%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP174-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n008.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 10:37:18 EDT 2022

% Result   : Unsatisfiable 0.52s 0.73s
% Output   : CNFRefutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   39
%            Number of leaves      :   79
% Syntax   : Number of clauses     :  331 ( 170 unt;   0 nHn; 179 RR)
%            Number of literals    :  561 ( 560 equ; 232 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  491 (   6 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_lub,axiom,
    least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).

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

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

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

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

cnf(p05b_1,hypothesis,
    greatest_lower_bound(identity,a) = a ).

cnf(p05b_2,hypothesis,
    greatest_lower_bound(identity,inverse(a)) = inverse(a) ).

cnf(prove_p05b,negated_conjecture,
    identity != a ).

cnf(refute_0_0,plain,
    ( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
    | least_upper_bound(X,greatest_lower_bound(X,Y)) != X
    | least_upper_bound(X,greatest_lower_bound(Y,X)) = X ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X) ),[0,1],$fot(greatest_lower_bound(Y,X))]]) ).

cnf(refute_0_1,plain,
    ( least_upper_bound(X,greatest_lower_bound(X,Y)) != X
    | least_upper_bound(X,greatest_lower_bound(Y,X)) = X ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_0]) ).

cnf(refute_0_2,plain,
    least_upper_bound(X,greatest_lower_bound(Y,X)) = X,
    inference(resolve,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X) )],[lub_absorbtion,refute_0_1]) ).

cnf(refute_0_3,plain,
    least_upper_bound(identity,greatest_lower_bound(a,identity)) = identity,
    inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(a))]]) ).

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

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

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

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

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

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

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

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

cnf(refute_0_12,plain,
    greatest_lower_bound(a,identity) = a,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,a),a) )],[p05b_1,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( greatest_lower_bound(a,identity) != a
    | least_upper_bound(identity,greatest_lower_bound(a,identity)) != identity
    | least_upper_bound(identity,a) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,identity)),identity) ),[0,1],$fot(a)]]) ).

cnf(refute_0_14,plain,
    ( least_upper_bound(identity,greatest_lower_bound(a,identity)) != identity
    | least_upper_bound(identity,a) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(a,identity),a) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    least_upper_bound(identity,a) = identity,
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(a,identity)),identity) )],[refute_0_3,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( least_upper_bound(X,Y) != least_upper_bound(Y,X)
    | least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).

cnf(refute_0_17,plain,
    least_upper_bound(Y,X) = least_upper_bound(X,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_16]) ).

cnf(refute_0_18,plain,
    least_upper_bound(identity,a) = least_upper_bound(a,identity),
    inference(subst,[],[refute_0_17:[bind(X,$fot(a)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_19,plain,
    ( least_upper_bound(identity,a) != identity
    | least_upper_bound(identity,a) != least_upper_bound(a,identity)
    | least_upper_bound(a,identity) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,a),identity) ),[0],$fot(least_upper_bound(a,identity))]]) ).

cnf(refute_0_20,plain,
    ( least_upper_bound(identity,a) != identity
    | least_upper_bound(a,identity) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,a),least_upper_bound(a,identity)) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    least_upper_bound(a,identity) = identity,
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,a),identity) )],[refute_0_15,refute_0_20]) ).

cnf(refute_0_22,plain,
    least_upper_bound(a,a) = a,
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(a))]]) ).

cnf(refute_0_23,plain,
    greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) = X_12,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).

cnf(refute_0_24,plain,
    least_upper_bound(X_13,X_12) = least_upper_bound(X_12,X_13),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).

cnf(refute_0_25,plain,
    ( least_upper_bound(X_13,X_12) != least_upper_bound(X_12,X_13)
    | least_upper_bound(X_12,X_13) = least_upper_bound(X_13,X_12) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_13,X_12))),bind(Y0,$fot(least_upper_bound(X_12,X_13)))]]) ).

cnf(refute_0_26,plain,
    least_upper_bound(X_12,X_13) = least_upper_bound(X_13,X_12),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_13,X_12),least_upper_bound(X_12,X_13)) )],[refute_0_24,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) != X_12
    | least_upper_bound(X_12,X_13) != least_upper_bound(X_13,X_12)
    | greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12 ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)),X_12) ),[0,1],$fot(least_upper_bound(X_13,X_12))]]) ).

cnf(refute_0_28,plain,
    ( greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) != X_12
    | greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12 ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_12,X_13),least_upper_bound(X_13,X_12)) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)),X_12) )],[refute_0_23,refute_0_28]) ).

cnf(refute_0_30,plain,
    greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,least_upper_bound(X_32,inverse(a)))) = least_upper_bound(X_32,inverse(a)),
    inference(subst,[],[refute_0_29:[bind(X_12,$fot(least_upper_bound(X_32,inverse(a)))),bind(X_13,$fot(identity))]]) ).

cnf(refute_0_31,plain,
    least_upper_bound(least_upper_bound(Y,X_13),greatest_lower_bound(Y,least_upper_bound(Y,X_13))) = least_upper_bound(Y,X_13),
    inference(subst,[],[refute_0_2:[bind(X,$fot(least_upper_bound(Y,X_13)))]]) ).

cnf(refute_0_32,plain,
    greatest_lower_bound(Y,least_upper_bound(Y,X_13)) = Y,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(Y)),bind(Y,$fot(X_13))]]) ).

cnf(refute_0_33,plain,
    ( greatest_lower_bound(Y,least_upper_bound(Y,X_13)) != Y
    | least_upper_bound(least_upper_bound(Y,X_13),greatest_lower_bound(Y,least_upper_bound(Y,X_13))) != least_upper_bound(Y,X_13)
    | least_upper_bound(least_upper_bound(Y,X_13),Y) = least_upper_bound(Y,X_13) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_13),greatest_lower_bound(Y,least_upper_bound(Y,X_13))),least_upper_bound(Y,X_13)) ),[0,1],$fot(Y)]]) ).

