity)
    | multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) != multiply(b,inverse(greatest_lower_bound(a,identity)))
    | multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) = least_upper_bound(b,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))))),bind(Y0,$fot(multiply(b,inverse(greatest_lower_bound(a,identity))))),bind(Z0,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_4396,plain,
    ( multiply(b,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(b,identity)
    | multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) = least_upper_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))),multiply(b,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_4394,refute_0_4395]) ).

cnf(refute_0_4397,plain,
    multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(a,identity))),least_upper_bound(b,identity)) )],[refute_0_3558,refute_0_4396]) ).

cnf(refute_0_4398,plain,
    multiply(b,inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b))) = multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))),
    inference(subst,[],[refute_0_1032:[bind(Y,$fot(inverse(greatest_lower_bound(a,identity)))),bind(X_99,$fot(b))]]) ).

cnf(refute_0_4399,plain,
    least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(b,inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b))),
    inference(subst,[],[refute_0_3398:[bind(X_219,$fot(inverse(greatest_lower_bound(a,identity)))),bind(X_220,$fot(b))]]) ).

cnf(refute_0_4400,plain,
    ( multiply(b,inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b))) != multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))))
    | least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) != multiply(b,inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)))
    | least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))))),bind(Y0,$fot(multiply(b,inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b))))),bind(Z0,$fot(multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))))))]]) ).

cnf(refute_0_4401,plain,
    ( multiply(b,inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b))) != multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))))
    | least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))),multiply(b,inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b)))) )],[refute_0_4399,refute_0_4400]) ).

cnf(refute_0_4402,plain,
    least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),b))),multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_4398,refute_0_4401]) ).

cnf(refute_0_4403,plain,
    ( multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) != least_upper_bound(b,identity)
    | least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) != multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))))
    | least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) = least_upper_bound(b,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))))),bind(Y0,$fot(multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))))),bind(Z0,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_4404,plain,
    ( multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))) != least_upper_bound(b,identity)
    | least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) = least_upper_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))),multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_4402,refute_0_4403]) ).

cnf(refute_0_4405,plain,
    least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(greatest_lower_bound(b,inverse(greatest_lower_bound(a,identity))))),least_upper_bound(b,identity)) )],[refute_0_4397,refute_0_4404]) ).

cnf(refute_0_4406,plain,
    ( multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) != least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))
    | least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))) != least_upper_bound(b,identity)
    | multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(b,identity) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)),least_upper_bound(b,identity)) ),[0],$fot(least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_4407,plain,
    ( multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) != least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity))))),least_upper_bound(b,identity)) )],[refute_0_4405,refute_0_4406]) ).

cnf(refute_0_4408,plain,
    ( multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))) != least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)),least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_4386,refute_0_4407]) ).

cnf(refute_0_4409,plain,
    multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),inverse(inverse(greatest_lower_bound(a,identity)))),least_upper_bound(identity,multiply(b,inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_4380,refute_0_4408]) ).

cnf(refute_0_4410,plain,
    multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),
    inference(subst,[],[refute_0_243:[bind(Y,$fot(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_4411,plain,
    multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),greatest_lower_bound(inverse(X),inverse(Y))) = identity,
    inference(subst,[],[refute_0_144:[bind(X_24,$fot(inverse(Y))),bind(X_25,$fot(inverse(X)))]]) ).

cnf(refute_0_4412,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),greatest_lower_bound(inverse(X),inverse(Y))) != identity
    | greatest_lower_bound(inverse(X),inverse(Y)) != inverse(least_upper_bound(X,Y))
    | multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),greatest_lower_bound(inverse(X),inverse(Y))),identity) ),[0,1],$fot(inverse(least_upper_bound(X,Y)))]]) ).

cnf(refute_0_4413,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),greatest_lower_bound(inverse(X),inverse(Y))) != identity
    | multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X),inverse(Y)),inverse(least_upper_bound(X,Y))) )],[refute_0_54,refute_0_4412]) ).

cnf(refute_0_4414,plain,
    multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),greatest_lower_bound(inverse(X),inverse(Y))),identity) )],[refute_0_4411,refute_0_4413]) ).

cnf(refute_0_4415,plain,
    multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))) = multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))))]]) ).

cnf(refute_0_4416,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))) != multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y)))
    | inverse(greatest_lower_bound(inverse(Y),inverse(X))) != inverse(inverse(least_upper_bound(Y,X)))
    | multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))) = multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))),multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y)))) ),[1,0],$fot(inverse(inverse(least_upper_bound(Y,X))))]]) ).

cnf(refute_0_4417,plain,
    ( inverse(greatest_lower_bound(inverse(Y),inverse(X))) != inverse(inverse(least_upper_bound(Y,X)))
    | multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))) = multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))),multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y)))) )],[refute_0_4415,refute_0_4416]) ).

cnf(refute_0_4418,plain,
    multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))) = multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(inverse(least_upper_bound(Y,X)))) )],[refute_0_600,refute_0_4417]) ).

cnf(refute_0_4419,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))) != multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y)))
    | multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))) != identity
    | multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))),identity) ),[0],$fot(multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))))]]) ).

cnf(refute_0_4420,plain,
    ( multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))) != identity
    | multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))),multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y)))) )],[refute_0_4418,refute_0_4419]) ).

cnf(refute_0_4421,plain,
    multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(inverse(Y),inverse(X))),inverse(least_upper_bound(X,Y))),identity) )],[refute_0_4414,refute_0_4420]) ).

cnf(refute_0_4422,plain,
    multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))) = multiply(least_upper_bound(Y,X),inverse(least_upper_bound(X,Y))),
    inference(subst,[],[refute_0_25:[bind(X_61,$fot(least_upper_bound(Y,X))),bind(X_62,$fot(inverse(least_upper_bound(X,Y))))]]) ).

cnf(refute_0_4423,plain,
    ( multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))) != multiply(least_upper_bound(Y,X),inverse(least_upper_bound(X,Y)))
    | multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))) != identity
    | multiply(least_upper_bound(Y,X),inverse(least_upper_bound(X,Y))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))),identity) ),[0],$fot(multiply(least_upper_bound(Y,X),inverse(least_upper_bound(X,Y))))]]) ).

cnf(refute_0_4424,plain,
    ( multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))) != identity
    | multiply(least_upper_bound(Y,X),inverse(least_upper_bound(X,Y))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))),multiply(least_upper_bound(Y,X),inverse(least_upper_bound(X,Y)))) )],[refute_0_4422,refute_0_4423]) ).

cnf(refute_0_4425,plain,
    multiply(least_upper_bound(Y,X),inverse(least_upper_bound(X,Y))) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(Y,X))),inverse(least_upper_bound(X,Y))),identity) )],[refute_0_4421,refute_0_4424]) ).

cnf(refute_0_4426,plain,
    multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = identity,
    inference(subst,[],[refute_0_4425:[bind(X,$fot(multiply(X_111,inverse(X_112)))),bind(Y,$fot(identity))]]) ).

cnf(refute_0_4427,plain,
    ( multiply(least_upper_bound(X_111,X_112),inverse(X_112)) != least_upper_bound(identity,multiply(X_111,inverse(X_112)))
    | least_upper_bound(identity,multiply(X_111,inverse(X_112))) = multiply(least_upper_bound(X_111,X_112),inverse(X_112)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_111,X_112),inverse(X_112)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_111,inverse(X_112)))))]]) ).

cnf(refute_0_4428,plain,
    least_upper_bound(identity,multiply(X_111,inverse(X_112))) = multiply(least_upper_bound(X_111,X_112),inverse(X_112)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),least_upper_bound(identity,multiply(X_111,inverse(X_112)))) )],[refute_0_363,refute_0_4427]) ).

cnf(refute_0_4429,plain,
    ( multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) != identity
    | least_upper_bound(identity,multiply(X_111,inverse(X_112))) != multiply(least_upper_bound(X_111,X_112),inverse(X_112))
    | multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))),identity) ),[0,0],$fot(multiply(least_upper_bound(X_111,X_112),inverse(X_112)))]]) ).

cnf(refute_0_4430,plain,
    ( multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) != identity
    | multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_111,inverse(X_112))),multiply(least_upper_bound(X_111,X_112),inverse(X_112))) )],[refute_0_4428,refute_0_4429]) ).

cnf(refute_0_4431,plain,
    multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = identity,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))),identity) )],[refute_0_4426,refute_0_4430]) ).

cnf(refute_0_4432,plain,
    inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) = inverse(least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110))),
    inference(subst,[],[refute_0_58:[bind(X_14,$fot(multiply(X_111,X_110))),bind(X_15,$fot(multiply(X_112,X_110)))]]) ).

cnf(refute_0_4433,plain,
    ( inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) != inverse(least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)))
    | least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)) != multiply(least_upper_bound(X_111,X_112),X_110)
    | inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) = inverse(multiply(least_upper_bound(X_111,X_112),X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))),inverse(least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)))) ),[1,0],$fot(multiply(least_upper_bound(X_111,X_112),X_110))]]) ).

cnf(refute_0_4434,plain,
    ( inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) != inverse(least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)))
    | inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) = inverse(multiply(least_upper_bound(X_111,X_112),X_110)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)),multiply(least_upper_bound(X_111,X_112),X_110)) )],[refute_0_402,refute_0_4433]) ).

cnf(refute_0_4435,plain,
    inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) = inverse(multiply(least_upper_bound(X_111,X_112),X_110)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))),inverse(least_upper_bound(multiply(X_111,X_110),multiply(X_112,X_110)))) )],[refute_0_4432,refute_0_4434]) ).

cnf(refute_0_4436,plain,
    inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) = inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))))]]) ).

cnf(refute_0_4437,plain,
    ( inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) != inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)))
    | least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) != multiply(least_upper_bound(X_112,X_111),X_110)
    | inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) = inverse(multiply(least_upper_bound(X_112,X_111),X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))),inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)))) ),[1,0],$fot(multiply(least_upper_bound(X_112,X_111),X_110))]]) ).

cnf(refute_0_4438,plain,
    ( least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)) != multiply(least_upper_bound(X_112,X_111),X_110)
    | inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) = inverse(multiply(least_upper_bound(X_112,X_111),X_110)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))),inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)))) )],[refute_0_4436,refute_0_4437]) ).

cnf(refute_0_4439,plain,
    inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) = inverse(multiply(least_upper_bound(X_112,X_111),X_110)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110)),multiply(least_upper_bound(X_112,X_111),X_110)) )],[refute_0_406,refute_0_4438]) ).

cnf(refute_0_4440,plain,
    ( inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) != inverse(multiply(least_upper_bound(X_111,X_112),X_110))
    | inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) != inverse(multiply(least_upper_bound(X_112,X_111),X_110))
    | inverse(multiply(least_upper_bound(X_112,X_111),X_110)) = inverse(multiply(least_upper_bound(X_111,X_112),X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))),inverse(multiply(least_upper_bound(X_111,X_112),X_110))) ),[0],$fot(inverse(multiply(least_upper_bound(X_112,X_111),X_110)))]]) ).

cnf(refute_0_4441,plain,
    ( inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))) != inverse(multiply(least_upper_bound(X_111,X_112),X_110))
    | inverse(multiply(least_upper_bound(X_112,X_111),X_110)) = inverse(multiply(least_upper_bound(X_111,X_112),X_110)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))),inverse(multiply(least_upper_bound(X_112,X_111),X_110))) )],[refute_0_4439,refute_0_4440]) ).

cnf(refute_0_4442,plain,
    inverse(multiply(least_upper_bound(X_112,X_111),X_110)) = inverse(multiply(least_upper_bound(X_111,X_112),X_110)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(multiply(X_112,X_110),multiply(X_111,X_110))),inverse(multiply(least_upper_bound(X_111,X_112),X_110))) )],[refute_0_4435,refute_0_4441]) ).

cnf(refute_0_4443,plain,
    ( inverse(multiply(least_upper_bound(X_112,X_111),X_110)) != inverse(multiply(least_upper_bound(X_111,X_112),X_110))
    | inverse(multiply(least_upper_bound(X_111,X_112),X_110)) = inverse(multiply(least_upper_bound(X_112,X_111),X_110)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(multiply(least_upper_bound(X_112,X_111),X_110)))),bind(Y0,$fot(inverse(multiply(least_upper_bound(X_111,X_112),X_110))))]]) ).

cnf(refute_0_4444,plain,
    inverse(multiply(least_upper_bound(X_111,X_112),X_110)) = inverse(multiply(least_upper_bound(X_112,X_111),X_110)),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_112,X_111),X_110)),inverse(multiply(least_upper_bound(X_111,X_112),X_110))) )],[refute_0_4442,refute_0_4443]) ).

cnf(refute_0_4445,plain,
    inverse(multiply(least_upper_bound(multiply(X_111,inverse(X_112)),identity),X_112)) = inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112)),
    inference(subst,[],[refute_0_4444:[bind(X_110,$fot(X_112)),bind(X_111,$fot(multiply(X_111,inverse(X_112)))),bind(X_112,$fot(identity))]]) ).

cnf(refute_0_4446,plain,
    multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = inverse(multiply(least_upper_bound(multiply(X_111,inverse(X_112)),identity),X_112)),
    inference(subst,[],[refute_0_667:[bind(X_198,$fot(least_upper_bound(multiply(X_111,inverse(X_112)),identity))),bind(X_59,$fot(X_112))]]) ).

cnf(refute_0_4447,plain,
    ( multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) != inverse(multiply(least_upper_bound(multiply(X_111,inverse(X_112)),identity),X_112))
    | inverse(multiply(least_upper_bound(multiply(X_111,inverse(X_112)),identity),X_112)) != inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))
    | multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(multiply(X_111,inverse(X_112)),identity),X_112)))),bind(Z0,$fot(inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))))]]) ).

cnf(refute_0_4448,plain,
    ( inverse(multiply(least_upper_bound(multiply(X_111,inverse(X_112)),identity),X_112)) != inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))
    | multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))),inverse(multiply(least_upper_bound(multiply(X_111,inverse(X_112)),identity),X_112))) )],[refute_0_4446,refute_0_4447]) ).

cnf(refute_0_4449,plain,
    multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112)),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(multiply(X_111,inverse(X_112)),identity),X_112)),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))) )],[refute_0_4445,refute_0_4448]) ).

cnf(refute_0_4450,plain,
    multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))) = multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))))]]) ).

cnf(refute_0_4451,plain,
    ( multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) != inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))
    | multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))) != multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))))
    | multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))) = multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))),multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))))) ),[1,1],$fot(inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112)))]]) ).

cnf(refute_0_4452,plain,
    ( multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) != inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))
    | multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))) = multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))),multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))))) )],[refute_0_4450,refute_0_4451]) ).

cnf(refute_0_4453,plain,
    multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))) = multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))) )],[refute_0_4449,refute_0_4452]) ).

cnf(refute_0_4454,plain,
    multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))),
    inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(X_111,X_112))),bind(Y,$fot(inverse(X_112))),bind(Z,$fot(inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))))]]) ).

cnf(refute_0_4455,plain,
    ( multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) != multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))))
    | multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))) != multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112)))
    | multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))))),bind(Y0,$fot(multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))))),bind(Z0,$fot(multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112)))))]]) ).

cnf(refute_0_4456,plain,
    ( multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))) != multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112)))
    | multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))),multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))))) )],[refute_0_4454,refute_0_4455]) ).

cnf(refute_0_4457,plain,
    multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) = multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,X_112),multiply(inverse(X_112),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity)))),multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112)))) )],[refute_0_4453,refute_0_4456]) ).

cnf(refute_0_4458,plain,
    ( multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) != multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112)))
    | multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) != identity
    | multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))),identity) ),[0],$fot(multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))))]]) ).

cnf(refute_0_4459,plain,
    ( multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))) != identity
    | multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))),multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112)))) )],[refute_0_4457,refute_0_4458]) ).

cnf(refute_0_4460,plain,
    multiply(least_upper_bound(X_111,X_112),inverse(multiply(least_upper_bound(identity,multiply(X_111,inverse(X_112))),X_112))) = identity,
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_111,X_112),inverse(X_112)),inverse(least_upper_bound(multiply(X_111,inverse(X_112)),identity))),identity) )],[refute_0_4431,refute_0_4459]) ).

cnf(refute_0_4461,plain,
    multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = identity,
    inference(subst,[],[refute_0_4460:[bind(X_111,$fot(greatest_lower_bound(a,greatest_lower_bound(c,identity)))),bind(X_112,$fot(least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_4462,plain,
    multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))))) = inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(greatest_lower_bound(a,greatest_lower_bound(c,identity)))),bind(X_59,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4463,plain,
    X_71 = multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(a,greatest_lower_bound(X_42,c)),X_71)),
    inference(subst,[],[refute_0_3591:[bind(X_24,$fot(greatest_lower_bound(X_42,c))),bind(X_25,$fot(a)),bind(X_60,$fot(X_71))]]) ).

cnf(refute_0_4464,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(b,greatest_lower_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(b)),bind(Z,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4465,plain,
    greatest_lower_bound(b,greatest_lower_bound(b,c)) = greatest_lower_bound(b,c),
    inference(subst,[],[refute_0_801:[bind(X_32,$fot(c)),bind(X_33,$fot(b))]]) ).

cnf(refute_0_4466,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | greatest_lower_bound(b,greatest_lower_bound(b,c)) != greatest_lower_bound(b,c)
    | greatest_lower_bound(b,greatest_lower_bound(a,c)) = greatest_lower_bound(b,c) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(b,c)),greatest_lower_bound(b,c)) ),[0,1],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_4467,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(b,c)) != greatest_lower_bound(b,c)
    | greatest_lower_bound(b,greatest_lower_bound(a,c)) = greatest_lower_bound(b,c) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_178,refute_0_4466]) ).

cnf(refute_0_4468,plain,
    greatest_lower_bound(b,greatest_lower_bound(a,c)) = greatest_lower_bound(b,c),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(b,c)),greatest_lower_bound(b,c)) )],[refute_0_4465,refute_0_4467]) ).

cnf(refute_0_4469,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | greatest_lower_bound(b,greatest_lower_bound(a,c)) != greatest_lower_bound(b,c)
    | greatest_lower_bound(b,greatest_lower_bound(a,c)) = greatest_lower_bound(a,c) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(a,c)),greatest_lower_bound(b,c)) ),[1],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_4470,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(a,c)) != greatest_lower_bound(b,c)
    | greatest_lower_bound(b,greatest_lower_bound(a,c)) = greatest_lower_bound(a,c) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_178,refute_0_4469]) ).

cnf(refute_0_4471,plain,
    greatest_lower_bound(b,greatest_lower_bound(a,c)) = greatest_lower_bound(a,c),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(a,c)),greatest_lower_bound(b,c)) )],[refute_0_4468,refute_0_4470]) ).

cnf(refute_0_4472,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(b,greatest_lower_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c))
    | greatest_lower_bound(b,greatest_lower_bound(a,c)) != greatest_lower_bound(a,c)
    | greatest_lower_bound(X_36,greatest_lower_bound(a,c)) = greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(b,greatest_lower_bound(a,c))),greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c))) ),[0,1],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_4473,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(b,greatest_lower_bound(a,c))) != greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c))
    | greatest_lower_bound(X_36,greatest_lower_bound(a,c)) = greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(a,c)),greatest_lower_bound(a,c)) )],[refute_0_4471,refute_0_4472]) ).

cnf(refute_0_4474,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(a,c)) = greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(b,greatest_lower_bound(a,c))),greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c))) )],[refute_0_4464,refute_0_4473]) ).

cnf(refute_0_4475,plain,
    greatest_lower_bound(c,greatest_lower_bound(X_36,b)) = greatest_lower_bound(b,greatest_lower_bound(c,X_36)),
    inference(subst,[],[refute_0_886:[bind(X,$fot(b)),bind(X_36,$fot(c)),bind(X_37,$fot(X_36))]]) ).

cnf(refute_0_4476,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))))]]) ).

cnf(refute_0_4477,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b)))
    | greatest_lower_bound(c,greatest_lower_bound(X_36,b)) != greatest_lower_bound(b,greatest_lower_bound(c,X_36))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))) = greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b)))) ),[1,1],$fot(greatest_lower_bound(b,greatest_lower_bound(c,X_36)))]]) ).

cnf(refute_0_4478,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(X_36,b)) != greatest_lower_bound(b,greatest_lower_bound(c,X_36))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))) = greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b)))) )],[refute_0_4476,refute_0_4477]) ).

cnf(refute_0_4479,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))) = greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(X_36,b)),greatest_lower_bound(b,greatest_lower_bound(c,X_36))) )],[refute_0_4475,refute_0_4478]) ).

cnf(refute_0_4480,plain,
    greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_36,b),a)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))),
    inference(subst,[],[refute_0_886:[bind(X,$fot(a)),bind(X_36,$fot(c)),bind(X_37,$fot(greatest_lower_bound(X_36,b)))]]) ).

cnf(refute_0_4481,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) = greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_36,b),a)),
    inference(subst,[],[refute_0_886:[bind(X,$fot(c)),bind(X_36,$fot(greatest_lower_bound(X_36,b))),bind(X_37,$fot(a))]]) ).

cnf(refute_0_4482,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_36,b),a)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b)))
    | greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) != greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_36,b),a))
    | greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)))),bind(Y0,$fot(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_36,b),a)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b)))))]]) ).

cnf(refute_0_4483,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_36,b),a)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b)))
    | greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)),greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_36,b),a))) )],[refute_0_4481,refute_0_4482]) ).

cnf(refute_0_4484,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(greatest_lower_bound(X_36,b),a)),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b)))) )],[refute_0_4480,refute_0_4483]) ).

cnf(refute_0_4485,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))) != greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))
    | greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b)))
    | greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))))]]) ).

cnf(refute_0_4486,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))) != greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))
    | greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b)))) )],[refute_0_4484,refute_0_4485]) ).

cnf(refute_0_4487,plain,
    greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_36,b))),greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))) )],[refute_0_4479,refute_0_4486]) ).

cnf(refute_0_4488,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(a,c)) != greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c))
    | greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))
    | greatest_lower_bound(X_36,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_36,greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4489,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(a,c)) != greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c))
    | greatest_lower_bound(X_36,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))) )],[refute_0_4487,refute_0_4488]) ).

cnf(refute_0_4490,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(a,c)),greatest_lower_bound(greatest_lower_bound(X_36,b),greatest_lower_bound(a,c))) )],[refute_0_4474,refute_0_4489]) ).

cnf(refute_0_4491,plain,
    greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,X_36))) = greatest_lower_bound(a,greatest_lower_bound(c,X_36)),
    inference(subst,[],[refute_0_801:[bind(X_32,$fot(greatest_lower_bound(c,X_36))),bind(X_33,$fot(a))]]) ).

cnf(refute_0_4492,plain,
    greatest_lower_bound(b,greatest_lower_bound(c,X_38)) = greatest_lower_bound(greatest_lower_bound(b,c),X_38),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(b)),bind(Y,$fot(c)),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_4493,plain,
    ( greatest_lower_bound(b,c) != greatest_lower_bound(a,c)
    | greatest_lower_bound(b,greatest_lower_bound(c,X_38)) != greatest_lower_bound(greatest_lower_bound(b,c),X_38)
    | greatest_lower_bound(b,greatest_lower_bound(c,X_38)) = greatest_lower_bound(greatest_lower_bound(a,c),X_38) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_38)),greatest_lower_bound(greatest_lower_bound(b,c),X_38)) ),[1,0],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_4494,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_38)) != greatest_lower_bound(greatest_lower_bound(b,c),X_38)
    | greatest_lower_bound(b,greatest_lower_bound(c,X_38)) = greatest_lower_bound(greatest_lower_bound(a,c),X_38) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,c),greatest_lower_bound(a,c)) )],[refute_0_178,refute_0_4493]) ).

cnf(refute_0_4495,plain,
    greatest_lower_bound(b,greatest_lower_bound(c,X_38)) = greatest_lower_bound(greatest_lower_bound(a,c),X_38),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_38)),greatest_lower_bound(greatest_lower_bound(b,c),X_38)) )],[refute_0_4492,refute_0_4494]) ).

cnf(refute_0_4496,plain,
    greatest_lower_bound(greatest_lower_bound(a,c),X_38) = greatest_lower_bound(a,greatest_lower_bound(c,X_38)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_4497,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_38)) != greatest_lower_bound(greatest_lower_bound(a,c),X_38)
    | greatest_lower_bound(greatest_lower_bound(a,c),X_38) != greatest_lower_bound(a,greatest_lower_bound(c,X_38))
    | greatest_lower_bound(b,greatest_lower_bound(c,X_38)) = greatest_lower_bound(a,greatest_lower_bound(c,X_38)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_38)),greatest_lower_bound(a,greatest_lower_bound(c,X_38))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(a,c),X_38))]]) ).

cnf(refute_0_4498,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_38)) != greatest_lower_bound(greatest_lower_bound(a,c),X_38)
    | greatest_lower_bound(b,greatest_lower_bound(c,X_38)) = greatest_lower_bound(a,greatest_lower_bound(c,X_38)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),X_38),greatest_lower_bound(a,greatest_lower_bound(c,X_38))) )],[refute_0_4496,refute_0_4497]) ).

cnf(refute_0_4499,plain,
    greatest_lower_bound(b,greatest_lower_bound(c,X_38)) = greatest_lower_bound(a,greatest_lower_bound(c,X_38)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_38)),greatest_lower_bound(greatest_lower_bound(a,c),X_38)) )],[refute_0_4495,refute_0_4498]) ).

cnf(refute_0_4500,plain,
    greatest_lower_bound(b,greatest_lower_bound(c,X_36)) = greatest_lower_bound(a,greatest_lower_bound(c,X_36)),
    inference(subst,[],[refute_0_4499:[bind(X_38,$fot(X_36))]]) ).

cnf(refute_0_4501,plain,
    greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) = greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))))]]) ).

cnf(refute_0_4502,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) != greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))
    | greatest_lower_bound(b,greatest_lower_bound(c,X_36)) != greatest_lower_bound(a,greatest_lower_bound(c,X_36))
    | greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,X_36))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))),greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))) ),[1,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_36)))]]) ).

cnf(refute_0_4503,plain,
    ( greatest_lower_bound(b,greatest_lower_bound(c,X_36)) != greatest_lower_bound(a,greatest_lower_bound(c,X_36))
    | greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,X_36))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))),greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))) )],[refute_0_4501,refute_0_4502]) ).

cnf(refute_0_4504,plain,
    greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,X_36))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,greatest_lower_bound(c,X_36)),greatest_lower_bound(a,greatest_lower_bound(c,X_36))) )],[refute_0_4500,refute_0_4503]) ).

cnf(refute_0_4505,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,X_36))) != greatest_lower_bound(a,greatest_lower_bound(c,X_36))
    | greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) != greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,X_36)))
    | greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) = greatest_lower_bound(a,greatest_lower_bound(c,X_36)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,X_36))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_36))))]]) ).

cnf(refute_0_4506,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,X_36))) != greatest_lower_bound(a,greatest_lower_bound(c,X_36))
    | greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) = greatest_lower_bound(a,greatest_lower_bound(c,X_36)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))),greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,X_36)))) )],[refute_0_4504,refute_0_4505]) ).

cnf(refute_0_4507,plain,
    greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) = greatest_lower_bound(a,greatest_lower_bound(c,X_36)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,X_36))),greatest_lower_bound(a,greatest_lower_bound(c,X_36))) )],[refute_0_4491,refute_0_4506]) ).

cnf(refute_0_4508,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))
    | greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))) != greatest_lower_bound(a,greatest_lower_bound(c,X_36))
    | greatest_lower_bound(X_36,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(c,X_36)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_36,greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(c,X_36))) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))))]]) ).

cnf(refute_0_4509,plain,
    ( greatest_lower_bound(X_36,greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))
    | greatest_lower_bound(X_36,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(c,X_36)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36))),greatest_lower_bound(a,greatest_lower_bound(c,X_36))) )],[refute_0_4507,refute_0_4508]) ).

cnf(refute_0_4510,plain,
    greatest_lower_bound(X_36,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(c,X_36)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X_36)))) )],[refute_0_4490,refute_0_4509]) ).

cnf(refute_0_4511,plain,
    greatest_lower_bound(X_42,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(c,X_42)),
    inference(subst,[],[refute_0_4510:[bind(X_36,$fot(X_42))]]) ).

cnf(refute_0_4512,plain,
    greatest_lower_bound(X_42,c) = greatest_lower_bound(c,X_42),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_42)),bind(Y,$fot(c))]]) ).

cnf(refute_0_4513,plain,
    ( greatest_lower_bound(X_42,c) != greatest_lower_bound(c,X_42)
    | greatest_lower_bound(c,X_42) = greatest_lower_bound(X_42,c) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_42,c))),bind(Y0,$fot(greatest_lower_bound(c,X_42)))]]) ).

cnf(refute_0_4514,plain,
    greatest_lower_bound(c,X_42) = greatest_lower_bound(X_42,c),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,c),greatest_lower_bound(c,X_42)) )],[refute_0_4512,refute_0_4513]) ).

cnf(refute_0_4515,plain,
    ( greatest_lower_bound(X_42,greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(c,X_42))
    | greatest_lower_bound(c,X_42) != greatest_lower_bound(X_42,c)
    | greatest_lower_bound(X_42,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(X_42,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(c,X_42))) ),[1,1],$fot(greatest_lower_bound(X_42,c))]]) ).

cnf(refute_0_4516,plain,
    ( greatest_lower_bound(X_42,greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(c,X_42))
    | greatest_lower_bound(X_42,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(X_42,c)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,X_42),greatest_lower_bound(X_42,c)) )],[refute_0_4514,refute_0_4515]) ).

cnf(refute_0_4517,plain,
    greatest_lower_bound(X_42,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(X_42,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(c,X_42))) )],[refute_0_4511,refute_0_4516]) ).

cnf(refute_0_4518,plain,
    ( greatest_lower_bound(X_42,greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(X_42,c))
    | greatest_lower_bound(a,greatest_lower_bound(X_42,c)) = greatest_lower_bound(X_42,greatest_lower_bound(a,c)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_42,greatest_lower_bound(a,c)))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(X_42,c))))]]) ).

cnf(refute_0_4519,plain,
    greatest_lower_bound(a,greatest_lower_bound(X_42,c)) = greatest_lower_bound(X_42,greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(X_42,c))) )],[refute_0_4517,refute_0_4518]) ).

cnf(refute_0_4520,plain,
    ( X_71 != multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(a,greatest_lower_bound(X_42,c)),X_71))
    | greatest_lower_bound(a,greatest_lower_bound(X_42,c)) != greatest_lower_bound(X_42,greatest_lower_bound(a,c))
    | X_71 = multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) ),
    introduced(tautology,[equality,[$cnf( $equal(X_71,multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(a,greatest_lower_bound(X_42,c)),X_71))) ),[1,1,0],$fot(greatest_lower_bound(X_42,greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4521,plain,
    ( X_71 != multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(a,greatest_lower_bound(X_42,c)),X_71))
    | X_71 = multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(X_42,c)),greatest_lower_bound(X_42,greatest_lower_bound(a,c))) )],[refute_0_4519,refute_0_4520]) ).

cnf(refute_0_4522,plain,
    X_71 = multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)),
    inference(resolve,[$cnf( $equal(X_71,multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(a,greatest_lower_bound(X_42,c)),X_71))) )],[refute_0_4463,refute_0_4521]) ).

cnf(refute_0_4523,plain,
    inverse(greatest_lower_bound(X,Y)) = multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y)))),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(inverse(inverse(greatest_lower_bound(Y,X))))),bind(X_60,$fot(inverse(greatest_lower_bound(X,Y))))]]) ).

cnf(refute_0_4524,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))) != identity
    | inverse(greatest_lower_bound(X,Y)) != multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))))
    | inverse(greatest_lower_bound(X,Y)) = multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_4525,plain,
    ( inverse(greatest_lower_bound(X,Y)) != multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))))
    | inverse(greatest_lower_bound(X,Y)) = multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))),identity) )],[refute_0_203,refute_0_4524]) ).

cnf(refute_0_4526,plain,
    inverse(greatest_lower_bound(X,Y)) = multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),identity),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))))) )],[refute_0_4523,refute_0_4525]) ).

cnf(refute_0_4527,plain,
    multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),identity) = multiply(inverse(greatest_lower_bound(Y,X)),identity),
    inference(subst,[],[refute_0_25:[bind(X_61,$fot(inverse(greatest_lower_bound(Y,X)))),bind(X_62,$fot(identity))]]) ).

cnf(refute_0_4528,plain,
    ( multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),identity) != multiply(inverse(greatest_lower_bound(Y,X)),identity)
    | inverse(greatest_lower_bound(X,Y)) != multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),identity)
    | inverse(greatest_lower_bound(X,Y)) = multiply(inverse(greatest_lower_bound(Y,X)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),identity)) ),[1],$fot(multiply(inverse(greatest_lower_bound(Y,X)),identity))]]) ).

cnf(refute_0_4529,plain,
    ( inverse(greatest_lower_bound(X,Y)) != multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),identity)
    | inverse(greatest_lower_bound(X,Y)) = multiply(inverse(greatest_lower_bound(Y,X)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),identity),multiply(inverse(greatest_lower_bound(Y,X)),identity)) )],[refute_0_4527,refute_0_4528]) ).

cnf(refute_0_4530,plain,
    inverse(greatest_lower_bound(X,Y)) = multiply(inverse(greatest_lower_bound(Y,X)),identity),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),multiply(inverse(inverse(inverse(greatest_lower_bound(Y,X)))),identity)) )],[refute_0_4526,refute_0_4529]) ).

cnf(refute_0_4531,plain,
    multiply(inverse(greatest_lower_bound(Y,X)),identity) = inverse(greatest_lower_bound(Y,X)),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(inverse(greatest_lower_bound(Y,X))))]]) ).

cnf(refute_0_4532,plain,
    ( multiply(inverse(greatest_lower_bound(Y,X)),identity) != inverse(greatest_lower_bound(Y,X))
    | inverse(greatest_lower_bound(X,Y)) != multiply(inverse(greatest_lower_bound(Y,X)),identity)
    | inverse(greatest_lower_bound(X,Y)) = inverse(greatest_lower_bound(Y,X)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),multiply(inverse(greatest_lower_bound(Y,X)),identity)) ),[1],$fot(inverse(greatest_lower_bound(Y,X)))]]) ).

cnf(refute_0_4533,plain,
    ( inverse(greatest_lower_bound(X,Y)) != multiply(inverse(greatest_lower_bound(Y,X)),identity)
    | inverse(greatest_lower_bound(X,Y)) = inverse(greatest_lower_bound(Y,X)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X)),identity),inverse(greatest_lower_bound(Y,X))) )],[refute_0_4531,refute_0_4532]) ).

cnf(refute_0_4534,plain,
    inverse(greatest_lower_bound(X,Y)) = inverse(greatest_lower_bound(Y,X)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),multiply(inverse(greatest_lower_bound(Y,X)),identity)) )],[refute_0_4530,refute_0_4533]) ).

cnf(refute_0_4535,plain,
    ( inverse(greatest_lower_bound(X,Y)) != inverse(greatest_lower_bound(Y,X))
    | inverse(greatest_lower_bound(Y,X)) = inverse(greatest_lower_bound(X,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(X,Y)))),bind(Y0,$fot(inverse(greatest_lower_bound(Y,X))))]]) ).

cnf(refute_0_4536,plain,
    inverse(greatest_lower_bound(Y,X)) = inverse(greatest_lower_bound(X,Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),inverse(greatest_lower_bound(Y,X))) )],[refute_0_4534,refute_0_4535]) ).

cnf(refute_0_4537,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)) = inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c))),
    inference(subst,[],[refute_0_4536:[bind(X,$fot(a)),bind(Y,$fot(greatest_lower_bound(X_42,c)))]]) ).

cnf(refute_0_4538,plain,
    multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) = multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)))]]) ).

cnf(refute_0_4539,plain,
    ( multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) != multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)) != inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c)))
    | multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c))),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)),multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71))) ),[1,0],$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c))))]]) ).

cnf(refute_0_4540,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)) != inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c)))
    | multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c))),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)),multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71))) )],[refute_0_4538,refute_0_4539]) ).

cnf(refute_0_4541,plain,
    multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c))),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c)))) )],[refute_0_4537,refute_0_4540]) ).

cnf(refute_0_4542,plain,
    ( X_71 != multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71))
    | multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c))),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71))
    | X_71 = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c))),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_71,multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c))),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71))) ),[0],$fot(multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)))]]) ).

cnf(refute_0_4543,plain,
    ( X_71 != multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71))
    | X_71 = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c))),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c))),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71))) )],[refute_0_4541,refute_0_4542]) ).

cnf(refute_0_4544,plain,
    X_71 = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(X_42,c))),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71)),
    inference(resolve,[$cnf( $equal(X_71,multiply(inverse(greatest_lower_bound(greatest_lower_bound(X_42,c),a)),multiply(greatest_lower_bound(X_42,greatest_lower_bound(a,c)),X_71))) )],[refute_0_4522,refute_0_4543]) ).

cnf(refute_0_4545,plain,
    X_174 = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),multiply(greatest_lower_bound(inverse(X_174),greatest_lower_bound(a,c)),X_174)),
    inference(subst,[],[refute_0_4544:[bind(X_42,$fot(inverse(X_174))),bind(X_71,$fot(X_174))]]) ).

cnf(refute_0_4546,plain,
    multiply(greatest_lower_bound(inverse(X_174),greatest_lower_bound(a,c)),X_174) = greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174)),
    inference(subst,[],[refute_0_1305:[bind(X_121,$fot(X_174)),bind(X_123,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4547,plain,
    ( X_174 != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),multiply(greatest_lower_bound(inverse(X_174),greatest_lower_bound(a,c)),X_174))
    | multiply(greatest_lower_bound(inverse(X_174),greatest_lower_bound(a,c)),X_174) != greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))
    | X_174 = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) ),
    introduced(tautology,[equality,[$cnf( $equal(X_174,multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),multiply(greatest_lower_bound(inverse(X_174),greatest_lower_bound(a,c)),X_174))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174)))]]) ).

cnf(refute_0_4548,plain,
    ( X_174 != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),multiply(greatest_lower_bound(inverse(X_174),greatest_lower_bound(a,c)),X_174))
    | X_174 = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_174),greatest_lower_bound(a,c)),X_174),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) )],[refute_0_4546,refute_0_4547]) ).

cnf(refute_0_4549,plain,
    X_174 = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))),
    inference(resolve,[$cnf( $equal(X_174,multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),multiply(greatest_lower_bound(inverse(X_174),greatest_lower_bound(a,c)),X_174))) )],[refute_0_4545,refute_0_4548]) ).

cnf(refute_0_4550,plain,
    inverse(greatest_lower_bound(X,greatest_lower_bound(a,c))) = least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c))),
    inference(subst,[],[p12x_3:[bind(Y,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4551,plain,
    greatest_lower_bound(X,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(c,X)),
    inference(subst,[],[refute_0_4510:[bind(X_36,$fot(X))]]) ).

cnf(refute_0_4552,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(c,X))
    | inverse(greatest_lower_bound(X,greatest_lower_bound(a,c))) != least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,X))) = least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X,greatest_lower_bound(a,c))),least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c)))) ),[0,0],$fot(greatest_lower_bound(a,greatest_lower_bound(c,X)))]]) ).

cnf(refute_0_4553,plain,
    ( inverse(greatest_lower_bound(X,greatest_lower_bound(a,c))) != least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,X))) = least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(c,X))) )],[refute_0_4551,refute_0_4552]) ).

cnf(refute_0_4554,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(c,X))) = least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,greatest_lower_bound(a,c))),least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c)))) )],[refute_0_4550,refute_0_4553]) ).

cnf(refute_0_4555,plain,
    least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c))) = inverse(greatest_lower_bound(X,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_136:[bind(Y,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4556,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(c,X))) != least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c)))
    | least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c))) != inverse(greatest_lower_bound(X,greatest_lower_bound(a,c)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,X))) = inverse(greatest_lower_bound(X,greatest_lower_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,X))),inverse(greatest_lower_bound(X,greatest_lower_bound(a,c)))) ),[0],$fot(least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_4557,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(c,X))) != least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,X))) = inverse(greatest_lower_bound(X,greatest_lower_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c))),inverse(greatest_lower_bound(X,greatest_lower_bound(a,c)))) )],[refute_0_4555,refute_0_4556]) ).

cnf(refute_0_4558,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(c,X))) = inverse(greatest_lower_bound(X,greatest_lower_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,X))),least_upper_bound(inverse(X),inverse(greatest_lower_bound(a,c)))) )],[refute_0_4554,refute_0_4557]) ).

cnf(refute_0_4559,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))) = inverse(greatest_lower_bound(X_163,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_4558:[bind(X,$fot(X_163))]]) ).

cnf(refute_0_4560,plain,
    greatest_lower_bound(X_163,greatest_lower_bound(a,c)) = greatest_lower_bound(a,greatest_lower_bound(X_163,c)),
    inference(subst,[],[refute_0_4517:[bind(X_42,$fot(X_163))]]) ).

cnf(refute_0_4561,plain,
    ( greatest_lower_bound(X_163,greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(X_163,c))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))) != inverse(greatest_lower_bound(X_163,greatest_lower_bound(a,c)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))) = inverse(greatest_lower_bound(a,greatest_lower_bound(X_163,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))),inverse(greatest_lower_bound(X_163,greatest_lower_bound(a,c)))) ),[1,0],$fot(greatest_lower_bound(a,greatest_lower_bound(X_163,c)))]]) ).

cnf(refute_0_4562,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))) != inverse(greatest_lower_bound(X_163,greatest_lower_bound(a,c)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))) = inverse(greatest_lower_bound(a,greatest_lower_bound(X_163,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_163,greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(X_163,c))) )],[refute_0_4560,refute_0_4561]) ).

cnf(refute_0_4563,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))) = inverse(greatest_lower_bound(a,greatest_lower_bound(X_163,c))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))),inverse(greatest_lower_bound(X_163,greatest_lower_bound(a,c)))) )],[refute_0_4559,refute_0_4562]) ).

cnf(refute_0_4564,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))) != inverse(greatest_lower_bound(a,greatest_lower_bound(X_163,c)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(X_163,c))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))))),bind(Y0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(X_163,c)))))]]) ).

cnf(refute_0_4565,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(X_163,c))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,X_163))),inverse(greatest_lower_bound(a,greatest_lower_bound(X_163,c)))) )],[refute_0_4563,refute_0_4564]) ).

cnf(refute_0_4566,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174)))),
    inference(subst,[],[refute_0_4565:[bind(X_163,$fot(inverse(X_174)))]]) ).

cnf(refute_0_4567,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))))]]) ).

cnf(refute_0_4568,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))) != inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174))))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174)))) ),[1,0],$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174)))))]]) ).

cnf(refute_0_4569,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))) != inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174))))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174)))) )],[refute_0_4567,refute_0_4568]) ).

cnf(refute_0_4570,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174))))) )],[refute_0_4566,refute_0_4569]) ).

cnf(refute_0_4571,plain,
    ( X_174 != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174)))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174)))
    | X_174 = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_174,multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174)))) ),[0],$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))))]]) ).

cnf(refute_0_4572,plain,
    ( X_174 != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174)))
    | X_174 = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174)))) )],[refute_0_4570,refute_0_4571]) ).

cnf(refute_0_4573,plain,
    X_174 = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_174)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174))),
    inference(resolve,[$cnf( $equal(X_174,multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(X_174),c))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),X_174)))) )],[refute_0_4549,refute_0_4572]) ).

cnf(refute_0_4574,plain,
    least_upper_bound(identity,greatest_lower_bound(a,c)) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_4573:[bind(X_174,$fot(least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_4575,plain,
    multiply(X_329,greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329))))) = greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))),
    inference(subst,[],[refute_0_1286:[bind(X_107,$fot(X_329)),bind(X_109,$fot(inverse(greatest_lower_bound(identity,inverse(X_329)))))]]) ).

cnf(refute_0_4576,plain,
    greatest_lower_bound(inverse(X_329),identity) = greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329)))),
    inference(subst,[],[refute_0_625:[bind(X_204,$fot(inverse(X_329)))]]) ).

cnf(refute_0_4577,plain,
    ( greatest_lower_bound(inverse(X_329),identity) != greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329))))
    | greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329)))) = greatest_lower_bound(inverse(X_329),identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(inverse(X_329),identity))),bind(Y0,$fot(greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329))))))]]) ).

cnf(refute_0_4578,plain,
    greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329)))) = greatest_lower_bound(inverse(X_329),identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_329),identity),greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329))))) )],[refute_0_4576,refute_0_4577]) ).

cnf(refute_0_4579,plain,
    ( multiply(X_329,greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329))))) != greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))
    | greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329)))) != greatest_lower_bound(inverse(X_329),identity)
    | multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) = greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_329,greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329))))),greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))) ),[0,1],$fot(greatest_lower_bound(inverse(X_329),identity))]]) ).

cnf(refute_0_4580,plain,
    ( multiply(X_329,greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329))))) != greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))
    | multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) = greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329)))),greatest_lower_bound(inverse(X_329),identity)) )],[refute_0_4578,refute_0_4579]) ).

cnf(refute_0_4581,plain,
    multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) = greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))),
    inference(resolve,[$cnf( $equal(multiply(X_329,greatest_lower_bound(inverse(X_329),inverse(greatest_lower_bound(identity,inverse(X_329))))),greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))) )],[refute_0_4575,refute_0_4580]) ).

cnf(refute_0_4582,plain,
    multiply(greatest_lower_bound(X_329,identity),identity) = greatest_lower_bound(X_329,identity),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(greatest_lower_bound(X_329,identity)))]]) ).

cnf(refute_0_4583,plain,
    greatest_lower_bound(identity,multiply(X_329,identity)) = multiply(greatest_lower_bound(X_329,identity),identity),
    inference(subst,[],[refute_0_2028:[bind(X_121,$fot(identity)),bind(X_122,$fot(X_329))]]) ).

cnf(refute_0_4584,plain,
    ( multiply(greatest_lower_bound(X_329,identity),identity) != greatest_lower_bound(X_329,identity)
    | greatest_lower_bound(identity,multiply(X_329,identity)) != multiply(greatest_lower_bound(X_329,identity),identity)
    | greatest_lower_bound(identity,multiply(X_329,identity)) = greatest_lower_bound(X_329,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_329,identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_329,identity),identity))),bind(Z0,$fot(greatest_lower_bound(X_329,identity)))]]) ).

cnf(refute_0_4585,plain,
    ( multiply(greatest_lower_bound(X_329,identity),identity) != greatest_lower_bound(X_329,identity)
    | greatest_lower_bound(identity,multiply(X_329,identity)) = greatest_lower_bound(X_329,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_329,identity)),multiply(greatest_lower_bound(X_329,identity),identity)) )],[refute_0_4583,refute_0_4584]) ).

cnf(refute_0_4586,plain,
    greatest_lower_bound(identity,multiply(X_329,identity)) = greatest_lower_bound(X_329,identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_329,identity),identity),greatest_lower_bound(X_329,identity)) )],[refute_0_4582,refute_0_4585]) ).

cnf(refute_0_4587,plain,
    multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))) = greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,inverse(X_107))),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_107)),bind(Y,$fot(X_108)),bind(Z,$fot(inverse(X_107)))]]) ).

cnf(refute_0_4588,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))) != greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,inverse(X_107)))
    | multiply(X_107,inverse(X_107)) != identity
    | multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))) = greatest_lower_bound(multiply(X_107,X_108),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,inverse(X_107)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_4589,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))) != greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,inverse(X_107)))
    | multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))) = greatest_lower_bound(multiply(X_107,X_108),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_107,inverse(X_107)),identity) )],[refute_0_1283,refute_0_4588]) ).

cnf(refute_0_4590,plain,
    multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))) = greatest_lower_bound(multiply(X_107,X_108),identity),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))),greatest_lower_bound(multiply(X_107,X_108),multiply(X_107,inverse(X_107)))) )],[refute_0_4587,refute_0_4589]) ).

cnf(refute_0_4591,plain,
    greatest_lower_bound(multiply(X_107,X_108),identity) = greatest_lower_bound(identity,multiply(X_107,X_108)),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(multiply(X_107,X_108))),bind(X_25,$fot(identity))]]) ).

cnf(refute_0_4592,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))) != greatest_lower_bound(multiply(X_107,X_108),identity)
    | greatest_lower_bound(multiply(X_107,X_108),identity) != greatest_lower_bound(identity,multiply(X_107,X_108))
    | multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))) = greatest_lower_bound(identity,multiply(X_107,X_108)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))),greatest_lower_bound(identity,multiply(X_107,X_108))) ),[0],$fot(greatest_lower_bound(multiply(X_107,X_108),identity))]]) ).

cnf(refute_0_4593,plain,
    ( multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))) != greatest_lower_bound(multiply(X_107,X_108),identity)
    | multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))) = greatest_lower_bound(identity,multiply(X_107,X_108)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_107,X_108),identity),greatest_lower_bound(identity,multiply(X_107,X_108))) )],[refute_0_4591,refute_0_4592]) ).

cnf(refute_0_4594,plain,
    multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))) = greatest_lower_bound(identity,multiply(X_107,X_108)),
    inference(resolve,[$cnf( $equal(multiply(X_107,greatest_lower_bound(X_108,inverse(X_107))),greatest_lower_bound(multiply(X_107,X_108),identity)) )],[refute_0_4590,refute_0_4593]) ).

cnf(refute_0_4595,plain,
    multiply(X_329,greatest_lower_bound(identity,inverse(X_329))) = greatest_lower_bound(identity,multiply(X_329,identity)),
    inference(subst,[],[refute_0_4594:[bind(X_107,$fot(X_329)),bind(X_108,$fot(identity))]]) ).

cnf(refute_0_4596,plain,
    ( multiply(X_329,greatest_lower_bound(identity,inverse(X_329))) != greatest_lower_bound(identity,multiply(X_329,identity))
    | greatest_lower_bound(identity,multiply(X_329,identity)) != greatest_lower_bound(X_329,identity)
    | multiply(X_329,greatest_lower_bound(identity,inverse(X_329))) = greatest_lower_bound(X_329,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(X_329,greatest_lower_bound(identity,inverse(X_329))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_329,identity)))),bind(Z0,$fot(greatest_lower_bound(X_329,identity)))]]) ).

cnf(refute_0_4597,plain,
    ( greatest_lower_bound(identity,multiply(X_329,identity)) != greatest_lower_bound(X_329,identity)
    | multiply(X_329,greatest_lower_bound(identity,inverse(X_329))) = greatest_lower_bound(X_329,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_329,greatest_lower_bound(identity,inverse(X_329))),greatest_lower_bound(identity,multiply(X_329,identity))) )],[refute_0_4595,refute_0_4596]) ).

cnf(refute_0_4598,plain,
    multiply(X_329,greatest_lower_bound(identity,inverse(X_329))) = greatest_lower_bound(X_329,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_329,identity)),greatest_lower_bound(X_329,identity)) )],[refute_0_4586,refute_0_4597]) ).