cnf(refute_0_34,plain,
    ( least_upper_bound(least_upper_bound(Y,X_13),greatest_lower_bound(Y,least_upper_bound(Y,X_13))) != least_upper_bound(Y,X_13)
    | least_upper_bound(least_upper_bound(Y,X_13),Y) = least_upper_bound(Y,X_13) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(Y,least_upper_bound(Y,X_13)),Y) )],[refute_0_32,refute_0_33]) ).

cnf(refute_0_35,plain,
    least_upper_bound(least_upper_bound(Y,X_13),Y) = least_upper_bound(Y,X_13),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_13),greatest_lower_bound(Y,least_upper_bound(Y,X_13))),least_upper_bound(Y,X_13)) )],[refute_0_31,refute_0_34]) ).

cnf(refute_0_36,plain,
    ( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
    | least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).

cnf(refute_0_37,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_36]) ).

cnf(refute_0_38,plain,
    least_upper_bound(least_upper_bound(Y,X_13),Y) = least_upper_bound(Y,least_upper_bound(X_13,Y)),
    inference(subst,[],[refute_0_37:[bind(X,$fot(Y)),bind(Y,$fot(X_13)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_39,plain,
    ( least_upper_bound(least_upper_bound(Y,X_13),Y) != least_upper_bound(Y,X_13)
    | least_upper_bound(least_upper_bound(Y,X_13),Y) != least_upper_bound(Y,least_upper_bound(X_13,Y))
    | least_upper_bound(Y,least_upper_bound(X_13,Y)) = least_upper_bound(Y,X_13) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_13),Y),least_upper_bound(Y,X_13)) ),[0],$fot(least_upper_bound(Y,least_upper_bound(X_13,Y)))]]) ).

cnf(refute_0_40,plain,
    ( least_upper_bound(least_upper_bound(Y,X_13),Y) != least_upper_bound(Y,X_13)
    | least_upper_bound(Y,least_upper_bound(X_13,Y)) = least_upper_bound(Y,X_13) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_13),Y),least_upper_bound(Y,least_upper_bound(X_13,Y))) )],[refute_0_38,refute_0_39]) ).

cnf(refute_0_41,plain,
    least_upper_bound(Y,least_upper_bound(X_13,Y)) = least_upper_bound(Y,X_13),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_13),Y),least_upper_bound(Y,X_13)) )],[refute_0_35,refute_0_40]) ).

cnf(refute_0_42,plain,
    least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,least_upper_bound(inverse(a),X_27))) = least_upper_bound(least_upper_bound(inverse(a),X_27),identity),
    inference(subst,[],[refute_0_41:[bind(Y,$fot(least_upper_bound(inverse(a),X_27))),bind(X_13,$fot(identity))]]) ).

cnf(refute_0_43,plain,
    least_upper_bound(identity,least_upper_bound(inverse(a),X_24)) = least_upper_bound(least_upper_bound(identity,inverse(a)),X_24),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(inverse(a))),bind(Z,$fot(X_24))]]) ).

cnf(refute_0_44,plain,
    least_upper_bound(identity,greatest_lower_bound(identity,inverse(a))) = identity,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(inverse(a)))]]) ).

cnf(refute_0_45,plain,
    ( greatest_lower_bound(identity,inverse(a)) != inverse(a)
    | least_upper_bound(identity,greatest_lower_bound(identity,inverse(a))) != identity
    | least_upper_bound(identity,inverse(a)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,inverse(a))),identity) ),[0,1],$fot(inverse(a))]]) ).

cnf(refute_0_46,plain,
    ( least_upper_bound(identity,greatest_lower_bound(identity,inverse(a))) != identity
    | least_upper_bound(identity,inverse(a)) = identity ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(a)),inverse(a)) )],[p05b_2,refute_0_45]) ).

cnf(refute_0_47,plain,
    least_upper_bound(identity,inverse(a)) = identity,
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,inverse(a))),identity) )],[refute_0_44,refute_0_46]) ).

cnf(refute_0_48,plain,
    ( least_upper_bound(identity,inverse(a)) != identity
    | least_upper_bound(identity,least_upper_bound(inverse(a),X_24)) != least_upper_bound(least_upper_bound(identity,inverse(a)),X_24)
    | least_upper_bound(identity,least_upper_bound(inverse(a),X_24)) = least_upper_bound(identity,X_24) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(a),X_24)),least_upper_bound(least_upper_bound(identity,inverse(a)),X_24)) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_49,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(a),X_24)) != least_upper_bound(least_upper_bound(identity,inverse(a)),X_24)
    | least_upper_bound(identity,least_upper_bound(inverse(a),X_24)) = least_upper_bound(identity,X_24) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),identity) )],[refute_0_47,refute_0_48]) ).

cnf(refute_0_50,plain,
    least_upper_bound(identity,least_upper_bound(inverse(a),X_24)) = least_upper_bound(identity,X_24),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(a),X_24)),least_upper_bound(least_upper_bound(identity,inverse(a)),X_24)) )],[refute_0_43,refute_0_49]) ).

cnf(refute_0_51,plain,
    least_upper_bound(identity,least_upper_bound(inverse(a),X_27)) = least_upper_bound(identity,X_27),
    inference(subst,[],[refute_0_50:[bind(X_24,$fot(X_27))]]) ).

cnf(refute_0_52,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(a),X_27)) != least_upper_bound(identity,X_27)
    | least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,least_upper_bound(inverse(a),X_27))) != least_upper_bound(least_upper_bound(inverse(a),X_27),identity)
    | least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) = least_upper_bound(least_upper_bound(inverse(a),X_27),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,least_upper_bound(inverse(a),X_27))),least_upper_bound(least_upper_bound(inverse(a),X_27),identity)) ),[0,1],$fot(least_upper_bound(identity,X_27))]]) ).

cnf(refute_0_53,plain,
    ( least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,least_upper_bound(inverse(a),X_27))) != least_upper_bound(least_upper_bound(inverse(a),X_27),identity)
    | least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) = least_upper_bound(least_upper_bound(inverse(a),X_27),identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(a),X_27)),least_upper_bound(identity,X_27)) )],[refute_0_51,refute_0_52]) ).

cnf(refute_0_54,plain,
    least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) = least_upper_bound(least_upper_bound(inverse(a),X_27),identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,least_upper_bound(inverse(a),X_27))),least_upper_bound(least_upper_bound(inverse(a),X_27),identity)) )],[refute_0_42,refute_0_53]) ).

cnf(refute_0_55,plain,
    least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)) = least_upper_bound(X_27,inverse(a)),
    inference(subst,[],[refute_0_41:[bind(Y,$fot(X_27)),bind(X_13,$fot(inverse(a)))]]) ).

cnf(refute_0_56,plain,
    least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))) = least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))))]]) ).

cnf(refute_0_57,plain,
    ( least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)) != least_upper_bound(X_27,inverse(a))
    | least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))) != least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)))
    | least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))) = least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))),least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)))) ),[1,1],$fot(least_upper_bound(X_27,inverse(a)))]]) ).

cnf(refute_0_58,plain,
    ( least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)) != least_upper_bound(X_27,inverse(a))
    | least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))) = least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))),least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)))) )],[refute_0_56,refute_0_57]) ).

cnf(refute_0_59,plain,
    least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))) = least_upper_bound(identity,least_upper_bound(X_27,inverse(a))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)),least_upper_bound(X_27,inverse(a))) )],[refute_0_55,refute_0_58]) ).

cnf(refute_0_60,plain,
    least_upper_bound(X_22,least_upper_bound(X_23,X_24)) = least_upper_bound(least_upper_bound(X_22,X_23),X_24),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X_24))]]) ).

cnf(refute_0_61,plain,
    least_upper_bound(X_24,X_23) = least_upper_bound(X_23,X_24),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_24)),bind(Y,$fot(X_23))]]) ).

cnf(refute_0_62,plain,
    ( least_upper_bound(X_24,X_23) != least_upper_bound(X_23,X_24)
    | least_upper_bound(X_23,X_24) = least_upper_bound(X_24,X_23) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_24,X_23))),bind(Y0,$fot(least_upper_bound(X_23,X_24)))]]) ).

cnf(refute_0_63,plain,
    least_upper_bound(X_23,X_24) = least_upper_bound(X_24,X_23),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_24,X_23),least_upper_bound(X_23,X_24)) )],[refute_0_61,refute_0_62]) ).

cnf(refute_0_64,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_23,X_24)) != least_upper_bound(least_upper_bound(X_22,X_23),X_24)
    | least_upper_bound(X_23,X_24) != least_upper_bound(X_24,X_23)
    | least_upper_bound(X_22,least_upper_bound(X_24,X_23)) = least_upper_bound(least_upper_bound(X_22,X_23),X_24) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,X_24)),least_upper_bound(least_upper_bound(X_22,X_23),X_24)) ),[0,1],$fot(least_upper_bound(X_24,X_23))]]) ).

cnf(refute_0_65,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_23,X_24)) != least_upper_bound(least_upper_bound(X_22,X_23),X_24)
    | least_upper_bound(X_22,least_upper_bound(X_24,X_23)) = least_upper_bound(least_upper_bound(X_22,X_23),X_24) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_23,X_24),least_upper_bound(X_24,X_23)) )],[refute_0_63,refute_0_64]) ).

cnf(refute_0_66,plain,
    least_upper_bound(X_22,least_upper_bound(X_24,X_23)) = least_upper_bound(least_upper_bound(X_22,X_23),X_24),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,X_24)),least_upper_bound(least_upper_bound(X_22,X_23),X_24)) )],[refute_0_60,refute_0_65]) ).

cnf(refute_0_67,plain,
    least_upper_bound(least_upper_bound(X_22,X_23),X_24) = least_upper_bound(X_22,least_upper_bound(X_23,X_24)),
    inference(subst,[],[refute_0_37:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X_24))]]) ).

cnf(refute_0_68,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_24,X_23)) != least_upper_bound(least_upper_bound(X_22,X_23),X_24)
    | least_upper_bound(least_upper_bound(X_22,X_23),X_24) != least_upper_bound(X_22,least_upper_bound(X_23,X_24))
    | least_upper_bound(X_22,least_upper_bound(X_24,X_23)) = least_upper_bound(X_22,least_upper_bound(X_23,X_24)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_22,least_upper_bound(X_24,X_23)),least_upper_bound(X_22,least_upper_bound(X_23,X_24))) ),[0],$fot(least_upper_bound(least_upper_bound(X_22,X_23),X_24))]]) ).

cnf(refute_0_69,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_24,X_23)) != least_upper_bound(least_upper_bound(X_22,X_23),X_24)
    | least_upper_bound(X_22,least_upper_bound(X_24,X_23)) = least_upper_bound(X_22,least_upper_bound(X_23,X_24)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_23),X_24),least_upper_bound(X_22,least_upper_bound(X_23,X_24))) )],[refute_0_67,refute_0_68]) ).

cnf(refute_0_70,plain,
    least_upper_bound(X_22,least_upper_bound(X_24,X_23)) = least_upper_bound(X_22,least_upper_bound(X_23,X_24)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_24,X_23)),least_upper_bound(least_upper_bound(X_22,X_23),X_24)) )],[refute_0_66,refute_0_69]) ).

cnf(refute_0_71,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_24,X_23)) != least_upper_bound(X_22,least_upper_bound(X_23,X_24))
    | least_upper_bound(X_22,least_upper_bound(X_23,X_24)) = least_upper_bound(X_22,least_upper_bound(X_24,X_23)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(X_24,X_23)))),bind(Y0,$fot(least_upper_bound(X_22,least_upper_bound(X_23,X_24))))]]) ).