cnf(refute_0_4599,plain,
    multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) = multiply(X_329,greatest_lower_bound(identity,inverse(X_329))),
    inference(subst,[],[refute_0_4221:[bind(X,$fot(X_329)),bind(Y,$fot(identity)),bind(Z,$fot(inverse(X_329)))]]) ).

cnf(refute_0_4600,plain,
    ( multiply(X_329,greatest_lower_bound(identity,inverse(X_329))) != greatest_lower_bound(X_329,identity)
    | multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) != multiply(X_329,greatest_lower_bound(identity,inverse(X_329)))
    | multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) = greatest_lower_bound(X_329,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(X_329,greatest_lower_bound(inverse(X_329),identity)))),bind(Y0,$fot(multiply(X_329,greatest_lower_bound(identity,inverse(X_329))))),bind(Z0,$fot(greatest_lower_bound(X_329,identity)))]]) ).

cnf(refute_0_4601,plain,
    ( multiply(X_329,greatest_lower_bound(identity,inverse(X_329))) != greatest_lower_bound(X_329,identity)
    | multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) = greatest_lower_bound(X_329,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_329,greatest_lower_bound(inverse(X_329),identity)),multiply(X_329,greatest_lower_bound(identity,inverse(X_329)))) )],[refute_0_4599,refute_0_4600]) ).

cnf(refute_0_4602,plain,
    multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) = greatest_lower_bound(X_329,identity),
    inference(resolve,[$cnf( $equal(multiply(X_329,greatest_lower_bound(identity,inverse(X_329))),greatest_lower_bound(X_329,identity)) )],[refute_0_4598,refute_0_4601]) ).

cnf(refute_0_4603,plain,
    ( multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) != greatest_lower_bound(X_329,identity)
    | multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) != greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))
    | greatest_lower_bound(X_329,identity) = greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_329,greatest_lower_bound(inverse(X_329),identity)),greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))) ),[0],$fot(greatest_lower_bound(X_329,identity))]]) ).

cnf(refute_0_4604,plain,
    ( multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) != greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))
    | greatest_lower_bound(X_329,identity) = greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) ),
    inference(resolve,[$cnf( $equal(multiply(X_329,greatest_lower_bound(inverse(X_329),identity)),greatest_lower_bound(X_329,identity)) )],[refute_0_4602,refute_0_4603]) ).

cnf(refute_0_4605,plain,
    least_upper_bound(inverse(identity),X_329) = least_upper_bound(inverse(identity),X_329),
    introduced(tautology,[refl,[$fot(least_upper_bound(inverse(identity),X_329))]]) ).

cnf(refute_0_4606,plain,
    ( inverse(identity) != identity
    | least_upper_bound(inverse(identity),X_329) != least_upper_bound(inverse(identity),X_329)
    | least_upper_bound(inverse(identity),X_329) = least_upper_bound(identity,X_329) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(identity),X_329),least_upper_bound(inverse(identity),X_329)) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_4607,plain,
    ( inverse(identity) != identity
    | least_upper_bound(inverse(identity),X_329) = least_upper_bound(identity,X_329) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),X_329),least_upper_bound(inverse(identity),X_329)) )],[refute_0_4605,refute_0_4606]) ).

cnf(refute_0_4608,plain,
    least_upper_bound(inverse(identity),X_329) = least_upper_bound(identity,X_329),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_4607]) ).

cnf(refute_0_4609,plain,
    inverse(greatest_lower_bound(identity,inverse(X_329))) = least_upper_bound(inverse(identity),X_329),
    inference(subst,[],[refute_0_1559:[bind(X,$fot(identity)),bind(X_89,$fot(X_329))]]) ).

cnf(refute_0_4610,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_329))) != least_upper_bound(inverse(identity),X_329)
    | least_upper_bound(inverse(identity),X_329) != least_upper_bound(identity,X_329)
    | inverse(greatest_lower_bound(identity,inverse(X_329))) = least_upper_bound(identity,X_329) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_329))))),bind(Y0,$fot(least_upper_bound(inverse(identity),X_329))),bind(Z0,$fot(least_upper_bound(identity,X_329)))]]) ).

cnf(refute_0_4611,plain,
    ( least_upper_bound(inverse(identity),X_329) != least_upper_bound(identity,X_329)
    | inverse(greatest_lower_bound(identity,inverse(X_329))) = least_upper_bound(identity,X_329) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_329))),least_upper_bound(inverse(identity),X_329)) )],[refute_0_4609,refute_0_4610]) ).

cnf(refute_0_4612,plain,
    inverse(greatest_lower_bound(identity,inverse(X_329))) = least_upper_bound(identity,X_329),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),X_329),least_upper_bound(identity,X_329)) )],[refute_0_4608,refute_0_4611]) ).

cnf(refute_0_4613,plain,
    multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))) = multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))),
    introduced(tautology,[refl,[$fot(multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))]]) ).

cnf(refute_0_4614,plain,
    ( multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))) != multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))
    | inverse(greatest_lower_bound(identity,inverse(X_329))) != least_upper_bound(identity,X_329)
    | multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))) = multiply(X_329,least_upper_bound(identity,X_329)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))),multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) ),[1,1],$fot(least_upper_bound(identity,X_329))]]) ).

cnf(refute_0_4615,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X_329))) != least_upper_bound(identity,X_329)
    | multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))) = multiply(X_329,least_upper_bound(identity,X_329)) ),
    inference(resolve,[$cnf( $equal(multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))),multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) )],[refute_0_4613,refute_0_4614]) ).

cnf(refute_0_4616,plain,
    multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))) = multiply(X_329,least_upper_bound(identity,X_329)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_329))),least_upper_bound(identity,X_329)) )],[refute_0_4612,refute_0_4615]) ).

cnf(refute_0_4617,plain,
    greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) = greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))))]]) ).

cnf(refute_0_4618,plain,
    ( multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))) != multiply(X_329,least_upper_bound(identity,X_329))
    | greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) != greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))
    | greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) = greatest_lower_bound(identity,multiply(X_329,least_upper_bound(identity,X_329))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))),greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))) ),[1,1],$fot(multiply(X_329,least_upper_bound(identity,X_329)))]]) ).

cnf(refute_0_4619,plain,
    ( multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))) != multiply(X_329,least_upper_bound(identity,X_329))
    | greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) = greatest_lower_bound(identity,multiply(X_329,least_upper_bound(identity,X_329))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))),greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))) )],[refute_0_4617,refute_0_4618]) ).

cnf(refute_0_4620,plain,
    greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) = greatest_lower_bound(identity,multiply(X_329,least_upper_bound(identity,X_329))),
    inference(resolve,[$cnf( $equal(multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))),multiply(X_329,least_upper_bound(identity,X_329))) )],[refute_0_4616,refute_0_4619]) ).

cnf(refute_0_4621,plain,
    ( greatest_lower_bound(X_329,identity) != greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))
    | greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))) != greatest_lower_bound(identity,multiply(X_329,least_upper_bound(identity,X_329)))
    | greatest_lower_bound(X_329,identity) = greatest_lower_bound(identity,multiply(X_329,least_upper_bound(identity,X_329))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_329,identity),greatest_lower_bound(identity,multiply(X_329,least_upper_bound(identity,X_329)))) ),[0],$fot(greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))))]]) ).

cnf(refute_0_4622,plain,
    ( greatest_lower_bound(X_329,identity) != greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))
    | greatest_lower_bound(X_329,identity) = greatest_lower_bound(identity,multiply(X_329,least_upper_bound(identity,X_329))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329))))),greatest_lower_bound(identity,multiply(X_329,least_upper_bound(identity,X_329)))) )],[refute_0_4620,refute_0_4621]) ).

cnf(refute_0_4623,plain,
    ( multiply(X_329,greatest_lower_bound(inverse(X_329),identity)) != greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))
    | greatest_lower_bound(X_329,identity) = greatest_lower_bound(identity,multiply(X_329,least_upper_bound(identity,X_329))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_329,identity),greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))) )],[refute_0_4604,refute_0_4622]) ).

cnf(refute_0_4624,plain,
    greatest_lower_bound(X_329,identity) = greatest_lower_bound(identity,multiply(X_329,least_upper_bound(identity,X_329))),
    inference(resolve,[$cnf( $equal(multiply(X_329,greatest_lower_bound(inverse(X_329),identity)),greatest_lower_bound(identity,multiply(X_329,inverse(greatest_lower_bound(identity,inverse(X_329)))))) )],[refute_0_4581,refute_0_4623]) ).

cnf(refute_0_4625,plain,
    greatest_lower_bound(greatest_lower_bound(a,c),identity) = greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_4624:[bind(X_329,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4626,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,c),identity) != greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c))))
    | greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c)))) = greatest_lower_bound(greatest_lower_bound(a,c),identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,c),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4627,plain,
    greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c)))) = greatest_lower_bound(greatest_lower_bound(a,c),identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),identity),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c))))) )],[refute_0_4625,refute_0_4626]) ).

cnf(refute_0_4628,plain,
    ( greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c)))) != greatest_lower_bound(greatest_lower_bound(a,c),identity)
    | least_upper_bound(identity,greatest_lower_bound(a,c)) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | least_upper_bound(identity,greatest_lower_bound(a,c)) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),[1,1],$fot(greatest_lower_bound(greatest_lower_bound(a,c),identity))]]) ).

cnf(refute_0_4629,plain,
    ( least_upper_bound(identity,greatest_lower_bound(a,c)) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | least_upper_bound(identity,greatest_lower_bound(a,c)) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) )],[refute_0_4627,refute_0_4628]) ).

cnf(refute_0_4630,plain,
    least_upper_bound(identity,greatest_lower_bound(a,c)) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4574,refute_0_4629]) ).

cnf(refute_0_4631,plain,
    least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) = least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_265,identity)),
    inference(subst,[],[refute_0_3215:[bind(X_45,$fot(least_upper_bound(X_265,identity)))]]) ).

cnf(refute_0_4632,plain,
    least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_265,identity)) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y)))),
    inference(subst,[],[refute_0_3904:[bind(X_211,$fot(inverse(greatest_lower_bound(X,Y)))),bind(X_230,$fot(X_265))]]) ).

cnf(refute_0_4633,plain,
    ( least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) != least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_265,identity))
    | least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_265,identity)) != least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y))))
    | least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))),least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y))))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_265,identity)))]]) ).

cnf(refute_0_4634,plain,
    ( least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) != least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_265,identity))
    | least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_265,identity)),least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y))))) )],[refute_0_4632,refute_0_4633]) ).

cnf(refute_0_4635,plain,
    least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))),least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_265,identity))) )],[refute_0_4631,refute_0_4634]) ).

cnf(refute_0_4636,plain,
    least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X))) = least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X))),
    inference(subst,[],[refute_0_3276:[bind(X,$fot(Y)),bind(Y,$fot(X)),bind(X_82,$fot(X_265))]]) ).

cnf(refute_0_4637,plain,
    least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))) = least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))))]]) ).

cnf(refute_0_4638,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))) != least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X))))
    | least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X))) != least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))
    | least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))),least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X))))) ),[1,1],$fot(least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X))))]]) ).

cnf(refute_0_4639,plain,
    ( least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X))) != least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))
    | least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))),least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X))))) )],[refute_0_4637,refute_0_4638]) ).

cnf(refute_0_4640,plain,
    least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X))),least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))) )],[refute_0_4636,refute_0_4639]) ).

cnf(refute_0_4641,plain,
    least_upper_bound(X_218,least_upper_bound(identity,least_upper_bound(X_192,X_193))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)),
    inference(subst,[],[refute_0_1726:[bind(X_166,$fot(least_upper_bound(X_192,X_193))),bind(X_211,$fot(X_218))]]) ).

cnf(refute_0_4642,plain,
    ( least_upper_bound(X_218,least_upper_bound(identity,least_upper_bound(X_192,X_193))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218))
    | least_upper_bound(identity,least_upper_bound(X_192,X_193)) != least_upper_bound(X_192,least_upper_bound(X_193,identity))
    | least_upper_bound(X_218,least_upper_bound(X_192,least_upper_bound(X_193,identity))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_218,least_upper_bound(identity,least_upper_bound(X_192,X_193))),least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218))) ),[0,1],$fot(least_upper_bound(X_192,least_upper_bound(X_193,identity)))]]) ).

cnf(refute_0_4643,plain,
    ( least_upper_bound(X_218,least_upper_bound(identity,least_upper_bound(X_192,X_193))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218))
    | least_upper_bound(X_218,least_upper_bound(X_192,least_upper_bound(X_193,identity))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_192,X_193)),least_upper_bound(X_192,least_upper_bound(X_193,identity))) )],[refute_0_3689,refute_0_4642]) ).

cnf(refute_0_4644,plain,
    least_upper_bound(X_218,least_upper_bound(X_192,least_upper_bound(X_193,identity))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_218,least_upper_bound(identity,least_upper_bound(X_192,X_193))),least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218))) )],[refute_0_4641,refute_0_4643]) ).

cnf(refute_0_4645,plain,
    least_upper_bound(least_upper_bound(X_192,X_193),X_218) = least_upper_bound(X_192,least_upper_bound(X_193,X_218)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(X_192)),bind(Y,$fot(X_193)),bind(Z,$fot(X_218))]]) ).

cnf(refute_0_4646,plain,
    least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)) = least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)))]]) ).

cnf(refute_0_4647,plain,
    ( least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)) != least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218))
    | least_upper_bound(least_upper_bound(X_192,X_193),X_218) != least_upper_bound(X_192,least_upper_bound(X_193,X_218))
    | least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)) = least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,X_218))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)),least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218))) ),[1,1],$fot(least_upper_bound(X_192,least_upper_bound(X_193,X_218)))]]) ).

cnf(refute_0_4648,plain,
    ( least_upper_bound(least_upper_bound(X_192,X_193),X_218) != least_upper_bound(X_192,least_upper_bound(X_193,X_218))
    | least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)) = least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,X_218))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)),least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218))) )],[refute_0_4646,refute_0_4647]) ).

cnf(refute_0_4649,plain,
    least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)) = least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,X_218))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_192,X_193),X_218),least_upper_bound(X_192,least_upper_bound(X_193,X_218))) )],[refute_0_4645,refute_0_4648]) ).

cnf(refute_0_4650,plain,
    ( least_upper_bound(X_218,least_upper_bound(X_192,least_upper_bound(X_193,identity))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218))
    | least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)) != least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,X_218)))
    | least_upper_bound(X_218,least_upper_bound(X_192,least_upper_bound(X_193,identity))) = least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,X_218))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_218,least_upper_bound(X_192,least_upper_bound(X_193,identity))),least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,X_218)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)))]]) ).

cnf(refute_0_4651,plain,
    ( least_upper_bound(X_218,least_upper_bound(X_192,least_upper_bound(X_193,identity))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218))
    | least_upper_bound(X_218,least_upper_bound(X_192,least_upper_bound(X_193,identity))) = least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,X_218))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218)),least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,X_218)))) )],[refute_0_4649,refute_0_4650]) ).

cnf(refute_0_4652,plain,
    least_upper_bound(X_218,least_upper_bound(X_192,least_upper_bound(X_193,identity))) = least_upper_bound(identity,least_upper_bound(X_192,least_upper_bound(X_193,X_218))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_218,least_upper_bound(X_192,least_upper_bound(X_193,identity))),least_upper_bound(identity,least_upper_bound(least_upper_bound(X_192,X_193),X_218))) )],[refute_0_4644,refute_0_4651]) ).

cnf(refute_0_4653,plain,
    least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) = least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))),
    inference(subst,[],[refute_0_4652:[bind(X_192,$fot(inverse(Y))),bind(X_193,$fot(X_265)),bind(X_218,$fot(inverse(X)))]]) ).

cnf(refute_0_4654,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))) != least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X))))
    | least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) != least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X))))
    | least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X))))))]]) ).

cnf(refute_0_4655,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))) != least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X))))
    | least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))),least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X))))) )],[refute_0_4653,refute_0_4654]) ).

cnf(refute_0_4656,plain,
    least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(Y),least_upper_bound(X_265,inverse(X)))),least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X))))) )],[refute_0_4640,refute_0_4655]) ).

cnf(refute_0_4657,plain,
    ( least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) != least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y))))
    | least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) != least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X))))
    | least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))),least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y))))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))))]]) ).

cnf(refute_0_4658,plain,
    ( least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))) != least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y))))
    | least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))),least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X))))) )],[refute_0_4656,refute_0_4657]) ).

cnf(refute_0_4659,plain,
    least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_265,identity))),least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y))))) )],[refute_0_4635,refute_0_4658]) ).

cnf(refute_0_4660,plain,
    ( least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))) != least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y))))
    | least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y)))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y))))))]]) ).

cnf(refute_0_4661,plain,
    least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y)))) = least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(Y,X)))),least_upper_bound(identity,least_upper_bound(X_265,inverse(greatest_lower_bound(X,Y))))) )],[refute_0_4659,refute_0_4660]) ).

cnf(refute_0_4662,plain,
    least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(c,a)))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_4661:[bind(X,$fot(c)),bind(Y,$fot(a)),bind(X_265,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4663,plain,
    least_upper_bound(X_43,least_upper_bound(Y,X_45)) = least_upper_bound(Y,least_upper_bound(X_45,X_43)),
    inference(subst,[],[refute_0_3111:[bind(X,$fot(X_43)),bind(X_145,$fot(X_45))]]) ).

cnf(refute_0_4664,plain,
    ( least_upper_bound(Y,least_upper_bound(X_43,X_45)) != least_upper_bound(X_43,least_upper_bound(Y,X_45))
    | least_upper_bound(X_43,least_upper_bound(Y,X_45)) != least_upper_bound(Y,least_upper_bound(X_45,X_43))
    | least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(Y,least_upper_bound(X_45,X_43)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(Y,least_upper_bound(X_43,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_43))) ),[0],$fot(least_upper_bound(X_43,least_upper_bound(Y,X_45)))]]) ).

cnf(refute_0_4665,plain,
    ( least_upper_bound(Y,least_upper_bound(X_43,X_45)) != least_upper_bound(X_43,least_upper_bound(Y,X_45))
    | least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(Y,least_upper_bound(X_45,X_43)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(Y,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_43))) )],[refute_0_4663,refute_0_4664]) ).

cnf(refute_0_4666,plain,
    least_upper_bound(Y,least_upper_bound(X_43,X_45)) = least_upper_bound(Y,least_upper_bound(X_45,X_43)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_43,X_45)),least_upper_bound(X_43,least_upper_bound(Y,X_45))) )],[refute_0_1102,refute_0_4665]) ).

cnf(refute_0_4667,plain,
    ( least_upper_bound(Y,least_upper_bound(X_43,X_45)) != least_upper_bound(Y,least_upper_bound(X_45,X_43))
    | least_upper_bound(Y,least_upper_bound(X_45,X_43)) = least_upper_bound(Y,least_upper_bound(X_43,X_45)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_43,X_45)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_45,X_43))))]]) ).

cnf(refute_0_4668,plain,
    least_upper_bound(Y,least_upper_bound(X_45,X_43)) = least_upper_bound(Y,least_upper_bound(X_43,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_43,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_43))) )],[refute_0_4666,refute_0_4667]) ).

cnf(refute_0_4669,plain,
    least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(c,a)))),
    inference(subst,[],[refute_0_4668:[bind(Y,$fot(identity)),bind(X_43,$fot(greatest_lower_bound(a,c))),bind(X_45,$fot(inverse(greatest_lower_bound(c,a))))]]) ).

cnf(refute_0_4670,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(c,a)))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(c,a))))
    | least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(c,a)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4671,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(c,a)))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(c,a))))) )],[refute_0_4669,refute_0_4670]) ).

cnf(refute_0_4672,plain,
    least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(c,a)))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_4662,refute_0_4671]) ).

cnf(refute_0_4673,plain,
    least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_4362:[bind(Y,$fot(identity)),bind(X_43,$fot(inverse(greatest_lower_bound(c,a)))),bind(X_45,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4674,plain,
    ( least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c)))
    | least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4675,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c)))) )],[refute_0_4673,refute_0_4674]) ).

cnf(refute_0_4676,plain,
    least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(c,a)),greatest_lower_bound(a,c))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_4672,refute_0_4675]) ).

cnf(refute_0_4677,plain,
    least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) = least_upper_bound(X_318,least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45))),
    inference(subst,[],[refute_0_3111:[bind(X,$fot(least_upper_bound(inverse(Y),X_45))),bind(Y,$fot(X_318)),bind(X_145,$fot(inverse(X)))]]) ).

cnf(refute_0_4678,plain,
    ( least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)) != least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45)
    | least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) != least_upper_bound(X_318,least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)))
    | least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) = least_upper_bound(X_318,least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))),least_upper_bound(X_318,least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)))) ),[1,1],$fot(least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45))]]) ).

cnf(refute_0_4679,plain,
    ( least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) != least_upper_bound(X_318,least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)))
    | least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) = least_upper_bound(X_318,least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)),least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45)) )],[refute_0_3215,refute_0_4678]) ).

cnf(refute_0_4680,plain,
    least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) = least_upper_bound(X_318,least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))),least_upper_bound(X_318,least_upper_bound(inverse(X),least_upper_bound(inverse(Y),X_45)))) )],[refute_0_4677,refute_0_4679]) ).

cnf(refute_0_4681,plain,
    least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_318,X_319))) = least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_318,X_319)),
    inference(subst,[],[refute_0_3215:[bind(X_45,$fot(least_upper_bound(X_318,X_319)))]]) ).

cnf(refute_0_4682,plain,
    least_upper_bound(inverse(Y),least_upper_bound(X_318,X_319)) = least_upper_bound(X_318,least_upper_bound(X_319,inverse(Y))),
    inference(subst,[],[refute_0_3111:[bind(X,$fot(inverse(Y))),bind(Y,$fot(X_318)),bind(X_145,$fot(X_319))]]) ).

cnf(refute_0_4683,plain,
    ( least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_318,X_319))) != least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_318,X_319))
    | least_upper_bound(inverse(Y),least_upper_bound(X_318,X_319)) != least_upper_bound(X_318,least_upper_bound(X_319,inverse(Y)))
    | least_upper_bound(inverse(X),least_upper_bound(X_318,least_upper_bound(X_319,inverse(Y)))) = least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_318,X_319)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_318,X_319))),least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_318,X_319))) ),[0,1],$fot(least_upper_bound(X_318,least_upper_bound(X_319,inverse(Y))))]]) ).

cnf(refute_0_4684,plain,
    ( least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_318,X_319))) != least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_318,X_319))
    | least_upper_bound(inverse(X),least_upper_bound(X_318,least_upper_bound(X_319,inverse(Y)))) = least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_318,X_319)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(Y),least_upper_bound(X_318,X_319)),least_upper_bound(X_318,least_upper_bound(X_319,inverse(Y)))) )],[refute_0_4682,refute_0_4683]) ).

cnf(refute_0_4685,plain,
    least_upper_bound(inverse(X),least_upper_bound(X_318,least_upper_bound(X_319,inverse(Y)))) = least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_318,X_319)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),least_upper_bound(inverse(Y),least_upper_bound(X_318,X_319))),least_upper_bound(inverse(greatest_lower_bound(X,Y)),least_upper_bound(X_318,X_319))) )],[refute_0_4681,refute_0_4684]) ).

cnf(refute_0_4686,plain,
    least_upper_bound(inverse(Y),least_upper_bound(X_45,least_upper_bound(X_318,inverse(X)))) = least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318)),
    inference(subst,[],[refute_0_4685:[bind(X,$fot(Y)),bind(Y,$fot(X)),bind(X_318,$fot(X_45)),bind(X_319,$fot(X_318))]]) ).

cnf(refute_0_4687,plain,
    least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) = least_upper_bound(inverse(Y),least_upper_bound(X_45,least_upper_bound(X_318,inverse(X)))),
    inference(subst,[],[refute_0_375:[bind(X,$fot(inverse(Y))),bind(Y,$fot(X_45)),bind(Z,$fot(least_upper_bound(X_318,inverse(X))))]]) ).

cnf(refute_0_4688,plain,
    ( least_upper_bound(inverse(Y),least_upper_bound(X_45,least_upper_bound(X_318,inverse(X)))) != least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318))
    | least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) != least_upper_bound(inverse(Y),least_upper_bound(X_45,least_upper_bound(X_318,inverse(X))))
    | least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) = least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))))),bind(Y0,$fot(least_upper_bound(inverse(Y),least_upper_bound(X_45,least_upper_bound(X_318,inverse(X)))))),bind(Z0,$fot(least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318))))]]) ).

cnf(refute_0_4689,plain,
    ( least_upper_bound(inverse(Y),least_upper_bound(X_45,least_upper_bound(X_318,inverse(X)))) != least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318))
    | least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) = least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))),least_upper_bound(inverse(Y),least_upper_bound(X_45,least_upper_bound(X_318,inverse(X))))) )],[refute_0_4687,refute_0_4688]) ).

cnf(refute_0_4690,plain,
    least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) = least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(Y),least_upper_bound(X_45,least_upper_bound(X_318,inverse(X)))),least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318))) )],[refute_0_4686,refute_0_4689]) ).

cnf(refute_0_4691,plain,
    ( least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) != least_upper_bound(X_318,least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45))
    | least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) != least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318))
    | least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318)) = least_upper_bound(X_318,least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))),least_upper_bound(X_318,least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318)))]]) ).

cnf(refute_0_4692,plain,
    ( least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))) != least_upper_bound(X_318,least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45))
    | least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318)) = least_upper_bound(X_318,least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))),least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318))) )],[refute_0_4690,refute_0_4691]) ).

cnf(refute_0_4693,plain,
    least_upper_bound(inverse(greatest_lower_bound(Y,X)),least_upper_bound(X_45,X_318)) = least_upper_bound(X_318,least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(Y),X_45),least_upper_bound(X_318,inverse(X))),least_upper_bound(X_318,least_upper_bound(inverse(greatest_lower_bound(X,Y)),X_45))) )],[refute_0_4680,refute_0_4692]) ).

cnf(refute_0_4694,plain,
    least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)),
    inference(subst,[],[refute_0_4693:[bind(X,$fot(c)),bind(Y,$fot(a)),bind(X_318,$fot(greatest_lower_bound(a,c))),bind(X_45,$fot(identity))]]) ).

cnf(refute_0_4695,plain,
    ( least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))) != least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity))
    | least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4696,plain,
    ( least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))),least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity))) )],[refute_0_4694,refute_0_4695]) ).

cnf(refute_0_4697,plain,
    least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(c,a)),identity)),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_4676,refute_0_4696]) ).

cnf(refute_0_4698,plain,
    least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))),
    inference(subst,[],[refute_0_4573:[bind(X_174,$fot(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))]]) ).

cnf(refute_0_4699,plain,
    multiply(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)) = least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)),
    inference(subst,[],[refute_0_236:[bind(X_93,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4700,plain,
    ( multiply(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)) != least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))
    | least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))
    | least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))) ),[1,1,1],$fot(least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))]]) ).

cnf(refute_0_4701,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))
    | least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)),least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))) )],[refute_0_4699,refute_0_4700]) ).

cnf(refute_0_4702,plain,
    least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,c),least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))) )],[refute_0_4698,refute_0_4701]) ).

cnf(refute_0_4703,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))))]]) ).

cnf(refute_0_4704,plain,
    greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))) = identity,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(greatest_lower_bound(a,c),X_95)))]]) ).

cnf(refute_0_4705,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))))]]) ).

cnf(refute_0_4706,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))
    | greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))) != identity
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_4707,plain,
    ( greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))) != identity
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))) )],[refute_0_4705,refute_0_4706]) ).

cnf(refute_0_4708,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))),identity) )],[refute_0_4704,refute_0_4707]) ).

cnf(refute_0_4709,plain,
    greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))),
    inference(subst,[],[refute_0_801:[bind(X_32,$fot(greatest_lower_bound(c,inverse(X_95)))),bind(X_33,$fot(a))]]) ).

cnf(refute_0_4710,plain,
    greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95))) = greatest_lower_bound(c,inverse(X_95)),
    inference(subst,[],[refute_0_801:[bind(X_32,$fot(inverse(X_95))),bind(X_33,$fot(c))]]) ).

cnf(refute_0_4711,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))))]]) ).

cnf(refute_0_4712,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95))))
    | greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95))) != greatest_lower_bound(c,inverse(X_95))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95))))) ),[1,1],$fot(greatest_lower_bound(c,inverse(X_95)))]]) ).

cnf(refute_0_4713,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95))) != greatest_lower_bound(c,inverse(X_95))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95))))) )],[refute_0_4711,refute_0_4712]) ).

cnf(refute_0_4714,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95))),greatest_lower_bound(c,inverse(X_95))) )],[refute_0_4710,refute_0_4713]) ).

cnf(refute_0_4715,plain,
    greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) = greatest_lower_bound(Y,greatest_lower_bound(a,greatest_lower_bound(c,X_295))),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(greatest_lower_bound(a,greatest_lower_bound(c,X_295))))]]) ).

cnf(refute_0_4716,plain,
    greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) = greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(a,c)),Z),
    inference(subst,[],[associativity_of_glb:[bind(Y,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4717,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(a,c)) != greatest_lower_bound(a,greatest_lower_bound(c,X))
    | greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) != greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(a,c)),Z)
    | greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)),greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(a,c)),Z)) ),[1,0],$fot(greatest_lower_bound(a,greatest_lower_bound(c,X)))]]) ).

cnf(refute_0_4718,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) != greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(a,c)),Z)
    | greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(a,c)),greatest_lower_bound(a,greatest_lower_bound(c,X))) )],[refute_0_4551,refute_0_4717]) ).

cnf(refute_0_4719,plain,
    greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)),greatest_lower_bound(greatest_lower_bound(X,greatest_lower_bound(a,c)),Z)) )],[refute_0_4716,refute_0_4718]) ).

cnf(refute_0_4720,plain,
    greatest_lower_bound(greatest_lower_bound(a,c),Z) = greatest_lower_bound(a,greatest_lower_bound(c,Z)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(a)),bind(Y,$fot(c))]]) ).

cnf(refute_0_4721,plain,
    greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) = greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)))]]) ).

cnf(refute_0_4722,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) != greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z))
    | greatest_lower_bound(greatest_lower_bound(a,c),Z) != greatest_lower_bound(a,greatest_lower_bound(c,Z))
    | greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) = greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)),greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z))) ),[1,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,Z)))]]) ).

cnf(refute_0_4723,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,c),Z) != greatest_lower_bound(a,greatest_lower_bound(c,Z))
    | greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) = greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)),greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z))) )],[refute_0_4721,refute_0_4722]) ).

cnf(refute_0_4724,plain,
    greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) = greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),Z),greatest_lower_bound(a,greatest_lower_bound(c,Z))) )],[refute_0_4720,refute_0_4723]) ).

cnf(refute_0_4725,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) != greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z)))
    | greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z)
    | greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z)) ),[0],$fot(greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))))]]) ).

cnf(refute_0_4726,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z)
    | greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)),greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z)))) )],[refute_0_4724,refute_0_4725]) ).

cnf(refute_0_4727,plain,
    greatest_lower_bound(greatest_lower_bound(c,X),Z) = greatest_lower_bound(c,greatest_lower_bound(X,Z)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(c)),bind(Y,$fot(X))]]) ).

cnf(refute_0_4728,plain,
    greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)))]]) ).

cnf(refute_0_4729,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z))
    | greatest_lower_bound(greatest_lower_bound(c,X),Z) != greatest_lower_bound(c,greatest_lower_bound(X,Z))
    | greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z))) ),[1,1],$fot(greatest_lower_bound(c,greatest_lower_bound(X,Z)))]]) ).

cnf(refute_0_4730,plain,
    ( greatest_lower_bound(greatest_lower_bound(c,X),Z) != greatest_lower_bound(c,greatest_lower_bound(X,Z))
    | greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z))) )],[refute_0_4728,refute_0_4729]) ).

cnf(refute_0_4731,plain,
    greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,X),Z),greatest_lower_bound(c,greatest_lower_bound(X,Z))) )],[refute_0_4727,refute_0_4730]) ).

cnf(refute_0_4732,plain,
    greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(a)),bind(Y,$fot(greatest_lower_bound(c,X)))]]) ).

cnf(refute_0_4733,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z)))))]]) ).

cnf(refute_0_4734,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z))) )],[refute_0_4732,refute_0_4733]) ).

cnf(refute_0_4735,plain,
    greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X),Z)),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z)))) )],[refute_0_4731,refute_0_4734]) ).

cnf(refute_0_4736,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z)
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z)))
    | greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z))]]) ).

cnf(refute_0_4737,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z)
    | greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z)))) )],[refute_0_4735,refute_0_4736]) ).

cnf(refute_0_4738,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z)
    | greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z)) )],[refute_0_4726,refute_0_4737]) ).

cnf(refute_0_4739,plain,
    greatest_lower_bound(X,greatest_lower_bound(a,greatest_lower_bound(c,Z))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X,Z))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(greatest_lower_bound(a,c),Z)),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X)),Z)) )],[refute_0_4719,refute_0_4738]) ).

cnf(refute_0_4740,plain,
    greatest_lower_bound(Y,greatest_lower_bound(a,greatest_lower_bound(c,X_295))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295))),
    inference(subst,[],[refute_0_4739:[bind(X,$fot(Y)),bind(Z,$fot(X_295))]]) ).

cnf(refute_0_4741,plain,
    ( greatest_lower_bound(Y,greatest_lower_bound(a,greatest_lower_bound(c,X_295))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) != greatest_lower_bound(Y,greatest_lower_bound(a,greatest_lower_bound(c,X_295)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y),greatest_lower_bound(Y,greatest_lower_bound(a,greatest_lower_bound(c,X_295)))) ),[1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295))))]]) ).

cnf(refute_0_4742,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) != greatest_lower_bound(Y,greatest_lower_bound(a,greatest_lower_bound(c,X_295)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(a,greatest_lower_bound(c,X_295))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295)))) )],[refute_0_4740,refute_0_4741]) ).

cnf(refute_0_4743,plain,
    greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y),greatest_lower_bound(Y,greatest_lower_bound(a,greatest_lower_bound(c,X_295)))) )],[refute_0_4715,refute_0_4742]) ).

cnf(refute_0_4744,plain,
    greatest_lower_bound(greatest_lower_bound(c,X_295),Y) = greatest_lower_bound(c,greatest_lower_bound(X_295,Y)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(c)),bind(Y,$fot(X_295)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_4745,plain,
    greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)))]]) ).

cnf(refute_0_4746,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y))
    | greatest_lower_bound(greatest_lower_bound(c,X_295),Y) != greatest_lower_bound(c,greatest_lower_bound(X_295,Y))
    | greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y))) ),[1,1],$fot(greatest_lower_bound(c,greatest_lower_bound(X_295,Y)))]]) ).

cnf(refute_0_4747,plain,
    ( greatest_lower_bound(greatest_lower_bound(c,X_295),Y) != greatest_lower_bound(c,greatest_lower_bound(X_295,Y))
    | greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y))) )],[refute_0_4745,refute_0_4746]) ).

cnf(refute_0_4748,plain,
    greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,X_295),Y),greatest_lower_bound(c,greatest_lower_bound(X_295,Y))) )],[refute_0_4744,refute_0_4747]) ).

cnf(refute_0_4749,plain,
    greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(a)),bind(Y,$fot(greatest_lower_bound(c,X_295))),bind(Z,$fot(Y))]]) ).

cnf(refute_0_4750,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y)))))]]) ).

cnf(refute_0_4751,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y))) )],[refute_0_4749,refute_0_4750]) ).

cnf(refute_0_4752,plain,
    greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,X_295),Y)),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y)))) )],[refute_0_4748,refute_0_4751]) ).

cnf(refute_0_4753,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y)))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295)))) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))))]]) ).

cnf(refute_0_4754,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295)))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y)))) )],[refute_0_4752,refute_0_4753]) ).

cnf(refute_0_4755,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,X_295)),Y),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295)))) )],[refute_0_4743,refute_0_4754]) ).

cnf(refute_0_4756,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295)))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295)))))]]) ).

cnf(refute_0_4757,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_295,Y))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Y,X_295)))) )],[refute_0_4755,refute_0_4756]) ).

cnf(refute_0_4758,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))),
    inference(subst,[],[refute_0_4757:[bind(Y,$fot(inverse(X_95))),bind(X_295,$fot(c))]]) ).

cnf(refute_0_4759,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95))))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))))]]) ).

cnf(refute_0_4760,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95))))) )],[refute_0_4758,refute_0_4759]) ).

cnf(refute_0_4761,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) )],[refute_0_4714,refute_0_4760]) ).

cnf(refute_0_4762,plain,
    least_upper_bound(greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) = greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))),
    inference(subst,[],[refute_0_4188:[bind(X_32,$fot(X_314)),bind(X_9,$fot(greatest_lower_bound(a,greatest_lower_bound(c,Z))))]]) ).

cnf(refute_0_4763,plain,
    greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),
    inference(subst,[],[refute_0_4739:[bind(X,$fot(X_314))]]) ).

cnf(refute_0_4764,plain,
    ( greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z)))
    | least_upper_bound(greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) != greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z)))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) = greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)),greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z)))) ),[0,0],$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))))]]) ).

cnf(refute_0_4765,plain,
    ( least_upper_bound(greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) != greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z)))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) = greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z)))) )],[refute_0_4763,refute_0_4764]) ).

cnf(refute_0_4766,plain,
    least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) = greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)),greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z)))) )],[refute_0_4762,refute_0_4765]) ).

cnf(refute_0_4767,plain,
    least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(X_315,greatest_lower_bound(a,greatest_lower_bound(c,Z)))) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),
    inference(subst,[],[refute_0_4188:[bind(X_32,$fot(greatest_lower_bound(a,greatest_lower_bound(c,Z)))),bind(X_9,$fot(X_315))]]) ).

cnf(refute_0_4768,plain,
    greatest_lower_bound(X_315,greatest_lower_bound(a,greatest_lower_bound(c,Z))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),
    inference(subst,[],[refute_0_4739:[bind(X,$fot(X_315))]]) ).

cnf(refute_0_4769,plain,
    ( greatest_lower_bound(X_315,greatest_lower_bound(a,greatest_lower_bound(c,Z))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))
    | least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(X_315,greatest_lower_bound(a,greatest_lower_bound(c,Z)))) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)
    | least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(X_315,greatest_lower_bound(a,greatest_lower_bound(c,Z)))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) ),[0,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))))]]) ).

cnf(refute_0_4770,plain,
    ( least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(X_315,greatest_lower_bound(a,greatest_lower_bound(c,Z)))) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)
    | least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_315,greatest_lower_bound(a,greatest_lower_bound(c,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) )],[refute_0_4768,refute_0_4769]) ).

cnf(refute_0_4771,plain,
    least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(X_315,greatest_lower_bound(a,greatest_lower_bound(c,Z)))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) )],[refute_0_4767,refute_0_4770]) ).

cnf(refute_0_4772,plain,
    greatest_lower_bound(greatest_lower_bound(c,Z),X_315) = greatest_lower_bound(c,greatest_lower_bound(Z,X_315)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(c)),bind(Y,$fot(Z)),bind(Z,$fot(X_315))]]) ).

cnf(refute_0_4773,plain,
    greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)))]]) ).

cnf(refute_0_4774,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315))
    | greatest_lower_bound(greatest_lower_bound(c,Z),X_315) != greatest_lower_bound(c,greatest_lower_bound(Z,X_315))
    | greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315))) ),[1,1],$fot(greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))]]) ).

cnf(refute_0_4775,plain,
    ( greatest_lower_bound(greatest_lower_bound(c,Z),X_315) != greatest_lower_bound(c,greatest_lower_bound(Z,X_315))
    | greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315))) )],[refute_0_4773,refute_0_4774]) ).

cnf(refute_0_4776,plain,
    greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,Z),X_315),greatest_lower_bound(c,greatest_lower_bound(Z,X_315))) )],[refute_0_4772,refute_0_4775]) ).

cnf(refute_0_4777,plain,
    greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(a)),bind(Y,$fot(greatest_lower_bound(c,Z))),bind(Z,$fot(X_315))]]) ).

cnf(refute_0_4778,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))))]]) ).

cnf(refute_0_4779,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315))) )],[refute_0_4777,refute_0_4778]) ).

cnf(refute_0_4780,plain,
    greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_315)),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) )],[refute_0_4776,refute_0_4779]) ).

cnf(refute_0_4781,plain,
    least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)),
    introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)))]]) ).

cnf(refute_0_4782,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) != least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)),least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315))) ),[1,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))))]]) ).

cnf(refute_0_4783,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)),least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315))) )],[refute_0_4781,refute_0_4782]) ).

cnf(refute_0_4784,plain,
    least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) )],[refute_0_4780,refute_0_4783]) ).

cnf(refute_0_4785,plain,
    least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315))),bind(X_17,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))))]]) ).

cnf(refute_0_4786,plain,
    ( least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) != least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))))
    | least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) != least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315))
    | least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)))),bind(Z0,$fot(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))))))]]) ).

cnf(refute_0_4787,plain,
    ( least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) != least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))))
    | least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))),least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315))) )],[refute_0_4785,refute_0_4786]) ).

cnf(refute_0_4788,plain,
    least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)),least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))))) )],[refute_0_4784,refute_0_4787]) ).

cnf(refute_0_4789,plain,
    ( least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)
    | least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) != least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) ),[0],$fot(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))))]]) ).

cnf(refute_0_4790,plain,
    ( least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) = greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))),least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))))) )],[refute_0_4788,refute_0_4789]) ).

cnf(refute_0_4791,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) ),[1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))))]]) ).

cnf(refute_0_4792,plain,
    ( least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) )],[refute_0_4780,refute_0_4791]) ).

cnf(refute_0_4793,plain,
    ( least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))) != greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) )],[refute_0_4790,refute_0_4792]) ).

cnf(refute_0_4794,plain,
    least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315)))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_315))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_315,Z)))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_315)) )],[refute_0_4771,refute_0_4793]) ).

cnf(refute_0_4795,plain,
    least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))),
    inference(subst,[],[refute_0_4794:[bind(X_315,$fot(X_314))]]) ).

cnf(refute_0_4796,plain,
    greatest_lower_bound(greatest_lower_bound(c,Z),X_314) = greatest_lower_bound(c,greatest_lower_bound(Z,X_314)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(c)),bind(Y,$fot(Z)),bind(Z,$fot(X_314))]]) ).

cnf(refute_0_4797,plain,
    greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)))]]) ).

cnf(refute_0_4798,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314))
    | greatest_lower_bound(greatest_lower_bound(c,Z),X_314) != greatest_lower_bound(c,greatest_lower_bound(Z,X_314))
    | greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314))) ),[1,1],$fot(greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))]]) ).

cnf(refute_0_4799,plain,
    ( greatest_lower_bound(greatest_lower_bound(c,Z),X_314) != greatest_lower_bound(c,greatest_lower_bound(Z,X_314))
    | greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314))) )],[refute_0_4797,refute_0_4798]) ).

cnf(refute_0_4800,plain,
    greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(c,Z),X_314),greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) )],[refute_0_4796,refute_0_4799]) ).

cnf(refute_0_4801,plain,
    greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314) = greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(a)),bind(Y,$fot(greatest_lower_bound(c,Z))),bind(Z,$fot(X_314))]]) ).

cnf(refute_0_4802,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314) != greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))))]]) ).

cnf(refute_0_4803,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))
    | greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314),greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314))) )],[refute_0_4801,refute_0_4802]) ).

cnf(refute_0_4804,plain,
    greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(c,Z),X_314)),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))) )],[refute_0_4800,refute_0_4803]) ).

cnf(refute_0_4805,plain,
    least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)),
    introduced(tautology,[refl,[$fot(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)))]]) ).

cnf(refute_0_4806,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) != least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)),least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314))) ),[1,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))))]]) ).

cnf(refute_0_4807,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)),least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314))) )],[refute_0_4805,refute_0_4806]) ).

cnf(refute_0_4808,plain,
    least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) = least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))) )],[refute_0_4804,refute_0_4807]) ).

cnf(refute_0_4809,plain,
    ( least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) != least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))))]]) ).

cnf(refute_0_4810,plain,
    ( least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)),least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))))) )],[refute_0_4808,refute_0_4809]) ).

cnf(refute_0_4811,plain,
    least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))) )],[refute_0_4795,refute_0_4810]) ).

cnf(refute_0_4812,plain,
    ( least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) != greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z)))
    | least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) = greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)),greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z)))) ),[0],$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))))]]) ).

cnf(refute_0_4813,plain,
    ( least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)) != greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z)))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) = greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314)))) )],[refute_0_4811,refute_0_4812]) ).

cnf(refute_0_4814,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) = greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(X_314,Z))),greatest_lower_bound(greatest_lower_bound(a,greatest_lower_bound(c,Z)),X_314)),greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z)))) )],[refute_0_4766,refute_0_4813]) ).

cnf(refute_0_4815,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) != greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z)))
    | greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))))),bind(Y0,$fot(greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z)))))]]) ).

cnf(refute_0_4816,plain,
    greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(Z,X_314))),greatest_lower_bound(X_314,greatest_lower_bound(a,greatest_lower_bound(c,Z)))) )],[refute_0_4814,refute_0_4815]) ).

cnf(refute_0_4817,plain,
    greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))),
    inference(subst,[],[refute_0_4816:[bind(Z,$fot(inverse(X_95))),bind(X_314,$fot(c))]]) ).

cnf(refute_0_4818,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c)))
    | greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))))]]) ).

cnf(refute_0_4819,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c)))) )],[refute_0_4817,refute_0_4818]) ).

cnf(refute_0_4820,plain,
    greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(X_95),c))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) )],[refute_0_4761,refute_0_4819]) ).

cnf(refute_0_4821,plain,
    greatest_lower_bound(greatest_lower_bound(a,c),inverse(X_95)) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))),
    inference(subst,[],[refute_0_790:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(inverse(X_95)))]]) ).

cnf(refute_0_4822,plain,
    inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)) = greatest_lower_bound(greatest_lower_bound(a,c),inverse(X_95)),
    inference(subst,[],[refute_0_101:[bind(Y,$fot(X_95)),bind(X_89,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4823,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,c),inverse(X_95)) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)) != greatest_lower_bound(greatest_lower_bound(a,c),inverse(X_95))
    | inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(a,c),inverse(X_95)))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))))]]) ).

cnf(refute_0_4824,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,c),inverse(X_95)) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)),greatest_lower_bound(greatest_lower_bound(a,c),inverse(X_95))) )],[refute_0_4822,refute_0_4823]) ).

cnf(refute_0_4825,plain,
    inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),inverse(X_95)),greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) )],[refute_0_4821,refute_0_4824]) ).

cnf(refute_0_4826,plain,
    greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))) = greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))]]) ).

cnf(refute_0_4827,plain,
    ( greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))) != greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))
    | inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))),greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) ),[1,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))]]) ).

cnf(refute_0_4828,plain,
    ( inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))),greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) )],[refute_0_4826,refute_0_4827]) ).

cnf(refute_0_4829,plain,
    greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))) = greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)),greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) )],[refute_0_4825,refute_0_4828]) ).

cnf(refute_0_4830,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))) != greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))
    | greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),bind(Y0,$fot(greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))))]]) ).

cnf(refute_0_4831,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))),greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))) )],[refute_0_4829,refute_0_4830]) ).

cnf(refute_0_4832,plain,
    greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) )],[refute_0_4820,refute_0_4831]) ).

cnf(refute_0_4833,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))))]]) ).

cnf(refute_0_4834,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))
    | greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))) ),[1,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))]]) ).

cnf(refute_0_4835,plain,
    ( greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))) )],[refute_0_4833,refute_0_4834]) ).

cnf(refute_0_4836,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) = greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) )],[refute_0_4832,refute_0_4835]) ).

cnf(refute_0_4837,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) != greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))
    | greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))))]]) ).

cnf(refute_0_4838,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))),greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))) )],[refute_0_4836,refute_0_4837]) ).

cnf(refute_0_4839,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) )],[refute_0_4709,refute_0_4838]) ).

cnf(refute_0_4840,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))))]]) ).

cnf(refute_0_4841,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))) != inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))))) ),[1,0],$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))]]) ).

cnf(refute_0_4842,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))))) )],[refute_0_4840,refute_0_4841]) ).

cnf(refute_0_4843,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95)))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) )],[refute_0_4839,refute_0_4842]) ).

cnf(refute_0_4844,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))))]]) ).

cnf(refute_0_4845,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))) != inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))) ),[1,0],$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))))]]) ).

cnf(refute_0_4846,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))) != inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))) )],[refute_0_4844,refute_0_4845]) ).

cnf(refute_0_4847,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))) )],[refute_0_4843,refute_0_4846]) ).

cnf(refute_0_4848,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity)
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity)))]]) ).

cnf(refute_0_4849,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity)
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))) )],[refute_0_4847,refute_0_4848]) ).

cnf(refute_0_4850,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity)) )],[refute_0_4708,refute_0_4849]) ).

cnf(refute_0_4851,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity) != inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity)
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))))]]) ).

cnf(refute_0_4852,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity) != inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity)) )],[refute_0_4850,refute_0_4851]) ).

cnf(refute_0_4853,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),identity),inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))) )],[refute_0_4703,refute_0_4852]) ).

cnf(refute_0_4854,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))) != inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))
    | least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))
    | least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))) ),[1],$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))))]]) ).

cnf(refute_0_4855,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))
    | least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95)))),inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))) )],[refute_0_4853,refute_0_4854]) ).

cnf(refute_0_4856,plain,
    least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) = inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))))),greatest_lower_bound(identity,least_upper_bound(identity,multiply(greatest_lower_bound(a,c),X_95))))) )],[refute_0_4702,refute_0_4855]) ).

cnf(refute_0_4857,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) != inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) = least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95))),bind(Y0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))))]]) ).

cnf(refute_0_4858,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95)))) = least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,c)),X_95),inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(X_95))))) )],[refute_0_4856,refute_0_4857]) ).

cnf(refute_0_4859,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) = least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_4858:[bind(X_95,$fot(least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_4860,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) != least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c)))
    | least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4861,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c)))) )],[refute_0_4859,refute_0_4860]) ).

cnf(refute_0_4862,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(a,c)),least_upper_bound(identity,greatest_lower_bound(a,c))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_4697,refute_0_4861]) ).

cnf(refute_0_4863,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))),
    introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))))]]) ).

cnf(refute_0_4864,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) = multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) ),[1,0],$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_4865,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) = multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) )],[refute_0_4863,refute_0_4864]) ).

cnf(refute_0_4866,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) = multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_4862,refute_0_4865]) ).

cnf(refute_0_4867,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,greatest_lower_bound(a,c))) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))),
    inference(subst,[],[refute_0_1518:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(X_231,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_4868,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_4221:[bind(X,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4869,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,greatest_lower_bound(a,c)))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,greatest_lower_bound(a,c))) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,greatest_lower_bound(a,c))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))))]]) ).

cnf(refute_0_4870,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,greatest_lower_bound(a,c))) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,greatest_lower_bound(a,c)))) )],[refute_0_4868,refute_0_4869]) ).