cnf(refute_0_72,plain,
    least_upper_bound(X_22,least_upper_bound(X_23,X_24)) = least_upper_bound(X_22,least_upper_bound(X_24,X_23)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_24,X_23)),least_upper_bound(X_22,least_upper_bound(X_23,X_24))) )],[refute_0_70,refute_0_71]) ).

cnf(refute_0_73,plain,
    least_upper_bound(identity,least_upper_bound(least_upper_bound(inverse(a),X_27),X_27)) = least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))),
    inference(subst,[],[refute_0_72:[bind(X_22,$fot(identity)),bind(X_23,$fot(least_upper_bound(inverse(a),X_27))),bind(X_24,$fot(X_27))]]) ).

cnf(refute_0_74,plain,
    least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) = least_upper_bound(least_upper_bound(X_22,least_upper_bound(X_13,X_22)),X_24),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_22)),bind(Y,$fot(least_upper_bound(X_13,X_22))),bind(Z,$fot(X_24))]]) ).

cnf(refute_0_75,plain,
    least_upper_bound(X_22,least_upper_bound(X_13,X_22)) = least_upper_bound(X_22,X_13),
    inference(subst,[],[refute_0_41:[bind(Y,$fot(X_22))]]) ).

cnf(refute_0_76,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_13,X_22)) != least_upper_bound(X_22,X_13)
    | least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) != least_upper_bound(least_upper_bound(X_22,least_upper_bound(X_13,X_22)),X_24)
    | least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) = least_upper_bound(least_upper_bound(X_22,X_13),X_24) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)),least_upper_bound(least_upper_bound(X_22,least_upper_bound(X_13,X_22)),X_24)) ),[1,0],$fot(least_upper_bound(X_22,X_13))]]) ).

cnf(refute_0_77,plain,
    ( least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) != least_upper_bound(least_upper_bound(X_22,least_upper_bound(X_13,X_22)),X_24)
    | least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) = least_upper_bound(least_upper_bound(X_22,X_13),X_24) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_13,X_22)),least_upper_bound(X_22,X_13)) )],[refute_0_75,refute_0_76]) ).

cnf(refute_0_78,plain,
    least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) = least_upper_bound(least_upper_bound(X_22,X_13),X_24),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)),least_upper_bound(least_upper_bound(X_22,least_upper_bound(X_13,X_22)),X_24)) )],[refute_0_74,refute_0_77]) ).

cnf(refute_0_79,plain,
    least_upper_bound(X_22,least_upper_bound(X_23,least_upper_bound(X_13,X_23))) = least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(least_upper_bound(X_13,X_23)))]]) ).

cnf(refute_0_80,plain,
    least_upper_bound(X_23,least_upper_bound(X_13,X_23)) = least_upper_bound(X_23,X_13),
    inference(subst,[],[refute_0_41:[bind(Y,$fot(X_23))]]) ).

cnf(refute_0_81,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_23,least_upper_bound(X_13,X_23))) != least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23))
    | least_upper_bound(X_23,least_upper_bound(X_13,X_23)) != least_upper_bound(X_23,X_13)
    | least_upper_bound(X_22,least_upper_bound(X_23,X_13)) = least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,least_upper_bound(X_13,X_23))),least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23))) ),[0,1],$fot(least_upper_bound(X_23,X_13))]]) ).

cnf(refute_0_82,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_23,least_upper_bound(X_13,X_23))) != least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23))
    | least_upper_bound(X_22,least_upper_bound(X_23,X_13)) = least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(X_13,X_23)),least_upper_bound(X_23,X_13)) )],[refute_0_80,refute_0_81]) ).

cnf(refute_0_83,plain,
    least_upper_bound(X_22,least_upper_bound(X_23,X_13)) = least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,least_upper_bound(X_13,X_23))),least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23))) )],[refute_0_79,refute_0_82]) ).

cnf(refute_0_84,plain,
    least_upper_bound(least_upper_bound(X_22,X_23),X_13) = least_upper_bound(X_22,least_upper_bound(X_23,X_13)),
    inference(subst,[],[refute_0_37:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X_13))]]) ).

cnf(refute_0_85,plain,
    least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)) = least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)))]]) ).

cnf(refute_0_86,plain,
    ( least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)) != least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13))
    | least_upper_bound(least_upper_bound(X_22,X_23),X_13) != least_upper_bound(X_22,least_upper_bound(X_23,X_13))
    | least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)),least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13))) ),[1,1],$fot(least_upper_bound(X_22,least_upper_bound(X_23,X_13)))]]) ).

cnf(refute_0_87,plain,
    ( least_upper_bound(least_upper_bound(X_22,X_23),X_13) != least_upper_bound(X_22,least_upper_bound(X_23,X_13))
    | least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)),least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13))) )],[refute_0_85,refute_0_86]) ).

cnf(refute_0_88,plain,
    least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_23),X_13),least_upper_bound(X_22,least_upper_bound(X_23,X_13))) )],[refute_0_84,refute_0_87]) ).

cnf(refute_0_89,plain,
    least_upper_bound(X,least_upper_bound(X_22,X_23)) = least_upper_bound(least_upper_bound(X_22,X_23),X),
    inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_22,X_23)))]]) ).

cnf(refute_0_90,plain,
    least_upper_bound(X_22,least_upper_bound(X_23,X)) = least_upper_bound(least_upper_bound(X_22,X_23),X),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X))]]) ).

cnf(refute_0_91,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_23,X)) != least_upper_bound(least_upper_bound(X_22,X_23),X)
    | least_upper_bound(least_upper_bound(X_22,X_23),X) = least_upper_bound(X_22,least_upper_bound(X_23,X)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(X_23,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_22,X_23),X)))]]) ).

cnf(refute_0_92,plain,
    least_upper_bound(least_upper_bound(X_22,X_23),X) = least_upper_bound(X_22,least_upper_bound(X_23,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,X)),least_upper_bound(least_upper_bound(X_22,X_23),X)) )],[refute_0_90,refute_0_91]) ).