cnf(refute_0_4871,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) = multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,greatest_lower_bound(a,c))),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) )],[refute_0_4867,refute_0_4870]) ).

cnf(refute_0_4872,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) != multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) = multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))))]]) ).

cnf(refute_0_4873,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) != multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))
    | multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) = multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) )],[refute_0_4871,refute_0_4872]) ).

cnf(refute_0_4874,plain,
    multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) = multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(a,greatest_lower_bound(c,identity))),multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) )],[refute_0_4866,refute_0_4873]) ).

cnf(refute_0_4875,plain,
    ( multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)) != multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))
    | least_upper_bound(identity,greatest_lower_bound(a,c)) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity))
    | least_upper_bound(identity,greatest_lower_bound(a,c)) = multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity))) ),[1],$fot(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))))]]) ).

cnf(refute_0_4876,plain,
    ( least_upper_bound(identity,greatest_lower_bound(a,c)) != multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity))
    | least_upper_bound(identity,greatest_lower_bound(a,c)) = multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity)),multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) )],[refute_0_4874,refute_0_4875]) ).

cnf(refute_0_4877,plain,
    least_upper_bound(identity,greatest_lower_bound(a,c)) = multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(inverse(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(greatest_lower_bound(a,c),identity))) )],[refute_0_4630,refute_0_4876]) ).

cnf(refute_0_4878,plain,
    ( least_upper_bound(identity,greatest_lower_bound(a,c)) != multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))
    | multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) = least_upper_bound(identity,greatest_lower_bound(a,c)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))))]]) ).

cnf(refute_0_4879,plain,
    multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) = least_upper_bound(identity,greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,c)),multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) )],[refute_0_4877,refute_0_4878]) ).

cnf(refute_0_4880,plain,
    ( multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))))) != inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))
    | multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))) != least_upper_bound(identity,greatest_lower_bound(a,c))
    | multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) = inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))))),inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))) ),[0,1,0],$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4881,plain,
    ( multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))))) != inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))
    | multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) = inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))),least_upper_bound(identity,greatest_lower_bound(a,c))) )],[refute_0_4879,refute_0_4880]) ).

cnf(refute_0_4882,plain,
    multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) = inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,identity))))),inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))) )],[refute_0_4462,refute_0_4881]) ).

cnf(refute_0_4883,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,c))),
    inference(subst,[],[refute_0_500:[bind(Y,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4884,plain,
    greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_4885,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))
    | greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))
    | greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))) ),[1,1],$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_4886,plain,
    ( greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))
    | greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))) )],[refute_0_4884,refute_0_4885]) ).

cnf(refute_0_4887,plain,
    greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) )],[refute_0_4883,refute_0_4886]) ).

cnf(refute_0_4888,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4889,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))))
    | greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))))) ),[1,1],$fot(greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_4890,plain,
    ( greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_4888,refute_0_4889]) ).

cnf(refute_0_4891,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) )],[refute_0_4887,refute_0_4890]) ).

cnf(refute_0_4892,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_4757:[bind(Y,$fot(inverse(greatest_lower_bound(a,c)))),bind(X_295,$fot(identity))]]) ).

cnf(refute_0_4893,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_4894,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_4892,refute_0_4893]) ).

cnf(refute_0_4895,plain,
    greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(identity,inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4891,refute_0_4894]) ).

cnf(refute_0_4896,plain,
    greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))),
    inference(subst,[],[refute_0_4816:[bind(Z,$fot(inverse(greatest_lower_bound(a,c)))),bind(X_314,$fot(identity))]]) ).

cnf(refute_0_4897,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity)))
    | greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_4898,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity)))) )],[refute_0_4896,refute_0_4897]) ).

cnf(refute_0_4899,plain,
    greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(inverse(greatest_lower_bound(a,c)),identity))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4895,refute_0_4898]) ).

cnf(refute_0_4900,plain,
    greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_790:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_4901,plain,
    greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_4902,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))
    | greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) ),[1,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_4903,plain,
    ( greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))
    | greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_4901,refute_0_4902]) ).

cnf(refute_0_4904,plain,
    greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_4900,refute_0_4903]) ).

cnf(refute_0_4905,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c)))))
    | greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_4906,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c)))))) )],[refute_0_4904,refute_0_4905]) ).

cnf(refute_0_4907,plain,
    greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4899,refute_0_4906]) ).

cnf(refute_0_4908,plain,
    inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_303))))),
    inference(subst,[],[refute_0_1547:[bind(X_14,$fot(inverse(greatest_lower_bound(identity,X_303))))]]) ).

cnf(refute_0_4909,plain,
    least_upper_bound(X_82,least_upper_bound(identity,inverse(Y))) = least_upper_bound(identity,least_upper_bound(X_82,inverse(Y))),
    inference(subst,[],[refute_0_1102:[bind(Y,$fot(X_82)),bind(X_43,$fot(identity)),bind(X_45,$fot(inverse(Y)))]]) ).

cnf(refute_0_4910,plain,
    ( least_upper_bound(X_82,least_upper_bound(identity,inverse(Y))) != least_upper_bound(identity,least_upper_bound(X_82,inverse(Y)))
    | least_upper_bound(identity,inverse(Y)) != inverse(greatest_lower_bound(identity,Y))
    | least_upper_bound(X_82,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(identity,least_upper_bound(X_82,inverse(Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_82,least_upper_bound(identity,inverse(Y))),least_upper_bound(identity,least_upper_bound(X_82,inverse(Y)))) ),[0,1],$fot(inverse(greatest_lower_bound(identity,Y)))]]) ).

cnf(refute_0_4911,plain,
    ( least_upper_bound(X_82,least_upper_bound(identity,inverse(Y))) != least_upper_bound(identity,least_upper_bound(X_82,inverse(Y)))
    | least_upper_bound(X_82,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(identity,least_upper_bound(X_82,inverse(Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(Y)),inverse(greatest_lower_bound(identity,Y))) )],[refute_0_488,refute_0_4910]) ).

cnf(refute_0_4912,plain,
    least_upper_bound(X_82,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(identity,least_upper_bound(X_82,inverse(Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_82,least_upper_bound(identity,inverse(Y))),least_upper_bound(identity,least_upper_bound(X_82,inverse(Y)))) )],[refute_0_4909,refute_0_4911]) ).

cnf(refute_0_4913,plain,
    least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_303))) = least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))),
    inference(subst,[],[refute_0_4912:[bind(Y,$fot(X_303)),bind(X_82,$fot(X_15))]]) ).

cnf(refute_0_4914,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) != inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_303)))))
    | least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_303))) != least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) = inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))),inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_303)))))) ),[1,0,1],$fot(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))]]) ).

cnf(refute_0_4915,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) != inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_303)))))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) = inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_303))),least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) )],[refute_0_4913,refute_0_4914]) ).

cnf(refute_0_4916,plain,
    inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) = inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))),inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(greatest_lower_bound(identity,X_303)))))) )],[refute_0_4908,refute_0_4915]) ).

cnf(refute_0_4917,plain,
    greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))) = greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))),
    inference(subst,[],[refute_0_801:[bind(X_32,$fot(greatest_lower_bound(X_303,inverse(X_15)))),bind(X_33,$fot(identity))]]) ).

cnf(refute_0_4918,plain,
    greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77)),
    inference(subst,[],[associativity_of_glb:[bind(Z,$fot(greatest_lower_bound(X_76,X_77)))]]) ).

cnf(refute_0_4919,plain,
    greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77)) = greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y)),
    inference(subst,[],[refute_0_839:[bind(X,$fot(Y)),bind(X_36,$fot(X_76)),bind(X_37,$fot(X_77))]]) ).

cnf(refute_0_4920,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77))
    | greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77)) != greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))
    | greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77))) ),[0,1],$fot(greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y)))]]) ).

cnf(refute_0_4921,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77))
    | greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77)),greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))) )],[refute_0_4919,refute_0_4920]) ).

cnf(refute_0_4922,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))) = greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77))) )],[refute_0_4918,refute_0_4921]) ).

cnf(refute_0_4923,plain,
    greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77)) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77))),
    inference(subst,[],[refute_0_790:[bind(Z,$fot(greatest_lower_bound(X_76,X_77)))]]) ).

cnf(refute_0_4924,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77))
    | greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77)) != greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77)))
    | greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))),greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77)))]]) ).

cnf(refute_0_4925,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))) != greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77))
    | greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77)),greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77)))) )],[refute_0_4923,refute_0_4924]) ).

cnf(refute_0_4926,plain,
    greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))) = greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))),greatest_lower_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X_76,X_77))) )],[refute_0_4922,refute_0_4925]) ).

cnf(refute_0_4927,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))) != greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77)))
    | greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77))) = greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77)))))]]) ).

cnf(refute_0_4928,plain,
    greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77))) = greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_76,greatest_lower_bound(X_77,Y))),greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X_76,X_77)))) )],[refute_0_4926,refute_0_4927]) ).

cnf(refute_0_4929,plain,
    greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))) = greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))),
    inference(subst,[],[refute_0_4928:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_15))),bind(X_76,$fot(identity)),bind(X_77,$fot(X_303))]]) ).

cnf(refute_0_4930,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))) != greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))) != greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))) = greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))))]]) ).

cnf(refute_0_4931,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))) != greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))) = greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))),greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))))) )],[refute_0_4929,refute_0_4930]) ).

cnf(refute_0_4932,plain,
    greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))) = greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))),greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))) )],[refute_0_4917,refute_0_4931]) ).

cnf(refute_0_4933,plain,
    inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))),
    inference(subst,[],[refute_0_2148:[bind(X_272,$fot(greatest_lower_bound(identity,X_303)))]]) ).

cnf(refute_0_4934,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))) != greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303)))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) = greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))))),bind(Z0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))))]]) ).

cnf(refute_0_4935,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))) != greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) = greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303)))) )],[refute_0_4933,refute_0_4934]) ).

cnf(refute_0_4936,plain,
    inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) = greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_15),greatest_lower_bound(identity,X_303))),greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))) )],[refute_0_4932,refute_0_4935]) ).

cnf(refute_0_4937,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) != greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))
    | inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) != inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))))
    | greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) = inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))),inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))))]]) ).

cnf(refute_0_4938,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) != inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))))
    | greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) = inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))),greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15)))) )],[refute_0_4936,refute_0_4937]) ).

cnf(refute_0_4939,plain,
    least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) = least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(least_upper_bound(X_15,inverse(X_303)))),bind(X_31,$fot(identity))]]) ).

cnf(refute_0_4940,plain,
    inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) = inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))))]]) ).

cnf(refute_0_4941,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) != inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))))
    | least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) != least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))
    | inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))),inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))))) ),[1,0],$fot(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))]]) ).

cnf(refute_0_4942,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) != least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))
    | inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))),inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))))) )],[refute_0_4940,refute_0_4941]) ).

cnf(refute_0_4943,plain,
    inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))),least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) )],[refute_0_4939,refute_0_4942]) ).

cnf(refute_0_4944,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) != inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))))
    | inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) != inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))
    | greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))),inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) ),[0],$fot(inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))))]]) ).

cnf(refute_0_4945,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) != inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))))
    | greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))),inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) )],[refute_0_4943,refute_0_4944]) ).

cnf(refute_0_4946,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))) != inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))))
    | greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))),inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))))) )],[refute_0_4938,refute_0_4945]) ).

cnf(refute_0_4947,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) = inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(identity,X_303)),X_15))),inverse(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))))) )],[refute_0_4916,refute_0_4946]) ).

cnf(refute_0_4948,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) != inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))
    | inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) = greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))))),bind(Y0,$fot(inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))))]]) ).

cnf(refute_0_4949,plain,
    inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303)))) = greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_303,inverse(X_15))),inverse(least_upper_bound(identity,least_upper_bound(X_15,inverse(X_303))))) )],[refute_0_4947,refute_0_4948]) ).

cnf(refute_0_4950,plain,
    inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),
    inference(subst,[],[refute_0_4949:[bind(X_15,$fot(greatest_lower_bound(a,c))),bind(X_303,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4951,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))),bind(Z0,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_4952,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) )],[refute_0_4950,refute_0_4951]) ).

cnf(refute_0_4953,plain,
    inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4907,refute_0_4952]) ).

cnf(refute_0_4954,plain,
    ( multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) != inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))
    | inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),[0],$fot(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4955,plain,
    ( multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) != inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))
    | multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c))))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4953,refute_0_4954]) ).

cnf(refute_0_4956,plain,
    multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) = greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(a,c)))))) )],[refute_0_4882,refute_0_4955]) ).

cnf(refute_0_4957,plain,
    ( multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))) != greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != identity
    | multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),identity) ),[0,1,0,0,1],$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4958,plain,
    ( multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != identity
    | multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))),greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4956,refute_0_4957]) ).

cnf(refute_0_4959,plain,
    multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = identity,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,greatest_lower_bound(c,identity)),inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),identity) )],[refute_0_4461,refute_0_4958]) ).

cnf(refute_0_4960,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))),bind(X_59,$fot(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_4961,plain,
    least_upper_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) = greatest_lower_bound(X_36,X_37),
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(greatest_lower_bound(X_36,X_37)))]]) ).

cnf(refute_0_4962,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))
    | least_upper_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) != greatest_lower_bound(X_36,X_37)
    | least_upper_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) = greatest_lower_bound(X_36,X_37) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),greatest_lower_bound(X_36,X_37)) ),[0,1],$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))]]) ).

cnf(refute_0_4963,plain,
    ( least_upper_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) != greatest_lower_bound(X_36,X_37)
    | least_upper_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) = greatest_lower_bound(X_36,X_37) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y),greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) )],[refute_0_880,refute_0_4962]) ).

cnf(refute_0_4964,plain,
    least_upper_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) = greatest_lower_bound(X_36,X_37),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),greatest_lower_bound(X_36,X_37)) )],[refute_0_4961,refute_0_4963]) ).

cnf(refute_0_4965,plain,
    least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity))) = greatest_lower_bound(a,c),
    inference(subst,[],[refute_0_4964:[bind(Y,$fot(identity)),bind(X_36,$fot(a)),bind(X_37,$fot(c))]]) ).

cnf(refute_0_4966,plain,
    least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))))]]) ).

cnf(refute_0_4967,plain,
    ( least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity))) != greatest_lower_bound(a,c)
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity))))
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) = least_upper_bound(identity,greatest_lower_bound(a,c)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity))))) ),[1,1],$fot(greatest_lower_bound(a,c))]]) ).

cnf(refute_0_4968,plain,
    ( least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity))) != greatest_lower_bound(a,c)
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) = least_upper_bound(identity,greatest_lower_bound(a,c)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity))))) )],[refute_0_4966,refute_0_4967]) ).

cnf(refute_0_4969,plain,
    least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) = least_upper_bound(identity,greatest_lower_bound(a,c)),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity))),greatest_lower_bound(a,c)) )],[refute_0_4965,refute_0_4968]) ).

cnf(refute_0_4970,plain,
    multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))))]]) ).

cnf(refute_0_4971,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) != least_upper_bound(identity,greatest_lower_bound(a,c))
    | multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),[1,0],$fot(least_upper_bound(identity,greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4972,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))) != least_upper_bound(identity,greatest_lower_bound(a,c))
    | multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4970,refute_0_4971]) ).

cnf(refute_0_4973,plain,
    multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),least_upper_bound(identity,greatest_lower_bound(a,c))) )],[refute_0_4969,refute_0_4972]) ).

cnf(refute_0_4974,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))
    | multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Y0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))]]) ).

cnf(refute_0_4975,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))
    | multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4973,refute_0_4974]) ).

cnf(refute_0_4976,plain,
    multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,c)),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) )],[refute_0_4960,refute_0_4975]) ).

cnf(refute_0_4977,plain,
    multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X)),
    inference(subst,[],[monotony_lub2:[bind(Z,$fot(least_upper_bound(X_318,X_319)))]]) ).

cnf(refute_0_4978,plain,
    least_upper_bound(Y,least_upper_bound(X_318,X_319)) = least_upper_bound(X_318,least_upper_bound(X_319,Y)),
    inference(subst,[],[refute_0_3111:[bind(X,$fot(Y)),bind(Y,$fot(X_318)),bind(X_145,$fot(X_319))]]) ).

cnf(refute_0_4979,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X))
    | least_upper_bound(Y,least_upper_bound(X_318,X_319)) != least_upper_bound(X_318,least_upper_bound(X_319,Y))
    | multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X))) ),[0,0],$fot(least_upper_bound(X_318,least_upper_bound(X_319,Y)))]]) ).

cnf(refute_0_4980,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X))
    | multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_318,X_319)),least_upper_bound(X_318,least_upper_bound(X_319,Y))) )],[refute_0_4978,refute_0_4979]) ).

cnf(refute_0_4981,plain,
    multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X))) )],[refute_0_4977,refute_0_4980]) ).

cnf(refute_0_4982,plain,
    least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X)) = multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X),
    inference(subst,[],[refute_0_384:[bind(Z,$fot(least_upper_bound(X_318,X_319)))]]) ).

cnf(refute_0_4983,plain,
    ( multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X))
    | least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X)) != multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X)
    | multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X) = multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X),multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X)) ),[0],$fot(least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X)))]]) ).

cnf(refute_0_4984,plain,
    ( multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X))
    | multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X) = multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X)),multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X)) )],[refute_0_4982,refute_0_4983]) ).

cnf(refute_0_4985,plain,
    multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X) = multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(X_318,X_319),X))) )],[refute_0_4981,refute_0_4984]) ).

cnf(refute_0_4986,plain,
    ( multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X) != multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X)
    | multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X) = multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X))),bind(Y0,$fot(multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X)))]]) ).

cnf(refute_0_4987,plain,
    multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X) = multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_318,least_upper_bound(X_319,Y)),X),multiply(least_upper_bound(Y,least_upper_bound(X_318,X_319)),X)) )],[refute_0_4985,refute_0_4986]) ).

cnf(refute_0_4988,plain,
    multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),
    inference(subst,[],[refute_0_4987:[bind(X,$fot(inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c)))))),bind(Y,$fot(greatest_lower_bound(a,greatest_lower_bound(c,identity)))),bind(X_318,$fot(identity)),bind(X_319,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_4989,plain,
    ( multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c)))))
    | multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))
    | multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))]]) ).

cnf(refute_0_4990,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))
    | multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c)))))) )],[refute_0_4988,refute_0_4989]) ).

cnf(refute_0_4991,plain,
    multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) = inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,greatest_lower_bound(c,identity)))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) )],[refute_0_4976,refute_0_4990]) ).

cnf(refute_0_4992,plain,
    ( multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != identity
    | multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),identity) ),[0],$fot(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_4993,plain,
    ( multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))) != identity
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) )],[refute_0_4991,refute_0_4992]) ).

cnf(refute_0_4994,plain,
    inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) = identity,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,identity)),least_upper_bound(identity,greatest_lower_bound(a,c))),inverse(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),least_upper_bound(identity,greatest_lower_bound(a,c))))),identity) )],[refute_0_4959,refute_0_4993]) ).

cnf(refute_0_4995,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) != least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) != identity
    | multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = least_upper_bound(identity,multiply(X_99,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))) ),[1,1,1],$fot(identity)]]) ).

cnf(refute_0_4996,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) != least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))
    | multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = least_upper_bound(identity,multiply(X_99,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),identity) )],[refute_0_4994,refute_0_4995]) ).

cnf(refute_0_4997,plain,
    multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = least_upper_bound(identity,multiply(X_99,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),least_upper_bound(identity,multiply(X_99,inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))) )],[refute_0_4410,refute_0_4996]) ).

cnf(refute_0_4998,plain,
    multiply(least_upper_bound(X_99,identity),identity) = least_upper_bound(X_99,identity),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(least_upper_bound(X_99,identity)))]]) ).

cnf(refute_0_4999,plain,
    least_upper_bound(identity,multiply(X_99,identity)) = multiply(least_upper_bound(X_99,identity),identity),
    inference(subst,[],[refute_0_730:[bind(X_110,$fot(identity)),bind(X_111,$fot(X_99))]]) ).

cnf(refute_0_5000,plain,
    ( multiply(least_upper_bound(X_99,identity),identity) != least_upper_bound(X_99,identity)
    | least_upper_bound(identity,multiply(X_99,identity)) != multiply(least_upper_bound(X_99,identity),identity)
    | least_upper_bound(identity,multiply(X_99,identity)) = least_upper_bound(X_99,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(X_99,identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_99,identity),identity))),bind(Z0,$fot(least_upper_bound(X_99,identity)))]]) ).

cnf(refute_0_5001,plain,
    ( multiply(least_upper_bound(X_99,identity),identity) != least_upper_bound(X_99,identity)
    | least_upper_bound(identity,multiply(X_99,identity)) = least_upper_bound(X_99,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_99,identity)),multiply(least_upper_bound(X_99,identity),identity)) )],[refute_0_4999,refute_0_5000]) ).

cnf(refute_0_5002,plain,
    least_upper_bound(identity,multiply(X_99,identity)) = least_upper_bound(X_99,identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_99,identity),identity),least_upper_bound(X_99,identity)) )],[refute_0_4998,refute_0_5001]) ).

cnf(refute_0_5003,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) != least_upper_bound(identity,multiply(X_99,identity))
    | least_upper_bound(identity,multiply(X_99,identity)) != least_upper_bound(X_99,identity)
    | multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = least_upper_bound(X_99,identity) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),least_upper_bound(X_99,identity)) ),[0],$fot(least_upper_bound(identity,multiply(X_99,identity)))]]) ).

cnf(refute_0_5004,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) != least_upper_bound(identity,multiply(X_99,identity))
    | multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = least_upper_bound(X_99,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_99,identity)),least_upper_bound(X_99,identity)) )],[refute_0_5002,refute_0_5003]) ).

cnf(refute_0_5005,plain,
    multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = least_upper_bound(X_99,identity),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),least_upper_bound(identity,multiply(X_99,identity))) )],[refute_0_4997,refute_0_5004]) ).

cnf(refute_0_5006,plain,
    multiply(X_99,inverse(greatest_lower_bound(X_99,identity))) = least_upper_bound(identity,X_99),
    inference(subst,[],[refute_0_3143:[bind(X_98,$fot(X_99))]]) ).

cnf(refute_0_5007,plain,
    multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) = inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),
    inference(subst,[],[refute_0_1864:[bind(X_103,$fot(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_5008,plain,
    ( multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) != inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) != identity
    | multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) = inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)),inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_5009,plain,
    ( multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) != inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))
    | multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) = inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),identity) )],[refute_0_4994,refute_0_5008]) ).

cnf(refute_0_5010,plain,
    multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) = inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)),inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) )],[refute_0_5007,refute_0_5009]) ).

cnf(refute_0_5011,plain,
    least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) = least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),
    inference(subst,[],[refute_0_433:[bind(X_30,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),bind(X_31,$fot(identity))]]) ).

cnf(refute_0_5012,plain,
    multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))]]) ).

cnf(refute_0_5013,plain,
    ( multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) != least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))
    | least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) != least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))
    | multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),bind(Z0,$fot(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_5014,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) != least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))
    | multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) )],[refute_0_5012,refute_0_5013]) ).

cnf(refute_0_5015,plain,
    multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) )],[refute_0_5011,refute_0_5014]) ).

cnf(refute_0_5016,plain,
    greatest_lower_bound(least_upper_bound(X_30,X_11),least_upper_bound(X_11,least_upper_bound(X_30,X_11))) = least_upper_bound(X_30,X_11),
    inference(subst,[],[refute_0_215:[bind(X_10,$fot(least_upper_bound(X_30,X_11)))]]) ).

cnf(refute_0_5017,plain,
    least_upper_bound(X_11,least_upper_bound(X_30,X_11)) = least_upper_bound(X_11,X_30),
    inference(subst,[],[refute_0_426:[bind(Y,$fot(X_30)),bind(X_21,$fot(X_11))]]) ).

cnf(refute_0_5018,plain,
    ( greatest_lower_bound(least_upper_bound(X_30,X_11),least_upper_bound(X_11,least_upper_bound(X_30,X_11))) != least_upper_bound(X_30,X_11)
    | least_upper_bound(X_11,least_upper_bound(X_30,X_11)) != least_upper_bound(X_11,X_30)
    | greatest_lower_bound(least_upper_bound(X_30,X_11),least_upper_bound(X_11,X_30)) = least_upper_bound(X_30,X_11) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_30,X_11),least_upper_bound(X_11,least_upper_bound(X_30,X_11))),least_upper_bound(X_30,X_11)) ),[0,1],$fot(least_upper_bound(X_11,X_30))]]) ).

cnf(refute_0_5019,plain,
    ( greatest_lower_bound(least_upper_bound(X_30,X_11),least_upper_bound(X_11,least_upper_bound(X_30,X_11))) != least_upper_bound(X_30,X_11)
    | greatest_lower_bound(least_upper_bound(X_30,X_11),least_upper_bound(X_11,X_30)) = least_upper_bound(X_30,X_11) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,least_upper_bound(X_30,X_11)),least_upper_bound(X_11,X_30)) )],[refute_0_5017,refute_0_5018]) ).

cnf(refute_0_5020,plain,
    greatest_lower_bound(least_upper_bound(X_30,X_11),least_upper_bound(X_11,X_30)) = least_upper_bound(X_30,X_11),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_30,X_11),least_upper_bound(X_11,least_upper_bound(X_30,X_11))),least_upper_bound(X_30,X_11)) )],[refute_0_5016,refute_0_5019]) ).

cnf(refute_0_5021,plain,
    greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
    inference(subst,[],[refute_0_5020:[bind(X_11,$fot(multiply(X,Y))),bind(X_30,$fot(multiply(X,Z)))]]) ).

cnf(refute_0_5022,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | least_upper_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).

cnf(refute_0_5023,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,Z)),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_540,refute_0_5022]) ).

cnf(refute_0_5024,plain,
    greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_5021,refute_0_5023]) ).

cnf(refute_0_5025,plain,
    greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) = least_upper_bound(Y,Z),
    inference(subst,[],[refute_0_5020:[bind(X_11,$fot(Z)),bind(X_30,$fot(Y))]]) ).

cnf(refute_0_5026,plain,
    multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
    introduced(tautology,[refl,[$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))]]) ).

cnf(refute_0_5027,plain,
    ( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
    | greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
    | multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) ),[1,1],$fot(least_upper_bound(Y,Z))]]) ).

cnf(refute_0_5028,plain,
    ( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
    | multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_5026,refute_0_5027]) ).

cnf(refute_0_5029,plain,
    multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_5025,refute_0_5028]) ).

cnf(refute_0_5030,plain,
    greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
    inference(subst,[],[refute_0_831:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).

cnf(refute_0_5031,plain,
    ( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Y0,$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).

cnf(refute_0_5032,plain,
    ( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_5030,refute_0_5031]) ).

cnf(refute_0_5033,plain,
    greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_5029,refute_0_5032]) ).

cnf(refute_0_5034,plain,
    least_upper_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,least_upper_bound(Z,Y)),
    inference(subst,[],[refute_0_540:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_5035,plain,
    greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).

cnf(refute_0_5036,plain,
    ( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
    | least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,least_upper_bound(Z,Y)))]]) ).

cnf(refute_0_5037,plain,
    ( least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_5035,refute_0_5036]) ).

cnf(refute_0_5038,plain,
    greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_5034,refute_0_5037]) ).

cnf(refute_0_5039,plain,
    ( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).

cnf(refute_0_5040,plain,
    ( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))) )],[refute_0_5038,refute_0_5039]) ).

cnf(refute_0_5041,plain,
    greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_5033,refute_0_5040]) ).

cnf(refute_0_5042,plain,
    greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(least_upper_bound(multiply(X,Z),multiply(X,Y)))),bind(X_25,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).

cnf(refute_0_5043,plain,
    ( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).

cnf(refute_0_5044,plain,
    ( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_5042,refute_0_5043]) ).

cnf(refute_0_5045,plain,
    greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_5041,refute_0_5044]) ).

cnf(refute_0_5046,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != multiply(X,least_upper_bound(Y,Z))
    | greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).

cnf(refute_0_5047,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_5045,refute_0_5046]) ).

cnf(refute_0_5048,plain,
    ( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
    | multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),[0],$fot(least_upper_bound(multiply(X,Z),multiply(X,Y)))]]) ).

cnf(refute_0_5049,plain,
    ( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_5034,refute_0_5048]) ).

cnf(refute_0_5050,plain,
    ( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
    | multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_5047,refute_0_5049]) ).

cnf(refute_0_5051,plain,
    multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_5024,refute_0_5050]) ).

cnf(refute_0_5052,plain,
    ( multiply(X,least_upper_bound(Y,Z)) != multiply(X,least_upper_bound(Z,Y))
    | multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(multiply(X,least_upper_bound(Z,Y))))]]) ).

cnf(refute_0_5053,plain,
    multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_5051,refute_0_5052]) ).

cnf(refute_0_5054,plain,
    multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) = multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),
    inference(subst,[],[refute_0_5053:[bind(X,$fot(identity)),bind(Y,$fot(identity)),bind(Z,$fot(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_5055,plain,
    ( multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) != least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))
    | multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) != multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))
    | multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) = least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))),bind(Z0,$fot(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_5056,plain,
    ( multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) != least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))
    | multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) = least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) ),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)),multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) )],[refute_0_5054,refute_0_5055]) ).

cnf(refute_0_5057,plain,
    multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) = least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) )],[refute_0_5015,refute_0_5056]) ).

cnf(refute_0_5058,plain,
    ( multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) != inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))
    | multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) != least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))
    | least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) = inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)),inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) ),[0],$fot(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_5059,plain,
    ( multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) != inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))
    | least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) = inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) ),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)),least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) )],[refute_0_5057,refute_0_5058]) ).

cnf(refute_0_5060,plain,
    greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) = identity,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))]]) ).

cnf(refute_0_5061,plain,
    inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))]]) ).

cnf(refute_0_5062,plain,
    ( greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) != identity
    | inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) != inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))
    | inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = inverse(identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_5063,plain,
    ( greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) != identity
    | inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = inverse(identity) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) )],[refute_0_5061,refute_0_5062]) ).

cnf(refute_0_5064,plain,
    inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = inverse(identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),identity) )],[refute_0_5060,refute_0_5063]) ).

cnf(refute_0_5065,plain,
    ( inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) != inverse(identity)
    | inverse(identity) != identity
    | inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = identity ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).

cnf(refute_0_5066,plain,
    ( inverse(identity) != identity
    | inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = identity ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),inverse(identity)) )],[refute_0_5064,refute_0_5065]) ).

cnf(refute_0_5067,plain,
    inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = identity,
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_5066]) ).

cnf(refute_0_5068,plain,
    ( inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) != identity
    | least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) != inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))
    | least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) ),[1],$fot(identity)]]) ).

cnf(refute_0_5069,plain,
    ( least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) != inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))
    | least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) = identity ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),identity) )],[refute_0_5067,refute_0_5068]) ).

cnf(refute_0_5070,plain,
    ( multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)) != inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))
    | least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) )],[refute_0_5059,refute_0_5069]) ).

cnf(refute_0_5071,plain,
    least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) = identity,
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity)),inverse(greatest_lower_bound(identity,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) )],[refute_0_5010,refute_0_5070]) ).

cnf(refute_0_5072,plain,
    greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) = greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_5073,plain,
    ( greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) != greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))
    | least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) != identity
    | greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) = greatest_lower_bound(X_99,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_5074,plain,
    ( least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) != identity
    | greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) = greatest_lower_bound(X_99,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) )],[refute_0_5072,refute_0_5073]) ).

cnf(refute_0_5075,plain,
    greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) = greatest_lower_bound(X_99,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity) )],[refute_0_5071,refute_0_5074]) ).

cnf(refute_0_5076,plain,
    inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))]]) ).

cnf(refute_0_5077,plain,
    ( greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) != greatest_lower_bound(X_99,identity)
    | inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) != inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))
    | inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = inverse(greatest_lower_bound(X_99,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) ),[1,0],$fot(greatest_lower_bound(X_99,identity))]]) ).

cnf(refute_0_5078,plain,
    ( greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) != greatest_lower_bound(X_99,identity)
    | inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = inverse(greatest_lower_bound(X_99,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) )],[refute_0_5076,refute_0_5077]) ).

cnf(refute_0_5079,plain,
    inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) = inverse(greatest_lower_bound(X_99,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),greatest_lower_bound(X_99,identity)) )],[refute_0_5075,refute_0_5078]) ).

cnf(refute_0_5080,plain,
    multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),
    introduced(tautology,[refl,[$fot(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))))]]) ).

cnf(refute_0_5081,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) != multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))
    | inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) != inverse(greatest_lower_bound(X_99,identity))
    | multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = multiply(X_99,inverse(greatest_lower_bound(X_99,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))) ),[1,1],$fot(inverse(greatest_lower_bound(X_99,identity)))]]) ).

cnf(refute_0_5082,plain,
    ( inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))) != inverse(greatest_lower_bound(X_99,identity))
    | multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = multiply(X_99,inverse(greatest_lower_bound(X_99,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))))) )],[refute_0_5080,refute_0_5081]) ).

cnf(refute_0_5083,plain,
    multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = multiply(X_99,inverse(greatest_lower_bound(X_99,identity))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))))),inverse(greatest_lower_bound(X_99,identity))) )],[refute_0_5079,refute_0_5082]) ).

cnf(refute_0_5084,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,identity))) != least_upper_bound(identity,X_99)
    | multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) != multiply(X_99,inverse(greatest_lower_bound(X_99,identity)))
    | multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = least_upper_bound(identity,X_99) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))))),bind(Y0,$fot(multiply(X_99,inverse(greatest_lower_bound(X_99,identity))))),bind(Z0,$fot(least_upper_bound(identity,X_99)))]]) ).

cnf(refute_0_5085,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,identity))) != least_upper_bound(identity,X_99)
    | multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = least_upper_bound(identity,X_99) ),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),multiply(X_99,inverse(greatest_lower_bound(X_99,identity)))) )],[refute_0_5083,refute_0_5084]) ).

cnf(refute_0_5086,plain,
    multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = least_upper_bound(identity,X_99),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,identity))),least_upper_bound(identity,X_99)) )],[refute_0_5006,refute_0_5085]) ).

cnf(refute_0_5087,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) != least_upper_bound(X_99,identity)
    | multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) != least_upper_bound(identity,X_99)
    | least_upper_bound(identity,X_99) = least_upper_bound(X_99,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),least_upper_bound(X_99,identity)) ),[0],$fot(least_upper_bound(identity,X_99))]]) ).

cnf(refute_0_5088,plain,
    ( multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) != least_upper_bound(X_99,identity)
    | least_upper_bound(identity,X_99) = least_upper_bound(X_99,identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),least_upper_bound(identity,X_99)) )],[refute_0_5086,refute_0_5087]) ).

cnf(refute_0_5089,plain,
    least_upper_bound(identity,X_99) = least_upper_bound(X_99,identity),
    inference(resolve,[$cnf( $equal(multiply(X_99,inverse(greatest_lower_bound(X_99,least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),least_upper_bound(X_99,identity)) )],[refute_0_5005,refute_0_5088]) ).

cnf(refute_0_5090,plain,
    least_upper_bound(identity,a) = least_upper_bound(a,identity),
    inference(subst,[],[refute_0_5089:[bind(X_99,$fot(a))]]) ).

cnf(refute_0_5091,plain,
    least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) = least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity))))),
    inference(subst,[],[refute_0_712:[bind(X_210,$fot(multiply(X_259,greatest_lower_bound(X_259,identity))))]]) ).

cnf(refute_0_5092,plain,
    multiply(X_220,inverse(greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity))))) = least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))),
    inference(subst,[],[refute_0_243:[bind(Y,$fot(inverse(greatest_lower_bound(X_220,identity)))),bind(X_99,$fot(X_220))]]) ).

cnf(refute_0_5093,plain,
    greatest_lower_bound(X_220,identity) = greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity))),
    inference(subst,[],[refute_0_1929:[bind(X_204,$fot(X_220))]]) ).

cnf(refute_0_5094,plain,
    ( greatest_lower_bound(X_220,identity) != greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity)))
    | greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity))) = greatest_lower_bound(X_220,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_220,identity))),bind(Y0,$fot(greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity)))))]]) ).

cnf(refute_0_5095,plain,
    greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity))) = greatest_lower_bound(X_220,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity)))) )],[refute_0_5093,refute_0_5094]) ).

cnf(refute_0_5096,plain,
    ( multiply(X_220,inverse(greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity))))) != least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))
    | greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity))) != greatest_lower_bound(X_220,identity)
    | multiply(X_220,inverse(greatest_lower_bound(X_220,identity))) = least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_220,inverse(greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity))))),least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))) ),[0,1,0],$fot(greatest_lower_bound(X_220,identity))]]) ).

cnf(refute_0_5097,plain,
    ( multiply(X_220,inverse(greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity))))) != least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))
    | multiply(X_220,inverse(greatest_lower_bound(X_220,identity))) = least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity))),greatest_lower_bound(X_220,identity)) )],[refute_0_5095,refute_0_5096]) ).

cnf(refute_0_5098,plain,
    multiply(X_220,inverse(greatest_lower_bound(X_220,identity))) = least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))),
    inference(resolve,[$cnf( $equal(multiply(X_220,inverse(greatest_lower_bound(X_220,inverse(greatest_lower_bound(X_220,identity))))),least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))) )],[refute_0_5092,refute_0_5097]) ).

cnf(refute_0_5099,plain,
    multiply(X_220,inverse(greatest_lower_bound(X_220,identity))) = least_upper_bound(identity,X_220),
    inference(subst,[],[refute_0_3143:[bind(X_98,$fot(X_220))]]) ).

cnf(refute_0_5100,plain,
    ( multiply(X_220,inverse(greatest_lower_bound(X_220,identity))) != least_upper_bound(identity,X_220)
    | multiply(X_220,inverse(greatest_lower_bound(X_220,identity))) != least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))
    | least_upper_bound(identity,X_220) = least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_220,inverse(greatest_lower_bound(X_220,identity))),least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))) ),[0],$fot(least_upper_bound(identity,X_220))]]) ).

cnf(refute_0_5101,plain,
    ( multiply(X_220,inverse(greatest_lower_bound(X_220,identity))) != least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))
    | least_upper_bound(identity,X_220) = least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(X_220,inverse(greatest_lower_bound(X_220,identity))),least_upper_bound(identity,X_220)) )],[refute_0_5099,refute_0_5100]) ).

cnf(refute_0_5102,plain,
    inverse(inverse(greatest_lower_bound(X_220,identity))) = greatest_lower_bound(X_220,identity),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(X_220,identity)))]]) ).

cnf(refute_0_5103,plain,
    multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))) = multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))),
    introduced(tautology,[refl,[$fot(multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))]]) ).

cnf(refute_0_5104,plain,
    ( multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))) != multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))
    | inverse(inverse(greatest_lower_bound(X_220,identity))) != greatest_lower_bound(X_220,identity)
    | multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))) = multiply(X_220,greatest_lower_bound(X_220,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))),multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) ),[1,1],$fot(greatest_lower_bound(X_220,identity))]]) ).

cnf(refute_0_5105,plain,
    ( inverse(inverse(greatest_lower_bound(X_220,identity))) != greatest_lower_bound(X_220,identity)
    | multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))) = multiply(X_220,greatest_lower_bound(X_220,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))),multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) )],[refute_0_5103,refute_0_5104]) ).

cnf(refute_0_5106,plain,
    multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))) = multiply(X_220,greatest_lower_bound(X_220,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_220,identity))),greatest_lower_bound(X_220,identity)) )],[refute_0_5102,refute_0_5105]) ).

cnf(refute_0_5107,plain,
    least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) = least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))))]]) ).

cnf(refute_0_5108,plain,
    ( multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))) != multiply(X_220,greatest_lower_bound(X_220,identity))
    | least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) != least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))
    | least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) = least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))),least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))) ),[1,1],$fot(multiply(X_220,greatest_lower_bound(X_220,identity)))]]) ).

cnf(refute_0_5109,plain,
    ( multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))) != multiply(X_220,greatest_lower_bound(X_220,identity))
    | least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) = least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))),least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))) )],[refute_0_5107,refute_0_5108]) ).

cnf(refute_0_5110,plain,
    least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) = least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))),
    inference(resolve,[$cnf( $equal(multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))),multiply(X_220,greatest_lower_bound(X_220,identity))) )],[refute_0_5106,refute_0_5109]) ).

cnf(refute_0_5111,plain,
    ( least_upper_bound(identity,X_220) != least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))
    | least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))) != least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))
    | least_upper_bound(identity,X_220) = least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,X_220),least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))) ),[0],$fot(least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))))]]) ).

cnf(refute_0_5112,plain,
    ( least_upper_bound(identity,X_220) != least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))
    | least_upper_bound(identity,X_220) = least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity))))),least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))) )],[refute_0_5110,refute_0_5111]) ).

cnf(refute_0_5113,plain,
    ( multiply(X_220,inverse(greatest_lower_bound(X_220,identity))) != least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))
    | least_upper_bound(identity,X_220) = least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_220),least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))) )],[refute_0_5101,refute_0_5112]) ).

cnf(refute_0_5114,plain,
    least_upper_bound(identity,X_220) = least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))),
    inference(resolve,[$cnf( $equal(multiply(X_220,inverse(greatest_lower_bound(X_220,identity))),least_upper_bound(identity,multiply(X_220,inverse(inverse(greatest_lower_bound(X_220,identity)))))) )],[refute_0_5098,refute_0_5113]) ).

cnf(refute_0_5115,plain,
    least_upper_bound(identity,X_259) = least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity))),
    inference(subst,[],[refute_0_5114:[bind(X_220,$fot(X_259))]]) ).

cnf(refute_0_5116,plain,
    ( least_upper_bound(identity,X_259) != least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity)))
    | least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity))) = least_upper_bound(identity,X_259) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,X_259))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity)))))]]) ).

cnf(refute_0_5117,plain,
    least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity))) = least_upper_bound(identity,X_259),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_259),least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity)))) )],[refute_0_5115,refute_0_5116]) ).

cnf(refute_0_5118,plain,
    ( least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) != least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity)))))
    | least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity))) != least_upper_bound(identity,X_259)
    | least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) = least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity),least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity)))))) ),[1,1,0],$fot(least_upper_bound(identity,X_259))]]) ).

cnf(refute_0_5119,plain,
    ( least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) != least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity)))))
    | least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) = least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity))),least_upper_bound(identity,X_259)) )],[refute_0_5117,refute_0_5118]) ).

cnf(refute_0_5120,plain,
    least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) = least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity),least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity)))))) )],[refute_0_5091,refute_0_5119]) ).

cnf(refute_0_5121,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) = least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45)))),
    inference(subst,[],[refute_0_712:[bind(X_210,$fot(least_upper_bound(greatest_lower_bound(identity,Y),X_45)))]]) ).

cnf(refute_0_5122,plain,
    least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45)) = least_upper_bound(identity,X_45),
    inference(subst,[],[refute_0_685:[bind(X_43,$fot(identity))]]) ).

cnf(refute_0_5123,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45)) != least_upper_bound(identity,X_45)
    | least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) != least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45))))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) = least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity),least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45))))) ),[1,1,0],$fot(least_upper_bound(identity,X_45))]]) ).

cnf(refute_0_5124,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) != least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45))))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) = least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45)),least_upper_bound(identity,X_45)) )],[refute_0_5122,refute_0_5123]) ).

cnf(refute_0_5125,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) = least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity),least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45))))) )],[refute_0_5121,refute_0_5124]) ).

cnf(refute_0_5126,plain,
    multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) = least_upper_bound(identity,multiply(inverse(X_59),multiply(X_59,X_60))),
    inference(subst,[],[refute_0_166:[bind(X_110,$fot(multiply(X_59,X_60))),bind(X_112,$fot(inverse(X_59)))]]) ).

cnf(refute_0_5127,plain,
    ( multiply(inverse(X_59),multiply(X_59,X_60)) != X_60
    | multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) != least_upper_bound(identity,multiply(inverse(X_59),multiply(X_59,X_60)))
    | multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) = least_upper_bound(identity,X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)),least_upper_bound(identity,multiply(inverse(X_59),multiply(X_59,X_60)))) ),[1,1],$fot(X_60)]]) ).

cnf(refute_0_5128,plain,
    ( multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) != least_upper_bound(identity,multiply(inverse(X_59),multiply(X_59,X_60)))
    | multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) = least_upper_bound(identity,X_60) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_59),multiply(X_59,X_60)),X_60) )],[refute_0_1308,refute_0_5127]) ).

cnf(refute_0_5129,plain,
    multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) = least_upper_bound(identity,X_60),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)),least_upper_bound(identity,multiply(inverse(X_59),multiply(X_59,X_60)))) )],[refute_0_5126,refute_0_5128]) ).

cnf(refute_0_5130,plain,
    multiply(multiply(least_upper_bound(X_114,inverse(Y)),Y),Z) = multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z)),
    inference(subst,[],[associativity:[bind(X,$fot(least_upper_bound(X_114,inverse(Y))))]]) ).

cnf(refute_0_5131,plain,
    multiply(least_upper_bound(X_114,inverse(Y)),Y) = least_upper_bound(identity,multiply(X_114,Y)),
    inference(subst,[],[refute_0_92:[bind(X_110,$fot(Y)),bind(X_111,$fot(X_114))]]) ).

cnf(refute_0_5132,plain,
    ( multiply(multiply(least_upper_bound(X_114,inverse(Y)),Y),Z) != multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z))
    | multiply(least_upper_bound(X_114,inverse(Y)),Y) != least_upper_bound(identity,multiply(X_114,Y))
    | multiply(least_upper_bound(identity,multiply(X_114,Y)),Z) = multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(least_upper_bound(X_114,inverse(Y)),Y),Z),multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z))) ),[0,0],$fot(least_upper_bound(identity,multiply(X_114,Y)))]]) ).

cnf(refute_0_5133,plain,
    ( multiply(multiply(least_upper_bound(X_114,inverse(Y)),Y),Z) != multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z))
    | multiply(least_upper_bound(identity,multiply(X_114,Y)),Z) = multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_114,inverse(Y)),Y),least_upper_bound(identity,multiply(X_114,Y))) )],[refute_0_5131,refute_0_5132]) ).

cnf(refute_0_5134,plain,
    multiply(least_upper_bound(identity,multiply(X_114,Y)),Z) = multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(multiply(least_upper_bound(X_114,inverse(Y)),Y),Z),multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z))) )],[refute_0_5130,refute_0_5133]) ).

cnf(refute_0_5135,plain,
    ( multiply(least_upper_bound(identity,multiply(X_114,Y)),Z) != multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z))
    | multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z)) = multiply(least_upper_bound(identity,multiply(X_114,Y)),Z) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(X_114,Y)),Z))),bind(Y0,$fot(multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z))))]]) ).

cnf(refute_0_5136,plain,
    multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z)) = multiply(least_upper_bound(identity,multiply(X_114,Y)),Z),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_114,Y)),Z),multiply(least_upper_bound(X_114,inverse(Y)),multiply(Y,Z))) )],[refute_0_5134,refute_0_5135]) ).

cnf(refute_0_5137,plain,
    multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) = multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),
    inference(subst,[],[refute_0_5136:[bind(Y,$fot(X_59)),bind(Z,$fot(X_60)),bind(X_114,$fot(inverse(multiply(X_59,X_60))))]]) ).

cnf(refute_0_5138,plain,
    ( multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) != multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60)
    | multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) != least_upper_bound(identity,X_60)
    | multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = least_upper_bound(identity,X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)),least_upper_bound(identity,X_60)) ),[0],$fot(multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60))]]) ).

cnf(refute_0_5139,plain,
    ( multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)) != least_upper_bound(identity,X_60)
    | multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = least_upper_bound(identity,X_60) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)),multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60)) )],[refute_0_5137,refute_0_5138]) ).

cnf(refute_0_5140,plain,
    multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = least_upper_bound(identity,X_60),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(multiply(X_59,X_60)),inverse(X_59)),multiply(X_59,X_60)),least_upper_bound(identity,X_60)) )],[refute_0_5129,refute_0_5139]) ).

cnf(refute_0_5141,plain,
    least_upper_bound(identity,inverse(X_60)) = inverse(greatest_lower_bound(identity,X_60)),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(X_60))]]) ).

cnf(refute_0_5142,plain,
    least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)))]]) ).

cnf(refute_0_5143,plain,
    ( multiply(inverse(multiply(X_59,X_60)),X_59) != inverse(X_60)
    | least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) != least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59))
    | least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = least_upper_bound(identity,inverse(X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59))) ),[1,1],$fot(inverse(X_60))]]) ).

cnf(refute_0_5144,plain,
    ( multiply(inverse(multiply(X_59,X_60)),X_59) != inverse(X_60)
    | least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = least_upper_bound(identity,inverse(X_60)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59))) )],[refute_0_5142,refute_0_5143]) ).

cnf(refute_0_5145,plain,
    least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = least_upper_bound(identity,inverse(X_60)),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_59,X_60)),X_59),inverse(X_60)) )],[refute_0_1336,refute_0_5144]) ).

cnf(refute_0_5146,plain,
    ( least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) != least_upper_bound(identity,inverse(X_60))
    | least_upper_bound(identity,inverse(X_60)) != inverse(greatest_lower_bound(identity,X_60))
    | least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = inverse(greatest_lower_bound(identity,X_60)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_60)))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,X_60))))]]) ).

cnf(refute_0_5147,plain,
    ( least_upper_bound(identity,inverse(X_60)) != inverse(greatest_lower_bound(identity,X_60))
    | least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = inverse(greatest_lower_bound(identity,X_60)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),least_upper_bound(identity,inverse(X_60))) )],[refute_0_5145,refute_0_5146]) ).

cnf(refute_0_5148,plain,
    least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) = inverse(greatest_lower_bound(identity,X_60)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_60)),inverse(greatest_lower_bound(identity,X_60))) )],[refute_0_5141,refute_0_5147]) ).

cnf(refute_0_5149,plain,
    multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60))]]) ).

cnf(refute_0_5150,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) != multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60)
    | least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) != inverse(greatest_lower_bound(identity,X_60))
    | multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = multiply(inverse(greatest_lower_bound(identity,X_60)),X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60)) ),[1,0],$fot(inverse(greatest_lower_bound(identity,X_60)))]]) ).

cnf(refute_0_5151,plain,
    ( least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)) != inverse(greatest_lower_bound(identity,X_60))
    | multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = multiply(inverse(greatest_lower_bound(identity,X_60)),X_60) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60)) )],[refute_0_5149,refute_0_5150]) ).

cnf(refute_0_5152,plain,
    multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = multiply(inverse(greatest_lower_bound(identity,X_60)),X_60),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),inverse(greatest_lower_bound(identity,X_60))) )],[refute_0_5148,refute_0_5151]) ).

cnf(refute_0_5153,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_60)),X_60) != least_upper_bound(X_60,identity)
    | multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) != multiply(inverse(greatest_lower_bound(identity,X_60)),X_60)
    | multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = least_upper_bound(X_60,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_60)),X_60))),bind(Z0,$fot(least_upper_bound(X_60,identity)))]]) ).

cnf(refute_0_5154,plain,
    ( multiply(inverse(greatest_lower_bound(identity,X_60)),X_60) != least_upper_bound(X_60,identity)
    | multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = least_upper_bound(X_60,identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),multiply(inverse(greatest_lower_bound(identity,X_60)),X_60)) )],[refute_0_5152,refute_0_5153]) ).

cnf(refute_0_5155,plain,
    multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) = least_upper_bound(X_60,identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_60)),X_60),least_upper_bound(X_60,identity)) )],[refute_0_1665,refute_0_5154]) ).

cnf(refute_0_5156,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) != least_upper_bound(X_60,identity)
    | multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) != least_upper_bound(identity,X_60)
    | least_upper_bound(X_60,identity) = least_upper_bound(identity,X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),least_upper_bound(identity,X_60)) ),[0],$fot(least_upper_bound(X_60,identity))]]) ).

cnf(refute_0_5157,plain,
    ( multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60) != least_upper_bound(identity,X_60)
    | least_upper_bound(X_60,identity) = least_upper_bound(identity,X_60) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),least_upper_bound(X_60,identity)) )],[refute_0_5155,refute_0_5156]) ).

cnf(refute_0_5158,plain,
    least_upper_bound(X_60,identity) = least_upper_bound(identity,X_60),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(inverse(multiply(X_59,X_60)),X_59)),X_60),least_upper_bound(identity,X_60)) )],[refute_0_5140,refute_0_5157]) ).

cnf(refute_0_5159,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45)),
    inference(subst,[],[refute_0_5158:[bind(X_60,$fot(least_upper_bound(greatest_lower_bound(identity,Y),X_45)))]]) ).

cnf(refute_0_5160,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45)) != least_upper_bound(identity,X_45)
    | least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) = least_upper_bound(identity,X_45) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45)))),bind(Z0,$fot(least_upper_bound(identity,X_45)))]]) ).

cnf(refute_0_5161,plain,
    ( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45)) != least_upper_bound(identity,X_45)
    | least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) = least_upper_bound(identity,X_45) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45))) )],[refute_0_5159,refute_0_5160]) ).

cnf(refute_0_5162,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) = least_upper_bound(identity,X_45),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,Y),X_45)),least_upper_bound(identity,X_45)) )],[refute_0_5122,refute_0_5161]) ).

cnf(refute_0_5163,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) != least_upper_bound(identity,X_45)
    | least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) != least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45)))
    | least_upper_bound(identity,X_45) = least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity),least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45)))) ),[0],$fot(least_upper_bound(identity,X_45))]]) ).

cnf(refute_0_5164,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) != least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45)))
    | least_upper_bound(identity,X_45) = least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity),least_upper_bound(identity,X_45)) )],[refute_0_5162,refute_0_5163]) ).

cnf(refute_0_5165,plain,
    least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),greatest_lower_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9)))) = least_upper_bound(X_192,least_upper_bound(X_193,X_9)),
    inference(subst,[],[refute_0_117:[bind(X_8,$fot(least_upper_bound(X_192,least_upper_bound(X_193,X_9))))]]) ).

cnf(refute_0_5166,plain,
    greatest_lower_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9))) = X_9,
    inference(subst,[],[refute_0_1684:[bind(X_10,$fot(X_9)),bind(X_43,$fot(X_192)),bind(X_44,$fot(X_193))]]) ).

cnf(refute_0_5167,plain,
    ( greatest_lower_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9))) != X_9
    | least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),greatest_lower_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9)))) != least_upper_bound(X_192,least_upper_bound(X_193,X_9))
    | least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9) = least_upper_bound(X_192,least_upper_bound(X_193,X_9)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),greatest_lower_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9)))),least_upper_bound(X_192,least_upper_bound(X_193,X_9))) ),[0,1],$fot(X_9)]]) ).

cnf(refute_0_5168,plain,
    ( least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),greatest_lower_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9)))) != least_upper_bound(X_192,least_upper_bound(X_193,X_9))
    | least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9) = least_upper_bound(X_192,least_upper_bound(X_193,X_9)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9))),X_9) )],[refute_0_5166,refute_0_5167]) ).

cnf(refute_0_5169,plain,
    least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9) = least_upper_bound(X_192,least_upper_bound(X_193,X_9)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),greatest_lower_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9)))),least_upper_bound(X_192,least_upper_bound(X_193,X_9))) )],[refute_0_5165,refute_0_5168]) ).

cnf(refute_0_5170,plain,
    least_upper_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9))) = least_upper_bound(X_9,least_upper_bound(X_192,X_193)),
    inference(subst,[],[refute_0_1695:[bind(X_21,$fot(X_9)),bind(X_43,$fot(X_192)),bind(X_44,$fot(X_193))]]) ).

cnf(refute_0_5171,plain,
    least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9) = least_upper_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9))),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(least_upper_bound(X_192,least_upper_bound(X_193,X_9)))),bind(X_17,$fot(X_9))]]) ).

cnf(refute_0_5172,plain,
    ( least_upper_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9))) != least_upper_bound(X_9,least_upper_bound(X_192,X_193))
    | least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9) != least_upper_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9)))
    | least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9) = least_upper_bound(X_9,least_upper_bound(X_192,X_193)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9))),bind(Y0,$fot(least_upper_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9))))),bind(Z0,$fot(least_upper_bound(X_9,least_upper_bound(X_192,X_193))))]]) ).

cnf(refute_0_5173,plain,
    ( least_upper_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9))) != least_upper_bound(X_9,least_upper_bound(X_192,X_193))
    | least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9) = least_upper_bound(X_9,least_upper_bound(X_192,X_193)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9),least_upper_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9)))) )],[refute_0_5171,refute_0_5172]) ).

cnf(refute_0_5174,plain,
    least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9) = least_upper_bound(X_9,least_upper_bound(X_192,X_193)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_9,least_upper_bound(X_192,least_upper_bound(X_193,X_9))),least_upper_bound(X_9,least_upper_bound(X_192,X_193))) )],[refute_0_5170,refute_0_5173]) ).

cnf(refute_0_5175,plain,
    ( least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9) != least_upper_bound(X_192,least_upper_bound(X_193,X_9))
    | least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9) != least_upper_bound(X_9,least_upper_bound(X_192,X_193))
    | least_upper_bound(X_9,least_upper_bound(X_192,X_193)) = least_upper_bound(X_192,least_upper_bound(X_193,X_9)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9),least_upper_bound(X_192,least_upper_bound(X_193,X_9))) ),[0],$fot(least_upper_bound(X_9,least_upper_bound(X_192,X_193)))]]) ).

cnf(refute_0_5176,plain,
    ( least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9) != least_upper_bound(X_192,least_upper_bound(X_193,X_9))
    | least_upper_bound(X_9,least_upper_bound(X_192,X_193)) = least_upper_bound(X_192,least_upper_bound(X_193,X_9)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9),least_upper_bound(X_9,least_upper_bound(X_192,X_193))) )],[refute_0_5174,refute_0_5175]) ).

cnf(refute_0_5177,plain,
    least_upper_bound(X_9,least_upper_bound(X_192,X_193)) = least_upper_bound(X_192,least_upper_bound(X_193,X_9)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_192,least_upper_bound(X_193,X_9)),X_9),least_upper_bound(X_192,least_upper_bound(X_193,X_9))) )],[refute_0_5169,refute_0_5176]) ).

cnf(refute_0_5178,plain,
    ( least_upper_bound(X_9,least_upper_bound(X_192,X_193)) != least_upper_bound(X_192,least_upper_bound(X_193,X_9))
    | least_upper_bound(X_192,least_upper_bound(X_193,X_9)) = least_upper_bound(X_9,least_upper_bound(X_192,X_193)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_9,least_upper_bound(X_192,X_193)))),bind(Y0,$fot(least_upper_bound(X_192,least_upper_bound(X_193,X_9))))]]) ).

cnf(refute_0_5179,plain,
    least_upper_bound(X_192,least_upper_bound(X_193,X_9)) = least_upper_bound(X_9,least_upper_bound(X_192,X_193)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_9,least_upper_bound(X_192,X_193)),least_upper_bound(X_192,least_upper_bound(X_193,X_9))) )],[refute_0_5177,refute_0_5178]) ).

cnf(refute_0_5180,plain,
    least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(greatest_lower_bound(identity,Y),X_45)) = least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))),
    inference(subst,[],[refute_0_5179:[bind(X_192,$fot(inverse(least_upper_bound(X_45,identity)))),bind(X_193,$fot(greatest_lower_bound(identity,Y))),bind(X_9,$fot(X_45))]]) ).

cnf(refute_0_5181,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))) = least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(greatest_lower_bound(identity,Y),X_45)),
    inference(subst,[],[refute_0_1834:[bind(X_16,$fot(X_45)),bind(X_17,$fot(identity)),bind(X_97,$fot(least_upper_bound(greatest_lower_bound(identity,Y),X_45)))]]) ).

cnf(refute_0_5182,plain,
    ( least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(greatest_lower_bound(identity,Y),X_45)) != least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y)))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))) != least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(greatest_lower_bound(identity,Y),X_45))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))) = least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(greatest_lower_bound(identity,Y),X_45)))),bind(Z0,$fot(least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y)))))]]) ).

cnf(refute_0_5183,plain,
    ( least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(greatest_lower_bound(identity,Y),X_45)) != least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y)))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))) = least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))),least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(greatest_lower_bound(identity,Y),X_45))) )],[refute_0_5181,refute_0_5182]) ).

cnf(refute_0_5184,plain,
    least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))) = least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_45,identity)),least_upper_bound(greatest_lower_bound(identity,Y),X_45)),least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y)))) )],[refute_0_5180,refute_0_5183]) ).

cnf(refute_0_5185,plain,
    ( least_upper_bound(identity,X_45) != least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45)))
    | least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))) != least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y)))
    | least_upper_bound(identity,X_45) = least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,X_45),least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))))]]) ).

cnf(refute_0_5186,plain,
    ( least_upper_bound(identity,X_45) != least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45)))
    | least_upper_bound(identity,X_45) = least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45))),least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y)))) )],[refute_0_5184,refute_0_5185]) ).

cnf(refute_0_5187,plain,
    ( least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity) != least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45)))
    | least_upper_bound(identity,X_45) = least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_45),least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45)))) )],[refute_0_5164,refute_0_5186]) ).

cnf(refute_0_5188,plain,
    least_upper_bound(identity,X_45) = least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),identity),least_upper_bound(least_upper_bound(greatest_lower_bound(identity,Y),X_45),inverse(least_upper_bound(identity,X_45)))) )],[refute_0_5125,refute_0_5187]) ).

cnf(refute_0_5189,plain,
    least_upper_bound(identity,greatest_lower_bound(identity,Y)) = identity,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity))]]) ).

cnf(refute_0_5190,plain,
    least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))) = least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))))]]) ).

cnf(refute_0_5191,plain,
    ( least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y)))
    | least_upper_bound(identity,greatest_lower_bound(identity,Y)) != identity
    | least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))) = least_upper_bound(X_45,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_5192,plain,
    ( least_upper_bound(identity,greatest_lower_bound(identity,Y)) != identity
    | least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))) = least_upper_bound(X_45,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y)))) )],[refute_0_5190,refute_0_5191]) ).

cnf(refute_0_5193,plain,
    least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))) = least_upper_bound(X_45,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,Y)),identity) )],[refute_0_5189,refute_0_5192]) ).

cnf(refute_0_5194,plain,
    least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)) = least_upper_bound(least_upper_bound(X,inverse(least_upper_bound(X,identity))),Z),
    inference(subst,[],[associativity_of_lub:[bind(Y,$fot(inverse(least_upper_bound(X,identity))))]]) ).

cnf(refute_0_5195,plain,
    least_upper_bound(X,identity) = least_upper_bound(X,inverse(least_upper_bound(X,identity))),
    inference(subst,[],[refute_0_1847:[bind(X_210,$fot(X))]]) ).

cnf(refute_0_5196,plain,
    ( least_upper_bound(X,identity) != least_upper_bound(X,inverse(least_upper_bound(X,identity)))
    | least_upper_bound(X,inverse(least_upper_bound(X,identity))) = least_upper_bound(X,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X,identity))),bind(Y0,$fot(least_upper_bound(X,inverse(least_upper_bound(X,identity)))))]]) ).

cnf(refute_0_5197,plain,
    least_upper_bound(X,inverse(least_upper_bound(X,identity))) = least_upper_bound(X,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,identity),least_upper_bound(X,inverse(least_upper_bound(X,identity)))) )],[refute_0_5195,refute_0_5196]) ).

cnf(refute_0_5198,plain,
    ( least_upper_bound(X,inverse(least_upper_bound(X,identity))) != least_upper_bound(X,identity)
    | least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)) != least_upper_bound(least_upper_bound(X,inverse(least_upper_bound(X,identity))),Z)
    | least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)) = least_upper_bound(least_upper_bound(X,identity),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)),least_upper_bound(least_upper_bound(X,inverse(least_upper_bound(X,identity))),Z)) ),[1,0],$fot(least_upper_bound(X,identity))]]) ).

cnf(refute_0_5199,plain,
    ( least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)) != least_upper_bound(least_upper_bound(X,inverse(least_upper_bound(X,identity))),Z)
    | least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)) = least_upper_bound(least_upper_bound(X,identity),Z) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,inverse(least_upper_bound(X,identity))),least_upper_bound(X,identity)) )],[refute_0_5197,refute_0_5198]) ).

cnf(refute_0_5200,plain,
    least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)) = least_upper_bound(least_upper_bound(X,identity),Z),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)),least_upper_bound(least_upper_bound(X,inverse(least_upper_bound(X,identity))),Z)) )],[refute_0_5194,refute_0_5199]) ).

cnf(refute_0_5201,plain,
    least_upper_bound(least_upper_bound(X,identity),Z) = least_upper_bound(X,least_upper_bound(identity,Z)),
    inference(subst,[],[refute_0_375:[bind(Y,$fot(identity))]]) ).

cnf(refute_0_5202,plain,
    ( least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)) != least_upper_bound(least_upper_bound(X,identity),Z)
    | least_upper_bound(least_upper_bound(X,identity),Z) != least_upper_bound(X,least_upper_bound(identity,Z))
    | least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)) = least_upper_bound(X,least_upper_bound(identity,Z)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)),least_upper_bound(X,least_upper_bound(identity,Z))) ),[0],$fot(least_upper_bound(least_upper_bound(X,identity),Z))]]) ).

cnf(refute_0_5203,plain,
    ( least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)) != least_upper_bound(least_upper_bound(X,identity),Z)
    | least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)) = least_upper_bound(X,least_upper_bound(identity,Z)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,identity),Z),least_upper_bound(X,least_upper_bound(identity,Z))) )],[refute_0_5201,refute_0_5202]) ).

cnf(refute_0_5204,plain,
    least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)) = least_upper_bound(X,least_upper_bound(identity,Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(inverse(least_upper_bound(X,identity)),Z)),least_upper_bound(least_upper_bound(X,identity),Z)) )],[refute_0_5200,refute_0_5203]) ).

cnf(refute_0_5205,plain,
    least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))) = least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))),
    inference(subst,[],[refute_0_5204:[bind(X,$fot(X_45)),bind(Z,$fot(greatest_lower_bound(identity,Y)))]]) ).

cnf(refute_0_5206,plain,
    ( least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(X_45,identity)
    | least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))) != least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y)))
    | least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))) = least_upper_bound(X_45,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))))),bind(Y0,$fot(least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))))),bind(Z0,$fot(least_upper_bound(X_45,identity)))]]) ).

cnf(refute_0_5207,plain,
    ( least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(X_45,identity)
    | least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))) = least_upper_bound(X_45,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))),least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y)))) )],[refute_0_5205,refute_0_5206]) ).

cnf(refute_0_5208,plain,
    least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))) = least_upper_bound(X_45,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(X_45,identity)) )],[refute_0_5193,refute_0_5207]) ).

cnf(refute_0_5209,plain,
    ( least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))) != least_upper_bound(X_45,identity)
    | least_upper_bound(identity,X_45) != least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y)))
    | least_upper_bound(identity,X_45) = least_upper_bound(X_45,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,X_45),least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y)))) ),[1],$fot(least_upper_bound(X_45,identity))]]) ).

cnf(refute_0_5210,plain,
    ( least_upper_bound(identity,X_45) != least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y)))
    | least_upper_bound(identity,X_45) = least_upper_bound(X_45,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y))),least_upper_bound(X_45,identity)) )],[refute_0_5208,refute_0_5209]) ).

cnf(refute_0_5211,plain,
    least_upper_bound(identity,X_45) = least_upper_bound(X_45,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_45),least_upper_bound(X_45,least_upper_bound(inverse(least_upper_bound(X_45,identity)),greatest_lower_bound(identity,Y)))) )],[refute_0_5188,refute_0_5210]) ).

cnf(refute_0_5212,plain,
    ( least_upper_bound(identity,X_45) != least_upper_bound(X_45,identity)
    | least_upper_bound(X_45,identity) = least_upper_bound(identity,X_45) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,X_45))),bind(Y0,$fot(least_upper_bound(X_45,identity)))]]) ).

cnf(refute_0_5213,plain,
    least_upper_bound(X_45,identity) = least_upper_bound(identity,X_45),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_45),least_upper_bound(X_45,identity)) )],[refute_0_5211,refute_0_5212]) ).

cnf(refute_0_5214,plain,
    least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) = least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity))),
    inference(subst,[],[refute_0_5213:[bind(X_45,$fot(multiply(X_259,greatest_lower_bound(X_259,identity))))]]) ).

cnf(refute_0_5215,plain,
    ( least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) != least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity)))
    | least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity))) != least_upper_bound(identity,X_259)
    | least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) = least_upper_bound(identity,X_259) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity))))),bind(Z0,$fot(least_upper_bound(identity,X_259)))]]) ).

cnf(refute_0_5216,plain,
    ( least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity))) != least_upper_bound(identity,X_259)
    | least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) = least_upper_bound(identity,X_259) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity),least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity)))) )],[refute_0_5214,refute_0_5215]) ).

cnf(refute_0_5217,plain,
    least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) = least_upper_bound(identity,X_259),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_259,greatest_lower_bound(X_259,identity))),least_upper_bound(identity,X_259)) )],[refute_0_5117,refute_0_5216]) ).

cnf(refute_0_5218,plain,
    ( least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) != least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259)))
    | least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) != least_upper_bound(identity,X_259)
    | least_upper_bound(identity,X_259) = least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity),least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259)))) ),[0],$fot(least_upper_bound(identity,X_259))]]) ).

cnf(refute_0_5219,plain,
    ( least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) != least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259)))
    | least_upper_bound(identity,X_259) = least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity),least_upper_bound(identity,X_259)) )],[refute_0_5217,refute_0_5218]) ).

cnf(refute_0_5220,plain,
    multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) = least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),multiply(inverse(X_233),greatest_lower_bound(X_233,identity))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(greatest_lower_bound(X_233,identity))),bind(Z,$fot(inverse(X_233)))]]) ).

cnf(refute_0_5221,plain,
    ( multiply(inverse(X_233),greatest_lower_bound(X_233,identity)) != inverse(least_upper_bound(identity,X_233))
    | multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) != least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),multiply(inverse(X_233),greatest_lower_bound(X_233,identity)))
    | multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) = least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)),least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),multiply(inverse(X_233),greatest_lower_bound(X_233,identity)))) ),[1,1],$fot(inverse(least_upper_bound(identity,X_233)))]]) ).

cnf(refute_0_5222,plain,
    ( multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) != least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),multiply(inverse(X_233),greatest_lower_bound(X_233,identity)))
    | multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) = least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_233),greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233))) )],[refute_0_1361,refute_0_5221]) ).

cnf(refute_0_5223,plain,
    multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) = least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)),least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),multiply(inverse(X_233),greatest_lower_bound(X_233,identity)))) )],[refute_0_5220,refute_0_5222]) ).

cnf(refute_0_5224,plain,
    least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233))) = least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity))),
    inference(subst,[],[refute_0_1834:[bind(X_16,$fot(X_233)),bind(X_17,$fot(identity)),bind(X_97,$fot(multiply(Y,greatest_lower_bound(X_233,identity))))]]) ).

cnf(refute_0_5225,plain,
    ( multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) != least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233)))
    | least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233))) != least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity)))
    | multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) = least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)),least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity)))) ),[0],$fot(least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233))))]]) ).

cnf(refute_0_5226,plain,
    ( multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) != least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233)))
    | multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) = least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233))),least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity)))) )],[refute_0_5224,refute_0_5225]) ).

cnf(refute_0_5227,plain,
    multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) = least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)),least_upper_bound(multiply(Y,greatest_lower_bound(X_233,identity)),inverse(least_upper_bound(identity,X_233)))) )],[refute_0_5223,refute_0_5226]) ).

cnf(refute_0_5228,plain,
    ( multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) != least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity)))
    | least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity))) = multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity)))))]]) ).

cnf(refute_0_5229,plain,
    least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity))) = multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,inverse(X_233)),greatest_lower_bound(X_233,identity)),least_upper_bound(inverse(least_upper_bound(X_233,identity)),multiply(Y,greatest_lower_bound(X_233,identity)))) )],[refute_0_5227,refute_0_5228]) ).

cnf(refute_0_5230,plain,
    least_upper_bound(inverse(least_upper_bound(X_259,identity)),multiply(X_259,greatest_lower_bound(X_259,identity))) = multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity)),
    inference(subst,[],[refute_0_5229:[bind(Y,$fot(X_259)),bind(X_233,$fot(X_259))]]) ).

cnf(refute_0_5231,plain,
    least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))) = least_upper_bound(inverse(least_upper_bound(X_259,identity)),multiply(X_259,greatest_lower_bound(X_259,identity))),
    inference(subst,[],[refute_0_1834:[bind(X_16,$fot(X_259)),bind(X_17,$fot(identity)),bind(X_97,$fot(multiply(X_259,greatest_lower_bound(X_259,identity))))]]) ).

cnf(refute_0_5232,plain,
    ( least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))) != least_upper_bound(inverse(least_upper_bound(X_259,identity)),multiply(X_259,greatest_lower_bound(X_259,identity)))
    | least_upper_bound(inverse(least_upper_bound(X_259,identity)),multiply(X_259,greatest_lower_bound(X_259,identity))) != multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity))
    | least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))) = multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))))),bind(Y0,$fot(least_upper_bound(inverse(least_upper_bound(X_259,identity)),multiply(X_259,greatest_lower_bound(X_259,identity))))),bind(Z0,$fot(multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity))))]]) ).

cnf(refute_0_5233,plain,
    ( least_upper_bound(inverse(least_upper_bound(X_259,identity)),multiply(X_259,greatest_lower_bound(X_259,identity))) != multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity))
    | least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))) = multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))),least_upper_bound(inverse(least_upper_bound(X_259,identity)),multiply(X_259,greatest_lower_bound(X_259,identity)))) )],[refute_0_5231,refute_0_5232]) ).

cnf(refute_0_5234,plain,
    least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))) = multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(least_upper_bound(X_259,identity)),multiply(X_259,greatest_lower_bound(X_259,identity))),multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity))) )],[refute_0_5230,refute_0_5233]) ).

cnf(refute_0_5235,plain,
    ( least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))) != multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity))
    | least_upper_bound(identity,X_259) != least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259)))
    | least_upper_bound(identity,X_259) = multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,X_259),least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259)))) ),[1],$fot(multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity)))]]) ).

cnf(refute_0_5236,plain,
    ( least_upper_bound(identity,X_259) != least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259)))
    | least_upper_bound(identity,X_259) = multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259))),multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity))) )],[refute_0_5234,refute_0_5235]) ).

cnf(refute_0_5237,plain,
    ( least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity) != least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259)))
    | least_upper_bound(identity,X_259) = multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_259),least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259)))) )],[refute_0_5219,refute_0_5236]) ).

cnf(refute_0_5238,plain,
    least_upper_bound(identity,X_259) = multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),identity),least_upper_bound(multiply(X_259,greatest_lower_bound(X_259,identity)),inverse(least_upper_bound(identity,X_259)))) )],[refute_0_5120,refute_0_5237]) ).

cnf(refute_0_5239,plain,
    ( least_upper_bound(identity,X_259) != multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity))
    | multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity)) = least_upper_bound(identity,X_259) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,X_259))),bind(Y0,$fot(multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity))))]]) ).

cnf(refute_0_5240,plain,
    multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity)) = least_upper_bound(identity,X_259),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_259),multiply(least_upper_bound(X_259,inverse(X_259)),greatest_lower_bound(X_259,identity))) )],[refute_0_5238,refute_0_5239]) ).

cnf(refute_0_5241,plain,
    multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(identity,a),
    inference(subst,[],[refute_0_5240:[bind(X_259,$fot(a))]]) ).

cnf(refute_0_5242,plain,
    ( multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)) != least_upper_bound(identity,a)
    | least_upper_bound(identity,a) != least_upper_bound(a,identity)
    | multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(a,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)))),bind(Y0,$fot(least_upper_bound(identity,a))),bind(Z0,$fot(least_upper_bound(a,identity)))]]) ).

cnf(refute_0_5243,plain,
    ( least_upper_bound(identity,a) != least_upper_bound(a,identity)
    | multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)),least_upper_bound(identity,a)) )],[refute_0_5241,refute_0_5242]) ).

cnf(refute_0_5244,plain,
    multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(a,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,a),least_upper_bound(a,identity)) )],[refute_0_5090,refute_0_5243]) ).

cnf(refute_0_5245,plain,
    multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) = least_upper_bound(a,multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity))))),
    inference(subst,[],[refute_0_480:[bind(X_93,$fot(a)),bind(X_94,$fot(inverse(multiply(a,greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_5246,plain,
    multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))) = inverse(greatest_lower_bound(a,identity)),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(multiply(a,least_upper_bound(b,identity)))),bind(X_59,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_5247,plain,
    multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))),
    inference(subst,[],[refute_0_334:[bind(X_129,$fot(multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_5248,plain,
    multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326)),
    inference(subst,[],[refute_0_4594:[bind(X_107,$fot(greatest_lower_bound(identity,X_326))),bind(X_108,$fot(X_326))]]) ).

cnf(refute_0_5249,plain,
    greatest_lower_bound(X_326,identity) = greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326))),
    inference(subst,[],[refute_0_625:[bind(X_204,$fot(X_326))]]) ).

cnf(refute_0_5250,plain,
    ( greatest_lower_bound(X_326,identity) != greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326)))
    | greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326))) = greatest_lower_bound(X_326,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_326,identity))),bind(Y0,$fot(greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326)))))]]) ).

cnf(refute_0_5251,plain,
    greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326))) = greatest_lower_bound(X_326,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_326,identity),greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326)))) )],[refute_0_5249,refute_0_5250]) ).

cnf(refute_0_5252,plain,
    ( multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326)))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326))
    | greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326))) != greatest_lower_bound(X_326,identity)
    | multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,identity)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326))) ),[0,1],$fot(greatest_lower_bound(X_326,identity))]]) ).

cnf(refute_0_5253,plain,
    ( multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326)))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326))
    | multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,identity)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326))),greatest_lower_bound(X_326,identity)) )],[refute_0_5251,refute_0_5252]) ).

cnf(refute_0_5254,plain,
    multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,identity)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,inverse(greatest_lower_bound(identity,X_326)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326))) )],[refute_0_5248,refute_0_5253]) ).

cnf(refute_0_5255,plain,
    multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),multiply(a,least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_5254:[bind(X_326,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_5256,plain,
    ( multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),multiply(a,least_upper_bound(b,identity))))
    | greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),multiply(a,least_upper_bound(b,identity))))) ),[1,1,0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_5257,plain,
    ( multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),multiply(a,least_upper_bound(b,identity))))
    | multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3860,refute_0_5256]) ).

cnf(refute_0_5258,plain,
    multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),multiply(a,least_upper_bound(b,identity))))) )],[refute_0_5255,refute_0_5257]) ).

cnf(refute_0_5259,plain,
    multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_5260,plain,
    ( multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) != multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))
    | greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))) ),[1,1],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_5261,plain,
    ( greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))) )],[refute_0_5259,refute_0_5260]) ).

cnf(refute_0_5262,plain,
    multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3860,refute_0_5261]) ).

cnf(refute_0_5263,plain,
    multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) = multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_5264,plain,
    ( multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) != multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))
    | greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))) ),[1,0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_5265,plain,
    ( greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))) )],[refute_0_5263,refute_0_5264]) ).

cnf(refute_0_5266,plain,
    multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3860,refute_0_5265]) ).

cnf(refute_0_5267,plain,
    ( multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) != multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))
    | multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) != multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))
    | multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))),bind(Y0,$fot(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))),bind(Z0,$fot(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_5268,plain,
    ( multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) != multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))
    | multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))) )],[refute_0_5266,refute_0_5267]) ).

cnf(refute_0_5269,plain,
    multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))) )],[refute_0_5262,refute_0_5268]) ).

cnf(refute_0_5270,plain,
    multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328)),
    inference(subst,[],[refute_0_5254:[bind(X_326,$fot(X_328))]]) ).

cnf(refute_0_5271,plain,
    greatest_lower_bound(identity,X_328) = greatest_lower_bound(X_328,identity),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_328))]]) ).

cnf(refute_0_5272,plain,
    ( greatest_lower_bound(identity,X_328) != greatest_lower_bound(X_328,identity)
    | greatest_lower_bound(X_328,identity) = greatest_lower_bound(identity,X_328) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(identity,X_328))),bind(Y0,$fot(greatest_lower_bound(X_328,identity)))]]) ).

cnf(refute_0_5273,plain,
    greatest_lower_bound(X_328,identity) = greatest_lower_bound(identity,X_328),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)) )],[refute_0_5271,refute_0_5272]) ).

cnf(refute_0_5274,plain,
    ( multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328))
    | greatest_lower_bound(X_328,identity) != greatest_lower_bound(identity,X_328)
    | multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328))) ),[0,1],$fot(greatest_lower_bound(identity,X_328))]]) ).

cnf(refute_0_5275,plain,
    ( multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328))
    | multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_328,identity),greatest_lower_bound(identity,X_328)) )],[refute_0_5273,refute_0_5274]) ).

cnf(refute_0_5276,plain,
    multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328))) )],[refute_0_5270,refute_0_5275]) ).

cnf(refute_0_5277,plain,
    ( multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,identity)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326))
    | greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326)) = multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326))))]]) ).

cnf(refute_0_5278,plain,
    greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326)) = multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,identity)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_326),greatest_lower_bound(X_326,identity)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_326),X_326))) )],[refute_0_5254,refute_0_5277]) ).

cnf(refute_0_5279,plain,
    greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328)) = multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)),
    inference(subst,[],[refute_0_5278:[bind(X_326,$fot(X_328))]]) ).

cnf(refute_0_5280,plain,
    ( multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328))
    | greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328)) != multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity))
    | multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)) = multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)),multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity))) ),[0],$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328)))]]) ).

cnf(refute_0_5281,plain,
    ( multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328))
    | multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)) = multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328)),multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity))) )],[refute_0_5279,refute_0_5280]) ).

cnf(refute_0_5282,plain,
    multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)) = multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)),greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_328),X_328))) )],[refute_0_5276,refute_0_5281]) ).

cnf(refute_0_5283,plain,
    ( multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)) != multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity))
    | multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)) = multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity))))]]) ).

cnf(refute_0_5284,plain,
    multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity)) = multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(identity,X_328)),multiply(greatest_lower_bound(identity,X_328),greatest_lower_bound(X_328,identity))) )],[refute_0_5282,refute_0_5283]) ).

cnf(refute_0_5285,plain,
    multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) = multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_5284:[bind(X_328,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_5286,plain,
    ( multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) != multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))
    | multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) != multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))
    | multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))),bind(Z0,$fot(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_5287,plain,
    ( multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) != multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))
    | multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)),multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))) )],[refute_0_5285,refute_0_5286]) ).

cnf(refute_0_5288,plain,
    multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))),multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))) )],[refute_0_5269,refute_0_5287]) ).

cnf(refute_0_5289,plain,
    ( multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) != multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))
    | multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))
    | multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))) ),[0],$fot(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_5290,plain,
    ( multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))
    | multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)),multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))) )],[refute_0_5288,refute_0_5289]) ).

cnf(refute_0_5291,plain,
    multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity)),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))) )],[refute_0_5258,refute_0_5290]) ).

cnf(refute_0_5292,plain,
    multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))),
    inference(subst,[],[refute_0_340:[bind(X_122,$fot(inverse(greatest_lower_bound(a,identity)))),bind(X_123,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_5293,plain,
    greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) = greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))),
    inference(subst,[],[refute_0_625:[bind(X_204,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_5294,plain,
    ( greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) != greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))
    | greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) = greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))) ),[1,1,0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_5295,plain,
    ( greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) != greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))
    | greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) = greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3860,refute_0_5294]) ).

cnf(refute_0_5296,plain,
    greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) = greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))))) )],[refute_0_5293,refute_0_5295]) ).

cnf(refute_0_5297,plain,
    greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) = greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_3839:[bind(X,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_5298,plain,
    ( greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) != greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) = greatest_lower_bound(a,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))))),bind(Z0,$fot(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_5299,plain,
    ( greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) = greatest_lower_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity),greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity)))) )],[refute_0_5297,refute_0_5298]) ).

cnf(refute_0_5300,plain,
    greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3860,refute_0_5299]) ).

cnf(refute_0_5301,plain,
    ( greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) != greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))
    | greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) != greatest_lower_bound(a,identity)
    | greatest_lower_bound(a,identity) = greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) ),[0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_5302,plain,
    ( greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) != greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))
    | greatest_lower_bound(a,identity) = greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity),greatest_lower_bound(a,identity)) )],[refute_0_5300,refute_0_5301]) ).

cnf(refute_0_5303,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) = multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330))),
    inference(subst,[],[refute_0_3591:[bind(X_60,$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330)))]]) ).

cnf(refute_0_5304,plain,
    multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330)),
    inference(subst,[],[refute_0_1286:[bind(X_107,$fot(greatest_lower_bound(X_25,X_24))),bind(X_109,$fot(X_330))]]) ).

cnf(refute_0_5305,plain,
    ( multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))
    | greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) != multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330)))
    | greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) = multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330)))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330)))]]) ).

cnf(refute_0_5306,plain,
    ( greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) != multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330)))
    | greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) = multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))) )],[refute_0_5304,refute_0_5305]) ).

cnf(refute_0_5307,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) = multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330)))) )],[refute_0_5303,refute_0_5306]) ).

cnf(refute_0_5308,plain,
    greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330))]]) ).

cnf(refute_0_5309,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),identity) != inverse(greatest_lower_bound(X_24,X_25))
    | greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330)
    | greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330)) ),[1,0],$fot(inverse(greatest_lower_bound(X_24,X_25)))]]) ).

cnf(refute_0_5310,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),identity) != inverse(greatest_lower_bound(X_24,X_25))
    | greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330)) )],[refute_0_5308,refute_0_5309]) ).

cnf(refute_0_5311,plain,
    greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(greatest_lower_bound(X_24,X_25))) )],[refute_0_3606,refute_0_5310]) ).

cnf(refute_0_5312,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_108,multiply(greatest_lower_bound(X_25,X_24),X_60))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_108),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60))),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(greatest_lower_bound(X_24,X_25)))),bind(Y,$fot(X_108)),bind(Z,$fot(multiply(greatest_lower_bound(X_25,X_24),X_60)))]]) ).

cnf(refute_0_5313,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)) != X_60
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_108,multiply(greatest_lower_bound(X_25,X_24),X_60))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_108),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_108,multiply(greatest_lower_bound(X_25,X_24),X_60))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_108),X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_108,multiply(greatest_lower_bound(X_25,X_24),X_60))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_108),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)))) ),[1,1],$fot(X_60)]]) ).

cnf(refute_0_5314,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_108,multiply(greatest_lower_bound(X_25,X_24),X_60))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_108),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)))
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_108,multiply(greatest_lower_bound(X_25,X_24),X_60))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_108),X_60) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)),X_60) )],[refute_0_3616,refute_0_5313]) ).

cnf(refute_0_5315,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_108,multiply(greatest_lower_bound(X_25,X_24),X_60))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_108),X_60),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(X_108,multiply(greatest_lower_bound(X_25,X_24),X_60))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),X_108),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),X_60)))) )],[refute_0_5312,refute_0_5314]) ).

cnf(refute_0_5316,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330),
    inference(subst,[],[refute_0_5315:[bind(X_108,$fot(identity)),bind(X_60,$fot(X_330))]]) ).

cnf(refute_0_5317,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330)
    | greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330) != greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330)
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330))),bind(Z0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330)))]]) ).

cnf(refute_0_5318,plain,
    ( greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330) != greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330)
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330)) )],[refute_0_5316,refute_0_5317]) ).

cnf(refute_0_5319,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_330),greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330)) )],[refute_0_5311,refute_0_5318]) ).

cnf(refute_0_5320,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))) != greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330)
    | greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) != multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330)))
    | greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330)))) ),[1],$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330))]]) ).

cnf(refute_0_5321,plain,
    ( greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) != multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330)))
    | greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330))),greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330)) )],[refute_0_5319,refute_0_5320]) ).

cnf(refute_0_5322,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_330)))) )],[refute_0_5307,refute_0_5321]) ).

cnf(refute_0_5323,plain,
    ( greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) != greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330)
    | greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330) = greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330)))]]) ).

cnf(refute_0_5324,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330) = greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(X_25,X_24)),X_330),greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_330)) )],[refute_0_5322,refute_0_5323]) ).

cnf(refute_0_5325,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,least_upper_bound(b,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_5324:[bind(X_24,$fot(identity)),bind(X_25,$fot(a)),bind(X_330,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_5326,plain,
    greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))) = multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))))),
    inference(subst,[],[refute_0_3591:[bind(X_60,$fot(greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24)))))]]) ).

cnf(refute_0_5327,plain,
    multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326)),
    inference(subst,[],[refute_0_4594:[bind(X_107,$fot(greatest_lower_bound(X_25,X_24))),bind(X_108,$fot(X_326))]]) ).

cnf(refute_0_5328,plain,
    ( multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24)))) != greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))
    | greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))) != multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24)))))
    | greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))) = multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24)))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326)))]]) ).

cnf(refute_0_5329,plain,
    ( greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))) != multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24)))))
    | greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))) = multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))) )],[refute_0_5327,refute_0_5328]) ).

cnf(refute_0_5330,plain,
    greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))) = multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))),multiply(inverse(greatest_lower_bound(X_24,X_25)),multiply(greatest_lower_bound(X_25,X_24),greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24)))))) )],[refute_0_5326,refute_0_5329]) ).

cnf(refute_0_5331,plain,
    greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326))]]) ).

cnf(refute_0_5332,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),identity) != inverse(greatest_lower_bound(X_24,X_25))
    | greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326)
    | greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326)) ),[1,0],$fot(inverse(greatest_lower_bound(X_24,X_25)))]]) ).

cnf(refute_0_5333,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),identity) != inverse(greatest_lower_bound(X_24,X_25))
    | greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326)) )],[refute_0_5331,refute_0_5332]) ).

cnf(refute_0_5334,plain,
    greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),inverse(greatest_lower_bound(X_24,X_25))) )],[refute_0_3606,refute_0_5333]) ).

cnf(refute_0_5335,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326),
    inference(subst,[],[refute_0_5315:[bind(X_108,$fot(identity)),bind(X_60,$fot(X_326))]]) ).

cnf(refute_0_5336,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326)
    | greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326) != greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326)
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326))),bind(Z0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326)))]]) ).

cnf(refute_0_5337,plain,
    ( greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326) != greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326)
    | multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326)) )],[refute_0_5335,refute_0_5336]) ).

cnf(refute_0_5338,plain,
    multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_24,X_25)),identity),X_326),greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326)) )],[refute_0_5334,refute_0_5337]) ).

cnf(refute_0_5339,plain,
    ( multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))) != greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326)
    | greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))) != multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326)))
    | greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326)))) ),[1],$fot(greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326))]]) ).

cnf(refute_0_5340,plain,
    ( greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))) != multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326)))
    | greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326))),greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326)) )],[refute_0_5338,refute_0_5339]) ).

cnf(refute_0_5341,plain,
    greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))) = greatest_lower_bound(inverse(greatest_lower_bound(X_24,X_25)),X_326),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_326,inverse(greatest_lower_bound(X_25,X_24))),multiply(inverse(greatest_lower_bound(X_24,X_25)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_25,X_24),X_326)))) )],[refute_0_5330,refute_0_5340]) ).

cnf(refute_0_5342,plain,
    greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,least_upper_bound(b,identity))),
    inference(subst,[],[refute_0_5341:[bind(X_24,$fot(identity)),bind(X_25,$fot(a)),bind(X_326,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_5343,plain,
    ( greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,least_upper_bound(b,identity))))),bind(Z0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_5344,plain,
    ( greatest_lower_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))),greatest_lower_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,least_upper_bound(b,identity)))) )],[refute_0_5342,refute_0_5343]) ).

cnf(refute_0_5345,plain,
    greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity)))) )],[refute_0_5325,refute_0_5344]) ).

cnf(refute_0_5346,plain,
    ( greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))) != greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(a,identity) != greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))
    | greatest_lower_bound(a,identity) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,identity),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) ),[1],$fot(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_5347,plain,
    ( greatest_lower_bound(a,identity) != greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))
    | greatest_lower_bound(a,identity) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity))),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity)))) )],[refute_0_5345,refute_0_5346]) ).

cnf(refute_0_5348,plain,
    ( greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity) != greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))
    | greatest_lower_bound(a,identity) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,identity),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) )],[refute_0_5302,refute_0_5347]) ).

cnf(refute_0_5349,plain,
    greatest_lower_bound(a,identity) = greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),identity),greatest_lower_bound(multiply(a,least_upper_bound(b,identity)),inverse(greatest_lower_bound(a,identity)))) )],[refute_0_5296,refute_0_5348]) ).

cnf(refute_0_5350,plain,
    ( greatest_lower_bound(a,identity) != greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity)))
    | greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))) = greatest_lower_bound(a,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(a,identity))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity)))))]]) ).

cnf(refute_0_5351,plain,
    greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))) = greatest_lower_bound(a,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity)))) )],[refute_0_5349,refute_0_5350]) ).

cnf(refute_0_5352,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))
    | greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))),greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))) ),[0,0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_5353,plain,
    ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_5351,refute_0_5352]) ).

cnf(refute_0_5354,plain,
    multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(a,identity)),multiply(a,least_upper_bound(b,identity))),inverse(inverse(greatest_lower_bound(a,identity)))),greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_5292,refute_0_5353]) ).

cnf(refute_0_5355,plain,
    multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_5356,plain,
    ( multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity))))
    | inverse(inverse(greatest_lower_bound(a,identity))) != greatest_lower_bound(a,identity)
    | multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity))))) ),[1,1],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_5357,plain,
    ( inverse(inverse(greatest_lower_bound(a,identity))) != greatest_lower_bound(a,identity)
    | multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity))))) )],[refute_0_5355,refute_0_5356]) ).

cnf(refute_0_5358,plain,
    multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(a,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3765,refute_0_5357]) ).

cnf(refute_0_5359,plain,
    ( multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))
    | multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))),greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))) ),[0],$fot(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_5360,plain,
    ( multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))) )],[refute_0_5358,refute_0_5359]) ).

cnf(refute_0_5361,plain,
    ( multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) != b
    | multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = b ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))),bind(Y0,$fot(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)))),bind(Z0,$fot(b))]]) ).

cnf(refute_0_5362,plain,
    ( multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)) != b
    | multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = b ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity))) )],[refute_0_3769,refute_0_5361]) ).

cnf(refute_0_5363,plain,
    multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) = b,
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),greatest_lower_bound(a,identity)),b) )],[refute_0_3810,refute_0_5362]) ).

cnf(refute_0_5364,plain,
    multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))),
    introduced(tautology,[refl,[$fot(multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_5365,plain,
    ( multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) != multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) != b
    | multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(a,b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))),multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))) ),[1,1],$fot(b)]]) ).

cnf(refute_0_5366,plain,
    ( multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))) != b
    | multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(a,b) ),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))),multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_5364,refute_0_5365]) ).

cnf(refute_0_5367,plain,
    multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) = multiply(a,b),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))),b) )],[refute_0_5363,refute_0_5366]) ).

cnf(refute_0_5368,plain,
    multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))),
    inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(least_upper_bound(b,identity))),bind(Z,$fot(inverse(inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_5369,plain,
    ( multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) != multiply(a,b)
    | multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(a,b) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))),bind(Y0,$fot(multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))))),bind(Z0,$fot(multiply(a,b)))]]) ).

cnf(refute_0_5370,plain,
    ( multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))) != multiply(a,b)
    | multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(a,b) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_5368,refute_0_5369]) ).

cnf(refute_0_5371,plain,
    multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) = multiply(a,b),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(least_upper_bound(b,identity),inverse(inverse(greatest_lower_bound(a,identity))))),multiply(a,b)) )],[refute_0_5367,refute_0_5370]) ).

cnf(refute_0_5372,plain,
    greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) = greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_5373,plain,
    ( multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(a,b)
    | greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) != greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))
    | greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) = greatest_lower_bound(identity,multiply(a,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))),greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))) ),[1,1],$fot(multiply(a,b))]]) ).

cnf(refute_0_5374,plain,
    ( multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))) != multiply(a,b)
    | greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) = greatest_lower_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))),greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_5372,refute_0_5373]) ).

cnf(refute_0_5375,plain,
    greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) = greatest_lower_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))),multiply(a,b)) )],[refute_0_5371,refute_0_5374]) ).

cnf(refute_0_5376,plain,
    ( multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))
    | greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) != greatest_lower_bound(identity,multiply(a,b))
    | multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(a,b)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,multiply(a,b))) ),[0],$fot(greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_5377,plain,
    ( multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity))))),greatest_lower_bound(identity,multiply(a,b))) )],[refute_0_5375,refute_0_5376]) ).

cnf(refute_0_5378,plain,
    ( multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))) != greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))
    | multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_5360,refute_0_5377]) ).

cnf(refute_0_5379,plain,
    multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),inverse(inverse(greatest_lower_bound(a,identity)))),greatest_lower_bound(identity,multiply(multiply(a,least_upper_bound(b,identity)),inverse(inverse(greatest_lower_bound(a,identity)))))) )],[refute_0_5354,refute_0_5378]) ).

cnf(refute_0_5380,plain,
    ( multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(a,b))
    | multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))
    | greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))) ),[0],$fot(greatest_lower_bound(identity,multiply(a,b)))]]) ).

cnf(refute_0_5381,plain,
    ( multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))
    | greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,multiply(a,b))) )],[refute_0_5379,refute_0_5380]) ).

cnf(refute_0_5382,plain,
    greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))) )],[refute_0_5291,refute_0_5381]) ).

cnf(refute_0_5383,plain,
    ( greatest_lower_bound(identity,multiply(a,b)) != greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))
    | greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) = greatest_lower_bound(identity,multiply(a,b)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(identity,multiply(a,b)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_5384,plain,
    greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) = greatest_lower_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))) )],[refute_0_5382,refute_0_5383]) ).

cnf(refute_0_5385,plain,
    ( multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))))
    | greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) != greatest_lower_bound(identity,multiply(a,b))
    | multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))))) ),[1,1],$fot(greatest_lower_bound(identity,multiply(a,b)))]]) ).

cnf(refute_0_5386,plain,
    ( multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))))
    | multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) )],[refute_0_5384,refute_0_5385]) ).

cnf(refute_0_5387,plain,
    multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))))) )],[refute_0_5247,refute_0_5386]) ).

cnf(refute_0_5388,plain,
    ( X_129 != multiply(least_upper_bound(identity,X_129),greatest_lower_bound(identity,X_129))
    | multiply(least_upper_bound(identity,X_129),greatest_lower_bound(identity,X_129)) = X_129 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_129)),bind(Y0,$fot(multiply(least_upper_bound(identity,X_129),greatest_lower_bound(identity,X_129))))]]) ).

cnf(refute_0_5389,plain,
    multiply(least_upper_bound(identity,X_129),greatest_lower_bound(identity,X_129)) = X_129,
    inference(resolve,[$cnf( $equal(X_129,multiply(least_upper_bound(identity,X_129),greatest_lower_bound(identity,X_129))) )],[refute_0_334,refute_0_5388]) ).

cnf(refute_0_5390,plain,
    multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(a,b))) = multiply(a,b),
    inference(subst,[],[refute_0_5389:[bind(X_129,$fot(multiply(a,b)))]]) ).

cnf(refute_0_5391,plain,
    multiply(least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110)))),X_110) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)),
    inference(subst,[],[refute_0_166:[bind(X_112,$fot(inverse(least_upper_bound(identity,inverse(X_110)))))]]) ).

cnf(refute_0_5392,plain,
    least_upper_bound(inverse(X_110),identity) = least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110)))),
    inference(subst,[],[refute_0_712:[bind(X_210,$fot(inverse(X_110)))]]) ).

cnf(refute_0_5393,plain,
    ( least_upper_bound(inverse(X_110),identity) != least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110))))
    | least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110)))) = least_upper_bound(inverse(X_110),identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(inverse(X_110),identity))),bind(Y0,$fot(least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110))))))]]) ).

cnf(refute_0_5394,plain,
    least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110)))) = least_upper_bound(inverse(X_110),identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_110),identity),least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110))))) )],[refute_0_5392,refute_0_5393]) ).

cnf(refute_0_5395,plain,
    ( multiply(least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110)))),X_110) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))
    | least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110)))) != least_upper_bound(inverse(X_110),identity)
    | multiply(least_upper_bound(inverse(X_110),identity),X_110) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110)))),X_110),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))) ),[0,0],$fot(least_upper_bound(inverse(X_110),identity))]]) ).

cnf(refute_0_5396,plain,
    ( multiply(least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110)))),X_110) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))
    | multiply(least_upper_bound(inverse(X_110),identity),X_110) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110)))),least_upper_bound(inverse(X_110),identity)) )],[refute_0_5394,refute_0_5395]) ).

cnf(refute_0_5397,plain,
    multiply(least_upper_bound(inverse(X_110),identity),X_110) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_110),inverse(least_upper_bound(identity,inverse(X_110)))),X_110),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))) )],[refute_0_5391,refute_0_5396]) ).