cnf(refute_0_93,plain,
    ( least_upper_bound(X,least_upper_bound(X_22,X_23)) != least_upper_bound(least_upper_bound(X_22,X_23),X)
    | least_upper_bound(least_upper_bound(X_22,X_23),X) != least_upper_bound(X_22,least_upper_bound(X_23,X))
    | least_upper_bound(X,least_upper_bound(X_22,X_23)) = least_upper_bound(X_22,least_upper_bound(X_23,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_22,X_23)),least_upper_bound(X_22,least_upper_bound(X_23,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_22,X_23),X))]]) ).

cnf(refute_0_94,plain,
    ( least_upper_bound(X,least_upper_bound(X_22,X_23)) != least_upper_bound(least_upper_bound(X_22,X_23),X)
    | least_upper_bound(X,least_upper_bound(X_22,X_23)) = least_upper_bound(X_22,least_upper_bound(X_23,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_23),X),least_upper_bound(X_22,least_upper_bound(X_23,X))) )],[refute_0_92,refute_0_93]) ).

cnf(refute_0_95,plain,
    least_upper_bound(X,least_upper_bound(X_22,X_23)) = least_upper_bound(X_22,least_upper_bound(X_23,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_22,X_23)),least_upper_bound(least_upper_bound(X_22,X_23),X)) )],[refute_0_89,refute_0_94]) ).

cnf(refute_0_96,plain,
    ( least_upper_bound(X,least_upper_bound(X_22,X_23)) != least_upper_bound(X_22,least_upper_bound(X_23,X))
    | least_upper_bound(X_22,least_upper_bound(X_23,X)) = least_upper_bound(X,least_upper_bound(X_22,X_23)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_22,X_23)))),bind(Y0,$fot(least_upper_bound(X_22,least_upper_bound(X_23,X))))]]) ).

cnf(refute_0_97,plain,
    least_upper_bound(X_22,least_upper_bound(X_23,X)) = least_upper_bound(X,least_upper_bound(X_22,X_23)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_22,X_23)),least_upper_bound(X_22,least_upper_bound(X_23,X))) )],[refute_0_95,refute_0_96]) ).

cnf(refute_0_98,plain,
    least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)) = least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)),
    inference(subst,[],[refute_0_97:[bind(X,$fot(X_23)),bind(X_22,$fot(least_upper_bound(X_22,X_23))),bind(X_23,$fot(X_13))]]) ).

cnf(refute_0_99,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_100,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_6,refute_0_99]) ).

cnf(refute_0_101,plain,
    ( least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)) != least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13)))
    | least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)) != least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13))
    | least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13))) ),
    inference(subst,[],[refute_0_100:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)))),bind(Y0,$fot(least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)))),bind(Z0,$fot(least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13)))))]]) ).

cnf(refute_0_102,plain,
    ( least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)) != least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13)))
    | least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)),least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13))) )],[refute_0_98,refute_0_101]) ).

cnf(refute_0_103,plain,
    least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_23,least_upper_bound(least_upper_bound(X_22,X_23),X_13)),least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13)))) )],[refute_0_88,refute_0_102]) ).

cnf(refute_0_104,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_23,X_13)) != least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23))
    | least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)) != least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13)))
    | least_upper_bound(X_22,least_upper_bound(X_23,X_13)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_22,least_upper_bound(X_23,X_13)),least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)))]]) ).

cnf(refute_0_105,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_23,X_13)) != least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23))
    | least_upper_bound(X_22,least_upper_bound(X_23,X_13)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23)),least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13)))) )],[refute_0_103,refute_0_104]) ).

cnf(refute_0_106,plain,
    least_upper_bound(X_22,least_upper_bound(X_23,X_13)) = least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,X_13)),least_upper_bound(least_upper_bound(X_22,X_23),least_upper_bound(X_13,X_23))) )],[refute_0_83,refute_0_105]) ).

cnf(refute_0_107,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_23,X_13)) != least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13)))
    | least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13))) = least_upper_bound(X_22,least_upper_bound(X_23,X_13)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(X_23,X_13)))),bind(Y0,$fot(least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13)))))]]) ).

cnf(refute_0_108,plain,
    least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13))) = least_upper_bound(X_22,least_upper_bound(X_23,X_13)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_23,X_13)),least_upper_bound(X_23,least_upper_bound(X_22,least_upper_bound(X_23,X_13)))) )],[refute_0_106,refute_0_107]) ).

cnf(refute_0_109,plain,
    least_upper_bound(X_22,least_upper_bound(X_13,least_upper_bound(X_22,X_24))) = least_upper_bound(X_13,least_upper_bound(X_22,X_24)),
    inference(subst,[],[refute_0_108:[bind(X_13,$fot(X_24)),bind(X_22,$fot(X_13)),bind(X_23,$fot(X_22))]]) ).

cnf(refute_0_110,plain,
    least_upper_bound(least_upper_bound(X_13,X_22),X_24) = least_upper_bound(X_13,least_upper_bound(X_22,X_24)),
    inference(subst,[],[refute_0_37:[bind(X,$fot(X_13)),bind(Y,$fot(X_22)),bind(Z,$fot(X_24))]]) ).

cnf(refute_0_111,plain,
    least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) = least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)))]]) ).

cnf(refute_0_112,plain,
    ( least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) != least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24))
    | least_upper_bound(least_upper_bound(X_13,X_22),X_24) != least_upper_bound(X_13,least_upper_bound(X_22,X_24))
    | least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) = least_upper_bound(X_22,least_upper_bound(X_13,least_upper_bound(X_22,X_24))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)),least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24))) ),[1,1],$fot(least_upper_bound(X_13,least_upper_bound(X_22,X_24)))]]) ).

cnf(refute_0_113,plain,
    ( least_upper_bound(least_upper_bound(X_13,X_22),X_24) != least_upper_bound(X_13,least_upper_bound(X_22,X_24))
    | least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) = least_upper_bound(X_22,least_upper_bound(X_13,least_upper_bound(X_22,X_24))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)),least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24))) )],[refute_0_111,refute_0_112]) ).