cnf(refute_0_5398,plain,
    multiply(identity,least_upper_bound(X_110,identity)) = least_upper_bound(X_110,identity),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_110,identity)))]]) ).

cnf(refute_0_5399,plain,
    least_upper_bound(identity,multiply(identity,X_110)) = multiply(identity,least_upper_bound(X_110,identity)),
    inference(subst,[],[refute_0_549:[bind(X_93,$fot(identity)),bind(X_94,$fot(X_110))]]) ).

cnf(refute_0_5400,plain,
    ( multiply(identity,least_upper_bound(X_110,identity)) != least_upper_bound(X_110,identity)
    | least_upper_bound(identity,multiply(identity,X_110)) != multiply(identity,least_upper_bound(X_110,identity))
    | least_upper_bound(identity,multiply(identity,X_110)) = least_upper_bound(X_110,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,multiply(identity,X_110)))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_110,identity)))),bind(Z0,$fot(least_upper_bound(X_110,identity)))]]) ).

cnf(refute_0_5401,plain,
    ( multiply(identity,least_upper_bound(X_110,identity)) != least_upper_bound(X_110,identity)
    | least_upper_bound(identity,multiply(identity,X_110)) = least_upper_bound(X_110,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_110)),multiply(identity,least_upper_bound(X_110,identity))) )],[refute_0_5399,refute_0_5400]) ).

cnf(refute_0_5402,plain,
    least_upper_bound(identity,multiply(identity,X_110)) = least_upper_bound(X_110,identity),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_110,identity)),least_upper_bound(X_110,identity)) )],[refute_0_5398,refute_0_5401]) ).

cnf(refute_0_5403,plain,
    multiply(least_upper_bound(inverse(X_110),identity),X_110) = least_upper_bound(identity,multiply(identity,X_110)),
    inference(subst,[],[refute_0_166:[bind(X_112,$fot(identity))]]) ).

cnf(refute_0_5404,plain,
    ( multiply(least_upper_bound(inverse(X_110),identity),X_110) != least_upper_bound(identity,multiply(identity,X_110))
    | least_upper_bound(identity,multiply(identity,X_110)) != least_upper_bound(X_110,identity)
    | multiply(least_upper_bound(inverse(X_110),identity),X_110) = least_upper_bound(X_110,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(inverse(X_110),identity),X_110))),bind(Y0,$fot(least_upper_bound(identity,multiply(identity,X_110)))),bind(Z0,$fot(least_upper_bound(X_110,identity)))]]) ).

cnf(refute_0_5405,plain,
    ( least_upper_bound(identity,multiply(identity,X_110)) != least_upper_bound(X_110,identity)
    | multiply(least_upper_bound(inverse(X_110),identity),X_110) = least_upper_bound(X_110,identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_110),identity),X_110),least_upper_bound(identity,multiply(identity,X_110))) )],[refute_0_5403,refute_0_5404]) ).

cnf(refute_0_5406,plain,
    multiply(least_upper_bound(inverse(X_110),identity),X_110) = least_upper_bound(X_110,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(identity,X_110)),least_upper_bound(X_110,identity)) )],[refute_0_5402,refute_0_5405]) ).

cnf(refute_0_5407,plain,
    ( multiply(least_upper_bound(inverse(X_110),identity),X_110) != least_upper_bound(X_110,identity)
    | multiply(least_upper_bound(inverse(X_110),identity),X_110) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))
    | least_upper_bound(X_110,identity) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_110),identity),X_110),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))) ),[0],$fot(least_upper_bound(X_110,identity))]]) ).

cnf(refute_0_5408,plain,
    ( multiply(least_upper_bound(inverse(X_110),identity),X_110) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))
    | least_upper_bound(X_110,identity) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_110),identity),X_110),least_upper_bound(X_110,identity)) )],[refute_0_5406,refute_0_5407]) ).

cnf(refute_0_5409,plain,
    greatest_lower_bound(inverse(identity),X_110) = greatest_lower_bound(inverse(identity),X_110),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(identity),X_110))]]) ).

cnf(refute_0_5410,plain,
    ( greatest_lower_bound(inverse(identity),X_110) != greatest_lower_bound(inverse(identity),X_110)
    | inverse(identity) != identity
    | greatest_lower_bound(inverse(identity),X_110) = greatest_lower_bound(identity,X_110) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(identity),X_110),greatest_lower_bound(inverse(identity),X_110)) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_5411,plain,
    ( inverse(identity) != identity
    | greatest_lower_bound(inverse(identity),X_110) = greatest_lower_bound(identity,X_110) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(identity),X_110),greatest_lower_bound(inverse(identity),X_110)) )],[refute_0_5409,refute_0_5410]) ).

cnf(refute_0_5412,plain,
    greatest_lower_bound(inverse(identity),X_110) = greatest_lower_bound(identity,X_110),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_296,refute_0_5411]) ).

cnf(refute_0_5413,plain,
    inverse(least_upper_bound(identity,inverse(X_110))) = greatest_lower_bound(inverse(identity),X_110),
    inference(subst,[],[refute_0_582:[bind(X,$fot(identity)),bind(X_89,$fot(X_110))]]) ).

cnf(refute_0_5414,plain,
    ( greatest_lower_bound(inverse(identity),X_110) != greatest_lower_bound(identity,X_110)
    | inverse(least_upper_bound(identity,inverse(X_110))) != greatest_lower_bound(inverse(identity),X_110)
    | inverse(least_upper_bound(identity,inverse(X_110))) = greatest_lower_bound(identity,X_110) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(least_upper_bound(identity,inverse(X_110))))),bind(Y0,$fot(greatest_lower_bound(inverse(identity),X_110))),bind(Z0,$fot(greatest_lower_bound(identity,X_110)))]]) ).

cnf(refute_0_5415,plain,
    ( greatest_lower_bound(inverse(identity),X_110) != greatest_lower_bound(identity,X_110)
    | inverse(least_upper_bound(identity,inverse(X_110))) = greatest_lower_bound(identity,X_110) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_110))),greatest_lower_bound(inverse(identity),X_110)) )],[refute_0_5413,refute_0_5414]) ).

cnf(refute_0_5416,plain,
    inverse(least_upper_bound(identity,inverse(X_110))) = greatest_lower_bound(identity,X_110),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(identity),X_110),greatest_lower_bound(identity,X_110)) )],[refute_0_5412,refute_0_5415]) ).

cnf(refute_0_5417,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110) = multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110),
    introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))]]) ).

cnf(refute_0_5418,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110) != multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)
    | inverse(least_upper_bound(identity,inverse(X_110))) != greatest_lower_bound(identity,X_110)
    | multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110) = multiply(greatest_lower_bound(identity,X_110),X_110) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110),multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) ),[1,0],$fot(greatest_lower_bound(identity,X_110))]]) ).

cnf(refute_0_5419,plain,
    ( inverse(least_upper_bound(identity,inverse(X_110))) != greatest_lower_bound(identity,X_110)
    | multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110) = multiply(greatest_lower_bound(identity,X_110),X_110) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110),multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) )],[refute_0_5417,refute_0_5418]) ).

cnf(refute_0_5420,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110) = multiply(greatest_lower_bound(identity,X_110),X_110),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,inverse(X_110))),greatest_lower_bound(identity,X_110)) )],[refute_0_5416,refute_0_5419]) ).

cnf(refute_0_5421,plain,
    least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)))]]) ).

cnf(refute_0_5422,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110) != multiply(greatest_lower_bound(identity,X_110),X_110)
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_110),X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))) ),[1,1],$fot(multiply(greatest_lower_bound(identity,X_110),X_110))]]) ).

cnf(refute_0_5423,plain,
    ( multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110) != multiply(greatest_lower_bound(identity,X_110),X_110)
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_110),X_110)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))) )],[refute_0_5421,refute_0_5422]) ).

cnf(refute_0_5424,plain,
    least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_110),X_110)),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110),multiply(greatest_lower_bound(identity,X_110),X_110)) )],[refute_0_5420,refute_0_5423]) ).

cnf(refute_0_5425,plain,
    ( least_upper_bound(X_110,identity) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))
    | least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_110),X_110))
    | least_upper_bound(X_110,identity) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_110),X_110)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_110,identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_110),X_110))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)))]]) ).

cnf(refute_0_5426,plain,
    ( least_upper_bound(X_110,identity) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))
    | least_upper_bound(X_110,identity) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_110),X_110)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110)),least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_110),X_110))) )],[refute_0_5424,refute_0_5425]) ).

cnf(refute_0_5427,plain,
    ( multiply(least_upper_bound(inverse(X_110),identity),X_110) != least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))
    | least_upper_bound(X_110,identity) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_110),X_110)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_110,identity),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))) )],[refute_0_5408,refute_0_5426]) ).

cnf(refute_0_5428,plain,
    least_upper_bound(X_110,identity) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,X_110),X_110)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_110),identity),X_110),least_upper_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X_110))),X_110))) )],[refute_0_5397,refute_0_5427]) ).

cnf(refute_0_5429,plain,
    least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),multiply(a,least_upper_bound(b,identity)))),
    inference(subst,[],[refute_0_5428:[bind(X_110,$fot(multiply(a,least_upper_bound(b,identity))))]]) ).

cnf(refute_0_5430,plain,
    ( greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))) != greatest_lower_bound(a,identity)
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),multiply(a,least_upper_bound(b,identity))))
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),multiply(a,least_upper_bound(b,identity))))) ),[1,1,0],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_5431,plain,
    ( least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),multiply(a,least_upper_bound(b,identity))))
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),greatest_lower_bound(a,identity)) )],[refute_0_3860,refute_0_5430]) ).

cnf(refute_0_5432,plain,
    least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),least_upper_bound(identity,multiply(greatest_lower_bound(identity,multiply(a,least_upper_bound(b,identity))),multiply(a,least_upper_bound(b,identity))))) )],[refute_0_5429,refute_0_5431]) ).

cnf(refute_0_5433,plain,
    ( least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(a,least_upper_bound(b,identity)))
    | least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(a,b))
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(a,b)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity))),bind(Y0,$fot(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))))),bind(Z0,$fot(least_upper_bound(identity,multiply(a,b))))]]) ).

cnf(refute_0_5434,plain,
    ( least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))) != least_upper_bound(identity,multiply(a,b))
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),least_upper_bound(identity,multiply(a,least_upper_bound(b,identity)))) )],[refute_0_4132,refute_0_5433]) ).

cnf(refute_0_5435,plain,
    least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) = least_upper_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,least_upper_bound(b,identity))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_4159,refute_0_5434]) ).

cnf(refute_0_5436,plain,
    ( least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(a,b))
    | least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))
    | least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))) ),[0],$fot(least_upper_bound(identity,multiply(a,b)))]]) ).

cnf(refute_0_5437,plain,
    ( least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity) != least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))
    | least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),least_upper_bound(identity,multiply(a,b))) )],[refute_0_5435,refute_0_5436]) ).

cnf(refute_0_5438,plain,
    least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(a,least_upper_bound(b,identity)),identity),least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))) )],[refute_0_5432,refute_0_5437]) ).

cnf(refute_0_5439,plain,
    ( least_upper_bound(identity,multiply(a,b)) != least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))
    | least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) = least_upper_bound(identity,multiply(a,b)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,multiply(a,b)))),bind(Y0,$fot(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))))]]) ).

cnf(refute_0_5440,plain,
    least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) = least_upper_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(a,b)),least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))) )],[refute_0_5438,refute_0_5439]) ).

cnf(refute_0_5441,plain,
    multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) = multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))))]]) ).

cnf(refute_0_5442,plain,
    ( multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b)))
    | least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) != least_upper_bound(identity,multiply(a,b))
    | multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(a,b))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b)))) ),[1,0],$fot(least_upper_bound(identity,multiply(a,b)))]]) ).

cnf(refute_0_5443,plain,
    ( least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))) != least_upper_bound(identity,multiply(a,b))
    | multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(a,b))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b)))) )],[refute_0_5441,refute_0_5442]) ).

cnf(refute_0_5444,plain,
    multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(a,b))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),least_upper_bound(identity,multiply(a,b))) )],[refute_0_5440,refute_0_5443]) ).

cnf(refute_0_5445,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(a,b))) != multiply(a,b)
    | multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) != multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(a,b)))
    | multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) = multiply(a,b) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(a,b))))),bind(Z0,$fot(multiply(a,b)))]]) ).

cnf(refute_0_5446,plain,
    ( multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(a,b))) != multiply(a,b)
    | multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) = multiply(a,b) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))),multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(a,b)))) )],[refute_0_5444,refute_0_5445]) ).

cnf(refute_0_5447,plain,
    multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) = multiply(a,b),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(a,b))),multiply(a,b)) )],[refute_0_5390,refute_0_5446]) ).

cnf(refute_0_5448,plain,
    ( multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b)))
    | multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))) != multiply(a,b)
    | multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) = multiply(a,b) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))),multiply(a,b)) ),[0],$fot(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))))]]) ).

cnf(refute_0_5449,plain,
    ( multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) != multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b)))
    | multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) = multiply(a,b) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b))),multiply(a,b)) )],[refute_0_5447,refute_0_5448]) ).

cnf(refute_0_5450,plain,
    multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) = multiply(a,b),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))),multiply(least_upper_bound(identity,multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity)))),greatest_lower_bound(identity,multiply(a,b)))) )],[refute_0_5387,refute_0_5449]) ).

cnf(refute_0_5451,plain,
    ( multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(a,identity))
    | multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))) != multiply(a,b)
    | multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))) = inverse(greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))),inverse(greatest_lower_bound(a,identity))) ),[0,1,0],$fot(multiply(a,b))]]) ).

cnf(refute_0_5452,plain,
    ( multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))) != inverse(greatest_lower_bound(a,identity))
    | multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))),multiply(a,b)) )],[refute_0_5450,refute_0_5451]) ).

cnf(refute_0_5453,plain,
    multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(greatest_lower_bound(a,identity),multiply(a,least_upper_bound(b,identity))))),inverse(greatest_lower_bound(a,identity))) )],[refute_0_5246,refute_0_5452]) ).

cnf(refute_0_5454,plain,
    multiply(a,greatest_lower_bound(b,identity)) = multiply(a,greatest_lower_bound(b,identity)),
    introduced(tautology,[refl,[$fot(multiply(a,greatest_lower_bound(b,identity)))]]) ).

cnf(refute_0_5455,plain,
    ( multiply(a,greatest_lower_bound(b,identity)) != multiply(a,greatest_lower_bound(b,identity))
    | greatest_lower_bound(b,identity) != greatest_lower_bound(a,identity)
    | multiply(a,greatest_lower_bound(b,identity)) = multiply(a,greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,greatest_lower_bound(b,identity)),multiply(a,greatest_lower_bound(b,identity))) ),[1,1],$fot(greatest_lower_bound(a,identity))]]) ).

cnf(refute_0_5456,plain,
    ( greatest_lower_bound(b,identity) != greatest_lower_bound(a,identity)
    | multiply(a,greatest_lower_bound(b,identity)) = multiply(a,greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(b,identity)),multiply(a,greatest_lower_bound(b,identity))) )],[refute_0_5454,refute_0_5455]) ).

cnf(refute_0_5457,plain,
    multiply(a,greatest_lower_bound(b,identity)) = multiply(a,greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),greatest_lower_bound(a,identity)) )],[refute_0_2212,refute_0_5456]) ).

cnf(refute_0_5458,plain,
    inverse(multiply(a,greatest_lower_bound(b,identity))) = inverse(multiply(a,greatest_lower_bound(b,identity))),
    introduced(tautology,[refl,[$fot(inverse(multiply(a,greatest_lower_bound(b,identity))))]]) ).

cnf(refute_0_5459,plain,
    ( multiply(a,greatest_lower_bound(b,identity)) != multiply(a,greatest_lower_bound(a,identity))
    | inverse(multiply(a,greatest_lower_bound(b,identity))) != inverse(multiply(a,greatest_lower_bound(b,identity)))
    | inverse(multiply(a,greatest_lower_bound(b,identity))) = inverse(multiply(a,greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(a,greatest_lower_bound(b,identity))),inverse(multiply(a,greatest_lower_bound(b,identity)))) ),[1,0],$fot(multiply(a,greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_5460,plain,
    ( multiply(a,greatest_lower_bound(b,identity)) != multiply(a,greatest_lower_bound(a,identity))
    | inverse(multiply(a,greatest_lower_bound(b,identity))) = inverse(multiply(a,greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(a,greatest_lower_bound(b,identity))),inverse(multiply(a,greatest_lower_bound(b,identity)))) )],[refute_0_5458,refute_0_5459]) ).

cnf(refute_0_5461,plain,
    inverse(multiply(a,greatest_lower_bound(b,identity))) = inverse(multiply(a,greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(a,greatest_lower_bound(b,identity)),multiply(a,greatest_lower_bound(a,identity))) )],[refute_0_5457,refute_0_5460]) ).

cnf(refute_0_5462,plain,
    multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))) = least_upper_bound(inverse(multiply(X_59,X_230)),multiply(X_230,inverse(multiply(X_59,X_230)))),
    inference(subst,[],[refute_0_728:[bind(X_110,$fot(inverse(multiply(X_59,X_230)))),bind(X_111,$fot(X_230))]]) ).

cnf(refute_0_5463,plain,
    multiply(X_230,inverse(multiply(X_59,X_230))) = inverse(X_59),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(X_230))]]) ).

cnf(refute_0_5464,plain,
    ( multiply(X_230,inverse(multiply(X_59,X_230))) != inverse(X_59)
    | multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))) != least_upper_bound(inverse(multiply(X_59,X_230)),multiply(X_230,inverse(multiply(X_59,X_230))))
    | multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))) = least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))),least_upper_bound(inverse(multiply(X_59,X_230)),multiply(X_230,inverse(multiply(X_59,X_230))))) ),[1,1],$fot(inverse(X_59))]]) ).

cnf(refute_0_5465,plain,
    ( multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))) != least_upper_bound(inverse(multiply(X_59,X_230)),multiply(X_230,inverse(multiply(X_59,X_230))))
    | multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))) = least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) ),
    inference(resolve,[$cnf( $equal(multiply(X_230,inverse(multiply(X_59,X_230))),inverse(X_59)) )],[refute_0_5463,refute_0_5464]) ).

cnf(refute_0_5466,plain,
    multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))) = least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))),least_upper_bound(inverse(multiply(X_59,X_230)),multiply(X_230,inverse(multiply(X_59,X_230))))) )],[refute_0_5462,refute_0_5465]) ).

cnf(refute_0_5467,plain,
    greatest_lower_bound(X_59,multiply(X_59,X_230)) = multiply(X_59,greatest_lower_bound(X_230,identity)),
    inference(subst,[],[refute_0_308:[bind(X_107,$fot(X_59)),bind(X_108,$fot(X_230))]]) ).

cnf(refute_0_5468,plain,
    inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))) = inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))))]]) ).

cnf(refute_0_5469,plain,
    ( greatest_lower_bound(X_59,multiply(X_59,X_230)) != multiply(X_59,greatest_lower_bound(X_230,identity))
    | inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))) != inverse(greatest_lower_bound(X_59,multiply(X_59,X_230)))
    | inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))) = inverse(multiply(X_59,greatest_lower_bound(X_230,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))),inverse(greatest_lower_bound(X_59,multiply(X_59,X_230)))) ),[1,0],$fot(multiply(X_59,greatest_lower_bound(X_230,identity)))]]) ).

cnf(refute_0_5470,plain,
    ( greatest_lower_bound(X_59,multiply(X_59,X_230)) != multiply(X_59,greatest_lower_bound(X_230,identity))
    | inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))) = inverse(multiply(X_59,greatest_lower_bound(X_230,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))),inverse(greatest_lower_bound(X_59,multiply(X_59,X_230)))) )],[refute_0_5468,refute_0_5469]) ).

cnf(refute_0_5471,plain,
    inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))) = inverse(multiply(X_59,greatest_lower_bound(X_230,identity))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_59,multiply(X_59,X_230)),multiply(X_59,greatest_lower_bound(X_230,identity))) )],[refute_0_5467,refute_0_5470]) ).

cnf(refute_0_5472,plain,
    least_upper_bound(inverse(X_59),inverse(multiply(X_59,X_230))) = inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))),
    inference(subst,[],[refute_0_136:[bind(X,$fot(X_59)),bind(Y,$fot(multiply(X_59,X_230)))]]) ).

cnf(refute_0_5473,plain,
    least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) = least_upper_bound(inverse(X_59),inverse(multiply(X_59,X_230))),
    inference(subst,[],[refute_0_88:[bind(X_16,$fot(inverse(multiply(X_59,X_230)))),bind(X_17,$fot(inverse(X_59)))]]) ).

cnf(refute_0_5474,plain,
    ( least_upper_bound(inverse(X_59),inverse(multiply(X_59,X_230))) != inverse(greatest_lower_bound(X_59,multiply(X_59,X_230)))
    | least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) != least_upper_bound(inverse(X_59),inverse(multiply(X_59,X_230)))
    | least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) = inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)))),bind(Y0,$fot(least_upper_bound(inverse(X_59),inverse(multiply(X_59,X_230))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_59,multiply(X_59,X_230)))))]]) ).

cnf(refute_0_5475,plain,
    ( least_upper_bound(inverse(X_59),inverse(multiply(X_59,X_230))) != inverse(greatest_lower_bound(X_59,multiply(X_59,X_230)))
    | least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) = inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)),least_upper_bound(inverse(X_59),inverse(multiply(X_59,X_230)))) )],[refute_0_5473,refute_0_5474]) ).

cnf(refute_0_5476,plain,
    least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) = inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_59),inverse(multiply(X_59,X_230))),inverse(greatest_lower_bound(X_59,multiply(X_59,X_230)))) )],[refute_0_5472,refute_0_5475]) ).

cnf(refute_0_5477,plain,
    ( inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))) != inverse(multiply(X_59,greatest_lower_bound(X_230,identity)))
    | least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) != inverse(greatest_lower_bound(X_59,multiply(X_59,X_230)))
    | least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) = inverse(multiply(X_59,greatest_lower_bound(X_230,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))))),bind(Z0,$fot(inverse(multiply(X_59,greatest_lower_bound(X_230,identity)))))]]) ).

cnf(refute_0_5478,plain,
    ( inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))) != inverse(multiply(X_59,greatest_lower_bound(X_230,identity)))
    | least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) = inverse(multiply(X_59,greatest_lower_bound(X_230,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)),inverse(greatest_lower_bound(X_59,multiply(X_59,X_230)))) )],[refute_0_5476,refute_0_5477]) ).

cnf(refute_0_5479,plain,
    least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) = inverse(multiply(X_59,greatest_lower_bound(X_230,identity))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_59,multiply(X_59,X_230))),inverse(multiply(X_59,greatest_lower_bound(X_230,identity)))) )],[refute_0_5471,refute_0_5478]) ).

cnf(refute_0_5480,plain,
    ( multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))) != least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59))
    | least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)) != inverse(multiply(X_59,greatest_lower_bound(X_230,identity)))
    | multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))) = inverse(multiply(X_59,greatest_lower_bound(X_230,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))),inverse(multiply(X_59,greatest_lower_bound(X_230,identity)))) ),[0],$fot(least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)))]]) ).

cnf(refute_0_5481,plain,
    ( multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))) != least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59))
    | multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))) = inverse(multiply(X_59,greatest_lower_bound(X_230,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59)),inverse(multiply(X_59,greatest_lower_bound(X_230,identity)))) )],[refute_0_5479,refute_0_5480]) ).

cnf(refute_0_5482,plain,
    multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))) = inverse(multiply(X_59,greatest_lower_bound(X_230,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_230,identity),inverse(multiply(X_59,X_230))),least_upper_bound(inverse(multiply(X_59,X_230)),inverse(X_59))) )],[refute_0_5466,refute_0_5481]) ).

cnf(refute_0_5483,plain,
    multiply(least_upper_bound(b,identity),inverse(multiply(a,b))) = inverse(multiply(a,greatest_lower_bound(b,identity))),
    inference(subst,[],[refute_0_5482:[bind(X_230,$fot(b)),bind(X_59,$fot(a))]]) ).

cnf(refute_0_5484,plain,
    ( multiply(least_upper_bound(b,identity),inverse(multiply(a,b))) != inverse(multiply(a,greatest_lower_bound(b,identity)))
    | inverse(multiply(a,greatest_lower_bound(b,identity))) != inverse(multiply(a,greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(b,identity),inverse(multiply(a,b))) = inverse(multiply(a,greatest_lower_bound(a,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(b,identity),inverse(multiply(a,b))))),bind(Y0,$fot(inverse(multiply(a,greatest_lower_bound(b,identity))))),bind(Z0,$fot(inverse(multiply(a,greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_5485,plain,
    ( inverse(multiply(a,greatest_lower_bound(b,identity))) != inverse(multiply(a,greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(b,identity),inverse(multiply(a,b))) = inverse(multiply(a,greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(multiply(a,b))),inverse(multiply(a,greatest_lower_bound(b,identity)))) )],[refute_0_5483,refute_0_5484]) ).

cnf(refute_0_5486,plain,
    multiply(least_upper_bound(b,identity),inverse(multiply(a,b))) = inverse(multiply(a,greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(inverse(multiply(a,greatest_lower_bound(b,identity))),inverse(multiply(a,greatest_lower_bound(a,identity)))) )],[refute_0_5461,refute_0_5485]) ).

cnf(refute_0_5487,plain,
    multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))) = multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))),
    introduced(tautology,[refl,[$fot(multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))))]]) ).

cnf(refute_0_5488,plain,
    ( multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))) != multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b))))
    | multiply(least_upper_bound(b,identity),inverse(multiply(a,b))) != inverse(multiply(a,greatest_lower_bound(a,identity)))
    | multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))) = multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))),multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b))))) ),[1,1],$fot(inverse(multiply(a,greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_5489,plain,
    ( multiply(least_upper_bound(b,identity),inverse(multiply(a,b))) != inverse(multiply(a,greatest_lower_bound(a,identity)))
    | multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))) = multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))),multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b))))) )],[refute_0_5487,refute_0_5488]) ).

cnf(refute_0_5490,plain,
    multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))) = multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),inverse(multiply(a,b))),inverse(multiply(a,greatest_lower_bound(a,identity)))) )],[refute_0_5486,refute_0_5489]) ).

cnf(refute_0_5491,plain,
    multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))) = multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))),
    inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(least_upper_bound(b,identity))),bind(Z,$fot(inverse(multiply(a,b))))]]) ).

cnf(refute_0_5492,plain,
    ( multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))) != multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b))))
    | multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))) != multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity))))
    | multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))) = multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))))),bind(Y0,$fot(multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))))),bind(Z0,$fot(multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_5493,plain,
    ( multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))) != multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity))))
    | multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))) = multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))),multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b))))) )],[refute_0_5491,refute_0_5492]) ).

cnf(refute_0_5494,plain,
    multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))) = multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(least_upper_bound(b,identity),inverse(multiply(a,b)))),multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity))))) )],[refute_0_5490,refute_0_5493]) ).

cnf(refute_0_5495,plain,
    ( multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))) != multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity))))
    | multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))) != inverse(greatest_lower_bound(a,identity))
    | multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))),inverse(greatest_lower_bound(a,identity))) ),[0],$fot(multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_5496,plain,
    ( multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))) != inverse(greatest_lower_bound(a,identity))
    | multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))),multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity))))) )],[refute_0_5494,refute_0_5495]) ).

cnf(refute_0_5497,plain,
    multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,least_upper_bound(b,identity)),inverse(multiply(a,b))),inverse(greatest_lower_bound(a,identity))) )],[refute_0_5453,refute_0_5496]) ).

cnf(refute_0_5498,plain,
    ( multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))) != inverse(greatest_lower_bound(a,identity))
    | multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) != least_upper_bound(a,multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))))
    | multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)),least_upper_bound(a,multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))))) ),[1,1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_5499,plain,
    ( multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) != least_upper_bound(a,multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))))
    | multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))),inverse(greatest_lower_bound(a,identity))) )],[refute_0_5497,refute_0_5498]) ).

cnf(refute_0_5500,plain,
    multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)),least_upper_bound(a,multiply(a,inverse(multiply(a,greatest_lower_bound(a,identity)))))) )],[refute_0_5245,refute_0_5499]) ).

cnf(refute_0_5501,plain,
    multiply(X_325,greatest_lower_bound(identity,inverse(X_325))) = greatest_lower_bound(identity,multiply(X_325,identity)),
    inference(subst,[],[refute_0_4594:[bind(X_107,$fot(X_325)),bind(X_108,$fot(identity))]]) ).

cnf(refute_0_5502,plain,
    inverse(least_upper_bound(identity,X_325)) = greatest_lower_bound(identity,inverse(X_325)),
    inference(subst,[],[refute_0_299:[bind(Y,$fot(X_325))]]) ).

cnf(refute_0_5503,plain,
    ( inverse(least_upper_bound(identity,X_325)) != greatest_lower_bound(identity,inverse(X_325))
    | greatest_lower_bound(identity,inverse(X_325)) = inverse(least_upper_bound(identity,X_325)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(least_upper_bound(identity,X_325)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_325))))]]) ).

cnf(refute_0_5504,plain,
    greatest_lower_bound(identity,inverse(X_325)) = inverse(least_upper_bound(identity,X_325)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_325)),greatest_lower_bound(identity,inverse(X_325))) )],[refute_0_5502,refute_0_5503]) ).

cnf(refute_0_5505,plain,
    ( multiply(X_325,greatest_lower_bound(identity,inverse(X_325))) != greatest_lower_bound(identity,multiply(X_325,identity))
    | greatest_lower_bound(identity,inverse(X_325)) != inverse(least_upper_bound(identity,X_325))
    | multiply(X_325,inverse(least_upper_bound(identity,X_325))) = greatest_lower_bound(identity,multiply(X_325,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_325,greatest_lower_bound(identity,inverse(X_325))),greatest_lower_bound(identity,multiply(X_325,identity))) ),[0,1],$fot(inverse(least_upper_bound(identity,X_325)))]]) ).

cnf(refute_0_5506,plain,
    ( multiply(X_325,greatest_lower_bound(identity,inverse(X_325))) != greatest_lower_bound(identity,multiply(X_325,identity))
    | multiply(X_325,inverse(least_upper_bound(identity,X_325))) = greatest_lower_bound(identity,multiply(X_325,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_325)),inverse(least_upper_bound(identity,X_325))) )],[refute_0_5504,refute_0_5505]) ).

cnf(refute_0_5507,plain,
    multiply(X_325,inverse(least_upper_bound(identity,X_325))) = greatest_lower_bound(identity,multiply(X_325,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_325,greatest_lower_bound(identity,inverse(X_325))),greatest_lower_bound(identity,multiply(X_325,identity))) )],[refute_0_5501,refute_0_5506]) ).

cnf(refute_0_5508,plain,
    multiply(greatest_lower_bound(X_325,identity),identity) = greatest_lower_bound(X_325,identity),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(greatest_lower_bound(X_325,identity)))]]) ).

cnf(refute_0_5509,plain,
    greatest_lower_bound(identity,multiply(X_325,identity)) = multiply(greatest_lower_bound(X_325,identity),identity),
    inference(subst,[],[refute_0_2028:[bind(X_121,$fot(identity)),bind(X_122,$fot(X_325))]]) ).

cnf(refute_0_5510,plain,
    ( multiply(greatest_lower_bound(X_325,identity),identity) != greatest_lower_bound(X_325,identity)
    | greatest_lower_bound(identity,multiply(X_325,identity)) != multiply(greatest_lower_bound(X_325,identity),identity)
    | greatest_lower_bound(identity,multiply(X_325,identity)) = greatest_lower_bound(X_325,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_325,identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_325,identity),identity))),bind(Z0,$fot(greatest_lower_bound(X_325,identity)))]]) ).

cnf(refute_0_5511,plain,
    ( multiply(greatest_lower_bound(X_325,identity),identity) != greatest_lower_bound(X_325,identity)
    | greatest_lower_bound(identity,multiply(X_325,identity)) = greatest_lower_bound(X_325,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_325,identity)),multiply(greatest_lower_bound(X_325,identity),identity)) )],[refute_0_5509,refute_0_5510]) ).

cnf(refute_0_5512,plain,
    greatest_lower_bound(identity,multiply(X_325,identity)) = greatest_lower_bound(X_325,identity),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_325,identity),identity),greatest_lower_bound(X_325,identity)) )],[refute_0_5508,refute_0_5511]) ).

cnf(refute_0_5513,plain,
    ( multiply(X_325,inverse(least_upper_bound(identity,X_325))) != greatest_lower_bound(identity,multiply(X_325,identity))
    | greatest_lower_bound(identity,multiply(X_325,identity)) != greatest_lower_bound(X_325,identity)
    | multiply(X_325,inverse(least_upper_bound(identity,X_325))) = greatest_lower_bound(X_325,identity) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_325,inverse(least_upper_bound(identity,X_325))),greatest_lower_bound(X_325,identity)) ),[0],$fot(greatest_lower_bound(identity,multiply(X_325,identity)))]]) ).

cnf(refute_0_5514,plain,
    ( multiply(X_325,inverse(least_upper_bound(identity,X_325))) != greatest_lower_bound(identity,multiply(X_325,identity))
    | multiply(X_325,inverse(least_upper_bound(identity,X_325))) = greatest_lower_bound(X_325,identity) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_325,identity)),greatest_lower_bound(X_325,identity)) )],[refute_0_5512,refute_0_5513]) ).

cnf(refute_0_5515,plain,
    multiply(X_325,inverse(least_upper_bound(identity,X_325))) = greatest_lower_bound(X_325,identity),
    inference(resolve,[$cnf( $equal(multiply(X_325,inverse(least_upper_bound(identity,X_325))),greatest_lower_bound(identity,multiply(X_325,identity))) )],[refute_0_5507,refute_0_5514]) ).

cnf(refute_0_5516,plain,
    multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))))) = greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity),
    inference(subst,[],[refute_0_5515:[bind(X_325,$fot(multiply(X_220,greatest_lower_bound(X_220,identity))))]]) ).

cnf(refute_0_5517,plain,
    ( least_upper_bound(identity,X_220) != least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))
    | least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) = least_upper_bound(identity,X_220) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,X_220))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))))]]) ).

cnf(refute_0_5518,plain,
    least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) = least_upper_bound(identity,X_220),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_220),least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))) )],[refute_0_5114,refute_0_5517]) ).

cnf(refute_0_5519,plain,
    ( multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))))) != greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)
    | least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) != least_upper_bound(identity,X_220)
    | multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) = greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))))),greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)) ),[0,1,0],$fot(least_upper_bound(identity,X_220))]]) ).

cnf(refute_0_5520,plain,
    ( multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))))) != greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)
    | multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) = greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))),least_upper_bound(identity,X_220)) )],[refute_0_5518,refute_0_5519]) ).

cnf(refute_0_5521,plain,
    multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) = greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))))),greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)) )],[refute_0_5516,refute_0_5520]) ).

cnf(refute_0_5522,plain,
    multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))) = greatest_lower_bound(multiply(X,Y),multiply(X,inverse(least_upper_bound(identity,X)))),
    inference(subst,[],[monotony_glb1:[bind(Z,$fot(inverse(least_upper_bound(identity,X))))]]) ).

cnf(refute_0_5523,plain,
    multiply(X,inverse(least_upper_bound(identity,X))) = greatest_lower_bound(X,identity),
    inference(subst,[],[refute_0_5515:[bind(X_325,$fot(X))]]) ).

cnf(refute_0_5524,plain,
    ( multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))) != greatest_lower_bound(multiply(X,Y),multiply(X,inverse(least_upper_bound(identity,X))))
    | multiply(X,inverse(least_upper_bound(identity,X))) != greatest_lower_bound(X,identity)
    | multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))) = greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))),greatest_lower_bound(multiply(X,Y),multiply(X,inverse(least_upper_bound(identity,X))))) ),[1,1],$fot(greatest_lower_bound(X,identity))]]) ).

cnf(refute_0_5525,plain,
    ( multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))) != greatest_lower_bound(multiply(X,Y),multiply(X,inverse(least_upper_bound(identity,X))))
    | multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))) = greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(X,inverse(least_upper_bound(identity,X))),greatest_lower_bound(X,identity)) )],[refute_0_5523,refute_0_5524]) ).

cnf(refute_0_5526,plain,
    multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))) = greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)),
    inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))),greatest_lower_bound(multiply(X,Y),multiply(X,inverse(least_upper_bound(identity,X))))) )],[refute_0_5522,refute_0_5525]) ).

cnf(refute_0_5527,plain,
    greatest_lower_bound(X,greatest_lower_bound(multiply(X,Y),identity)) = greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y))),
    inference(subst,[],[refute_0_1493:[bind(Y,$fot(identity)),bind(X_75,$fot(multiply(X,Y))),bind(X_77,$fot(X))]]) ).

cnf(refute_0_5528,plain,
    greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_314,X_315),greatest_lower_bound(X_315,X_314)),X_38)) = greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38),
    inference(subst,[],[refute_0_467:[bind(X_11,$fot(greatest_lower_bound(X_314,X_315))),bind(X_36,$fot(greatest_lower_bound(X_315,X_314)))]]) ).

cnf(refute_0_5529,plain,
    least_upper_bound(greatest_lower_bound(X_314,X_315),greatest_lower_bound(X_315,X_314)) = greatest_lower_bound(X_314,X_315),
    inference(subst,[],[refute_0_4188:[bind(X_32,$fot(X_314)),bind(X_9,$fot(X_315))]]) ).

cnf(refute_0_5530,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_314,X_315),greatest_lower_bound(X_315,X_314)),X_38)) != greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)
    | least_upper_bound(greatest_lower_bound(X_314,X_315),greatest_lower_bound(X_315,X_314)) != greatest_lower_bound(X_314,X_315)
    | greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_314,X_315),greatest_lower_bound(X_315,X_314)),X_38)),greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)) ),[0,1,0],$fot(greatest_lower_bound(X_314,X_315))]]) ).

cnf(refute_0_5531,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_314,X_315),greatest_lower_bound(X_315,X_314)),X_38)) != greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)
    | greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_314,X_315),greatest_lower_bound(X_315,X_314)),greatest_lower_bound(X_314,X_315)) )],[refute_0_5529,refute_0_5530]) ).

cnf(refute_0_5532,plain,
    greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(least_upper_bound(greatest_lower_bound(X_314,X_315),greatest_lower_bound(X_315,X_314)),X_38)),greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)) )],[refute_0_5528,refute_0_5531]) ).

cnf(refute_0_5533,plain,
    greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)),
    inference(subst,[],[refute_0_895:[bind(Y,$fot(X_38)),bind(X_36,$fot(X_314)),bind(X_37,$fot(X_315))]]) ).

cnf(refute_0_5534,plain,
    greatest_lower_bound(X_314,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)),
    inference(subst,[],[refute_0_801:[bind(X_32,$fot(greatest_lower_bound(X_315,X_38))),bind(X_33,$fot(X_314))]]) ).

cnf(refute_0_5535,plain,
    greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_314)),bind(Y,$fot(X_315)),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_5536,plain,
    greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)))]]) ).

cnf(refute_0_5537,plain,
    ( greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) != greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))
    | greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38) != greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))
    | greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)),greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) ),[1,1],$fot(greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)))]]) ).

cnf(refute_0_5538,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38) != greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))
    | greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)),greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) )],[refute_0_5536,refute_0_5537]) ).

cnf(refute_0_5539,plain,
    greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38),greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) )],[refute_0_5535,refute_0_5538]) ).

cnf(refute_0_5540,plain,
    ( greatest_lower_bound(X_314,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) != greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))
    | greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) != greatest_lower_bound(X_314,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)))
    | greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)))),bind(Y0,$fot(greatest_lower_bound(X_314,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))))),bind(Z0,$fot(greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))))]]) ).

cnf(refute_0_5541,plain,
    ( greatest_lower_bound(X_314,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) != greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))
    | greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)),greatest_lower_bound(X_314,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)))) )],[refute_0_5539,refute_0_5540]) ).

cnf(refute_0_5542,plain,
    greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_314,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))),greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) )],[refute_0_5534,refute_0_5541]) ).

cnf(refute_0_5543,plain,
    greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) = greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))))]]) ).

cnf(refute_0_5544,plain,
    ( greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) != greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))
    | greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) != greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)))
    | greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) = greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))),greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)))) ),[1,1],$fot(greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)))]]) ).

cnf(refute_0_5545,plain,
    ( greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) != greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))
    | greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) = greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))),greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)))) )],[refute_0_5543,refute_0_5544]) ).

cnf(refute_0_5546,plain,
    greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) = greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)),greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) )],[refute_0_5542,refute_0_5545]) ).

cnf(refute_0_5547,plain,
    ( greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) != greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))
    | greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) != greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)))
    | greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))))),bind(Y0,$fot(greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))))),bind(Z0,$fot(greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))))]]) ).

cnf(refute_0_5548,plain,
    ( greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) != greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))
    | greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))),greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)))) )],[refute_0_5546,refute_0_5547]) ).

cnf(refute_0_5549,plain,
    greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))),greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) )],[refute_0_5533,refute_0_5548]) ).

cnf(refute_0_5550,plain,
    greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_315)),bind(Y,$fot(X_314)),bind(Z,$fot(greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)))]]) ).

cnf(refute_0_5551,plain,
    ( greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) != greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))
    | greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) != greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)))
    | greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)))),bind(Y0,$fot(greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))))),bind(Z0,$fot(greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))))]]) ).

cnf(refute_0_5552,plain,
    ( greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))) != greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))
    | greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)),greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)))) )],[refute_0_5550,refute_0_5551]) ).

cnf(refute_0_5553,plain,
    greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_315,greatest_lower_bound(X_314,greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38))),greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) )],[refute_0_5549,refute_0_5552]) ).

cnf(refute_0_5554,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) != greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))
    | greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) != greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)
    | greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) = greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)),greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)) ),[0],$fot(greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)))]]) ).

cnf(refute_0_5555,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) != greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)
    | greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) = greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)),greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38))) )],[refute_0_5553,refute_0_5554]) ).

cnf(refute_0_5556,plain,
    greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38) = greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38)),
    inference(subst,[],[refute_0_790:[bind(X,$fot(X_315)),bind(Y,$fot(X_314)),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_5557,plain,
    ( greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) != greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)
    | greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38) != greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38))
    | greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) = greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)),greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38))]]) ).

cnf(refute_0_5558,plain,
    ( greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) != greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)
    | greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) = greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38),greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38))) )],[refute_0_5556,refute_0_5557]) ).

cnf(refute_0_5559,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)) != greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)
    | greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) = greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)),greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)) )],[refute_0_5555,refute_0_5558]) ).

cnf(refute_0_5560,plain,
    greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) = greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_315,X_314),greatest_lower_bound(greatest_lower_bound(X_314,X_315),X_38)),greatest_lower_bound(greatest_lower_bound(X_315,X_314),X_38)) )],[refute_0_5532,refute_0_5559]) ).

cnf(refute_0_5561,plain,
    ( greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) != greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38))
    | greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)))),bind(Y0,$fot(greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38))))]]) ).

cnf(refute_0_5562,plain,
    greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38)) = greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_314,greatest_lower_bound(X_315,X_38)),greatest_lower_bound(X_315,greatest_lower_bound(X_314,X_38))) )],[refute_0_5560,refute_0_5561]) ).

cnf(refute_0_5563,plain,
    greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)) = greatest_lower_bound(X,greatest_lower_bound(multiply(X,Y),identity)),
    inference(subst,[],[refute_0_5562:[bind(X_314,$fot(X)),bind(X_315,$fot(multiply(X,Y))),bind(X_38,$fot(identity))]]) ).

cnf(refute_0_5564,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(multiply(X,Y),identity)) != greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y)))
    | greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)) != greatest_lower_bound(X,greatest_lower_bound(multiply(X,Y),identity))
    | greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)) = greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)))),bind(Y0,$fot(greatest_lower_bound(X,greatest_lower_bound(multiply(X,Y),identity)))),bind(Z0,$fot(greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y)))))]]) ).

cnf(refute_0_5565,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(multiply(X,Y),identity)) != greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y)))
    | greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)) = greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)),greatest_lower_bound(X,greatest_lower_bound(multiply(X,Y),identity))) )],[refute_0_5563,refute_0_5564]) ).

cnf(refute_0_5566,plain,
    greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)) = greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(multiply(X,Y),identity)),greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y)))) )],[refute_0_5527,refute_0_5565]) ).

cnf(refute_0_5567,plain,
    ( multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))) != greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity))
    | greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)) != greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y)))
    | multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))) = greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))),greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y)))) ),[0],$fot(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)))]]) ).

cnf(refute_0_5568,plain,
    ( multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))) != greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity))
    | multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))) = greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity)),greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y)))) )],[refute_0_5566,refute_0_5567]) ).

cnf(refute_0_5569,plain,
    multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))) = greatest_lower_bound(X,greatest_lower_bound(identity,multiply(X,Y))),
    inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,inverse(least_upper_bound(identity,X)))),greatest_lower_bound(multiply(X,Y),greatest_lower_bound(X,identity))) )],[refute_0_5526,refute_0_5568]) ).

cnf(refute_0_5570,plain,
    multiply(X_220,greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220)))) = greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))),
    inference(subst,[],[refute_0_5569:[bind(X,$fot(X_220)),bind(Y,$fot(X_220))]]) ).

cnf(refute_0_5571,plain,
    multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) = greatest_lower_bound(greatest_lower_bound(X_132,identity),multiply(greatest_lower_bound(X_132,identity),inverse(X_132))),
    inference(subst,[],[refute_0_161:[bind(X_107,$fot(greatest_lower_bound(X_132,identity))),bind(X_108,$fot(inverse(X_132)))]]) ).

cnf(refute_0_5572,plain,
    ( multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) != greatest_lower_bound(greatest_lower_bound(X_132,identity),multiply(greatest_lower_bound(X_132,identity),inverse(X_132)))
    | multiply(greatest_lower_bound(X_132,identity),inverse(X_132)) != inverse(least_upper_bound(identity,X_132))
    | multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) = greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)),greatest_lower_bound(greatest_lower_bound(X_132,identity),multiply(greatest_lower_bound(X_132,identity),inverse(X_132)))) ),[1,1],$fot(inverse(least_upper_bound(identity,X_132)))]]) ).

cnf(refute_0_5573,plain,
    ( multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) != greatest_lower_bound(greatest_lower_bound(X_132,identity),multiply(greatest_lower_bound(X_132,identity),inverse(X_132)))
    | multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) = greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),inverse(X_132)),inverse(least_upper_bound(identity,X_132))) )],[refute_0_640,refute_0_5572]) ).

cnf(refute_0_5574,plain,
    multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) = greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)),greatest_lower_bound(greatest_lower_bound(X_132,identity),multiply(greatest_lower_bound(X_132,identity),inverse(X_132)))) )],[refute_0_5571,refute_0_5573]) ).

cnf(refute_0_5575,plain,
    multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))) = multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))))]]) ).

cnf(refute_0_5576,plain,
    ( multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))) != multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132)))
    | greatest_lower_bound(identity,inverse(X_132)) != inverse(least_upper_bound(identity,X_132))
    | multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))) = multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))),multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132)))) ),[1,1],$fot(inverse(least_upper_bound(identity,X_132)))]]) ).

cnf(refute_0_5577,plain,
    ( greatest_lower_bound(identity,inverse(X_132)) != inverse(least_upper_bound(identity,X_132))
    | multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))) = multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))),multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132)))) )],[refute_0_5575,refute_0_5576]) ).

cnf(refute_0_5578,plain,
    multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))) = multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_132)),inverse(least_upper_bound(identity,X_132))) )],[refute_0_637,refute_0_5577]) ).

cnf(refute_0_5579,plain,
    multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) = multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))),
    inference(subst,[],[refute_0_925:[bind(X_232,$fot(inverse(X_132))),bind(X_33,$fot(greatest_lower_bound(X_132,identity)))]]) ).

cnf(refute_0_5580,plain,
    ( multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))) != multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))
    | multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) != multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132)))
    | multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) = multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))))]]) ).

cnf(refute_0_5581,plain,
    ( multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))) != multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))
    | multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) = multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)),multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132)))) )],[refute_0_5579,refute_0_5580]) ).

cnf(refute_0_5582,plain,
    multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) = multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(identity,inverse(X_132))),multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))) )],[refute_0_5578,refute_0_5581]) ).

cnf(refute_0_5583,plain,
    ( multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) != multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))
    | multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) != greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))
    | multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)),greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))) ),[0],$fot(multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))))]]) ).

cnf(refute_0_5584,plain,
    ( multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) != greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))
    | multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)),multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))) )],[refute_0_5582,refute_0_5583]) ).

cnf(refute_0_5585,plain,
    greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) = greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))))]]) ).

cnf(refute_0_5586,plain,
    ( greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) != greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))
    | greatest_lower_bound(identity,inverse(X_132)) != inverse(least_upper_bound(identity,X_132))
    | greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) = greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))),greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))) ),[1,1],$fot(inverse(least_upper_bound(identity,X_132)))]]) ).

cnf(refute_0_5587,plain,
    ( greatest_lower_bound(identity,inverse(X_132)) != inverse(least_upper_bound(identity,X_132))
    | greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) = greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))),greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))) )],[refute_0_5585,refute_0_5586]) ).

cnf(refute_0_5588,plain,
    greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) = greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_132)),inverse(least_upper_bound(identity,X_132))) )],[refute_0_637,refute_0_5587]) ).

cnf(refute_0_5589,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))) = greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))),
    inference(subst,[],[refute_0_895:[bind(Y,$fot(inverse(X_132))),bind(X_36,$fot(X_132)),bind(X_37,$fot(identity))]]) ).

cnf(refute_0_5590,plain,
    greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))) = greatest_lower_bound(identity,greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))),
    inference(subst,[],[refute_0_1480:[bind(X,$fot(identity)),bind(X_36,$fot(identity)),bind(X_75,$fot(X_132)),bind(X_77,$fot(inverse(X_132)))]]) ).

cnf(refute_0_5591,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))) != greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))) != greatest_lower_bound(identity,greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))) = greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))))),bind(Z0,$fot(greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))))]]) ).

cnf(refute_0_5592,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))) != greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))) = greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))),greatest_lower_bound(identity,greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))))) )],[refute_0_5590,refute_0_5591]) ).

cnf(refute_0_5593,plain,
    greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))) = greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))),greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))) )],[refute_0_5589,refute_0_5592]) ).

cnf(refute_0_5594,plain,
    greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))),
    inference(subst,[],[refute_0_1493:[bind(Y,$fot(inverse(X_132))),bind(X_75,$fot(greatest_lower_bound(X_132,identity))),bind(X_77,$fot(identity))]]) ).

cnf(refute_0_5595,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity)))
    | greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))) != greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))
    | greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))) = greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))))),bind(Z0,$fot(greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))))]]) ).

cnf(refute_0_5596,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))) != greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))
    | greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))) = greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity)))) )],[refute_0_5594,refute_0_5595]) ).

cnf(refute_0_5597,plain,
    greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))) = greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_132),greatest_lower_bound(X_132,identity))),greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))) )],[refute_0_5593,refute_0_5596]) ).

cnf(refute_0_5598,plain,
    greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))),
    inference(subst,[],[refute_0_1402:[bind(Y,$fot(X_132)),bind(X_76,$fot(greatest_lower_bound(X_132,identity)))]]) ).

cnf(refute_0_5599,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) != greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132)))
    | greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))) != greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))
    | greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))))),bind(Z0,$fot(greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))))]]) ).

cnf(refute_0_5600,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))) != greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))
    | greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))),greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132)))) )],[refute_0_5598,refute_0_5599]) ).

cnf(refute_0_5601,plain,
    greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(X_132))),greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))) )],[refute_0_5597,refute_0_5600]) ).

cnf(refute_0_5602,plain,
    ( greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) != greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132)))
    | greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) != greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))
    | greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))))),bind(Y0,$fot(greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))))),bind(Z0,$fot(greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132)))))]]) ).

cnf(refute_0_5603,plain,
    ( greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))) != greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132)))
    | greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))),greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132)))) )],[refute_0_5601,refute_0_5602]) ).

cnf(refute_0_5604,plain,
    greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_132,greatest_lower_bound(identity,inverse(X_132))),greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132)))) )],[refute_0_5588,refute_0_5603]) ).

cnf(refute_0_5605,plain,
    ( multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) != greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))
    | greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) != greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132)))
    | multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))),greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))))]]) ).

cnf(refute_0_5606,plain,
    ( multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) != greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))
    | multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))),greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132)))) )],[refute_0_5604,refute_0_5605]) ).

cnf(refute_0_5607,plain,
    ( multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)) != greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))
    | multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))),greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))) )],[refute_0_5584,refute_0_5606]) ).

cnf(refute_0_5608,plain,
    multiply(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132))) = greatest_lower_bound(X_132,inverse(least_upper_bound(identity,X_132))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_132,identity),greatest_lower_bound(inverse(X_132),identity)),greatest_lower_bound(greatest_lower_bound(X_132,identity),inverse(least_upper_bound(identity,X_132)))) )],[refute_0_5574,refute_0_5607]) ).

cnf(refute_0_5609,plain,
    multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220))) = greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220))),
    inference(subst,[],[refute_0_5608:[bind(X_132,$fot(X_220))]]) ).

cnf(refute_0_5610,plain,
    multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))) = multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))),
    introduced(tautology,[refl,[$fot(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))))]]) ).

cnf(refute_0_5611,plain,
    ( multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))) != multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220))))
    | multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220))) != greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220)))
    | multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))) = multiply(X_220,greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))),multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220))))) ),[1,1],$fot(greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220))))]]) ).

cnf(refute_0_5612,plain,
    ( multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220))) != greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220)))
    | multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))) = multiply(X_220,greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))),multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220))))) )],[refute_0_5610,refute_0_5611]) ).

cnf(refute_0_5613,plain,
    multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))) = multiply(X_220,greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220))),greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220)))) )],[refute_0_5609,refute_0_5612]) ).

cnf(refute_0_5614,plain,
    ( multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))) != multiply(X_220,greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220))))
    | multiply(X_220,greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220)))) != greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220)))
    | multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))) = greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))))),bind(Y0,$fot(multiply(X_220,greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220)))))),bind(Z0,$fot(greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220)))))]]) ).

cnf(refute_0_5615,plain,
    ( multiply(X_220,greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220)))) != greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220)))
    | multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))) = greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) ),
    inference(resolve,[$cnf( $equal(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))),multiply(X_220,greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220))))) )],[refute_0_5613,refute_0_5614]) ).

cnf(refute_0_5616,plain,
    multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))) = greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))),
    inference(resolve,[$cnf( $equal(multiply(X_220,greatest_lower_bound(X_220,inverse(least_upper_bound(identity,X_220)))),greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220)))) )],[refute_0_5570,refute_0_5615]) ).

cnf(refute_0_5617,plain,
    multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) = multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))),
    inference(subst,[],[associativity:[bind(X,$fot(X_220)),bind(Y,$fot(greatest_lower_bound(X_220,identity))),bind(Z,$fot(inverse(least_upper_bound(identity,X_220))))]]) ).

cnf(refute_0_5618,plain,
    ( multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))) != greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220)))
    | multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) != multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220))))
    | multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) = greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))))),bind(Y0,$fot(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))))),bind(Z0,$fot(greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220)))))]]) ).

cnf(refute_0_5619,plain,
    ( multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))) != greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220)))
    | multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) = greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))),multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220))))) )],[refute_0_5617,refute_0_5618]) ).

cnf(refute_0_5620,plain,
    multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) = greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))),
    inference(resolve,[$cnf( $equal(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),inverse(least_upper_bound(identity,X_220)))),greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220)))) )],[refute_0_5616,refute_0_5619]) ).

cnf(refute_0_5621,plain,
    ( multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) != greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220)))
    | multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) != greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)
    | greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) = greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))),greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)) ),[0],$fot(greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))))]]) ).

cnf(refute_0_5622,plain,
    ( multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) != greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)
    | greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) = greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))),greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220)))) )],[refute_0_5620,refute_0_5621]) ).

cnf(refute_0_5623,plain,
    multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity))),inverse(inverse(greatest_lower_bound(X_122,identity)))) = greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))),
    inference(subst,[],[refute_0_3421:[bind(X_123,$fot(inverse(greatest_lower_bound(X_122,identity))))]]) ).

cnf(refute_0_5624,plain,
    greatest_lower_bound(X_122,identity) = greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity))),
    inference(subst,[],[refute_0_1929:[bind(X_204,$fot(X_122))]]) ).

cnf(refute_0_5625,plain,
    ( greatest_lower_bound(X_122,identity) != greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity)))
    | greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity))) = greatest_lower_bound(X_122,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_122,identity))),bind(Y0,$fot(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity)))))]]) ).

cnf(refute_0_5626,plain,
    greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity))) = greatest_lower_bound(X_122,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity)))) )],[refute_0_5624,refute_0_5625]) ).

cnf(refute_0_5627,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity))),inverse(inverse(greatest_lower_bound(X_122,identity)))) != greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))
    | greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity))) != greatest_lower_bound(X_122,identity)
    | multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) = greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity))),inverse(inverse(greatest_lower_bound(X_122,identity)))),greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))) ),[0,0],$fot(greatest_lower_bound(X_122,identity))]]) ).

cnf(refute_0_5628,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity))),inverse(inverse(greatest_lower_bound(X_122,identity)))) != greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))
    | multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) = greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity))),greatest_lower_bound(X_122,identity)) )],[refute_0_5626,refute_0_5627]) ).

cnf(refute_0_5629,plain,
    multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) = greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_122,identity))),inverse(inverse(greatest_lower_bound(X_122,identity)))),greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))) )],[refute_0_5623,refute_0_5628]) ).

cnf(refute_0_5630,plain,
    inverse(inverse(greatest_lower_bound(X_122,identity))) = greatest_lower_bound(X_122,identity),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(X_122,identity)))]]) ).

cnf(refute_0_5631,plain,
    multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) = multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))))]]) ).

cnf(refute_0_5632,plain,
    ( multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) != multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity))))
    | inverse(inverse(greatest_lower_bound(X_122,identity))) != greatest_lower_bound(X_122,identity)
    | multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) = multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))),multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity))))) ),[1,1],$fot(greatest_lower_bound(X_122,identity))]]) ).

cnf(refute_0_5633,plain,
    ( inverse(inverse(greatest_lower_bound(X_122,identity))) != greatest_lower_bound(X_122,identity)
    | multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) = multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))),multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity))))) )],[refute_0_5631,refute_0_5632]) ).

cnf(refute_0_5634,plain,
    multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) = multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_122,identity))),greatest_lower_bound(X_122,identity)) )],[refute_0_5630,refute_0_5633]) ).

cnf(refute_0_5635,plain,
    ( multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) != multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity))
    | multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) != greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))
    | multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) = greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))),greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))) ),[0],$fot(multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)))]]) ).

cnf(refute_0_5636,plain,
    ( multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) != greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))
    | multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) = greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))),multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity))) )],[refute_0_5634,refute_0_5635]) ).

cnf(refute_0_5637,plain,
    multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))) = multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))),
    introduced(tautology,[refl,[$fot(multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))]]) ).

cnf(refute_0_5638,plain,
    ( multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))) != multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))
    | inverse(inverse(greatest_lower_bound(X_122,identity))) != greatest_lower_bound(X_122,identity)
    | multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))) = multiply(X_122,greatest_lower_bound(X_122,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))),multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) ),[1,1],$fot(greatest_lower_bound(X_122,identity))]]) ).

cnf(refute_0_5639,plain,
    ( inverse(inverse(greatest_lower_bound(X_122,identity))) != greatest_lower_bound(X_122,identity)
    | multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))) = multiply(X_122,greatest_lower_bound(X_122,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))),multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) )],[refute_0_5637,refute_0_5638]) ).

cnf(refute_0_5640,plain,
    multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))) = multiply(X_122,greatest_lower_bound(X_122,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_122,identity))),greatest_lower_bound(X_122,identity)) )],[refute_0_5630,refute_0_5639]) ).

cnf(refute_0_5641,plain,
    greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) = greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))))]]) ).

cnf(refute_0_5642,plain,
    ( multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))) != multiply(X_122,greatest_lower_bound(X_122,identity))
    | greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) != greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))
    | greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) = greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))),greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))) ),[1,1],$fot(multiply(X_122,greatest_lower_bound(X_122,identity)))]]) ).

cnf(refute_0_5643,plain,
    ( multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))) != multiply(X_122,greatest_lower_bound(X_122,identity))
    | greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) = greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))),greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))) )],[refute_0_5641,refute_0_5642]) ).

cnf(refute_0_5644,plain,
    greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) = greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity))),
    inference(resolve,[$cnf( $equal(multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))),multiply(X_122,greatest_lower_bound(X_122,identity))) )],[refute_0_5640,refute_0_5643]) ).

cnf(refute_0_5645,plain,
    ( multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) != greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))
    | greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))) != greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity)))
    | multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) = greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)),greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity)))) ),[0],$fot(greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))))]]) ).

cnf(refute_0_5646,plain,
    ( multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) != greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))
    | multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) = greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity))))),greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity)))) )],[refute_0_5644,refute_0_5645]) ).

cnf(refute_0_5647,plain,
    ( multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))) != greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))
    | multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) = greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)),greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))) )],[refute_0_5636,refute_0_5646]) ).

cnf(refute_0_5648,plain,
    multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) = greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),inverse(inverse(greatest_lower_bound(X_122,identity)))),greatest_lower_bound(identity,multiply(X_122,inverse(inverse(greatest_lower_bound(X_122,identity)))))) )],[refute_0_5629,refute_0_5647]) ).

cnf(refute_0_5649,plain,
    ( multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) != greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity)))
    | greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity))) = multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity)))))]]) ).

cnf(refute_0_5650,plain,
    greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity))) = multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,identity),greatest_lower_bound(X_122,identity)),greatest_lower_bound(identity,multiply(X_122,greatest_lower_bound(X_122,identity)))) )],[refute_0_5648,refute_0_5649]) ).

cnf(refute_0_5651,plain,
    greatest_lower_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) = multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)),
    inference(subst,[],[refute_0_5650:[bind(X_122,$fot(X_220))]]) ).

cnf(refute_0_5652,plain,
    greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) = greatest_lower_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))),
    inference(subst,[],[refute_0_3839:[bind(X,$fot(multiply(X_220,greatest_lower_bound(X_220,identity))))]]) ).

cnf(refute_0_5653,plain,
    ( greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) != greatest_lower_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))
    | greatest_lower_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) != multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity))
    | greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) = multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity))))]]) ).

cnf(refute_0_5654,plain,
    ( greatest_lower_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) != multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity))
    | greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) = multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity),greatest_lower_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))) )],[refute_0_5652,refute_0_5653]) ).

cnf(refute_0_5655,plain,
    greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) = multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))),multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity))) )],[refute_0_5651,refute_0_5654]) ).

cnf(refute_0_5656,plain,
    ( greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) != greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)
    | greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) != multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity))
    | greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) = multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))),multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity))) ),[0],$fot(greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity))]]) ).

cnf(refute_0_5657,plain,
    ( greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) != greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)
    | greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) = multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity),multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity))) )],[refute_0_5655,refute_0_5656]) ).

cnf(refute_0_5658,plain,
    ( multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))) != greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)
    | greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) = multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))),greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)) )],[refute_0_5622,refute_0_5657]) ).

cnf(refute_0_5659,plain,
    greatest_lower_bound(X_220,greatest_lower_bound(identity,multiply(X_220,X_220))) = multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),inverse(least_upper_bound(identity,X_220))),greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity)) )],[refute_0_5521,refute_0_5658]) ).

cnf(refute_0_5660,plain,
    greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))) = multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),
    inference(subst,[],[refute_0_5659:[bind(X_220,$fot(a))]]) ).

cnf(refute_0_5661,plain,
    ( multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(a,b))
    | greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))) != multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))
    | greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))) = greatest_lower_bound(identity,multiply(a,b)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))),bind(Y0,$fot(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)))),bind(Z0,$fot(greatest_lower_bound(identity,multiply(a,b))))]]) ).

cnf(refute_0_5662,plain,
    ( multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(a,b))
    | greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))) = greatest_lower_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))),multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity))) )],[refute_0_5660,refute_0_5661]) ).

cnf(refute_0_5663,plain,
    greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))) = greatest_lower_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,multiply(a,b))) )],[refute_0_5379,refute_0_5662]) ).

cnf(refute_0_5664,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))))]]) ).

cnf(refute_0_5665,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))) != greatest_lower_bound(identity,multiply(a,b))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))) = inverse(greatest_lower_bound(identity,multiply(a,b))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))),inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(a,b)))]]) ).

cnf(refute_0_5666,plain,
    ( greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))) != greatest_lower_bound(identity,multiply(a,b))
    | inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))) = inverse(greatest_lower_bound(identity,multiply(a,b))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))),inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))) )],[refute_0_5664,refute_0_5665]) ).

cnf(refute_0_5667,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))) = inverse(greatest_lower_bound(identity,multiply(a,b))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))),greatest_lower_bound(identity,multiply(a,b))) )],[refute_0_5663,refute_0_5666]) ).

cnf(refute_0_5668,plain,
    inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) = inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24))),
    inference(subst,[],[refute_0_2824:[bind(X_13,$fot(X_24)),bind(X_36,$fot(X_25)),bind(X_37,$fot(Y))]]) ).

cnf(refute_0_5669,plain,
    ( inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))) != inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24)))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))) ),[1],$fot(inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24))))]]) ).

cnf(refute_0_5670,plain,
    ( inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) != inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y))),inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24)))) )],[refute_0_5668,refute_0_5669]) ).

cnf(refute_0_5671,plain,
    inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) = inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))),inverse(greatest_lower_bound(X_24,greatest_lower_bound(X_25,Y)))) )],[refute_0_1013,refute_0_5670]) ).

cnf(refute_0_5672,plain,
    ( inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) != inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24)))
    | inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24))) = inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))))),bind(Y0,$fot(inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24)))))]]) ).

cnf(refute_0_5673,plain,
    inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24))) = inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_25,greatest_lower_bound(X_24,Y))),inverse(greatest_lower_bound(X_25,greatest_lower_bound(Y,X_24)))) )],[refute_0_5671,refute_0_5672]) ).

cnf(refute_0_5674,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),identity))) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))),
    inference(subst,[],[refute_0_5673:[bind(Y,$fot(multiply(a,a))),bind(X_24,$fot(identity)),bind(X_25,$fot(a))]]) ).

cnf(refute_0_5675,plain,
    inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,multiply(X_36,X_232)))) = inverse(greatest_lower_bound(X_36,greatest_lower_bound(multiply(X_36,X_232),X_13))),
    inference(subst,[],[refute_0_2824:[bind(X_37,$fot(multiply(X_36,X_232)))]]) ).

cnf(refute_0_5676,plain,
    multiply(X_36,greatest_lower_bound(X_232,identity)) = greatest_lower_bound(X_36,multiply(X_36,X_232)),
    inference(subst,[],[refute_0_161:[bind(X_107,$fot(X_36)),bind(X_108,$fot(X_232))]]) ).

cnf(refute_0_5677,plain,
    ( multiply(X_36,greatest_lower_bound(X_232,identity)) != greatest_lower_bound(X_36,multiply(X_36,X_232))
    | greatest_lower_bound(X_36,multiply(X_36,X_232)) = multiply(X_36,greatest_lower_bound(X_232,identity)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_36,greatest_lower_bound(X_232,identity)))),bind(Y0,$fot(greatest_lower_bound(X_36,multiply(X_36,X_232))))]]) ).

cnf(refute_0_5678,plain,
    greatest_lower_bound(X_36,multiply(X_36,X_232)) = multiply(X_36,greatest_lower_bound(X_232,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_36,greatest_lower_bound(X_232,identity)),greatest_lower_bound(X_36,multiply(X_36,X_232))) )],[refute_0_5676,refute_0_5677]) ).

cnf(refute_0_5679,plain,
    ( greatest_lower_bound(X_36,multiply(X_36,X_232)) != multiply(X_36,greatest_lower_bound(X_232,identity))
    | inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,multiply(X_36,X_232)))) != inverse(greatest_lower_bound(X_36,greatest_lower_bound(multiply(X_36,X_232),X_13)))
    | inverse(greatest_lower_bound(X_13,multiply(X_36,greatest_lower_bound(X_232,identity)))) = inverse(greatest_lower_bound(X_36,greatest_lower_bound(multiply(X_36,X_232),X_13))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,multiply(X_36,X_232)))),inverse(greatest_lower_bound(X_36,greatest_lower_bound(multiply(X_36,X_232),X_13)))) ),[0,0,1],$fot(multiply(X_36,greatest_lower_bound(X_232,identity)))]]) ).

cnf(refute_0_5680,plain,
    ( inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,multiply(X_36,X_232)))) != inverse(greatest_lower_bound(X_36,greatest_lower_bound(multiply(X_36,X_232),X_13)))
    | inverse(greatest_lower_bound(X_13,multiply(X_36,greatest_lower_bound(X_232,identity)))) = inverse(greatest_lower_bound(X_36,greatest_lower_bound(multiply(X_36,X_232),X_13))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,multiply(X_36,X_232)),multiply(X_36,greatest_lower_bound(X_232,identity))) )],[refute_0_5678,refute_0_5679]) ).

cnf(refute_0_5681,plain,
    inverse(greatest_lower_bound(X_13,multiply(X_36,greatest_lower_bound(X_232,identity)))) = inverse(greatest_lower_bound(X_36,greatest_lower_bound(multiply(X_36,X_232),X_13))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_13,greatest_lower_bound(X_36,multiply(X_36,X_232)))),inverse(greatest_lower_bound(X_36,greatest_lower_bound(multiply(X_36,X_232),X_13)))) )],[refute_0_5675,refute_0_5680]) ).

cnf(refute_0_5682,plain,
    inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),identity))),
    inference(subst,[],[refute_0_5681:[bind(X_13,$fot(identity)),bind(X_232,$fot(a)),bind(X_36,$fot(a))]]) ).

cnf(refute_0_5683,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),identity))) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))
    | inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))) != inverse(greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),identity)))
    | inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))))),bind(Y0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),identity))))),bind(Z0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))))]]) ).

cnf(refute_0_5684,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),identity))) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))
    | inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))),inverse(greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),identity)))) )],[refute_0_5682,refute_0_5683]) ).

cnf(refute_0_5685,plain,
    inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(multiply(a,a),identity))),inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))) )],[refute_0_5674,refute_0_5684]) ).

cnf(refute_0_5686,plain,
    least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(multiply(a,greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_5687,plain,
    ( inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))
    | least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))) != inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity))))
    | least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))))),bind(Z0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))))]]) ).

cnf(refute_0_5688,plain,
    ( inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))
    | least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))),inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity))))) )],[refute_0_5686,refute_0_5687]) ).

cnf(refute_0_5689,plain,
    least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(a,greatest_lower_bound(a,identity)))),inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))) )],[refute_0_5685,refute_0_5688]) ).

cnf(refute_0_5690,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))) != inverse(greatest_lower_bound(identity,multiply(a,b)))
    | least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))) != inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))
    | least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(identity,multiply(a,b))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))))),bind(Y0,$fot(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))))),bind(Z0,$fot(inverse(greatest_lower_bound(identity,multiply(a,b)))))]]) ).

cnf(refute_0_5691,plain,
    ( inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))) != inverse(greatest_lower_bound(identity,multiply(a,b)))
    | least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(identity,multiply(a,b))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))),inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a))))) )],[refute_0_5689,refute_0_5690]) ).

cnf(refute_0_5692,plain,
    least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))) = inverse(greatest_lower_bound(identity,multiply(a,b))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,a)))),inverse(greatest_lower_bound(identity,multiply(a,b)))) )],[refute_0_5667,refute_0_5691]) ).

cnf(refute_0_5693,plain,
    multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))) = multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))),
    introduced(tautology,[refl,[$fot(multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))))]]) ).

cnf(refute_0_5694,plain,
    ( multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))) != multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))))
    | least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))) != inverse(greatest_lower_bound(identity,multiply(a,b)))
    | multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))) = multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))),multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,multiply(a,b))))]]) ).

cnf(refute_0_5695,plain,
    ( least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))) != inverse(greatest_lower_bound(identity,multiply(a,b)))
    | multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))) = multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) ),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))),multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))))) )],[refute_0_5693,refute_0_5694]) ).

cnf(refute_0_5696,plain,
    multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))) = multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))),inverse(greatest_lower_bound(identity,multiply(a,b)))) )],[refute_0_5692,refute_0_5695]) ).

cnf(refute_0_5697,plain,
    multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) = multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))),
    inference(subst,[],[refute_0_5053:[bind(X,$fot(a)),bind(Y,$fot(identity)),bind(Z,$fot(inverse(multiply(a,greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_5698,plain,
    ( multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))) != multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b))))
    | multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) != multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))))
    | multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) = multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)))),bind(Y0,$fot(multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))))),bind(Z0,$fot(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b))))))]]) ).

cnf(refute_0_5699,plain,
    ( multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))) != multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b))))
    | multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) = multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) ),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)),multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity)))))) )],[refute_0_5697,refute_0_5698]) ).

cnf(refute_0_5700,plain,
    multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) = multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(identity,inverse(multiply(a,greatest_lower_bound(a,identity))))),multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b))))) )],[refute_0_5696,refute_0_5699]) ).

cnf(refute_0_5701,plain,
    ( multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) != multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b))))
    | multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) ),[0],$fot(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))))]]) ).

cnf(refute_0_5702,plain,
    ( multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)),multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b))))) )],[refute_0_5700,refute_0_5701]) ).

cnf(refute_0_5703,plain,
    multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(a,least_upper_bound(inverse(multiply(a,greatest_lower_bound(a,identity))),identity)),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_5500,refute_0_5702]) ).

cnf(refute_0_5704,plain,
    multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) = least_upper_bound(X_93,multiply(X_93,inverse(multiply(X_198,X_93)))),
    inference(subst,[],[refute_0_480:[bind(X_94,$fot(inverse(multiply(X_198,X_93))))]]) ).

cnf(refute_0_5705,plain,
    multiply(X_93,inverse(multiply(X_198,X_93))) = inverse(X_198),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(X_93)),bind(X_59,$fot(X_198))]]) ).

cnf(refute_0_5706,plain,
    ( multiply(X_93,inverse(multiply(X_198,X_93))) != inverse(X_198)
    | multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) != least_upper_bound(X_93,multiply(X_93,inverse(multiply(X_198,X_93))))
    | multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) = least_upper_bound(X_93,inverse(X_198)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)),least_upper_bound(X_93,multiply(X_93,inverse(multiply(X_198,X_93))))) ),[1,1],$fot(inverse(X_198))]]) ).

cnf(refute_0_5707,plain,
    ( multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) != least_upper_bound(X_93,multiply(X_93,inverse(multiply(X_198,X_93))))
    | multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) = least_upper_bound(X_93,inverse(X_198)) ),
    inference(resolve,[$cnf( $equal(multiply(X_93,inverse(multiply(X_198,X_93))),inverse(X_198)) )],[refute_0_5705,refute_0_5706]) ).

cnf(refute_0_5708,plain,
    multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) = least_upper_bound(X_93,inverse(X_198)),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)),least_upper_bound(X_93,multiply(X_93,inverse(multiply(X_198,X_93))))) )],[refute_0_5704,refute_0_5707]) ).

cnf(refute_0_5709,plain,
    least_upper_bound(identity,inverse(multiply(X_198,X_93))) = inverse(greatest_lower_bound(identity,multiply(X_198,X_93))),
    inference(subst,[],[refute_0_488:[bind(Y,$fot(multiply(X_198,X_93)))]]) ).

cnf(refute_0_5710,plain,
    multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))) = multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))),
    introduced(tautology,[refl,[$fot(multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))))]]) ).

cnf(refute_0_5711,plain,
    ( multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))) != multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93))))
    | least_upper_bound(identity,inverse(multiply(X_198,X_93))) != inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))
    | multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))) = multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))),multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,multiply(X_198,X_93))))]]) ).

cnf(refute_0_5712,plain,
    ( least_upper_bound(identity,inverse(multiply(X_198,X_93))) != inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))
    | multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))) = multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))),multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93))))) )],[refute_0_5710,refute_0_5711]) ).

cnf(refute_0_5713,plain,
    multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))) = multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(multiply(X_198,X_93))),inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))) )],[refute_0_5709,refute_0_5712]) ).

cnf(refute_0_5714,plain,
    multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) = multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))),
    inference(subst,[],[refute_0_564:[bind(X_165,$fot(inverse(multiply(X_198,X_93)))),bind(X_31,$fot(X_93))]]) ).

cnf(refute_0_5715,plain,
    ( multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))) != multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93))))
    | multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) != multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93))))
    | multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) = multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)))),bind(Y0,$fot(multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))))),bind(Z0,$fot(multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93))))))]]) ).

cnf(refute_0_5716,plain,
    ( multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))) != multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93))))
    | multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) = multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))) ),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)),multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93))))) )],[refute_0_5714,refute_0_5715]) ).

cnf(refute_0_5717,plain,
    multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) = multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(identity,inverse(multiply(X_198,X_93)))),multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93))))) )],[refute_0_5713,refute_0_5716]) ).

cnf(refute_0_5718,plain,
    ( multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) != multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93))))
    | multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) != least_upper_bound(X_93,inverse(X_198))
    | multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))) = least_upper_bound(X_93,inverse(X_198)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)),least_upper_bound(X_93,inverse(X_198))) ),[0],$fot(multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))))]]) ).

cnf(refute_0_5719,plain,
    ( multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)) != least_upper_bound(X_93,inverse(X_198))
    | multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))) = least_upper_bound(X_93,inverse(X_198)) ),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)),multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93))))) )],[refute_0_5717,refute_0_5718]) ).

cnf(refute_0_5720,plain,
    multiply(X_93,inverse(greatest_lower_bound(identity,multiply(X_198,X_93)))) = least_upper_bound(X_93,inverse(X_198)),
    inference(resolve,[$cnf( $equal(multiply(X_93,least_upper_bound(inverse(multiply(X_198,X_93)),identity)),least_upper_bound(X_93,inverse(X_198))) )],[refute_0_5708,refute_0_5719]) ).

cnf(refute_0_5721,plain,
    multiply(a,inverse(greatest_lower_bound(identity,multiply(a,a)))) = least_upper_bound(a,inverse(a)),
    inference(subst,[],[refute_0_5720:[bind(X_198,$fot(a)),bind(X_93,$fot(a))]]) ).

cnf(refute_0_5722,plain,
    greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) = greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))))),
    inference(subst,[],[refute_0_4624:[bind(X_329,$fot(multiply(X_220,greatest_lower_bound(X_220,identity))))]]) ).

cnf(refute_0_5723,plain,
    ( greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) != greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))))
    | least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))) != least_upper_bound(identity,X_220)
    | greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) = greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity),greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))))) ),[1,1,1],$fot(least_upper_bound(identity,X_220))]]) ).

cnf(refute_0_5724,plain,
    ( greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) != greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))))
    | greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) = greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity))),least_upper_bound(identity,X_220)) )],[refute_0_5518,refute_0_5723]) ).

cnf(refute_0_5725,plain,
    greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) = greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity),greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,multiply(X_220,greatest_lower_bound(X_220,identity)))))) )],[refute_0_5722,refute_0_5724]) ).

cnf(refute_0_5726,plain,
    ( greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) != multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity))
    | greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) != greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))
    | multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) = greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity),greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))) ),[0],$fot(multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)))]]) ).

cnf(refute_0_5727,plain,
    ( greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) != greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))
    | multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) = greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity),multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity))) )],[refute_0_5655,refute_0_5726]) ).

cnf(refute_0_5728,plain,
    X_60 = multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),multiply(inverse(greatest_lower_bound(X_60,identity)),X_60)),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(inverse(greatest_lower_bound(X_60,identity))))]]) ).

cnf(refute_0_5729,plain,
    multiply(inverse(greatest_lower_bound(X_60,identity)),X_60) = least_upper_bound(X_60,identity),
    inference(subst,[],[refute_0_2750:[bind(X_117,$fot(X_60))]]) ).

cnf(refute_0_5730,plain,
    ( X_60 != multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),multiply(inverse(greatest_lower_bound(X_60,identity)),X_60))
    | multiply(inverse(greatest_lower_bound(X_60,identity)),X_60) != least_upper_bound(X_60,identity)
    | X_60 = multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(X_60,multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),multiply(inverse(greatest_lower_bound(X_60,identity)),X_60))) ),[1,1],$fot(least_upper_bound(X_60,identity))]]) ).

cnf(refute_0_5731,plain,
    ( X_60 != multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),multiply(inverse(greatest_lower_bound(X_60,identity)),X_60))
    | X_60 = multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_60,identity)),X_60),least_upper_bound(X_60,identity)) )],[refute_0_5729,refute_0_5730]) ).

cnf(refute_0_5732,plain,
    X_60 = multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)),
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),multiply(inverse(greatest_lower_bound(X_60,identity)),X_60))) )],[refute_0_5728,refute_0_5731]) ).

cnf(refute_0_5733,plain,
    inverse(inverse(greatest_lower_bound(X_60,identity))) = greatest_lower_bound(X_60,identity),
    inference(subst,[],[refute_0_42:[bind(X_87,$fot(greatest_lower_bound(X_60,identity)))]]) ).

cnf(refute_0_5734,plain,
    multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)) = multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)),
    introduced(tautology,[refl,[$fot(multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)))]]) ).

cnf(refute_0_5735,plain,
    ( multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)) != multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity))
    | inverse(inverse(greatest_lower_bound(X_60,identity))) != greatest_lower_bound(X_60,identity)
    | multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)) = multiply(greatest_lower_bound(X_60,identity),least_upper_bound(X_60,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)),multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity))) ),[1,0],$fot(greatest_lower_bound(X_60,identity))]]) ).

cnf(refute_0_5736,plain,
    ( inverse(inverse(greatest_lower_bound(X_60,identity))) != greatest_lower_bound(X_60,identity)
    | multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)) = multiply(greatest_lower_bound(X_60,identity),least_upper_bound(X_60,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)),multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity))) )],[refute_0_5734,refute_0_5735]) ).

cnf(refute_0_5737,plain,
    multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)) = multiply(greatest_lower_bound(X_60,identity),least_upper_bound(X_60,identity)),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_60,identity))),greatest_lower_bound(X_60,identity)) )],[refute_0_5733,refute_0_5736]) ).

cnf(refute_0_5738,plain,
    ( X_60 != multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity))
    | multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)) != multiply(greatest_lower_bound(X_60,identity),least_upper_bound(X_60,identity))
    | X_60 = multiply(greatest_lower_bound(X_60,identity),least_upper_bound(X_60,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_60,multiply(greatest_lower_bound(X_60,identity),least_upper_bound(X_60,identity))) ),[0],$fot(multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)))]]) ).

cnf(refute_0_5739,plain,
    ( X_60 != multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity))
    | X_60 = multiply(greatest_lower_bound(X_60,identity),least_upper_bound(X_60,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity)),multiply(greatest_lower_bound(X_60,identity),least_upper_bound(X_60,identity))) )],[refute_0_5737,refute_0_5738]) ).

cnf(refute_0_5740,plain,
    X_60 = multiply(greatest_lower_bound(X_60,identity),least_upper_bound(X_60,identity)),
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(inverse(greatest_lower_bound(X_60,identity))),least_upper_bound(X_60,identity))) )],[refute_0_5732,refute_0_5739]) ).

cnf(refute_0_5741,plain,
    X_139 = multiply(greatest_lower_bound(X_139,identity),least_upper_bound(X_139,identity)),
    inference(subst,[],[refute_0_5740:[bind(X_60,$fot(X_139))]]) ).

cnf(refute_0_5742,plain,
    least_upper_bound(identity,X_139) = least_upper_bound(X_139,identity),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_139))]]) ).

cnf(refute_0_5743,plain,
    ( least_upper_bound(identity,X_139) != least_upper_bound(X_139,identity)
    | least_upper_bound(X_139,identity) = least_upper_bound(identity,X_139) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,X_139))),bind(Y0,$fot(least_upper_bound(X_139,identity)))]]) ).

cnf(refute_0_5744,plain,
    least_upper_bound(X_139,identity) = least_upper_bound(identity,X_139),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_139),least_upper_bound(X_139,identity)) )],[refute_0_5742,refute_0_5743]) ).

cnf(refute_0_5745,plain,
    ( X_139 != multiply(greatest_lower_bound(X_139,identity),least_upper_bound(X_139,identity))
    | least_upper_bound(X_139,identity) != least_upper_bound(identity,X_139)
    | X_139 = multiply(greatest_lower_bound(X_139,identity),least_upper_bound(identity,X_139)) ),
    introduced(tautology,[equality,[$cnf( $equal(X_139,multiply(greatest_lower_bound(X_139,identity),least_upper_bound(X_139,identity))) ),[1,1],$fot(least_upper_bound(identity,X_139))]]) ).

cnf(refute_0_5746,plain,
    ( X_139 != multiply(greatest_lower_bound(X_139,identity),least_upper_bound(X_139,identity))
    | X_139 = multiply(greatest_lower_bound(X_139,identity),least_upper_bound(identity,X_139)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_139,identity),least_upper_bound(identity,X_139)) )],[refute_0_5744,refute_0_5745]) ).

cnf(refute_0_5747,plain,
    X_139 = multiply(greatest_lower_bound(X_139,identity),least_upper_bound(identity,X_139)),
    inference(resolve,[$cnf( $equal(X_139,multiply(greatest_lower_bound(X_139,identity),least_upper_bound(X_139,identity))) )],[refute_0_5741,refute_0_5746]) ).

cnf(refute_0_5748,plain,
    ( X_139 != multiply(greatest_lower_bound(X_139,identity),least_upper_bound(identity,X_139))
    | multiply(greatest_lower_bound(X_139,identity),least_upper_bound(identity,X_139)) = X_139 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_139)),bind(Y0,$fot(multiply(greatest_lower_bound(X_139,identity),least_upper_bound(identity,X_139))))]]) ).

cnf(refute_0_5749,plain,
    multiply(greatest_lower_bound(X_139,identity),least_upper_bound(identity,X_139)) = X_139,
    inference(resolve,[$cnf( $equal(X_139,multiply(greatest_lower_bound(X_139,identity),least_upper_bound(identity,X_139))) )],[refute_0_5747,refute_0_5748]) ).

cnf(refute_0_5750,plain,
    multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220)) = X_220,
    inference(subst,[],[refute_0_5749:[bind(X_139,$fot(X_220))]]) ).

cnf(refute_0_5751,plain,
    multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))) = multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))),
    introduced(tautology,[refl,[$fot(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))))]]) ).

cnf(refute_0_5752,plain,
    ( multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))) != multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220)))
    | multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220)) != X_220
    | multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))) = multiply(X_220,X_220) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))),multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220)))) ),[1,1],$fot(X_220)]]) ).

cnf(refute_0_5753,plain,
    ( multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220)) != X_220
    | multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))) = multiply(X_220,X_220) ),
    inference(resolve,[$cnf( $equal(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))),multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220)))) )],[refute_0_5751,refute_0_5752]) ).

cnf(refute_0_5754,plain,
    multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))) = multiply(X_220,X_220),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220)),X_220) )],[refute_0_5750,refute_0_5753]) ).

cnf(refute_0_5755,plain,
    multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)) = multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))),
    inference(subst,[],[associativity:[bind(X,$fot(X_220)),bind(Y,$fot(greatest_lower_bound(X_220,identity))),bind(Z,$fot(least_upper_bound(identity,X_220)))]]) ).

cnf(refute_0_5756,plain,
    ( multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))) != multiply(X_220,X_220)
    | multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)) != multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220)))
    | multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)) = multiply(X_220,X_220) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))),bind(Y0,$fot(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))))),bind(Z0,$fot(multiply(X_220,X_220)))]]) ).

cnf(refute_0_5757,plain,
    ( multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))) != multiply(X_220,X_220)
    | multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)) = multiply(X_220,X_220) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)),multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220)))) )],[refute_0_5755,refute_0_5756]) ).

cnf(refute_0_5758,plain,
    multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)) = multiply(X_220,X_220),
    inference(resolve,[$cnf( $equal(multiply(X_220,multiply(greatest_lower_bound(X_220,identity),least_upper_bound(identity,X_220))),multiply(X_220,X_220)) )],[refute_0_5754,refute_0_5757]) ).

cnf(refute_0_5759,plain,
    greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))) = greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))))]]) ).

cnf(refute_0_5760,plain,
    ( multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)) != multiply(X_220,X_220)
    | greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))) != greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))
    | greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))) = greatest_lower_bound(identity,multiply(X_220,X_220)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))),greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))) ),[1,1],$fot(multiply(X_220,X_220))]]) ).

cnf(refute_0_5761,plain,
    ( multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)) != multiply(X_220,X_220)
    | greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))) = greatest_lower_bound(identity,multiply(X_220,X_220)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))),greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))) )],[refute_0_5759,refute_0_5760]) ).

cnf(refute_0_5762,plain,
    greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))) = greatest_lower_bound(identity,multiply(X_220,X_220)),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)),multiply(X_220,X_220)) )],[refute_0_5758,refute_0_5761]) ).

cnf(refute_0_5763,plain,
    ( multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) != greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))
    | greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))) != greatest_lower_bound(identity,multiply(X_220,X_220))
    | multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) = greatest_lower_bound(identity,multiply(X_220,X_220)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)),greatest_lower_bound(identity,multiply(X_220,X_220))) ),[0],$fot(greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))))]]) ).

cnf(refute_0_5764,plain,
    ( multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) != greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))
    | multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) = greatest_lower_bound(identity,multiply(X_220,X_220)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220))),greatest_lower_bound(identity,multiply(X_220,X_220))) )],[refute_0_5762,refute_0_5763]) ).

cnf(refute_0_5765,plain,
    ( greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity) != greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))
    | multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) = greatest_lower_bound(identity,multiply(X_220,X_220)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)),greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))) )],[refute_0_5727,refute_0_5764]) ).

cnf(refute_0_5766,plain,
    multiply(greatest_lower_bound(X_220,identity),greatest_lower_bound(X_220,identity)) = greatest_lower_bound(identity,multiply(X_220,X_220)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_220,greatest_lower_bound(X_220,identity)),identity),greatest_lower_bound(identity,multiply(multiply(X_220,greatest_lower_bound(X_220,identity)),least_upper_bound(identity,X_220)))) )],[refute_0_5725,refute_0_5765]) ).

cnf(refute_0_5767,plain,
    multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(a,a)),
    inference(subst,[],[refute_0_5766:[bind(X_220,$fot(a))]]) ).

cnf(refute_0_5768,plain,
    ( multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(a,a))
    | multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(a,b))
    | greatest_lower_bound(identity,multiply(a,a)) = greatest_lower_bound(identity,multiply(a,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,multiply(a,b))) ),[0],$fot(greatest_lower_bound(identity,multiply(a,a)))]]) ).

cnf(refute_0_5769,plain,
    ( multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)) != greatest_lower_bound(identity,multiply(a,b))
    | greatest_lower_bound(identity,multiply(a,a)) = greatest_lower_bound(identity,multiply(a,b)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,multiply(a,a))) )],[refute_0_5767,refute_0_5768]) ).

cnf(refute_0_5770,plain,
    greatest_lower_bound(identity,multiply(a,a)) = greatest_lower_bound(identity,multiply(a,b)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,identity),greatest_lower_bound(a,identity)),greatest_lower_bound(identity,multiply(a,b))) )],[refute_0_5379,refute_0_5769]) ).

cnf(refute_0_5771,plain,
    ( greatest_lower_bound(identity,multiply(a,a)) != greatest_lower_bound(identity,multiply(a,b))
    | greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(identity,multiply(a,a)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(identity,multiply(a,a)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(a,b))))]]) ).

cnf(refute_0_5772,plain,
    greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(identity,multiply(a,a)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,a)),greatest_lower_bound(identity,multiply(a,b))) )],[refute_0_5770,refute_0_5771]) ).

cnf(refute_0_5773,plain,
    inverse(greatest_lower_bound(identity,multiply(a,b))) = inverse(greatest_lower_bound(identity,multiply(a,b))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,multiply(a,b))))]]) ).

cnf(refute_0_5774,plain,
    ( greatest_lower_bound(identity,multiply(a,b)) != greatest_lower_bound(identity,multiply(a,a))
    | inverse(greatest_lower_bound(identity,multiply(a,b))) != inverse(greatest_lower_bound(identity,multiply(a,b)))
    | inverse(greatest_lower_bound(identity,multiply(a,b))) = inverse(greatest_lower_bound(identity,multiply(a,a))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(a,b))),inverse(greatest_lower_bound(identity,multiply(a,b)))) ),[1,0],$fot(greatest_lower_bound(identity,multiply(a,a)))]]) ).

cnf(refute_0_5775,plain,
    ( greatest_lower_bound(identity,multiply(a,b)) != greatest_lower_bound(identity,multiply(a,a))
    | inverse(greatest_lower_bound(identity,multiply(a,b))) = inverse(greatest_lower_bound(identity,multiply(a,a))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(a,b))),inverse(greatest_lower_bound(identity,multiply(a,b)))) )],[refute_0_5773,refute_0_5774]) ).

cnf(refute_0_5776,plain,
    inverse(greatest_lower_bound(identity,multiply(a,b))) = inverse(greatest_lower_bound(identity,multiply(a,a))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,b)),greatest_lower_bound(identity,multiply(a,a))) )],[refute_0_5772,refute_0_5775]) ).

cnf(refute_0_5777,plain,
    multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) = multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))),
    introduced(tautology,[refl,[$fot(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))))]]) ).

cnf(refute_0_5778,plain,
    ( multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) != multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b))))
    | inverse(greatest_lower_bound(identity,multiply(a,b))) != inverse(greatest_lower_bound(identity,multiply(a,a)))
    | multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) = multiply(a,inverse(greatest_lower_bound(identity,multiply(a,a)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))),multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,multiply(a,a))))]]) ).

cnf(refute_0_5779,plain,
    ( inverse(greatest_lower_bound(identity,multiply(a,b))) != inverse(greatest_lower_bound(identity,multiply(a,a)))
    | multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) = multiply(a,inverse(greatest_lower_bound(identity,multiply(a,a)))) ),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))),multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b))))) )],[refute_0_5777,refute_0_5778]) ).

cnf(refute_0_5780,plain,
    multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) = multiply(a,inverse(greatest_lower_bound(identity,multiply(a,a)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(a,b))),inverse(greatest_lower_bound(identity,multiply(a,a)))) )],[refute_0_5776,refute_0_5779]) ).

cnf(refute_0_5781,plain,
    ( multiply(a,inverse(greatest_lower_bound(identity,multiply(a,a)))) != least_upper_bound(a,inverse(a))
    | multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) != multiply(a,inverse(greatest_lower_bound(identity,multiply(a,a))))
    | multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) = least_upper_bound(a,inverse(a)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))))),bind(Y0,$fot(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,a)))))),bind(Z0,$fot(least_upper_bound(a,inverse(a))))]]) ).

cnf(refute_0_5782,plain,
    ( multiply(a,inverse(greatest_lower_bound(identity,multiply(a,a)))) != least_upper_bound(a,inverse(a))
    | multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) = least_upper_bound(a,inverse(a)) ),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))),multiply(a,inverse(greatest_lower_bound(identity,multiply(a,a))))) )],[refute_0_5780,refute_0_5781]) ).

cnf(refute_0_5783,plain,
    multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) = least_upper_bound(a,inverse(a)),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,a)))),least_upper_bound(a,inverse(a))) )],[refute_0_5721,refute_0_5782]) ).

cnf(refute_0_5784,plain,
    ( multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) != least_upper_bound(a,inverse(a))
    | multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(a,inverse(a)) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) ),[0],$fot(least_upper_bound(a,inverse(a)))]]) ).

cnf(refute_0_5785,plain,
    ( multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(a,inverse(a)) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))),least_upper_bound(a,inverse(a))) )],[refute_0_5783,refute_0_5784]) ).

cnf(refute_0_5786,plain,
    least_upper_bound(a,inverse(a)) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(greatest_lower_bound(identity,multiply(a,b)))),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_5703,refute_0_5785]) ).

cnf(refute_0_5787,plain,
    ( least_upper_bound(a,inverse(a)) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(a)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(a,inverse(a)))),bind(Y0,$fot(least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_5788,plain,
    least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(a)),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,inverse(a)),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_5786,refute_0_5787]) ).

cnf(refute_0_5789,plain,
    inverse(greatest_lower_bound(X_180,greatest_lower_bound(identity,inverse(Y)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y)))),
    inference(subst,[],[refute_0_1013:[bind(Y,$fot(inverse(Y))),bind(X_24,$fot(identity)),bind(X_25,$fot(X_180))]]) ).

cnf(refute_0_5790,plain,
    ( greatest_lower_bound(identity,inverse(Y)) != inverse(least_upper_bound(identity,Y))
    | inverse(greatest_lower_bound(X_180,greatest_lower_bound(identity,inverse(Y)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y))))
    | inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_180,greatest_lower_bound(identity,inverse(Y)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y))))) ),[0,0,1],$fot(inverse(least_upper_bound(identity,Y)))]]) ).

cnf(refute_0_5791,plain,
    ( inverse(greatest_lower_bound(X_180,greatest_lower_bound(identity,inverse(Y)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y))))
    | inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(Y)),inverse(least_upper_bound(identity,Y))) )],[refute_0_500,refute_0_5790]) ).

cnf(refute_0_5792,plain,
    inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_180,greatest_lower_bound(identity,inverse(Y)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y))))) )],[refute_0_5789,refute_0_5791]) ).

cnf(refute_0_5793,plain,
    least_upper_bound(inverse(X_180),least_upper_bound(identity,Y)) = least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))),
    inference(subst,[],[refute_0_3111:[bind(X,$fot(inverse(X_180))),bind(Y,$fot(identity)),bind(X_145,$fot(Y))]]) ).

cnf(refute_0_5794,plain,
    inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))) = least_upper_bound(inverse(X_180),least_upper_bound(identity,Y)),
    inference(subst,[],[refute_0_1559:[bind(X,$fot(X_180)),bind(X_89,$fot(least_upper_bound(identity,Y)))]]) ).

cnf(refute_0_5795,plain,
    ( inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))) != least_upper_bound(inverse(X_180),least_upper_bound(identity,Y))
    | least_upper_bound(inverse(X_180),least_upper_bound(identity,Y)) != least_upper_bound(identity,least_upper_bound(Y,inverse(X_180)))
    | inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))) = least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))))),bind(Y0,$fot(least_upper_bound(inverse(X_180),least_upper_bound(identity,Y)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(Y,inverse(X_180)))))]]) ).

cnf(refute_0_5796,plain,
    ( least_upper_bound(inverse(X_180),least_upper_bound(identity,Y)) != least_upper_bound(identity,least_upper_bound(Y,inverse(X_180)))
    | inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))) = least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))),least_upper_bound(inverse(X_180),least_upper_bound(identity,Y))) )],[refute_0_5794,refute_0_5795]) ).

cnf(refute_0_5797,plain,
    inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))) = least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_180),least_upper_bound(identity,Y)),least_upper_bound(identity,least_upper_bound(Y,inverse(X_180)))) )],[refute_0_5793,refute_0_5796]) ).

cnf(refute_0_5798,plain,
    ( inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y))))
    | inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))) != least_upper_bound(identity,least_upper_bound(Y,inverse(X_180)))
    | least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y))))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))))]]) ).

cnf(refute_0_5799,plain,
    ( inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y))))
    | least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y)))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))),least_upper_bound(identity,least_upper_bound(Y,inverse(X_180)))) )],[refute_0_5797,refute_0_5798]) ).

cnf(refute_0_5800,plain,
    least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y)))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_180,inverse(least_upper_bound(identity,Y)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y))))) )],[refute_0_5792,refute_0_5799]) ).

cnf(refute_0_5801,plain,
    least_upper_bound(identity,least_upper_bound(b,inverse(X_180))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(b)))),
    inference(subst,[],[refute_0_5800:[bind(Y,$fot(b))]]) ).

cnf(refute_0_5802,plain,
    multiply(inverse(least_upper_bound(a,c)),inverse(multiply(b,inverse(least_upper_bound(a,c))))) = inverse(b),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(inverse(least_upper_bound(a,c)))),bind(X_59,$fot(b))]]) ).

cnf(refute_0_5803,plain,
    multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_121,identity))),X_121) = greatest_lower_bound(multiply(X_122,X_121),multiply(inverse(greatest_lower_bound(X_121,identity)),X_121)),
    inference(subst,[],[monotony_glb2:[bind(X,$fot(X_121)),bind(Y,$fot(X_122)),bind(Z,$fot(inverse(greatest_lower_bound(X_121,identity))))]]) ).