cnf(refute_0_114,plain,
    least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) = least_upper_bound(X_22,least_upper_bound(X_13,least_upper_bound(X_22,X_24))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,X_22),X_24),least_upper_bound(X_13,least_upper_bound(X_22,X_24))) )],[refute_0_110,refute_0_113]) ).

cnf(refute_0_115,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_13,least_upper_bound(X_22,X_24))) != least_upper_bound(X_13,least_upper_bound(X_22,X_24))
    | least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) != least_upper_bound(X_22,least_upper_bound(X_13,least_upper_bound(X_22,X_24)))
    | least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) = least_upper_bound(X_13,least_upper_bound(X_22,X_24)) ),
    inference(subst,[],[refute_0_100:[bind(X0,$fot(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)))),bind(Y0,$fot(least_upper_bound(X_22,least_upper_bound(X_13,least_upper_bound(X_22,X_24))))),bind(Z0,$fot(least_upper_bound(X_13,least_upper_bound(X_22,X_24))))]]) ).

cnf(refute_0_116,plain,
    ( least_upper_bound(X_22,least_upper_bound(X_13,least_upper_bound(X_22,X_24))) != least_upper_bound(X_13,least_upper_bound(X_22,X_24))
    | least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) = least_upper_bound(X_13,least_upper_bound(X_22,X_24)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)),least_upper_bound(X_22,least_upper_bound(X_13,least_upper_bound(X_22,X_24)))) )],[refute_0_114,refute_0_115]) ).

cnf(refute_0_117,plain,
    least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) = least_upper_bound(X_13,least_upper_bound(X_22,X_24)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(X_13,least_upper_bound(X_22,X_24))),least_upper_bound(X_13,least_upper_bound(X_22,X_24))) )],[refute_0_109,refute_0_116]) ).

cnf(refute_0_118,plain,
    ( least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) != least_upper_bound(X_13,least_upper_bound(X_22,X_24))
    | least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) != least_upper_bound(least_upper_bound(X_22,X_13),X_24)
    | least_upper_bound(X_13,least_upper_bound(X_22,X_24)) = least_upper_bound(least_upper_bound(X_22,X_13),X_24) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)),least_upper_bound(least_upper_bound(X_22,X_13),X_24)) ),[0],$fot(least_upper_bound(X_13,least_upper_bound(X_22,X_24)))]]) ).

cnf(refute_0_119,plain,
    ( least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) != least_upper_bound(least_upper_bound(X_22,X_13),X_24)
    | least_upper_bound(X_13,least_upper_bound(X_22,X_24)) = least_upper_bound(least_upper_bound(X_22,X_13),X_24) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)),least_upper_bound(X_13,least_upper_bound(X_22,X_24))) )],[refute_0_117,refute_0_118]) ).

cnf(refute_0_120,plain,
    least_upper_bound(least_upper_bound(X_22,X_13),X_24) = least_upper_bound(X_22,least_upper_bound(X_13,X_24)),
    inference(subst,[],[refute_0_37:[bind(X,$fot(X_22)),bind(Y,$fot(X_13)),bind(Z,$fot(X_24))]]) ).

cnf(refute_0_121,plain,
    ( least_upper_bound(X_13,least_upper_bound(X_22,X_24)) != least_upper_bound(least_upper_bound(X_22,X_13),X_24)
    | least_upper_bound(least_upper_bound(X_22,X_13),X_24) != least_upper_bound(X_22,least_upper_bound(X_13,X_24))
    | least_upper_bound(X_13,least_upper_bound(X_22,X_24)) = least_upper_bound(X_22,least_upper_bound(X_13,X_24)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_13,least_upper_bound(X_22,X_24)),least_upper_bound(X_22,least_upper_bound(X_13,X_24))) ),[0],$fot(least_upper_bound(least_upper_bound(X_22,X_13),X_24))]]) ).

cnf(refute_0_122,plain,
    ( least_upper_bound(X_13,least_upper_bound(X_22,X_24)) != least_upper_bound(least_upper_bound(X_22,X_13),X_24)
    | least_upper_bound(X_13,least_upper_bound(X_22,X_24)) = least_upper_bound(X_22,least_upper_bound(X_13,X_24)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_22,X_13),X_24),least_upper_bound(X_22,least_upper_bound(X_13,X_24))) )],[refute_0_120,refute_0_121]) ).

cnf(refute_0_123,plain,
    ( least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)) != least_upper_bound(least_upper_bound(X_22,X_13),X_24)
    | least_upper_bound(X_13,least_upper_bound(X_22,X_24)) = least_upper_bound(X_22,least_upper_bound(X_13,X_24)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(X_22,X_24)),least_upper_bound(least_upper_bound(X_22,X_13),X_24)) )],[refute_0_119,refute_0_122]) ).

cnf(refute_0_124,plain,
    least_upper_bound(X_13,least_upper_bound(X_22,X_24)) = least_upper_bound(X_22,least_upper_bound(X_13,X_24)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_22,least_upper_bound(least_upper_bound(X_13,X_22),X_24)),least_upper_bound(least_upper_bound(X_22,X_13),X_24)) )],[refute_0_78,refute_0_123]) ).

cnf(refute_0_125,plain,
    ( least_upper_bound(X_13,least_upper_bound(X_22,X_24)) != least_upper_bound(X_22,least_upper_bound(X_13,X_24))
    | least_upper_bound(X_22,least_upper_bound(X_13,X_24)) = least_upper_bound(X_13,least_upper_bound(X_22,X_24)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_13,least_upper_bound(X_22,X_24)))),bind(Y0,$fot(least_upper_bound(X_22,least_upper_bound(X_13,X_24))))]]) ).

cnf(refute_0_126,plain,
    least_upper_bound(X_22,least_upper_bound(X_13,X_24)) = least_upper_bound(X_13,least_upper_bound(X_22,X_24)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(X_22,X_24)),least_upper_bound(X_22,least_upper_bound(X_13,X_24))) )],[refute_0_124,refute_0_125]) ).