cnf(refute_0_5804,plain,
    multiply(inverse(greatest_lower_bound(X_121,identity)),X_121) = least_upper_bound(X_121,identity),
    inference(subst,[],[refute_0_2750:[bind(X_117,$fot(X_121))]]) ).

cnf(refute_0_5805,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_121,identity))),X_121) != greatest_lower_bound(multiply(X_122,X_121),multiply(inverse(greatest_lower_bound(X_121,identity)),X_121))
    | multiply(inverse(greatest_lower_bound(X_121,identity)),X_121) != least_upper_bound(X_121,identity)
    | multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_121,identity))),X_121) = greatest_lower_bound(multiply(X_122,X_121),least_upper_bound(X_121,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_121,identity))),X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(inverse(greatest_lower_bound(X_121,identity)),X_121))) ),[1,1],$fot(least_upper_bound(X_121,identity))]]) ).

cnf(refute_0_5806,plain,
    ( multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_121,identity))),X_121) != greatest_lower_bound(multiply(X_122,X_121),multiply(inverse(greatest_lower_bound(X_121,identity)),X_121))
    | multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_121,identity))),X_121) = greatest_lower_bound(multiply(X_122,X_121),least_upper_bound(X_121,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_121,identity)),X_121),least_upper_bound(X_121,identity)) )],[refute_0_5804,refute_0_5805]) ).

cnf(refute_0_5807,plain,
    multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_121,identity))),X_121) = greatest_lower_bound(multiply(X_122,X_121),least_upper_bound(X_121,identity)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,inverse(greatest_lower_bound(X_121,identity))),X_121),greatest_lower_bound(multiply(X_122,X_121),multiply(inverse(greatest_lower_bound(X_121,identity)),X_121))) )],[refute_0_5803,refute_0_5806]) ).

cnf(refute_0_5808,plain,
    multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) = greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)),
    inference(subst,[],[refute_0_5807:[bind(X_121,$fot(inverse(c))),bind(X_122,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_5809,plain,
    multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) = greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),
    inference(subst,[],[refute_0_340:[bind(X_122,$fot(least_upper_bound(a,c))),bind(X_123,$fot(b))]]) ).

cnf(refute_0_5810,plain,
    multiply(greatest_lower_bound(b,least_upper_bound(a,c)),inverse(least_upper_bound(a,c))) = greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),
    inference(subst,[],[refute_0_3421:[bind(X_122,$fot(b)),bind(X_123,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_5811,plain,
    ( multiply(greatest_lower_bound(b,least_upper_bound(a,c)),inverse(least_upper_bound(a,c))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
    | greatest_lower_bound(b,least_upper_bound(a,c)) != b
    | multiply(b,inverse(least_upper_bound(a,c))) = greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(b,least_upper_bound(a,c)),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))) ),[0,0],$fot(b)]]) ).

cnf(refute_0_5812,plain,
    ( multiply(greatest_lower_bound(b,least_upper_bound(a,c)),inverse(least_upper_bound(a,c))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
    | multiply(b,inverse(least_upper_bound(a,c))) = greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,c)),b) )],[refute_0_2900,refute_0_5811]) ).

cnf(refute_0_5813,plain,
    multiply(b,inverse(least_upper_bound(a,c))) = greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(b,least_upper_bound(a,c)),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_5810,refute_0_5812]) ).

cnf(refute_0_5814,plain,
    ( multiply(b,inverse(least_upper_bound(a,c))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
    | greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(b,inverse(least_upper_bound(a,c))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))))]]) ).

cnf(refute_0_5815,plain,
    greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_5813,refute_0_5814]) ).

cnf(refute_0_5816,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
    | greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
    | multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))),multiply(b,inverse(least_upper_bound(a,c)))) ),[0],$fot(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))))]]) ).

cnf(refute_0_5817,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
    | multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_5815,refute_0_5816]) ).

cnf(refute_0_5818,plain,
    multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) = multiply(b,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))),greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_5809,refute_0_5817]) ).

cnf(refute_0_5819,plain,
    multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)) = multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)))]]) ).

cnf(refute_0_5820,plain,
    ( multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)) != multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b))
    | least_upper_bound(a,least_upper_bound(b,c)) != least_upper_bound(a,c)
    | multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)) = multiply(least_upper_bound(a,c),inverse(b)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)),multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b))) ),[1,0],$fot(least_upper_bound(a,c))]]) ).

cnf(refute_0_5821,plain,
    ( least_upper_bound(a,least_upper_bound(b,c)) != least_upper_bound(a,c)
    | multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)) = multiply(least_upper_bound(a,c),inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)),multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b))) )],[refute_0_5819,refute_0_5820]) ).

cnf(refute_0_5822,plain,
    multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)) = multiply(least_upper_bound(a,c),inverse(b)),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,c)),least_upper_bound(a,c)) )],[refute_0_1048,refute_0_5821]) ).

cnf(refute_0_5823,plain,
    multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110) = least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110)),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(X_110)),bind(Y,$fot(X_111)),bind(Z,$fot(least_upper_bound(Y,X_45)))]]) ).

cnf(refute_0_5824,plain,
    least_upper_bound(Y,least_upper_bound(X_111,X_45)) = least_upper_bound(X_111,least_upper_bound(Y,X_45)),
    inference(subst,[],[refute_0_1102:[bind(X_43,$fot(X_111))]]) ).

cnf(refute_0_5825,plain,
    ( least_upper_bound(Y,least_upper_bound(X_111,X_45)) != least_upper_bound(X_111,least_upper_bound(Y,X_45))
    | least_upper_bound(X_111,least_upper_bound(Y,X_45)) = least_upper_bound(Y,least_upper_bound(X_111,X_45)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_111,X_45)))),bind(Y0,$fot(least_upper_bound(X_111,least_upper_bound(Y,X_45))))]]) ).

cnf(refute_0_5826,plain,
    least_upper_bound(X_111,least_upper_bound(Y,X_45)) = least_upper_bound(Y,least_upper_bound(X_111,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_111,X_45)),least_upper_bound(X_111,least_upper_bound(Y,X_45))) )],[refute_0_5824,refute_0_5825]) ).

cnf(refute_0_5827,plain,
    ( multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110) != least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110))
    | least_upper_bound(X_111,least_upper_bound(Y,X_45)) != least_upper_bound(Y,least_upper_bound(X_111,X_45))
    | multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110) = least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110),least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110))) ),[0,0],$fot(least_upper_bound(Y,least_upper_bound(X_111,X_45)))]]) ).

cnf(refute_0_5828,plain,
    ( multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110) != least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110))
    | multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110) = least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_111,least_upper_bound(Y,X_45)),least_upper_bound(Y,least_upper_bound(X_111,X_45))) )],[refute_0_5826,refute_0_5827]) ).

cnf(refute_0_5829,plain,
    multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110) = least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110),least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110))) )],[refute_0_5823,refute_0_5828]) ).

cnf(refute_0_5830,plain,
    least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110)) = multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110),
    inference(subst,[],[refute_0_384:[bind(X,$fot(X_110)),bind(Y,$fot(X_111)),bind(Z,$fot(least_upper_bound(Y,X_45)))]]) ).

cnf(refute_0_5831,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110) != least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110))
    | least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110)) != multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110)
    | multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110) = multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110),multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110)) ),[0],$fot(least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110)))]]) ).

cnf(refute_0_5832,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110) != least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110))
    | multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110) = multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110)),multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110)) )],[refute_0_5830,refute_0_5831]) ).

cnf(refute_0_5833,plain,
    multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110) = multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110),least_upper_bound(multiply(X_111,X_110),multiply(least_upper_bound(Y,X_45),X_110))) )],[refute_0_5829,refute_0_5832]) ).

cnf(refute_0_5834,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110) != multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110)
    | multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110) = multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110))),bind(Y0,$fot(multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110)))]]) ).

cnf(refute_0_5835,plain,
    multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110) = multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_111,X_45)),X_110),multiply(least_upper_bound(X_111,least_upper_bound(Y,X_45)),X_110)) )],[refute_0_5833,refute_0_5834]) ).

cnf(refute_0_5836,plain,
    multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)) = multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)),
    inference(subst,[],[refute_0_5835:[bind(Y,$fot(a)),bind(X_110,$fot(inverse(b))),bind(X_111,$fot(b)),bind(X_45,$fot(c))]]) ).

cnf(refute_0_5837,plain,
    ( multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)) != multiply(least_upper_bound(a,c),inverse(b))
    | multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)) != multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b))
    | multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)) = multiply(least_upper_bound(a,c),inverse(b)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)))),bind(Y0,$fot(multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)))),bind(Z0,$fot(multiply(least_upper_bound(a,c),inverse(b))))]]) ).

cnf(refute_0_5838,plain,
    ( multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)) != multiply(least_upper_bound(a,c),inverse(b))
    | multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)) = multiply(least_upper_bound(a,c),inverse(b)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)),multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b))) )],[refute_0_5836,refute_0_5837]) ).

cnf(refute_0_5839,plain,
    multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)) = multiply(least_upper_bound(a,c),inverse(b)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,least_upper_bound(b,c)),inverse(b)),multiply(least_upper_bound(a,c),inverse(b))) )],[refute_0_5822,refute_0_5838]) ).

cnf(refute_0_5840,plain,
    inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))) = inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))),
    introduced(tautology,[refl,[$fot(inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))))]]) ).

cnf(refute_0_5841,plain,
    ( multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)) != multiply(least_upper_bound(a,c),inverse(b))
    | inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))) != inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)))
    | inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))) = inverse(multiply(least_upper_bound(a,c),inverse(b))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))),inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)))) ),[1,0],$fot(multiply(least_upper_bound(a,c),inverse(b)))]]) ).

cnf(refute_0_5842,plain,
    ( multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)) != multiply(least_upper_bound(a,c),inverse(b))
    | inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))) = inverse(multiply(least_upper_bound(a,c),inverse(b))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))),inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)))) )],[refute_0_5840,refute_0_5841]) ).

cnf(refute_0_5843,plain,
    inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))) = inverse(multiply(least_upper_bound(a,c),inverse(b))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)),multiply(least_upper_bound(a,c),inverse(b))) )],[refute_0_5839,refute_0_5842]) ).

cnf(refute_0_5844,plain,
    multiply(greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))),inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) = greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))),
    inference(subst,[],[refute_0_3421:[bind(X_122,$fot(identity)),bind(X_123,$fot(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))]]) ).

cnf(refute_0_5845,plain,
    identity = greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))),
    inference(subst,[],[refute_0_349:[bind(Y,$fot(X_189)),bind(X_132,$fot(X_190))]]) ).

cnf(refute_0_5846,plain,
    ( identity != greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))) = identity ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))]]) ).

cnf(refute_0_5847,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))) = identity,
    inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) )],[refute_0_5845,refute_0_5846]) ).

cnf(refute_0_5848,plain,
    ( multiply(greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))),inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) != greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))
    | greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))) != identity
    | multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) = greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))),inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_5849,plain,
    ( multiply(greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))),inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) != greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))
    | multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) = greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity) )],[refute_0_5847,refute_0_5848]) ).

cnf(refute_0_5850,plain,
    multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) = greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))),inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))) )],[refute_0_5844,refute_0_5849]) ).

cnf(refute_0_5851,plain,
    multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) = inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),
    inference(subst,[],[left_identity:[bind(X,$fot(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))]]) ).

cnf(refute_0_5852,plain,
    ( multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) != greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))
    | multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) != inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))
    | inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))) = greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))) ),[0],$fot(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))]]) ).

cnf(refute_0_5853,plain,
    ( multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) != greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))
    | inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))) = greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) ),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) )],[refute_0_5851,refute_0_5852]) ).

cnf(refute_0_5854,plain,
    least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))) = least_upper_bound(identity,multiply(X_189,inverse(X_190))),
    inference(subst,[],[refute_0_438:[bind(X_112,$fot(X_189)),bind(X_119,$fot(X_190))]]) ).

cnf(refute_0_5855,plain,
    inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) = inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))]]) ).

cnf(refute_0_5856,plain,
    ( inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) != inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))
    | least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))) != least_upper_bound(identity,multiply(X_189,inverse(X_190)))
    | inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) = inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) ),[1,0],$fot(least_upper_bound(identity,multiply(X_189,inverse(X_190))))]]) ).

cnf(refute_0_5857,plain,
    ( least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))) != least_upper_bound(identity,multiply(X_189,inverse(X_190)))
    | inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) = inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) )],[refute_0_5855,refute_0_5856]) ).

cnf(refute_0_5858,plain,
    inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) = inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))),least_upper_bound(identity,multiply(X_189,inverse(X_190)))) )],[refute_0_5854,refute_0_5857]) ).

cnf(refute_0_5859,plain,
    greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) = inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),
    inference(subst,[],[refute_0_500:[bind(Y,$fot(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))]]) ).

cnf(refute_0_5860,plain,
    multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) = greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),
    inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))))]]) ).

cnf(refute_0_5861,plain,
    ( multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) != greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))
    | greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) != inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))
    | multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) = inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))))]]) ).

cnf(refute_0_5862,plain,
    ( greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) != inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))
    | multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) = inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) ),
    inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))),greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) )],[refute_0_5860,refute_0_5861]) ).

cnf(refute_0_5863,plain,
    multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) = inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) )],[refute_0_5859,refute_0_5862]) ).

cnf(refute_0_5864,plain,
    multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)) = multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))),
    inference(subst,[],[refute_0_857:[bind(X_107,$fot(identity)),bind(X_108,$fot(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))),bind(X_109,$fot(identity))]]) ).

cnf(refute_0_5865,plain,
    ( multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) != inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))
    | multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)) != multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))
    | multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)) = inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))))]]) ).

cnf(refute_0_5866,plain,
    ( multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) != inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))
    | multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)) = inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) ),
    inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)),multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))) )],[refute_0_5864,refute_0_5865]) ).

cnf(refute_0_5867,plain,
    multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)) = inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),
    inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))),inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) )],[refute_0_5863,refute_0_5866]) ).

cnf(refute_0_5868,plain,
    greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) = multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)),
    inference(subst,[],[refute_0_308:[bind(X_107,$fot(identity)),bind(X_108,$fot(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))]]) ).

cnf(refute_0_5869,plain,
    ( multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)) != inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))
    | greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) != multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity))
    | greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) = inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))))]]) ).

cnf(refute_0_5870,plain,
    ( multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)) != inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))
    | greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) = inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))),multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity))) )],[refute_0_5868,refute_0_5869]) ).

cnf(refute_0_5871,plain,
    greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) = inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),
    inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),identity)),inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) )],[refute_0_5867,refute_0_5870]) ).

cnf(refute_0_5872,plain,
    ( greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) != inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))
    | inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) != inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190))))
    | greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) = inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))))),bind(Y0,$fot(inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))),bind(Z0,$fot(inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190))))))]]) ).

cnf(refute_0_5873,plain,
    ( inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) != inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190))))
    | greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) = inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))),inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) )],[refute_0_5871,refute_0_5872]) ).

cnf(refute_0_5874,plain,
    greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) = inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190))))) )],[refute_0_5858,refute_0_5873]) ).

cnf(refute_0_5875,plain,
    ( greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))) != inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190))))
    | inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))) != greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))
    | inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))) = inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))) ),[1],$fot(inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))))]]) ).

cnf(refute_0_5876,plain,
    ( inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))) != greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))
    | inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))) = inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))),inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190))))) )],[refute_0_5874,refute_0_5875]) ).

cnf(refute_0_5877,plain,
    ( multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))) != greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))
    | inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))) = inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))) )],[refute_0_5853,refute_0_5876]) ).

cnf(refute_0_5878,plain,
    inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))) = inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))),greatest_lower_bound(identity,multiply(identity,inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190)))))) )],[refute_0_5850,refute_0_5877]) ).

cnf(refute_0_5879,plain,
    ( inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))) != inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190))))
    | inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))) = inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))))),bind(Y0,$fot(inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190))))))]]) ).

cnf(refute_0_5880,plain,
    inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190)))) = inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(X_190,X_189),inverse(X_190))),inverse(least_upper_bound(identity,multiply(X_189,inverse(X_190))))) )],[refute_0_5878,refute_0_5879]) ).

cnf(refute_0_5881,plain,
    inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b)))) = inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))),
    inference(subst,[],[refute_0_5880:[bind(X_189,$fot(least_upper_bound(a,c))),bind(X_190,$fot(b))]]) ).

cnf(refute_0_5882,plain,
    multiply(greatest_lower_bound(identity,multiply(X_122,inverse(X_123))),inverse(multiply(X_122,inverse(X_123)))) = inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123)))),
    inference(subst,[],[refute_0_508:[bind(Y,$fot(multiply(X_122,inverse(X_123))))]]) ).

cnf(refute_0_5883,plain,
    ( multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) != greatest_lower_bound(identity,multiply(X_122,inverse(X_123)))
    | greatest_lower_bound(identity,multiply(X_122,inverse(X_123))) = multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_122,inverse(X_123)))))]]) ).

cnf(refute_0_5884,plain,
    greatest_lower_bound(identity,multiply(X_122,inverse(X_123))) = multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),greatest_lower_bound(identity,multiply(X_122,inverse(X_123)))) )],[refute_0_3421,refute_0_5883]) ).

cnf(refute_0_5885,plain,
    ( multiply(greatest_lower_bound(identity,multiply(X_122,inverse(X_123))),inverse(multiply(X_122,inverse(X_123)))) != inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123))))
    | greatest_lower_bound(identity,multiply(X_122,inverse(X_123))) != multiply(greatest_lower_bound(X_122,X_123),inverse(X_123))
    | multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))) = inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_122,inverse(X_123))),inverse(multiply(X_122,inverse(X_123)))),inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123))))) ),[0,0],$fot(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)))]]) ).

cnf(refute_0_5886,plain,
    ( multiply(greatest_lower_bound(identity,multiply(X_122,inverse(X_123))),inverse(multiply(X_122,inverse(X_123)))) != inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123))))
    | multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))) = inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_122,inverse(X_123))),multiply(greatest_lower_bound(X_122,X_123),inverse(X_123))) )],[refute_0_5884,refute_0_5885]) ).

cnf(refute_0_5887,plain,
    multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))) = inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123)))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,multiply(X_122,inverse(X_123))),inverse(multiply(X_122,inverse(X_123)))),inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123))))) )],[refute_0_5882,refute_0_5886]) ).

cnf(refute_0_5888,plain,
    multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123)))) = inverse(X_122),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(inverse(X_123))),bind(X_59,$fot(X_122))]]) ).

cnf(refute_0_5889,plain,
    multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))) = multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))),
    introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))))]]) ).

cnf(refute_0_5890,plain,
    ( multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))) != multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123)))))
    | multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123)))) != inverse(X_122)
    | multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))) = multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))),multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123)))))) ),[1,1],$fot(inverse(X_122))]]) ).

cnf(refute_0_5891,plain,
    ( multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123)))) != inverse(X_122)
    | multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))) = multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))),multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123)))))) )],[refute_0_5889,refute_0_5890]) ).

cnf(refute_0_5892,plain,
    multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))) = multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123)))),inverse(X_122)) )],[refute_0_5888,refute_0_5891]) ).

cnf(refute_0_5893,plain,
    multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))) = multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))),
    inference(subst,[],[associativity:[bind(X,$fot(greatest_lower_bound(X_122,X_123))),bind(Y,$fot(inverse(X_123))),bind(Z,$fot(inverse(multiply(X_122,inverse(X_123)))))]]) ).

cnf(refute_0_5894,plain,
    ( multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))) != multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123)))))
    | multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))) != multiply(greatest_lower_bound(X_122,X_123),inverse(X_122))
    | multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))) = multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))))),bind(Y0,$fot(multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))))),bind(Z0,$fot(multiply(greatest_lower_bound(X_122,X_123),inverse(X_122))))]]) ).

cnf(refute_0_5895,plain,
    ( multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))) != multiply(greatest_lower_bound(X_122,X_123),inverse(X_122))
    | multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))) = multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))),multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123)))))) )],[refute_0_5893,refute_0_5894]) ).

cnf(refute_0_5896,plain,
    multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))) = multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_122,X_123),multiply(inverse(X_123),inverse(multiply(X_122,inverse(X_123))))),multiply(greatest_lower_bound(X_122,X_123),inverse(X_122))) )],[refute_0_5892,refute_0_5895]) ).

cnf(refute_0_5897,plain,
    ( multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))) != multiply(greatest_lower_bound(X_122,X_123),inverse(X_122))
    | multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))) != inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123))))
    | multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) = inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))),inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123))))) ),[0],$fot(multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)))]]) ).

cnf(refute_0_5898,plain,
    ( multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))) != inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123))))
    | multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) = inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))),multiply(greatest_lower_bound(X_122,X_123),inverse(X_122))) )],[refute_0_5896,refute_0_5897]) ).

cnf(refute_0_5899,plain,
    multiply(greatest_lower_bound(X_122,X_123),inverse(X_122)) = inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123)))),
    inference(resolve,[$cnf( $equal(multiply(multiply(greatest_lower_bound(X_122,X_123),inverse(X_123)),inverse(multiply(X_122,inverse(X_123)))),inverse(least_upper_bound(identity,multiply(X_122,inverse(X_123))))) )],[refute_0_5887,refute_0_5898]) ).

cnf(refute_0_5900,plain,
    multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) = inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b)))),
    inference(subst,[],[refute_0_5899:[bind(X_122,$fot(least_upper_bound(a,c))),bind(X_123,$fot(b))]]) ).

cnf(refute_0_5901,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) != inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b))))
    | inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b)))) != inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)))
    | multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) = inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))))),bind(Y0,$fot(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b)))))),bind(Z0,$fot(inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)))))]]) ).

cnf(refute_0_5902,plain,
    ( inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b)))) != inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)))
    | multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) = inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))),inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b))))) )],[refute_0_5900,refute_0_5901]) ).

cnf(refute_0_5903,plain,
    multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) = inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,multiply(least_upper_bound(a,c),inverse(b)))),inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)))) )],[refute_0_5881,refute_0_5902]) ).

cnf(refute_0_5904,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) != inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)))
    | inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))) != inverse(multiply(least_upper_bound(a,c),inverse(b)))
    | multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) = inverse(multiply(least_upper_bound(a,c),inverse(b))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))))),bind(Y0,$fot(inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))))),bind(Z0,$fot(inverse(multiply(least_upper_bound(a,c),inverse(b)))))]]) ).

cnf(refute_0_5905,plain,
    ( inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))) != inverse(multiply(least_upper_bound(a,c),inverse(b)))
    | multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) = inverse(multiply(least_upper_bound(a,c),inverse(b))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))),inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b)))) )],[refute_0_5903,refute_0_5904]) ).

cnf(refute_0_5906,plain,
    multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) = inverse(multiply(least_upper_bound(a,c),inverse(b))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(b,least_upper_bound(a,c)),inverse(b))),inverse(multiply(least_upper_bound(a,c),inverse(b)))) )],[refute_0_5843,refute_0_5905]) ).

cnf(refute_0_5907,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) != multiply(b,inverse(least_upper_bound(a,c)))
    | multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) != inverse(multiply(least_upper_bound(a,c),inverse(b)))
    | inverse(multiply(least_upper_bound(a,c),inverse(b))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))),multiply(b,inverse(least_upper_bound(a,c)))) ),[0],$fot(inverse(multiply(least_upper_bound(a,c),inverse(b))))]]) ).

cnf(refute_0_5908,plain,
    ( multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))) != multiply(b,inverse(least_upper_bound(a,c)))
    | inverse(multiply(least_upper_bound(a,c),inverse(b))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))),inverse(multiply(least_upper_bound(a,c),inverse(b)))) )],[refute_0_5906,refute_0_5907]) ).

cnf(refute_0_5909,plain,
    inverse(multiply(least_upper_bound(a,c),inverse(b))) = multiply(b,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(a,c),b),inverse(least_upper_bound(a,c))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_5818,refute_0_5908]) ).

cnf(refute_0_5910,plain,
    inverse(multiply(least_upper_bound(a,c),inverse(b))) = inverse(multiply(least_upper_bound(a,c),inverse(b))),
    introduced(tautology,[refl,[$fot(inverse(multiply(least_upper_bound(a,c),inverse(b))))]]) ).

cnf(refute_0_5911,plain,
    ( multiply(least_upper_bound(a,c),inverse(b)) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | inverse(multiply(least_upper_bound(a,c),inverse(b))) != inverse(multiply(least_upper_bound(a,c),inverse(b)))
    | inverse(multiply(least_upper_bound(a,c),inverse(b))) = inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(a,c),inverse(b))),inverse(multiply(least_upper_bound(a,c),inverse(b)))) ),[1,0],$fot(multiply(c,inverse(greatest_lower_bound(a,c))))]]) ).

cnf(refute_0_5912,plain,
    ( multiply(least_upper_bound(a,c),inverse(b)) != multiply(c,inverse(greatest_lower_bound(a,c)))
    | inverse(multiply(least_upper_bound(a,c),inverse(b))) = inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(a,c),inverse(b))),inverse(multiply(least_upper_bound(a,c),inverse(b)))) )],[refute_0_5910,refute_0_5911]) ).

cnf(refute_0_5913,plain,
    inverse(multiply(least_upper_bound(a,c),inverse(b))) = inverse(multiply(c,inverse(greatest_lower_bound(a,c)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,c),inverse(b)),multiply(c,inverse(greatest_lower_bound(a,c)))) )],[refute_0_458,refute_0_5912]) ).

cnf(refute_0_5914,plain,
    ( inverse(multiply(least_upper_bound(a,c),inverse(b))) != multiply(b,inverse(least_upper_bound(a,c)))
    | inverse(multiply(least_upper_bound(a,c),inverse(b))) != inverse(multiply(c,inverse(greatest_lower_bound(a,c))))
    | inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(least_upper_bound(a,c),inverse(b))),multiply(b,inverse(least_upper_bound(a,c)))) ),[0],$fot(inverse(multiply(c,inverse(greatest_lower_bound(a,c)))))]]) ).

cnf(refute_0_5915,plain,
    ( inverse(multiply(least_upper_bound(a,c),inverse(b))) != multiply(b,inverse(least_upper_bound(a,c)))
    | inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(a,c),inverse(b))),inverse(multiply(c,inverse(greatest_lower_bound(a,c))))) )],[refute_0_5913,refute_0_5914]) ).

cnf(refute_0_5916,plain,
    inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(multiply(least_upper_bound(a,c),inverse(b))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_5909,refute_0_5915]) ).

cnf(refute_0_5917,plain,
    multiply(multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))),X_60) = multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(inverse(greatest_lower_bound(Y,X))))),bind(Y,$fot(inverse(greatest_lower_bound(X,Y)))),bind(Z,$fot(X_60))]]) ).

cnf(refute_0_5918,plain,
    ( multiply(multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))),X_60) != multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60))
    | multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))) != identity
    | multiply(identity,X_60) = multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))),X_60),multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_5919,plain,
    ( multiply(multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))),X_60) != multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60))
    | multiply(identity,X_60) = multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))),identity) )],[refute_0_203,refute_0_5918]) ).

cnf(refute_0_5920,plain,
    multiply(identity,X_60) = multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(greatest_lower_bound(Y,X))),inverse(greatest_lower_bound(X,Y))),X_60),multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60))) )],[refute_0_5917,refute_0_5919]) ).

cnf(refute_0_5921,plain,
    ( multiply(identity,X_60) != X_60
    | multiply(identity,X_60) != multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60))
    | X_60 = multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_60),multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60))) ),[0],$fot(X_60)]]) ).

cnf(refute_0_5922,plain,
    ( multiply(identity,X_60) != multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60))
    | X_60 = multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_60),X_60) )],[refute_0_5,refute_0_5921]) ).

cnf(refute_0_5923,plain,
    X_60 = multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_60),multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60))) )],[refute_0_5920,refute_0_5922]) ).

cnf(refute_0_5924,plain,
    multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60)) = multiply(greatest_lower_bound(Y,X),multiply(inverse(greatest_lower_bound(X,Y)),X_60)),
    inference(subst,[],[refute_0_25:[bind(X_61,$fot(greatest_lower_bound(Y,X))),bind(X_62,$fot(multiply(inverse(greatest_lower_bound(X,Y)),X_60)))]]) ).

cnf(refute_0_5925,plain,
    ( X_60 != multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60))
    | multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60)) != multiply(greatest_lower_bound(Y,X),multiply(inverse(greatest_lower_bound(X,Y)),X_60))
    | X_60 = multiply(greatest_lower_bound(Y,X),multiply(inverse(greatest_lower_bound(X,Y)),X_60)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_60,multiply(greatest_lower_bound(Y,X),multiply(inverse(greatest_lower_bound(X,Y)),X_60))) ),[0],$fot(multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60)))]]) ).

cnf(refute_0_5926,plain,
    ( X_60 != multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60))
    | X_60 = multiply(greatest_lower_bound(Y,X),multiply(inverse(greatest_lower_bound(X,Y)),X_60)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60)),multiply(greatest_lower_bound(Y,X),multiply(inverse(greatest_lower_bound(X,Y)),X_60))) )],[refute_0_5924,refute_0_5925]) ).

cnf(refute_0_5927,plain,
    X_60 = multiply(greatest_lower_bound(Y,X),multiply(inverse(greatest_lower_bound(X,Y)),X_60)),
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(inverse(greatest_lower_bound(Y,X))),multiply(inverse(greatest_lower_bound(X,Y)),X_60))) )],[refute_0_5923,refute_0_5926]) ).

cnf(refute_0_5928,plain,
    multiply(greatest_lower_bound(X_347,X_348),X_60) = multiply(greatest_lower_bound(X_348,X_347),multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60))),
    inference(subst,[],[refute_0_5927:[bind(X,$fot(X_347)),bind(Y,$fot(X_348)),bind(X_60,$fot(multiply(greatest_lower_bound(X_347,X_348),X_60)))]]) ).

cnf(refute_0_5929,plain,
    X_60 = multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60)),
    inference(subst,[],[refute_0_8:[bind(X_59,$fot(greatest_lower_bound(X_347,X_348)))]]) ).

cnf(refute_0_5930,plain,
    ( X_60 != multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60))
    | multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60)) = X_60 ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(X_60)),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60))))]]) ).

cnf(refute_0_5931,plain,
    multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60)) = X_60,
    inference(resolve,[$cnf( $equal(X_60,multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60))) )],[refute_0_5929,refute_0_5930]) ).

cnf(refute_0_5932,plain,
    ( multiply(greatest_lower_bound(X_347,X_348),X_60) != multiply(greatest_lower_bound(X_348,X_347),multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60)))
    | multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60)) != X_60
    | multiply(greatest_lower_bound(X_347,X_348),X_60) = multiply(greatest_lower_bound(X_348,X_347),X_60) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_347,X_348),X_60),multiply(greatest_lower_bound(X_348,X_347),multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60)))) ),[1,1],$fot(X_60)]]) ).

cnf(refute_0_5933,plain,
    ( multiply(greatest_lower_bound(X_347,X_348),X_60) != multiply(greatest_lower_bound(X_348,X_347),multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60)))
    | multiply(greatest_lower_bound(X_347,X_348),X_60) = multiply(greatest_lower_bound(X_348,X_347),X_60) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60)),X_60) )],[refute_0_5931,refute_0_5932]) ).

cnf(refute_0_5934,plain,
    multiply(greatest_lower_bound(X_347,X_348),X_60) = multiply(greatest_lower_bound(X_348,X_347),X_60),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_347,X_348),X_60),multiply(greatest_lower_bound(X_348,X_347),multiply(inverse(greatest_lower_bound(X_347,X_348)),multiply(greatest_lower_bound(X_347,X_348),X_60)))) )],[refute_0_5928,refute_0_5933]) ).

cnf(refute_0_5935,plain,
    ( multiply(greatest_lower_bound(X_347,X_348),X_60) != multiply(greatest_lower_bound(X_348,X_347),X_60)
    | multiply(greatest_lower_bound(X_348,X_347),X_60) = multiply(greatest_lower_bound(X_347,X_348),X_60) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(X_347,X_348),X_60))),bind(Y0,$fot(multiply(greatest_lower_bound(X_348,X_347),X_60)))]]) ).

cnf(refute_0_5936,plain,
    multiply(greatest_lower_bound(X_348,X_347),X_60) = multiply(greatest_lower_bound(X_347,X_348),X_60),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_347,X_348),X_60),multiply(greatest_lower_bound(X_348,X_347),X_60)) )],[refute_0_5934,refute_0_5935]) ).

cnf(refute_0_5937,plain,
    multiply(greatest_lower_bound(c,a),inverse(c)) = multiply(greatest_lower_bound(a,c),inverse(c)),
    inference(subst,[],[refute_0_5936:[bind(X_347,$fot(a)),bind(X_348,$fot(c)),bind(X_60,$fot(inverse(c)))]]) ).

cnf(refute_0_5938,plain,
    inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348)))) = multiply(greatest_lower_bound(X_348,X_347),multiply(inverse(greatest_lower_bound(X_347,X_348)),inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348)))))),
    inference(subst,[],[refute_0_5927:[bind(X,$fot(X_347)),bind(Y,$fot(X_348)),bind(X_60,$fot(inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348))))))]]) ).

cnf(refute_0_5939,plain,
    multiply(inverse(greatest_lower_bound(X_347,X_348)),inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348))))) = inverse(X_59),
    inference(subst,[],[refute_0_661:[bind(X_138,$fot(inverse(greatest_lower_bound(X_347,X_348))))]]) ).

cnf(refute_0_5940,plain,
    ( multiply(inverse(greatest_lower_bound(X_347,X_348)),inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348))))) != inverse(X_59)
    | inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348)))) != multiply(greatest_lower_bound(X_348,X_347),multiply(inverse(greatest_lower_bound(X_347,X_348)),inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348))))))
    | inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348)))) = multiply(greatest_lower_bound(X_348,X_347),inverse(X_59)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348)))),multiply(greatest_lower_bound(X_348,X_347),multiply(inverse(greatest_lower_bound(X_347,X_348)),inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348))))))) ),[1,1],$fot(inverse(X_59))]]) ).

cnf(refute_0_5941,plain,
    ( inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348)))) != multiply(greatest_lower_bound(X_348,X_347),multiply(inverse(greatest_lower_bound(X_347,X_348)),inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348))))))
    | inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348)))) = multiply(greatest_lower_bound(X_348,X_347),inverse(X_59)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_347,X_348)),inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348))))),inverse(X_59)) )],[refute_0_5939,refute_0_5940]) ).

cnf(refute_0_5942,plain,
    inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348)))) = multiply(greatest_lower_bound(X_348,X_347),inverse(X_59)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348)))),multiply(greatest_lower_bound(X_348,X_347),multiply(inverse(greatest_lower_bound(X_347,X_348)),inverse(multiply(X_59,inverse(greatest_lower_bound(X_347,X_348))))))) )],[refute_0_5938,refute_0_5941]) ).

cnf(refute_0_5943,plain,
    inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(greatest_lower_bound(c,a),inverse(c)),
    inference(subst,[],[refute_0_5942:[bind(X_347,$fot(a)),bind(X_348,$fot(c)),bind(X_59,$fot(c))]]) ).

cnf(refute_0_5944,plain,
    ( multiply(greatest_lower_bound(c,a),inverse(c)) != multiply(greatest_lower_bound(a,c),inverse(c))
    | inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) != multiply(greatest_lower_bound(c,a),inverse(c))
    | inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(greatest_lower_bound(a,c),inverse(c)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(multiply(c,inverse(greatest_lower_bound(a,c)))))),bind(Y0,$fot(multiply(greatest_lower_bound(c,a),inverse(c)))),bind(Z0,$fot(multiply(greatest_lower_bound(a,c),inverse(c))))]]) ).

cnf(refute_0_5945,plain,
    ( multiply(greatest_lower_bound(c,a),inverse(c)) != multiply(greatest_lower_bound(a,c),inverse(c))
    | inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(greatest_lower_bound(a,c),inverse(c)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(c,inverse(greatest_lower_bound(a,c)))),multiply(greatest_lower_bound(c,a),inverse(c))) )],[refute_0_5943,refute_0_5944]) ).

cnf(refute_0_5946,plain,
    inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) = multiply(greatest_lower_bound(a,c),inverse(c)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(c,a),inverse(c)),multiply(greatest_lower_bound(a,c),inverse(c))) )],[refute_0_5937,refute_0_5945]) ).

cnf(refute_0_5947,plain,
    ( inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
    | inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) != multiply(greatest_lower_bound(a,c),inverse(c))
    | multiply(greatest_lower_bound(a,c),inverse(c)) = multiply(b,inverse(least_upper_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(c,inverse(greatest_lower_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) ),[0],$fot(multiply(greatest_lower_bound(a,c),inverse(c)))]]) ).

cnf(refute_0_5948,plain,
    ( inverse(multiply(c,inverse(greatest_lower_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
    | multiply(greatest_lower_bound(a,c),inverse(c)) = multiply(b,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(c,inverse(greatest_lower_bound(a,c)))),multiply(greatest_lower_bound(a,c),inverse(c))) )],[refute_0_5946,refute_0_5947]) ).

cnf(refute_0_5949,plain,
    multiply(greatest_lower_bound(a,c),inverse(c)) = multiply(b,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(inverse(multiply(c,inverse(greatest_lower_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_5916,refute_0_5948]) ).

cnf(refute_0_5950,plain,
    ( multiply(greatest_lower_bound(a,c),inverse(c)) != multiply(b,inverse(least_upper_bound(a,c)))
    | multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) != greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity))
    | multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) = greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)),greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity))) ),[1,0],$fot(multiply(b,inverse(least_upper_bound(a,c))))]]) ).

cnf(refute_0_5951,plain,
    ( multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) != greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity))
    | multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) = greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,c),inverse(c)),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_5949,refute_0_5950]) ).

cnf(refute_0_5952,plain,
    multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) = greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)),greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity))) )],[refute_0_5808,refute_0_5951]) ).

cnf(refute_0_5953,plain,
    multiply(X_329,greatest_lower_bound(inverse(X_329),inverse(Y))) = greatest_lower_bound(identity,multiply(X_329,inverse(Y))),
    inference(subst,[],[refute_0_1286:[bind(X_107,$fot(X_329)),bind(X_109,$fot(inverse(Y)))]]) ).

cnf(refute_0_5954,plain,
    inverse(least_upper_bound(X_329,Y)) = greatest_lower_bound(inverse(X_329),inverse(Y)),
    inference(subst,[],[p12x_4:[bind(X,$fot(X_329))]]) ).

cnf(refute_0_5955,plain,
    ( inverse(least_upper_bound(X_329,Y)) != greatest_lower_bound(inverse(X_329),inverse(Y))
    | greatest_lower_bound(inverse(X_329),inverse(Y)) = inverse(least_upper_bound(X_329,Y)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(least_upper_bound(X_329,Y)))),bind(Y0,$fot(greatest_lower_bound(inverse(X_329),inverse(Y))))]]) ).

cnf(refute_0_5956,plain,
    greatest_lower_bound(inverse(X_329),inverse(Y)) = inverse(least_upper_bound(X_329,Y)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_329,Y)),greatest_lower_bound(inverse(X_329),inverse(Y))) )],[refute_0_5954,refute_0_5955]) ).

cnf(refute_0_5957,plain,
    ( multiply(X_329,greatest_lower_bound(inverse(X_329),inverse(Y))) != greatest_lower_bound(identity,multiply(X_329,inverse(Y)))
    | greatest_lower_bound(inverse(X_329),inverse(Y)) != inverse(least_upper_bound(X_329,Y))
    | multiply(X_329,inverse(least_upper_bound(X_329,Y))) = greatest_lower_bound(identity,multiply(X_329,inverse(Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_329,greatest_lower_bound(inverse(X_329),inverse(Y))),greatest_lower_bound(identity,multiply(X_329,inverse(Y)))) ),[0,1],$fot(inverse(least_upper_bound(X_329,Y)))]]) ).

cnf(refute_0_5958,plain,
    ( multiply(X_329,greatest_lower_bound(inverse(X_329),inverse(Y))) != greatest_lower_bound(identity,multiply(X_329,inverse(Y)))
    | multiply(X_329,inverse(least_upper_bound(X_329,Y))) = greatest_lower_bound(identity,multiply(X_329,inverse(Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_329),inverse(Y)),inverse(least_upper_bound(X_329,Y))) )],[refute_0_5956,refute_0_5957]) ).

cnf(refute_0_5959,plain,
    multiply(X_329,inverse(least_upper_bound(X_329,Y))) = greatest_lower_bound(identity,multiply(X_329,inverse(Y))),
    inference(resolve,[$cnf( $equal(multiply(X_329,greatest_lower_bound(inverse(X_329),inverse(Y))),greatest_lower_bound(identity,multiply(X_329,inverse(Y)))) )],[refute_0_5953,refute_0_5958]) ).

cnf(refute_0_5960,plain,
    ( multiply(X_329,inverse(least_upper_bound(X_329,Y))) != greatest_lower_bound(identity,multiply(X_329,inverse(Y)))
    | greatest_lower_bound(identity,multiply(X_329,inverse(Y))) = multiply(X_329,inverse(least_upper_bound(X_329,Y))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_329,inverse(least_upper_bound(X_329,Y))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_329,inverse(Y)))))]]) ).

cnf(refute_0_5961,plain,
    greatest_lower_bound(identity,multiply(X_329,inverse(Y))) = multiply(X_329,inverse(least_upper_bound(X_329,Y))),
    inference(resolve,[$cnf( $equal(multiply(X_329,inverse(least_upper_bound(X_329,Y))),greatest_lower_bound(identity,multiply(X_329,inverse(Y)))) )],[refute_0_5959,refute_0_5960]) ).

cnf(refute_0_5962,plain,
    greatest_lower_bound(identity,multiply(a,inverse(c))) = multiply(a,inverse(least_upper_bound(a,c))),
    inference(subst,[],[refute_0_5961:[bind(Y,$fot(c)),bind(X_329,$fot(a))]]) ).

cnf(refute_0_5963,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108)),
    inference(subst,[],[refute_0_4594:[bind(X_107,$fot(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_5964,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108))
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) != identity
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108))) ),[0,1,1],$fot(identity)]]) ).

cnf(refute_0_5965,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),identity) )],[refute_0_4994,refute_0_5964]) ).

cnf(refute_0_5966,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108))) )],[refute_0_5963,refute_0_5965]) ).

cnf(refute_0_5967,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),X_109)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109)),
    inference(subst,[],[refute_0_1286:[bind(X_107,$fot(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))))]]) ).

cnf(refute_0_5968,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),X_109)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109))
    | inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))) != identity
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_109)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),X_109)),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109))) ),[0,1,0],$fot(identity)]]) ).

cnf(refute_0_5969,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),X_109)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_109)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),identity) )],[refute_0_4994,refute_0_5968]) ).

cnf(refute_0_5970,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_109)) = greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(inverse(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c))))))),X_109)),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109))) )],[refute_0_5967,refute_0_5969]) ).

cnf(refute_0_5971,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_109)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109))
    | greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_109)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_109)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109))))]]) ).

cnf(refute_0_5972,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_109)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_109)),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_109))) )],[refute_0_5970,refute_0_5971]) ).

cnf(refute_0_5973,plain,
    greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)),
    inference(subst,[],[refute_0_5972:[bind(X_109,$fot(X_108))]]) ).

cnf(refute_0_5974,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108))
    | greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108)) != multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))) ),[0],$fot(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108)))]]) ).

cnf(refute_0_5975,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) != greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108)),multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))) )],[refute_0_5973,refute_0_5974]) ).

cnf(refute_0_5976,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)),greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),X_108))) )],[refute_0_5966,refute_0_5975]) ).

cnf(refute_0_5977,plain,
    multiply(identity,greatest_lower_bound(X_108,identity)) = greatest_lower_bound(X_108,identity),
    inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(X_108,identity)))]]) ).

cnf(refute_0_5978,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)))]]) ).

cnf(refute_0_5979,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) != multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity))
    | least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) != identity
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = multiply(identity,greatest_lower_bound(X_108,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_5980,plain,
    ( least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) != identity
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = multiply(identity,greatest_lower_bound(X_108,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity))) )],[refute_0_5978,refute_0_5979]) ).

cnf(refute_0_5981,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = multiply(identity,greatest_lower_bound(X_108,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity) )],[refute_0_5071,refute_0_5980]) ).

cnf(refute_0_5982,plain,
    ( multiply(identity,greatest_lower_bound(X_108,identity)) != greatest_lower_bound(X_108,identity)
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) != multiply(identity,greatest_lower_bound(X_108,identity))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(X_108,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(X_108,identity)))),bind(Z0,$fot(greatest_lower_bound(X_108,identity)))]]) ).

cnf(refute_0_5983,plain,
    ( multiply(identity,greatest_lower_bound(X_108,identity)) != greatest_lower_bound(X_108,identity)
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(X_108,identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)),multiply(identity,greatest_lower_bound(X_108,identity))) )],[refute_0_5981,refute_0_5982]) ).

cnf(refute_0_5984,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) = greatest_lower_bound(X_108,identity),
    inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(X_108,identity)),greatest_lower_bound(X_108,identity)) )],[refute_0_5977,refute_0_5983]) ).

cnf(refute_0_5985,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) != multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) != greatest_lower_bound(X_108,identity)
    | greatest_lower_bound(X_108,identity) = multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))) ),[0],$fot(greatest_lower_bound(X_108,identity))]]) ).

cnf(refute_0_5986,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) != multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))
    | greatest_lower_bound(X_108,identity) = multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)),greatest_lower_bound(X_108,identity)) )],[refute_0_5984,refute_0_5985]) ).

cnf(refute_0_5987,plain,
    multiply(identity,greatest_lower_bound(identity,X_108)) = greatest_lower_bound(identity,X_108),
    inference(subst,[],[left_identity:[bind(X,$fot(greatest_lower_bound(identity,X_108)))]]) ).

cnf(refute_0_5988,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) = multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)))]]) ).

cnf(refute_0_5989,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) != multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))
    | least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) != identity
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) = multiply(identity,greatest_lower_bound(identity,X_108)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)),multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_5990,plain,
    ( least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))) != identity
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) = multiply(identity,greatest_lower_bound(identity,X_108)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)),multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))) )],[refute_0_5988,refute_0_5989]) ).

cnf(refute_0_5991,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) = multiply(identity,greatest_lower_bound(identity,X_108)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),identity) )],[refute_0_5071,refute_0_5990]) ).

cnf(refute_0_5992,plain,
    ( multiply(identity,greatest_lower_bound(identity,X_108)) != greatest_lower_bound(identity,X_108)
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) != multiply(identity,greatest_lower_bound(identity,X_108))
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) = greatest_lower_bound(identity,X_108) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)))),bind(Y0,$fot(multiply(identity,greatest_lower_bound(identity,X_108)))),bind(Z0,$fot(greatest_lower_bound(identity,X_108)))]]) ).

cnf(refute_0_5993,plain,
    ( multiply(identity,greatest_lower_bound(identity,X_108)) != greatest_lower_bound(identity,X_108)
    | multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) = greatest_lower_bound(identity,X_108) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)),multiply(identity,greatest_lower_bound(identity,X_108))) )],[refute_0_5991,refute_0_5992]) ).

cnf(refute_0_5994,plain,
    multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) = greatest_lower_bound(identity,X_108),
    inference(resolve,[$cnf( $equal(multiply(identity,greatest_lower_bound(identity,X_108)),greatest_lower_bound(identity,X_108)) )],[refute_0_5987,refute_0_5993]) ).

cnf(refute_0_5995,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)) != greatest_lower_bound(identity,X_108)
    | greatest_lower_bound(X_108,identity) != multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))
    | greatest_lower_bound(X_108,identity) = greatest_lower_bound(identity,X_108) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_108,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))) ),[1],$fot(greatest_lower_bound(identity,X_108))]]) ).

cnf(refute_0_5996,plain,
    ( greatest_lower_bound(X_108,identity) != multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))
    | greatest_lower_bound(X_108,identity) = greatest_lower_bound(identity,X_108) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108)),greatest_lower_bound(identity,X_108)) )],[refute_0_5994,refute_0_5995]) ).

cnf(refute_0_5997,plain,
    ( multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)) != multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))
    | greatest_lower_bound(X_108,identity) = greatest_lower_bound(identity,X_108) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_108,identity),multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))) )],[refute_0_5986,refute_0_5996]) ).

cnf(refute_0_5998,plain,
    greatest_lower_bound(X_108,identity) = greatest_lower_bound(identity,X_108),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(X_108,identity)),multiply(least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(c,inverse(least_upper_bound(identity,greatest_lower_bound(a,c)))))),greatest_lower_bound(identity,X_108))) )],[refute_0_5976,refute_0_5997]) ).

cnf(refute_0_5999,plain,
    greatest_lower_bound(multiply(a,inverse(c)),identity) = greatest_lower_bound(identity,multiply(a,inverse(c))),
    inference(subst,[],[refute_0_5998:[bind(X_108,$fot(multiply(a,inverse(c))))]]) ).

cnf(refute_0_6000,plain,
    ( greatest_lower_bound(multiply(a,inverse(c)),identity) != greatest_lower_bound(identity,multiply(a,inverse(c)))
    | greatest_lower_bound(identity,multiply(a,inverse(c))) != multiply(a,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(multiply(a,inverse(c)),identity) = multiply(a,inverse(least_upper_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(a,inverse(c)),identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(a,inverse(c))))),bind(Z0,$fot(multiply(a,inverse(least_upper_bound(a,c)))))]]) ).

cnf(refute_0_6001,plain,
    ( greatest_lower_bound(identity,multiply(a,inverse(c))) != multiply(a,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(multiply(a,inverse(c)),identity) = multiply(a,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(a,inverse(c)),identity),greatest_lower_bound(identity,multiply(a,inverse(c)))) )],[refute_0_5999,refute_0_6000]) ).

cnf(refute_0_6002,plain,
    greatest_lower_bound(multiply(a,inverse(c)),identity) = multiply(a,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(a,inverse(c))),multiply(a,inverse(least_upper_bound(a,c)))) )],[refute_0_5962,refute_0_6001]) ).

cnf(refute_0_6003,plain,
    greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))) = greatest_lower_bound(multiply(a,inverse(c)),identity),
    inference(subst,[],[refute_0_2852:[bind(Y,$fot(inverse(c))),bind(X_76,$fot(multiply(a,inverse(c)))),bind(X_77,$fot(identity))]]) ).

cnf(refute_0_6004,plain,
    ( greatest_lower_bound(multiply(a,inverse(c)),identity) != multiply(a,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))) != greatest_lower_bound(multiply(a,inverse(c)),identity)
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))) = multiply(a,inverse(least_upper_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))))),bind(Y0,$fot(greatest_lower_bound(multiply(a,inverse(c)),identity))),bind(Z0,$fot(multiply(a,inverse(least_upper_bound(a,c)))))]]) ).

cnf(refute_0_6005,plain,
    ( greatest_lower_bound(multiply(a,inverse(c)),identity) != multiply(a,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))) = multiply(a,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))),greatest_lower_bound(multiply(a,inverse(c)),identity)) )],[refute_0_6003,refute_0_6004]) ).

cnf(refute_0_6006,plain,
    greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))) = multiply(a,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(a,inverse(c)),identity),multiply(a,inverse(least_upper_bound(a,c)))) )],[refute_0_6002,refute_0_6005]) ).

cnf(refute_0_6007,plain,
    greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)) = greatest_lower_bound(greatest_lower_bound(identity,multiply(X_130,inverse(X_131))),Z),
    inference(subst,[],[associativity_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_130,inverse(X_131))))]]) ).

cnf(refute_0_6008,plain,
    ( multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)) != greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))
    | greatest_lower_bound(identity,multiply(X_130,inverse(X_131))) = multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))))]]) ).

cnf(refute_0_6009,plain,
    greatest_lower_bound(identity,multiply(X_130,inverse(X_131))) = multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)),greatest_lower_bound(identity,multiply(X_130,inverse(X_131)))) )],[refute_0_3422,refute_0_6008]) ).

cnf(refute_0_6010,plain,
    ( greatest_lower_bound(identity,multiply(X_130,inverse(X_131))) != multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)) != greatest_lower_bound(greatest_lower_bound(identity,multiply(X_130,inverse(X_131))),Z)
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)) = greatest_lower_bound(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_130,inverse(X_131))),Z)) ),[1,0],$fot(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)))]]) ).

cnf(refute_0_6011,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)) != greatest_lower_bound(greatest_lower_bound(identity,multiply(X_130,inverse(X_131))),Z)
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)) = greatest_lower_bound(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)),Z) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_130,inverse(X_131))),multiply(greatest_lower_bound(X_130,X_131),inverse(X_131))) )],[refute_0_6009,refute_0_6010]) ).

cnf(refute_0_6012,plain,
    greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)) = greatest_lower_bound(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)),Z),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)),greatest_lower_bound(greatest_lower_bound(identity,multiply(X_130,inverse(X_131))),Z)) )],[refute_0_6007,refute_0_6011]) ).

cnf(refute_0_6013,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)) != greatest_lower_bound(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)),Z)
    | greatest_lower_bound(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)),Z) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)),Z)))]]) ).

cnf(refute_0_6014,plain,
    greatest_lower_bound(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)),Z) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(X_130,inverse(X_131)),Z)),greatest_lower_bound(multiply(greatest_lower_bound(X_130,X_131),inverse(X_131)),Z)) )],[refute_0_6012,refute_0_6013]) ).

cnf(refute_0_6015,plain,
    greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))),
    inference(subst,[],[refute_0_6014:[bind(Z,$fot(least_upper_bound(identity,inverse(c)))),bind(X_130,$fot(a)),bind(X_131,$fot(c))]]) ).

cnf(refute_0_6016,plain,
    ( greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))) != greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c))))
    | greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))) != multiply(a,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))) = multiply(a,inverse(least_upper_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))))),bind(Z0,$fot(multiply(a,inverse(least_upper_bound(a,c)))))]]) ).

cnf(refute_0_6017,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))) != multiply(a,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))) = multiply(a,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))),greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c))))) )],[refute_0_6015,refute_0_6016]) ).

cnf(refute_0_6018,plain,
    greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))) = multiply(a,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(multiply(a,inverse(c)),least_upper_bound(identity,inverse(c)))),multiply(a,inverse(least_upper_bound(a,c)))) )],[refute_0_6006,refute_0_6017]) ).

cnf(refute_0_6019,plain,
    multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227) = greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(X_227,identity)),
    inference(subst,[],[refute_0_5807:[bind(X_121,$fot(X_227)),bind(X_122,$fot(X_228))]]) ).

cnf(refute_0_6020,plain,
    least_upper_bound(identity,X_227) = least_upper_bound(X_227,identity),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_227))]]) ).

cnf(refute_0_6021,plain,
    ( least_upper_bound(identity,X_227) != least_upper_bound(X_227,identity)
    | least_upper_bound(X_227,identity) = least_upper_bound(identity,X_227) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,X_227))),bind(Y0,$fot(least_upper_bound(X_227,identity)))]]) ).

cnf(refute_0_6022,plain,
    least_upper_bound(X_227,identity) = least_upper_bound(identity,X_227),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_227),least_upper_bound(X_227,identity)) )],[refute_0_6020,refute_0_6021]) ).

cnf(refute_0_6023,plain,
    ( multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227) != greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(X_227,identity))
    | least_upper_bound(X_227,identity) != least_upper_bound(identity,X_227)
    | multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227) = greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(identity,X_227)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227),greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(X_227,identity))) ),[1,1],$fot(least_upper_bound(identity,X_227))]]) ).

cnf(refute_0_6024,plain,
    ( multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227) != greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(X_227,identity))
    | multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227) = greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(identity,X_227)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_227,identity),least_upper_bound(identity,X_227)) )],[refute_0_6022,refute_0_6023]) ).

cnf(refute_0_6025,plain,
    multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227) = greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(identity,X_227)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227),greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(X_227,identity))) )],[refute_0_6019,refute_0_6024]) ).

cnf(refute_0_6026,plain,
    ( multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227) != greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(X_227,identity))
    | multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227) != greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(identity,X_227))
    | greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(X_227,identity)) = greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(identity,X_227)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227),greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(identity,X_227))) ),[0],$fot(greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(X_227,identity)))]]) ).

cnf(refute_0_6027,plain,
    ( multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227) != greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(identity,X_227))
    | greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(X_227,identity)) = greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(identity,X_227)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227),greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(X_227,identity))) )],[refute_0_6019,refute_0_6026]) ).

cnf(refute_0_6028,plain,
    greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(X_227,identity)) = greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(identity,X_227)),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_228,inverse(greatest_lower_bound(X_227,identity))),X_227),greatest_lower_bound(multiply(X_228,X_227),least_upper_bound(identity,X_227))) )],[refute_0_6025,refute_0_6027]) ).

cnf(refute_0_6029,plain,
    greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)) = greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))),
    inference(subst,[],[refute_0_6028:[bind(X_227,$fot(inverse(c))),bind(X_228,$fot(greatest_lower_bound(a,c)))]]) ).

cnf(refute_0_6030,plain,
    ( greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))) != multiply(a,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)) != greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c)))
    | greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)) = multiply(a,inverse(least_upper_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)))),bind(Y0,$fot(greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))))),bind(Z0,$fot(multiply(a,inverse(least_upper_bound(a,c)))))]]) ).

cnf(refute_0_6031,plain,
    ( greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))) != multiply(a,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)) = multiply(a,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)),greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c)))) )],[refute_0_6029,refute_0_6030]) ).

cnf(refute_0_6032,plain,
    greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)) = multiply(a,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(identity,inverse(c))),multiply(a,inverse(least_upper_bound(a,c)))) )],[refute_0_6018,refute_0_6031]) ).

cnf(refute_0_6033,plain,
    ( multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) != greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity))
    | greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)) != multiply(a,inverse(least_upper_bound(a,c)))
    | multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) = multiply(a,inverse(least_upper_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)))),bind(Y0,$fot(greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)))),bind(Z0,$fot(multiply(a,inverse(least_upper_bound(a,c)))))]]) ).

cnf(refute_0_6034,plain,
    ( greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)) != multiply(a,inverse(least_upper_bound(a,c)))
    | multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) = multiply(a,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)),greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity))) )],[refute_0_5808,refute_0_6033]) ).

cnf(refute_0_6035,plain,
    multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) = multiply(a,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(greatest_lower_bound(a,c),inverse(c)),least_upper_bound(inverse(c),identity)),multiply(a,inverse(least_upper_bound(a,c)))) )],[refute_0_6032,refute_0_6034]) ).

cnf(refute_0_6036,plain,
    ( multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) != multiply(a,inverse(least_upper_bound(a,c)))
    | multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) != greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity))
    | multiply(a,inverse(least_upper_bound(a,c))) = greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)),greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity))) ),[0],$fot(multiply(a,inverse(least_upper_bound(a,c))))]]) ).

cnf(refute_0_6037,plain,
    ( multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) != greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity))
    | multiply(a,inverse(least_upper_bound(a,c))) = greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)) ),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)),multiply(a,inverse(least_upper_bound(a,c)))) )],[refute_0_6035,refute_0_6036]) ).

cnf(refute_0_6038,plain,
    greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))) = greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),
    inference(subst,[],[refute_0_467:[bind(X_11,$fot(X_203)),bind(X_36,$fot(identity)),bind(X_38,$fot(multiply(b,inverse(least_upper_bound(a,c)))))]]) ).

cnf(refute_0_6039,plain,
    ( greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
    | greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))) ),[1],$fot(multiply(b,inverse(least_upper_bound(a,c))))]]) ).

cnf(refute_0_6040,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))) != greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))
    | greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_5815,refute_0_6039]) ).

cnf(refute_0_6041,plain,
    greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))) = multiply(b,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_6038,refute_0_6040]) ).

cnf(refute_0_6042,plain,
    greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)) = greatest_lower_bound(X_36,greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c))))),
    inference(subst,[],[refute_0_839:[bind(X,$fot(multiply(b,inverse(least_upper_bound(a,c))))),bind(X_37,$fot(identity))]]) ).

cnf(refute_0_6043,plain,
    ( greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)) != greatest_lower_bound(X_36,greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))))
    | greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)) = greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)),greatest_lower_bound(X_36,greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))))) ),[1,1],$fot(multiply(b,inverse(least_upper_bound(a,c))))]]) ).

cnf(refute_0_6044,plain,
    ( greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)) != greatest_lower_bound(X_36,greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))))
    | greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)) = greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_5815,refute_0_6043]) ).

cnf(refute_0_6045,plain,
    greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)) = greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)),greatest_lower_bound(X_36,greatest_lower_bound(identity,multiply(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_6042,refute_0_6044]) ).

cnf(refute_0_6046,plain,
    greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c))))),
    inference(subst,[],[refute_0_909:[bind(Y,$fot(multiply(b,inverse(least_upper_bound(a,c))))),bind(X_75,$fot(identity)),bind(X_76,$fot(X_36))]]) ).

cnf(refute_0_6047,plain,
    ( greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)) != greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c))))
    | greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)) != greatest_lower_bound(identity,greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c)))))
    | greatest_lower_bound(identity,greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c))))) = greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c)))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)),greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c))))) ),[0],$fot(greatest_lower_bound(identity,greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c))))))]]) ).

cnf(refute_0_6048,plain,
    ( greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)) != greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c))))
    | greatest_lower_bound(identity,greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c))))) = greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c)))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)),greatest_lower_bound(identity,greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c)))))) )],[refute_0_6046,refute_0_6047]) ).

cnf(refute_0_6049,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c))))) = greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c)))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),greatest_lower_bound(X_36,identity)),greatest_lower_bound(X_36,multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_6045,refute_0_6048]) ).

cnf(refute_0_6050,plain,
    greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))) = greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c)))),
    inference(subst,[],[refute_0_6049:[bind(X_36,$fot(least_upper_bound(X_203,identity)))]]) ).

cnf(refute_0_6051,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))) != multiply(b,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))) != greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))
    | greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))),multiply(b,inverse(least_upper_bound(a,c)))) ),[0],$fot(greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c)))))]]) ).

cnf(refute_0_6052,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))) != multiply(b,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))),greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_6050,refute_0_6051]) ).

cnf(refute_0_6053,plain,
    greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(X_203,identity),multiply(b,inverse(least_upper_bound(a,c))))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_6041,refute_0_6052]) ).

cnf(refute_0_6054,plain,
    greatest_lower_bound(least_upper_bound(inverse(c),identity),multiply(b,inverse(least_upper_bound(a,c)))) = multiply(b,inverse(least_upper_bound(a,c))),
    inference(subst,[],[refute_0_6053:[bind(X_203,$fot(inverse(c)))]]) ).

cnf(refute_0_6055,plain,
    greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)) = greatest_lower_bound(least_upper_bound(inverse(c),identity),multiply(b,inverse(least_upper_bound(a,c)))),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(multiply(b,inverse(least_upper_bound(a,c))))),bind(X_25,$fot(least_upper_bound(inverse(c),identity)))]]) ).

cnf(refute_0_6056,plain,
    ( greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)) != greatest_lower_bound(least_upper_bound(inverse(c),identity),multiply(b,inverse(least_upper_bound(a,c))))
    | greatest_lower_bound(least_upper_bound(inverse(c),identity),multiply(b,inverse(least_upper_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)) = multiply(b,inverse(least_upper_bound(a,c))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(inverse(c),identity),multiply(b,inverse(least_upper_bound(a,c)))))),bind(Z0,$fot(multiply(b,inverse(least_upper_bound(a,c)))))]]) ).

cnf(refute_0_6057,plain,
    ( greatest_lower_bound(least_upper_bound(inverse(c),identity),multiply(b,inverse(least_upper_bound(a,c)))) != multiply(b,inverse(least_upper_bound(a,c)))
    | greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)) = multiply(b,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)),greatest_lower_bound(least_upper_bound(inverse(c),identity),multiply(b,inverse(least_upper_bound(a,c))))) )],[refute_0_6055,refute_0_6056]) ).

cnf(refute_0_6058,plain,
    greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)) = multiply(b,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(inverse(c),identity),multiply(b,inverse(least_upper_bound(a,c)))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_6054,refute_0_6057]) ).

cnf(refute_0_6059,plain,
    ( multiply(a,inverse(least_upper_bound(a,c))) != greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity))
    | greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)) != multiply(b,inverse(least_upper_bound(a,c)))
    | multiply(a,inverse(least_upper_bound(a,c))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,inverse(least_upper_bound(a,c))),multiply(b,inverse(least_upper_bound(a,c)))) ),[0],$fot(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)))]]) ).

cnf(refute_0_6060,plain,
    ( multiply(a,inverse(least_upper_bound(a,c))) != greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity))
    | multiply(a,inverse(least_upper_bound(a,c))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity)),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_6058,refute_0_6059]) ).

cnf(refute_0_6061,plain,
    ( multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)) != greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity))
    | multiply(a,inverse(least_upper_bound(a,c))) = multiply(b,inverse(least_upper_bound(a,c))) ),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(least_upper_bound(a,c))),greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity))) )],[refute_0_6037,refute_0_6060]) ).

cnf(refute_0_6062,plain,
    multiply(a,inverse(least_upper_bound(a,c))) = multiply(b,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(a,c),inverse(greatest_lower_bound(inverse(c),identity))),inverse(c)),greatest_lower_bound(multiply(b,inverse(least_upper_bound(a,c))),least_upper_bound(inverse(c),identity))) )],[refute_0_5952,refute_0_6061]) ).

cnf(refute_0_6063,plain,
    ( multiply(a,inverse(least_upper_bound(a,c))) != multiply(b,inverse(least_upper_bound(a,c)))
    | multiply(b,inverse(least_upper_bound(a,c))) = multiply(a,inverse(least_upper_bound(a,c))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(a,inverse(least_upper_bound(a,c))))),bind(Y0,$fot(multiply(b,inverse(least_upper_bound(a,c)))))]]) ).

cnf(refute_0_6064,plain,
    multiply(b,inverse(least_upper_bound(a,c))) = multiply(a,inverse(least_upper_bound(a,c))),
    inference(resolve,[$cnf( $equal(multiply(a,inverse(least_upper_bound(a,c))),multiply(b,inverse(least_upper_bound(a,c)))) )],[refute_0_6062,refute_0_6063]) ).

cnf(refute_0_6065,plain,
    ( multiply(b,inverse(least_upper_bound(a,c))) != multiply(a,inverse(least_upper_bound(a,c)))
    | multiply(inverse(least_upper_bound(a,c)),inverse(multiply(b,inverse(least_upper_bound(a,c))))) != inverse(b)
    | multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))) = inverse(b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),inverse(multiply(b,inverse(least_upper_bound(a,c))))),inverse(b)) ),[0,1,0],$fot(multiply(a,inverse(least_upper_bound(a,c))))]]) ).

cnf(refute_0_6066,plain,
    ( multiply(inverse(least_upper_bound(a,c)),inverse(multiply(b,inverse(least_upper_bound(a,c))))) != inverse(b)
    | multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))) = inverse(b) ),
    inference(resolve,[$cnf( $equal(multiply(b,inverse(least_upper_bound(a,c))),multiply(a,inverse(least_upper_bound(a,c)))) )],[refute_0_6064,refute_0_6065]) ).

cnf(refute_0_6067,plain,
    multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))) = inverse(b),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),inverse(multiply(b,inverse(least_upper_bound(a,c))))),inverse(b)) )],[refute_0_5802,refute_0_6066]) ).

cnf(refute_0_6068,plain,
    multiply(a,identity) = a,
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(a))]]) ).

cnf(refute_0_6069,plain,
    multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_6070,plain,
    multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) = multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))),
    introduced(tautology,[refl,[$fot(multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))))]]) ).

cnf(refute_0_6071,plain,
    ( multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) != multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c)))
    | multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c)) != identity
    | multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) = multiply(a,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))),multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_6072,plain,
    ( multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c)) != identity
    | multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) = multiply(a,identity) ),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))),multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c)))) )],[refute_0_6070,refute_0_6071]) ).

cnf(refute_0_6073,plain,
    multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) = multiply(a,identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c)),identity) )],[refute_0_6069,refute_0_6072]) ).

cnf(refute_0_6074,plain,
    ( multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) != multiply(a,identity)
    | multiply(a,identity) != a
    | multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) = a ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))))),bind(Y0,$fot(multiply(a,identity))),bind(Z0,$fot(a))]]) ).

cnf(refute_0_6075,plain,
    ( multiply(a,identity) != a
    | multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) = a ),
    inference(resolve,[$cnf( $equal(multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))),multiply(a,identity)) )],[refute_0_6073,refute_0_6074]) ).

cnf(refute_0_6076,plain,
    multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) = a,
    inference(resolve,[$cnf( $equal(multiply(a,identity),a) )],[refute_0_6068,refute_0_6075]) ).

cnf(refute_0_6077,plain,
    multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)) = multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))),
    inference(subst,[],[associativity:[bind(X,$fot(a)),bind(Y,$fot(inverse(least_upper_bound(a,c)))),bind(Z,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_6078,plain,
    ( multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)) != multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c)))
    | multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) != a
    | multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)) = a ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)))),bind(Y0,$fot(multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))))),bind(Z0,$fot(a))]]) ).

cnf(refute_0_6079,plain,
    ( multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))) != a
    | multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)) = a ),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)),multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c)))) )],[refute_0_6077,refute_0_6078]) ).

cnf(refute_0_6080,plain,
    multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)) = a,
    inference(resolve,[$cnf( $equal(multiply(a,multiply(inverse(least_upper_bound(a,c)),least_upper_bound(a,c))),a) )],[refute_0_6076,refute_0_6079]) ).

cnf(refute_0_6081,plain,
    inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))) = inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))),
    introduced(tautology,[refl,[$fot(inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))))]]) ).

cnf(refute_0_6082,plain,
    ( multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)) != a
    | inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))) != inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)))
    | inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))) = inverse(a) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))),inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)))) ),[1,0],$fot(a)]]) ).

cnf(refute_0_6083,plain,
    ( multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)) != a
    | inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))) = inverse(a) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))),inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)))) )],[refute_0_6081,refute_0_6082]) ).

cnf(refute_0_6084,plain,
    inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))) = inverse(a),
    inference(resolve,[$cnf( $equal(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)),a) )],[refute_0_6080,refute_0_6083]) ).

cnf(refute_0_6085,plain,
    multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))) = inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))),
    inference(subst,[],[refute_0_667:[bind(X_198,$fot(multiply(a,inverse(least_upper_bound(a,c))))),bind(X_59,$fot(least_upper_bound(a,c)))]]) ).

cnf(refute_0_6086,plain,
    ( multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))) != inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)))
    | inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))) != inverse(a)
    | multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))) = inverse(a) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))))),bind(Y0,$fot(inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))))),bind(Z0,$fot(inverse(a)))]]) ).

cnf(refute_0_6087,plain,
    ( inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))) != inverse(a)
    | multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))) = inverse(a) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))),inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c)))) )],[refute_0_6085,refute_0_6086]) ).

cnf(refute_0_6088,plain,
    multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))) = inverse(a),
    inference(resolve,[$cnf( $equal(inverse(multiply(multiply(a,inverse(least_upper_bound(a,c))),least_upper_bound(a,c))),inverse(a)) )],[refute_0_6084,refute_0_6087]) ).

cnf(refute_0_6089,plain,
    ( multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))) != inverse(a)
    | multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))) != inverse(b)
    | inverse(a) = inverse(b) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))),inverse(b)) ),[0],$fot(inverse(a))]]) ).

cnf(refute_0_6090,plain,
    ( multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))) != inverse(b)
    | inverse(a) = inverse(b) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))),inverse(a)) )],[refute_0_6088,refute_0_6089]) ).

cnf(refute_0_6091,plain,
    inverse(a) = inverse(b),
    inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,c)),inverse(multiply(a,inverse(least_upper_bound(a,c))))),inverse(b)) )],[refute_0_6067,refute_0_6090]) ).

cnf(refute_0_6092,plain,
    ( inverse(a) != inverse(b)
    | inverse(b) = inverse(a) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(inverse(a))),bind(Y0,$fot(inverse(b)))]]) ).

cnf(refute_0_6093,plain,
    inverse(b) = inverse(a),
    inference(resolve,[$cnf( $equal(inverse(a),inverse(b)) )],[refute_0_6091,refute_0_6092]) ).

cnf(refute_0_6094,plain,
    ( inverse(b) != inverse(a)
    | least_upper_bound(identity,least_upper_bound(b,inverse(X_180))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(b))))
    | least_upper_bound(identity,least_upper_bound(b,inverse(X_180))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(b,inverse(X_180))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(b))))) ),[1,0,1,1],$fot(inverse(a))]]) ).

cnf(refute_0_6095,plain,
    ( least_upper_bound(identity,least_upper_bound(b,inverse(X_180))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(b))))
    | least_upper_bound(identity,least_upper_bound(b,inverse(X_180))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))) ),
    inference(resolve,[$cnf( $equal(inverse(b),inverse(a)) )],[refute_0_6093,refute_0_6094]) ).

cnf(refute_0_6096,plain,
    least_upper_bound(identity,least_upper_bound(b,inverse(X_180))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(b,inverse(X_180))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(b))))) )],[refute_0_5801,refute_0_6095]) ).

cnf(refute_0_6097,plain,
    greatest_lower_bound(least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) = least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))),
    inference(subst,[],[refute_0_5020:[bind(X_11,$fot(inverse(greatest_lower_bound(identity,Y)))),bind(X_30,$fot(X_311))]]) ).

cnf(refute_0_6098,plain,
    least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))) = least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),
    inference(subst,[],[refute_0_4912:[bind(X_82,$fot(X_311))]]) ).

cnf(refute_0_6099,plain,
    ( greatest_lower_bound(least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) != least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y)))
    | least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))) != least_upper_bound(identity,least_upper_bound(X_311,inverse(Y)))
    | greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) = least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)),least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y)))) ),[0,0],$fot(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))))]]) ).

cnf(refute_0_6100,plain,
    ( greatest_lower_bound(least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) != least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y)))
    | greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) = least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))),least_upper_bound(identity,least_upper_bound(X_311,inverse(Y)))) )],[refute_0_6098,refute_0_6099]) ).

cnf(refute_0_6101,plain,
    greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) = least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)),least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_6097,refute_0_6100]) ).

cnf(refute_0_6102,plain,
    greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(X_310,least_upper_bound(Y,X_45))) = least_upper_bound(least_upper_bound(Y,X_45),X_310),
    inference(subst,[],[refute_0_5020:[bind(X_11,$fot(X_310)),bind(X_30,$fot(least_upper_bound(Y,X_45)))]]) ).

cnf(refute_0_6103,plain,
    least_upper_bound(Y,least_upper_bound(X_310,X_45)) = least_upper_bound(X_310,least_upper_bound(Y,X_45)),
    inference(subst,[],[refute_0_1102:[bind(X_43,$fot(X_310))]]) ).

cnf(refute_0_6104,plain,
    ( least_upper_bound(Y,least_upper_bound(X_310,X_45)) != least_upper_bound(X_310,least_upper_bound(Y,X_45))
    | least_upper_bound(X_310,least_upper_bound(Y,X_45)) = least_upper_bound(Y,least_upper_bound(X_310,X_45)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_310,X_45)))),bind(Y0,$fot(least_upper_bound(X_310,least_upper_bound(Y,X_45))))]]) ).

cnf(refute_0_6105,plain,
    least_upper_bound(X_310,least_upper_bound(Y,X_45)) = least_upper_bound(Y,least_upper_bound(X_310,X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(X_310,least_upper_bound(Y,X_45))) )],[refute_0_6103,refute_0_6104]) ).

cnf(refute_0_6106,plain,
    ( greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(X_310,least_upper_bound(Y,X_45))) != least_upper_bound(least_upper_bound(Y,X_45),X_310)
    | least_upper_bound(X_310,least_upper_bound(Y,X_45)) != least_upper_bound(Y,least_upper_bound(X_310,X_45))
    | greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) = least_upper_bound(least_upper_bound(Y,X_45),X_310) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(X_310,least_upper_bound(Y,X_45))),least_upper_bound(least_upper_bound(Y,X_45),X_310)) ),[0,1],$fot(least_upper_bound(Y,least_upper_bound(X_310,X_45)))]]) ).

cnf(refute_0_6107,plain,
    ( greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(X_310,least_upper_bound(Y,X_45))) != least_upper_bound(least_upper_bound(Y,X_45),X_310)
    | greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) = least_upper_bound(least_upper_bound(Y,X_45),X_310) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_310,least_upper_bound(Y,X_45)),least_upper_bound(Y,least_upper_bound(X_310,X_45))) )],[refute_0_6105,refute_0_6106]) ).

cnf(refute_0_6108,plain,
    greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) = least_upper_bound(least_upper_bound(Y,X_45),X_310),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(X_310,least_upper_bound(Y,X_45))),least_upper_bound(least_upper_bound(Y,X_45),X_310)) )],[refute_0_6102,refute_0_6107]) ).

cnf(refute_0_6109,plain,
    least_upper_bound(least_upper_bound(Y,X_45),X_310) = least_upper_bound(Y,least_upper_bound(X_45,X_310)),
    inference(subst,[],[refute_0_375:[bind(X,$fot(Y)),bind(Y,$fot(X_45)),bind(Z,$fot(X_310))]]) ).

cnf(refute_0_6110,plain,
    greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)) = greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)))]]) ).

cnf(refute_0_6111,plain,
    ( greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)) != greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310))
    | least_upper_bound(least_upper_bound(Y,X_45),X_310) != least_upper_bound(Y,least_upper_bound(X_45,X_310))
    | greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)) = greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)),greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310))) ),[1,1],$fot(least_upper_bound(Y,least_upper_bound(X_45,X_310)))]]) ).

cnf(refute_0_6112,plain,
    ( least_upper_bound(least_upper_bound(Y,X_45),X_310) != least_upper_bound(Y,least_upper_bound(X_45,X_310))
    | greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)) = greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)),greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310))) )],[refute_0_6110,refute_0_6111]) ).

cnf(refute_0_6113,plain,
    greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)) = greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_45,X_310))) )],[refute_0_6109,refute_0_6112]) ).

cnf(refute_0_6114,plain,
    greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) = greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)),
    inference(subst,[],[refute_0_157:[bind(X_24,$fot(least_upper_bound(least_upper_bound(Y,X_45),X_310))),bind(X_25,$fot(least_upper_bound(Y,least_upper_bound(X_310,X_45))))]]) ).

cnf(refute_0_6115,plain,
    ( greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)) != greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310)))
    | greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) != greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310))
    | greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) = greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310)))))]]) ).

cnf(refute_0_6116,plain,
    ( greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)) != greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310)))
    | greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) = greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))),greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310))) )],[refute_0_6114,refute_0_6115]) ).

cnf(refute_0_6117,plain,
    greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) = greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(least_upper_bound(Y,X_45),X_310)),greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310)))) )],[refute_0_6113,refute_0_6116]) ).

cnf(refute_0_6118,plain,
    ( greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) != greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310)))
    | greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) != least_upper_bound(least_upper_bound(Y,X_45),X_310)
    | greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) = least_upper_bound(least_upper_bound(Y,X_45),X_310) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))),least_upper_bound(least_upper_bound(Y,X_45),X_310)) ),[0],$fot(greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))))]]) ).

cnf(refute_0_6119,plain,
    ( greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) != least_upper_bound(least_upper_bound(Y,X_45),X_310)
    | greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) = least_upper_bound(least_upper_bound(Y,X_45),X_310) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))),greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310)))) )],[refute_0_6117,refute_0_6118]) ).

cnf(refute_0_6120,plain,
    ( greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) != least_upper_bound(least_upper_bound(Y,X_45),X_310)
    | least_upper_bound(least_upper_bound(Y,X_45),X_310) != least_upper_bound(Y,least_upper_bound(X_45,X_310))
    | greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) = least_upper_bound(Y,least_upper_bound(X_45,X_310)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))),least_upper_bound(Y,least_upper_bound(X_45,X_310))) ),[0],$fot(least_upper_bound(least_upper_bound(Y,X_45),X_310))]]) ).

cnf(refute_0_6121,plain,
    ( greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) != least_upper_bound(least_upper_bound(Y,X_45),X_310)
    | greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) = least_upper_bound(Y,least_upper_bound(X_45,X_310)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_45,X_310))) )],[refute_0_6109,refute_0_6120]) ).

cnf(refute_0_6122,plain,
    ( greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))) != least_upper_bound(least_upper_bound(Y,X_45),X_310)
    | greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) = least_upper_bound(Y,least_upper_bound(X_45,X_310)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))),least_upper_bound(least_upper_bound(Y,X_45),X_310)) )],[refute_0_6119,refute_0_6121]) ).

cnf(refute_0_6123,plain,
    greatest_lower_bound(least_upper_bound(Y,least_upper_bound(X_310,X_45)),least_upper_bound(Y,least_upper_bound(X_45,X_310))) = least_upper_bound(Y,least_upper_bound(X_45,X_310)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(least_upper_bound(Y,X_45),X_310),least_upper_bound(Y,least_upper_bound(X_310,X_45))),least_upper_bound(least_upper_bound(Y,X_45),X_310)) )],[refute_0_6108,refute_0_6122]) ).

cnf(refute_0_6124,plain,
    greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))) = least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)),
    inference(subst,[],[refute_0_6123:[bind(Y,$fot(identity)),bind(X_310,$fot(X_311)),bind(X_45,$fot(inverse(Y)))]]) ).

cnf(refute_0_6125,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311) = least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)),
    inference(subst,[],[refute_0_2549:[bind(Z,$fot(X_311)),bind(X_64,$fot(Y))]]) ).

cnf(refute_0_6126,plain,
    greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) = greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)))]]) ).

cnf(refute_0_6127,plain,
    ( greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) != greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311))
    | least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311) != least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))
    | greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) = greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)),greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311))) ),[1,1],$fot(least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)))]]) ).

cnf(refute_0_6128,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311) != least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))
    | greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) = greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)),greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311))) )],[refute_0_6126,refute_0_6127]) ).

cnf(refute_0_6129,plain,
    greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) = greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))) )],[refute_0_6125,refute_0_6128]) ).

cnf(refute_0_6130,plain,
    ( greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))) != least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))
    | greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) != greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)))
    | greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) = least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))))]]) ).

cnf(refute_0_6131,plain,
    ( greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))) != least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))
    | greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) = least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)),greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)))) )],[refute_0_6129,refute_0_6130]) ).

cnf(refute_0_6132,plain,
    greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) = least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))) )],[refute_0_6124,refute_0_6131]) ).

cnf(refute_0_6133,plain,
    ( greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) != least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y)))
    | greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) != least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))
    | least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)) = least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)),least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)))]]) ).

cnf(refute_0_6134,plain,
    ( greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)) != least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y)))
    | least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)) = least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)),least_upper_bound(identity,least_upper_bound(inverse(Y),X_311))) )],[refute_0_6132,refute_0_6133]) ).

cnf(refute_0_6135,plain,
    least_upper_bound(identity,least_upper_bound(inverse(Y),X_311)) = least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,least_upper_bound(X_311,inverse(Y))),least_upper_bound(inverse(greatest_lower_bound(identity,Y)),X_311)),least_upper_bound(X_311,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_6101,refute_0_6134]) ).

cnf(refute_0_6136,plain,
    least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)) = least_upper_bound(X_311,inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331))))),
    inference(subst,[],[refute_0_6135:[bind(Y,$fot(multiply(X_331,least_upper_bound(identity,X_331))))]]) ).

cnf(refute_0_6137,plain,
    greatest_lower_bound(X_331,identity) = greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331))),
    inference(subst,[],[refute_0_4624:[bind(X_329,$fot(X_331))]]) ).

cnf(refute_0_6138,plain,
    ( greatest_lower_bound(X_331,identity) != greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))
    | greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331))) = greatest_lower_bound(X_331,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(greatest_lower_bound(X_331,identity))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))))]]) ).

cnf(refute_0_6139,plain,
    greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331))) = greatest_lower_bound(X_331,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_331,identity),greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))) )],[refute_0_6137,refute_0_6138]) ).

cnf(refute_0_6140,plain,
    ( greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331))) != greatest_lower_bound(X_331,identity)
    | least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)) != least_upper_bound(X_311,inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))))
    | least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)) = least_upper_bound(X_311,inverse(greatest_lower_bound(X_331,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)),least_upper_bound(X_311,inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))))) ),[1,1,0],$fot(greatest_lower_bound(X_331,identity))]]) ).

cnf(refute_0_6141,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)) != least_upper_bound(X_311,inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))))
    | least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)) = least_upper_bound(X_311,inverse(greatest_lower_bound(X_331,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331))),greatest_lower_bound(X_331,identity)) )],[refute_0_6139,refute_0_6140]) ).

cnf(refute_0_6142,plain,
    least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)) = least_upper_bound(X_311,inverse(greatest_lower_bound(X_331,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)),least_upper_bound(X_311,inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))))) )],[refute_0_6136,refute_0_6141]) ).

cnf(refute_0_6143,plain,
    least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45),
    inference(subst,[],[refute_0_3215:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_331,least_upper_bound(identity,X_331))))]]) ).

cnf(refute_0_6144,plain,
    ( greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331))) != greatest_lower_bound(X_331,identity)
    | least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) != least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45)
    | least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)),least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45)) ),[1,0,0],$fot(greatest_lower_bound(X_331,identity))]]) ).

cnf(refute_0_6145,plain,
    ( least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) != least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45)
    | least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331))),greatest_lower_bound(X_331,identity)) )],[refute_0_6139,refute_0_6144]) ).

cnf(refute_0_6146,plain,
    least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)),least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45)) )],[refute_0_6143,refute_0_6145]) ).

cnf(refute_0_6147,plain,
    least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45) = least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)),
    inference(subst,[],[refute_0_2549:[bind(Z,$fot(X_45)),bind(X_64,$fot(multiply(X_331,least_upper_bound(identity,X_331))))]]) ).

cnf(refute_0_6148,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45) != least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45))
    | least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) != least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45)
    | least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45))))]]) ).

cnf(refute_0_6149,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45) != least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45))
    | least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)),least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45)) )],[refute_0_6143,refute_0_6148]) ).

cnf(refute_0_6150,plain,
    least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(identity,multiply(X_331,least_upper_bound(identity,X_331)))),X_45),least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45))) )],[refute_0_6147,refute_0_6149]) ).

cnf(refute_0_6151,plain,
    ( least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) != least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45))
    | least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) != least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45)
    | least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)),least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)))]]) ).

cnf(refute_0_6152,plain,
    ( least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) != least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45)
    | least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)),least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45))) )],[refute_0_6150,refute_0_6151]) ).

cnf(refute_0_6153,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45) = least_upper_bound(identity,least_upper_bound(X_45,inverse(X_331))),
    inference(subst,[],[refute_0_3225:[bind(X_249,$fot(X_331)),bind(X_251,$fot(X_45))]]) ).

cnf(refute_0_6154,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) != least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45)
    | least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45) != least_upper_bound(identity,least_upper_bound(X_45,inverse(X_331)))
    | least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(identity,least_upper_bound(X_45,inverse(X_331))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)),least_upper_bound(identity,least_upper_bound(X_45,inverse(X_331)))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45))]]) ).

cnf(refute_0_6155,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) != least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45)
    | least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(identity,least_upper_bound(X_45,inverse(X_331))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45),least_upper_bound(identity,least_upper_bound(X_45,inverse(X_331)))) )],[refute_0_6153,refute_0_6154]) ).

cnf(refute_0_6156,plain,
    ( least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) != least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45)
    | least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(identity,least_upper_bound(X_45,inverse(X_331))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)),least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45)) )],[refute_0_6152,refute_0_6155]) ).

cnf(refute_0_6157,plain,
    least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)) = least_upper_bound(identity,least_upper_bound(X_45,inverse(X_331))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_45)),least_upper_bound(inverse(greatest_lower_bound(X_331,identity)),X_45)) )],[refute_0_6146,refute_0_6156]) ).

cnf(refute_0_6158,plain,
    least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)) = least_upper_bound(identity,least_upper_bound(X_311,inverse(X_331))),
    inference(subst,[],[refute_0_6157:[bind(X_45,$fot(X_311))]]) ).

cnf(refute_0_6159,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)) != least_upper_bound(X_311,inverse(greatest_lower_bound(X_331,identity)))
    | least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)) != least_upper_bound(identity,least_upper_bound(X_311,inverse(X_331)))
    | least_upper_bound(identity,least_upper_bound(X_311,inverse(X_331))) = least_upper_bound(X_311,inverse(greatest_lower_bound(X_331,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)),least_upper_bound(X_311,inverse(greatest_lower_bound(X_331,identity)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_311,inverse(X_331))))]]) ).

cnf(refute_0_6160,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)) != least_upper_bound(X_311,inverse(greatest_lower_bound(X_331,identity)))
    | least_upper_bound(identity,least_upper_bound(X_311,inverse(X_331))) = least_upper_bound(X_311,inverse(greatest_lower_bound(X_331,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)),least_upper_bound(identity,least_upper_bound(X_311,inverse(X_331)))) )],[refute_0_6158,refute_0_6159]) ).

cnf(refute_0_6161,plain,
    least_upper_bound(identity,least_upper_bound(X_311,inverse(X_331))) = least_upper_bound(X_311,inverse(greatest_lower_bound(X_331,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(multiply(X_331,least_upper_bound(identity,X_331))),X_311)),least_upper_bound(X_311,inverse(greatest_lower_bound(X_331,identity)))) )],[refute_0_6142,refute_0_6160]) ).

cnf(refute_0_6162,plain,
    least_upper_bound(identity,least_upper_bound(b,inverse(X_180))) = least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))),
    inference(subst,[],[refute_0_6161:[bind(X_311,$fot(b)),bind(X_331,$fot(X_180))]]) ).

cnf(refute_0_6163,plain,
    ( least_upper_bound(identity,least_upper_bound(b,inverse(X_180))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a))))
    | least_upper_bound(identity,least_upper_bound(b,inverse(X_180))) != least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity)))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(b,inverse(X_180))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a))))) ),[0],$fot(least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))))]]) ).

cnf(refute_0_6164,plain,
    ( least_upper_bound(identity,least_upper_bound(b,inverse(X_180))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a))))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))) = inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(b,inverse(X_180))),least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity)))) )],[refute_0_6162,refute_0_6163]) ).

cnf(refute_0_6165,plain,
    least_upper_bound(identity,least_upper_bound(a,inverse(X_180))) = least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity))),
    inference(subst,[],[refute_0_6161:[bind(X_311,$fot(a)),bind(X_331,$fot(X_180))]]) ).

cnf(refute_0_6166,plain,
    ( least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y))))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y)))) = least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))))),bind(Y0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y))))))]]) ).

cnf(refute_0_6167,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y)))) = least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(Y,inverse(X_180))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(Y))))) )],[refute_0_5800,refute_0_6166]) ).

cnf(refute_0_6168,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))) = least_upper_bound(identity,least_upper_bound(a,inverse(X_180))),
    inference(subst,[],[refute_0_6167:[bind(Y,$fot(a))]]) ).

cnf(refute_0_6169,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))) != least_upper_bound(identity,least_upper_bound(a,inverse(X_180)))
    | least_upper_bound(identity,least_upper_bound(a,inverse(X_180))) != least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity)))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))) = least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity))) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(a,inverse(X_180))))),bind(Z0,$fot(least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity)))))]]) ).

cnf(refute_0_6170,plain,
    ( least_upper_bound(identity,least_upper_bound(a,inverse(X_180))) != least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity)))
    | inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))) = least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))),least_upper_bound(identity,least_upper_bound(a,inverse(X_180)))) )],[refute_0_6168,refute_0_6169]) ).

cnf(refute_0_6171,plain,
    inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))) = least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(a,inverse(X_180))),least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity)))) )],[refute_0_6165,refute_0_6170]) ).

cnf(refute_0_6172,plain,
    ( inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))) != least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity)))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a))))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))) = least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a))))) ),[1],$fot(least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity))))]]) ).

cnf(refute_0_6173,plain,
    ( least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a))))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))) = least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a)))),least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity)))) )],[refute_0_6171,refute_0_6172]) ).

cnf(refute_0_6174,plain,
    ( least_upper_bound(identity,least_upper_bound(b,inverse(X_180))) != inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a))))
    | least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))) = least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a))))) )],[refute_0_6164,refute_0_6173]) ).

cnf(refute_0_6175,plain,
    least_upper_bound(b,inverse(greatest_lower_bound(X_180,identity))) = least_upper_bound(a,inverse(greatest_lower_bound(X_180,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(b,inverse(X_180))),inverse(greatest_lower_bound(identity,greatest_lower_bound(X_180,inverse(a))))) )],[refute_0_6096,refute_0_6174]) ).

cnf(refute_0_6176,plain,
    least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),
    inference(subst,[],[refute_0_6175:[bind(X_180,$fot(a))]]) ).

cnf(refute_0_6177,plain,
    ( least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,inverse(a))
    | least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(a)) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))))),bind(Y0,$fot(least_upper_bound(a,inverse(greatest_lower_bound(a,identity))))),bind(Z0,$fot(least_upper_bound(a,inverse(a))))]]) ).

cnf(refute_0_6178,plain,
    ( least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,inverse(a))
    | least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(a)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_6176,refute_0_6177]) ).

cnf(refute_0_6179,plain,
    least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(a)),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),least_upper_bound(a,inverse(a))) )],[refute_0_5788,refute_0_6178]) ).

cnf(refute_0_6180,plain,
    ( least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,inverse(a))
    | least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(b,inverse(a))
    | least_upper_bound(a,inverse(a)) = least_upper_bound(b,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),least_upper_bound(b,inverse(a))) ),[0],$fot(least_upper_bound(a,inverse(a)))]]) ).

cnf(refute_0_6181,plain,
    ( least_upper_bound(b,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(b,inverse(a))
    | least_upper_bound(a,inverse(a)) = least_upper_bound(b,inverse(a)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),least_upper_bound(a,inverse(a))) )],[refute_0_6179,refute_0_6180]) ).

cnf(refute_0_6182,plain,
    least_upper_bound(a,inverse(a)) = least_upper_bound(b,inverse(a)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(greatest_lower_bound(a,identity))),least_upper_bound(b,inverse(a))) )],[refute_0_4377,refute_0_6181]) ).

cnf(refute_0_6183,plain,
    ( least_upper_bound(a,inverse(a)) != least_upper_bound(b,inverse(a))
    | least_upper_bound(b,inverse(a)) = least_upper_bound(a,inverse(a)) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(a,inverse(a)))),bind(Y0,$fot(least_upper_bound(b,inverse(a))))]]) ).

cnf(refute_0_6184,plain,
    least_upper_bound(b,inverse(a)) = least_upper_bound(a,inverse(a)),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(a))) )],[refute_0_6182,refute_0_6183]) ).

cnf(refute_0_6185,plain,
    multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_6186,plain,
    ( multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) != multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity))
    | least_upper_bound(b,inverse(a)) != least_upper_bound(a,inverse(a))
    | multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)),multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity))) ),[1,0],$fot(least_upper_bound(a,inverse(a)))]]) ).

cnf(refute_0_6187,plain,
    ( least_upper_bound(b,inverse(a)) != least_upper_bound(a,inverse(a))
    | multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)),multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity))) )],[refute_0_6185,refute_0_6186]) ).

cnf(refute_0_6188,plain,
    multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,inverse(a)),least_upper_bound(a,inverse(a))) )],[refute_0_6184,refute_0_6187]) ).

cnf(refute_0_6189,plain,
    ( multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)) != least_upper_bound(a,identity)
    | multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) != multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity))
    | multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(a,identity) ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)))),bind(Y0,$fot(multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)))),bind(Z0,$fot(least_upper_bound(a,identity)))]]) ).

cnf(refute_0_6190,plain,
    ( multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)) != least_upper_bound(a,identity)
    | multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(a,identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)),multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity))) )],[refute_0_6188,refute_0_6189]) ).

cnf(refute_0_6191,plain,
    multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) = least_upper_bound(a,identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,inverse(a)),greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) )],[refute_0_5244,refute_0_6190]) ).

cnf(refute_0_6192,plain,
    ( multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) != least_upper_bound(a,identity)
    | multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) != least_upper_bound(b,identity)
    | least_upper_bound(a,identity) = least_upper_bound(b,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)),least_upper_bound(b,identity)) ),[0],$fot(least_upper_bound(a,identity))]]) ).

cnf(refute_0_6193,plain,
    ( multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)) != least_upper_bound(b,identity)
    | least_upper_bound(a,identity) = least_upper_bound(b,identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) )],[refute_0_6191,refute_0_6192]) ).

cnf(refute_0_6194,plain,
    least_upper_bound(a,identity) = least_upper_bound(b,identity),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,inverse(a)),greatest_lower_bound(a,identity)),least_upper_bound(b,identity)) )],[refute_0_4409,refute_0_6193]) ).

cnf(refute_0_6195,plain,
    ( least_upper_bound(a,identity) != least_upper_bound(b,identity)
    | least_upper_bound(b,identity) = least_upper_bound(a,identity) ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(a,identity))),bind(Y0,$fot(least_upper_bound(b,identity)))]]) ).

cnf(refute_0_6196,plain,
    least_upper_bound(b,identity) = least_upper_bound(a,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),least_upper_bound(b,identity)) )],[refute_0_6194,refute_0_6195]) ).

cnf(refute_0_6197,plain,
    greatest_lower_bound(a,least_upper_bound(b,identity)) = greatest_lower_bound(a,least_upper_bound(b,identity)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(a,least_upper_bound(b,identity)))]]) ).

cnf(refute_0_6198,plain,
    ( greatest_lower_bound(a,least_upper_bound(b,identity)) != greatest_lower_bound(a,least_upper_bound(b,identity))
    | least_upper_bound(b,identity) != least_upper_bound(a,identity)
    | greatest_lower_bound(a,least_upper_bound(b,identity)) = greatest_lower_bound(a,least_upper_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(b,identity)),greatest_lower_bound(a,least_upper_bound(b,identity))) ),[1,1],$fot(least_upper_bound(a,identity))]]) ).

cnf(refute_0_6199,plain,
    ( least_upper_bound(b,identity) != least_upper_bound(a,identity)
    | greatest_lower_bound(a,least_upper_bound(b,identity)) = greatest_lower_bound(a,least_upper_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(b,identity)),greatest_lower_bound(a,least_upper_bound(b,identity))) )],[refute_0_6197,refute_0_6198]) ).

cnf(refute_0_6200,plain,
    greatest_lower_bound(a,least_upper_bound(b,identity)) = greatest_lower_bound(a,least_upper_bound(a,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),least_upper_bound(a,identity)) )],[refute_0_6196,refute_0_6199]) ).

cnf(refute_0_6201,plain,
    ( greatest_lower_bound(a,least_upper_bound(a,identity)) != a
    | greatest_lower_bound(a,least_upper_bound(b,identity)) != greatest_lower_bound(a,least_upper_bound(a,identity))
    | greatest_lower_bound(a,least_upper_bound(b,identity)) = a ),
    inference(subst,[],[refute_0_222:[bind(X0,$fot(greatest_lower_bound(a,least_upper_bound(b,identity)))),bind(Y0,$fot(greatest_lower_bound(a,least_upper_bound(a,identity)))),bind(Z0,$fot(a))]]) ).

cnf(refute_0_6202,plain,
    ( greatest_lower_bound(a,least_upper_bound(a,identity)) != a
    | greatest_lower_bound(a,least_upper_bound(b,identity)) = a ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(b,identity)),greatest_lower_bound(a,least_upper_bound(a,identity))) )],[refute_0_6200,refute_0_6201]) ).

cnf(refute_0_6203,plain,
    greatest_lower_bound(a,least_upper_bound(b,identity)) = a,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(a,identity)),a) )],[refute_0_1276,refute_0_6202]) ).

cnf(refute_0_6204,plain,
    ( b != greatest_lower_bound(a,least_upper_bound(b,identity))
    | greatest_lower_bound(a,least_upper_bound(b,identity)) != a
    | b = a ),
    introduced(tautology,[equality,[$cnf( ~ $equal(b,a) ),[0],$fot(greatest_lower_bound(a,least_upper_bound(b,identity)))]]) ).

cnf(refute_0_6205,plain,
    ( b != greatest_lower_bound(a,least_upper_bound(b,identity))
    | b = a ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(b,identity)),a) )],[refute_0_6203,refute_0_6204]) ).

cnf(refute_0_6206,plain,
    b = a,
    inference(resolve,[$cnf( $equal(b,greatest_lower_bound(a,least_upper_bound(b,identity))) )],[refute_0_1275,refute_0_6205]) ).

cnf(refute_0_6207,plain,
    ( b != a
    | a = b ),
    inference(subst,[],[refute_0_18:[bind(X0,$fot(b)),bind(Y0,$fot(a))]]) ).

cnf(refute_0_6208,plain,
    b != a,
    inference(resolve,[$cnf( $equal(a,b) )],[refute_0_6207,prove_p12x]) ).

cnf(refute_0_6209,plain,
    $false,
    inference(resolve,[$cnf( $equal(b,a) )],[refute_0_6206,refute_0_6208]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : GRP181-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.10  % Command  : metis --show proof --show saturation %s
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 600
% 0.09/0.29  % DateTime : Mon Jun 13 23:06:12 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.09/0.29  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 30.57/30.75  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.57/30.75  
% 30.57/30.75  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 31.55/31.72  
%------------------------------------------------------------------------------