cnf(refute_0_127,plain,
    least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) = least_upper_bound(identity,least_upper_bound(least_upper_bound(inverse(a),X_27),X_27)),
    inference(subst,[],[refute_0_126:[bind(X_13,$fot(identity)),bind(X_22,$fot(least_upper_bound(inverse(a),X_27))),bind(X_24,$fot(X_27))]]) ).

cnf(refute_0_128,plain,
    ( least_upper_bound(identity,least_upper_bound(least_upper_bound(inverse(a),X_27),X_27)) != least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)))
    | least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) != least_upper_bound(identity,least_upper_bound(least_upper_bound(inverse(a),X_27),X_27))
    | least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) = least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))) ),
    inference(subst,[],[refute_0_100:[bind(X0,$fot(least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(inverse(a),X_27),X_27)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)))))]]) ).

cnf(refute_0_129,plain,
    ( least_upper_bound(identity,least_upper_bound(least_upper_bound(inverse(a),X_27),X_27)) != least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)))
    | least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) = least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)),least_upper_bound(identity,least_upper_bound(least_upper_bound(inverse(a),X_27),X_27))) )],[refute_0_127,refute_0_128]) ).

cnf(refute_0_130,plain,
    least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) = least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(inverse(a),X_27),X_27)),least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)))) )],[refute_0_73,refute_0_129]) ).

cnf(refute_0_131,plain,
    ( least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))) != least_upper_bound(identity,least_upper_bound(X_27,inverse(a)))
    | least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) != least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)))
    | least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) = least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) ),
    inference(subst,[],[refute_0_100:[bind(X0,$fot(least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_27,inverse(a)))))]]) ).

cnf(refute_0_132,plain,
    ( least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))) != least_upper_bound(identity,least_upper_bound(X_27,inverse(a)))
    | least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) = least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)),least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27)))) )],[refute_0_130,refute_0_131]) ).

cnf(refute_0_133,plain,
    least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) = least_upper_bound(identity,least_upper_bound(X_27,inverse(a))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_27,least_upper_bound(inverse(a),X_27))),least_upper_bound(identity,least_upper_bound(X_27,inverse(a)))) )],[refute_0_59,refute_0_132]) ).

cnf(refute_0_134,plain,
    ( least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) != least_upper_bound(identity,least_upper_bound(X_27,inverse(a)))
    | least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) != least_upper_bound(least_upper_bound(inverse(a),X_27),identity)
    | least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) = least_upper_bound(least_upper_bound(inverse(a),X_27),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)),least_upper_bound(least_upper_bound(inverse(a),X_27),identity)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_27,inverse(a))))]]) ).

cnf(refute_0_135,plain,
    ( least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) != least_upper_bound(least_upper_bound(inverse(a),X_27),identity)
    | least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) = least_upper_bound(least_upper_bound(inverse(a),X_27),identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)),least_upper_bound(identity,least_upper_bound(X_27,inverse(a)))) )],[refute_0_133,refute_0_134]) ).

cnf(refute_0_136,plain,
    least_upper_bound(inverse(a),least_upper_bound(X_27,identity)) = least_upper_bound(identity,least_upper_bound(inverse(a),X_27)),
    inference(subst,[],[refute_0_97:[bind(X,$fot(identity)),bind(X_22,$fot(inverse(a))),bind(X_23,$fot(X_27))]]) ).

cnf(refute_0_137,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(a),X_27)) != least_upper_bound(identity,X_27)
    | least_upper_bound(inverse(a),least_upper_bound(X_27,identity)) != least_upper_bound(identity,least_upper_bound(inverse(a),X_27))
    | least_upper_bound(inverse(a),least_upper_bound(X_27,identity)) = least_upper_bound(identity,X_27) ),
    inference(subst,[],[refute_0_100:[bind(X0,$fot(least_upper_bound(inverse(a),least_upper_bound(X_27,identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(a),X_27)))),bind(Z0,$fot(least_upper_bound(identity,X_27)))]]) ).

cnf(refute_0_138,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(a),X_27)) != least_upper_bound(identity,X_27)
    | least_upper_bound(inverse(a),least_upper_bound(X_27,identity)) = least_upper_bound(identity,X_27) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),least_upper_bound(X_27,identity)),least_upper_bound(identity,least_upper_bound(inverse(a),X_27))) )],[refute_0_136,refute_0_137]) ).

cnf(refute_0_139,plain,
    least_upper_bound(inverse(a),least_upper_bound(X_27,identity)) = least_upper_bound(identity,X_27),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(a),X_27)),least_upper_bound(identity,X_27)) )],[refute_0_51,refute_0_138]) ).

cnf(refute_0_140,plain,
    least_upper_bound(least_upper_bound(inverse(a),X_27),identity) = least_upper_bound(inverse(a),least_upper_bound(X_27,identity)),
    inference(subst,[],[refute_0_37:[bind(X,$fot(inverse(a))),bind(Y,$fot(X_27)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_141,plain,
    ( least_upper_bound(inverse(a),least_upper_bound(X_27,identity)) != least_upper_bound(identity,X_27)
    | least_upper_bound(least_upper_bound(inverse(a),X_27),identity) != least_upper_bound(inverse(a),least_upper_bound(X_27,identity))
    | least_upper_bound(least_upper_bound(inverse(a),X_27),identity) = least_upper_bound(identity,X_27) ),
    inference(subst,[],[refute_0_100:[bind(X0,$fot(least_upper_bound(least_upper_bound(inverse(a),X_27),identity))),bind(Y0,$fot(least_upper_bound(inverse(a),least_upper_bound(X_27,identity)))),bind(Z0,$fot(least_upper_bound(identity,X_27)))]]) ).

cnf(refute_0_142,plain,
    ( least_upper_bound(inverse(a),least_upper_bound(X_27,identity)) != least_upper_bound(identity,X_27)
    | least_upper_bound(least_upper_bound(inverse(a),X_27),identity) = least_upper_bound(identity,X_27) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(a),X_27),identity),least_upper_bound(inverse(a),least_upper_bound(X_27,identity))) )],[refute_0_140,refute_0_141]) ).

cnf(refute_0_143,plain,
    least_upper_bound(least_upper_bound(inverse(a),X_27),identity) = least_upper_bound(identity,X_27),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),least_upper_bound(X_27,identity)),least_upper_bound(identity,X_27)) )],[refute_0_139,refute_0_142]) ).

cnf(refute_0_144,plain,
    ( least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) != least_upper_bound(least_upper_bound(inverse(a),X_27),identity)
    | least_upper_bound(least_upper_bound(inverse(a),X_27),identity) != least_upper_bound(identity,X_27)
    | least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) = least_upper_bound(identity,X_27) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,least_upper_bound(X_27,inverse(a))),least_upper_bound(identity,X_27)) ),[0],$fot(least_upper_bound(least_upper_bound(inverse(a),X_27),identity))]]) ).

cnf(refute_0_145,plain,
    ( least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) != least_upper_bound(least_upper_bound(inverse(a),X_27),identity)
    | least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) = least_upper_bound(identity,X_27) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(a),X_27),identity),least_upper_bound(identity,X_27)) )],[refute_0_143,refute_0_144]) ).

cnf(refute_0_146,plain,
    ( least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)) != least_upper_bound(least_upper_bound(inverse(a),X_27),identity)
    | least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) = least_upper_bound(identity,X_27) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_27,inverse(a))),least_upper_bound(least_upper_bound(inverse(a),X_27),identity)) )],[refute_0_135,refute_0_145]) ).

cnf(refute_0_147,plain,
    least_upper_bound(identity,least_upper_bound(X_27,inverse(a))) = least_upper_bound(identity,X_27),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(a),X_27),least_upper_bound(identity,X_27)),least_upper_bound(least_upper_bound(inverse(a),X_27),identity)) )],[refute_0_54,refute_0_146]) ).

cnf(refute_0_148,plain,
    least_upper_bound(identity,least_upper_bound(X_32,inverse(a))) = least_upper_bound(identity,X_32),
    inference(subst,[],[refute_0_147:[bind(X_27,$fot(X_32))]]) ).

cnf(refute_0_149,plain,
    ( greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,least_upper_bound(X_32,inverse(a)))) != least_upper_bound(X_32,inverse(a))
    | least_upper_bound(identity,least_upper_bound(X_32,inverse(a))) != least_upper_bound(identity,X_32)
    | greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,X_32)) = least_upper_bound(X_32,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,least_upper_bound(X_32,inverse(a)))),least_upper_bound(X_32,inverse(a))) ),[0,1],$fot(least_upper_bound(identity,X_32))]]) ).

cnf(refute_0_150,plain,
    ( greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,least_upper_bound(X_32,inverse(a)))) != least_upper_bound(X_32,inverse(a))
    | greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,X_32)) = least_upper_bound(X_32,inverse(a)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_32,inverse(a))),least_upper_bound(identity,X_32)) )],[refute_0_148,refute_0_149]) ).

cnf(refute_0_151,plain,
    greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,X_32)) = least_upper_bound(X_32,inverse(a)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,least_upper_bound(X_32,inverse(a)))),least_upper_bound(X_32,inverse(a))) )],[refute_0_30,refute_0_150]) ).

cnf(refute_0_152,plain,
    greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,X_32)) = greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))),
    inference(subst,[],[refute_0_8:[bind(X,$fot(least_upper_bound(identity,X_32))),bind(Y,$fot(least_upper_bound(X_32,inverse(a))))]]) ).

cnf(refute_0_153,plain,
    ( greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,X_32)) != greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a)))
    | greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,X_32)) != least_upper_bound(X_32,inverse(a))
    | greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) = least_upper_bound(X_32,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,X_32)),least_upper_bound(X_32,inverse(a))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))))]]) ).

cnf(refute_0_154,plain,
    ( greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,X_32)) != least_upper_bound(X_32,inverse(a))
    | greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) = least_upper_bound(X_32,inverse(a)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,X_32)),greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a)))) )],[refute_0_152,refute_0_153]) ).

cnf(refute_0_155,plain,
    greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) = least_upper_bound(X_32,inverse(a)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_32,inverse(a)),least_upper_bound(identity,X_32)),least_upper_bound(X_32,inverse(a))) )],[refute_0_151,refute_0_154]) ).

cnf(refute_0_156,plain,
    greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,least_upper_bound(X_13,X_17))) = least_upper_bound(X_13,X_17),
    inference(subst,[],[refute_0_29:[bind(X_12,$fot(least_upper_bound(X_13,X_17))),bind(X_13,$fot(X_17))]]) ).

cnf(refute_0_157,plain,
    least_upper_bound(X_17,least_upper_bound(X_13,X_17)) = least_upper_bound(X_17,X_13),
    inference(subst,[],[refute_0_41:[bind(Y,$fot(X_17))]]) ).

cnf(refute_0_158,plain,
    ( greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,least_upper_bound(X_13,X_17))) != least_upper_bound(X_13,X_17)
    | least_upper_bound(X_17,least_upper_bound(X_13,X_17)) != least_upper_bound(X_17,X_13)
    | greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,X_13)) = least_upper_bound(X_13,X_17) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,least_upper_bound(X_13,X_17))),least_upper_bound(X_13,X_17)) ),[0,1],$fot(least_upper_bound(X_17,X_13))]]) ).

cnf(refute_0_159,plain,
    ( greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,least_upper_bound(X_13,X_17))) != least_upper_bound(X_13,X_17)
    | greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,X_13)) = least_upper_bound(X_13,X_17) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_17,least_upper_bound(X_13,X_17)),least_upper_bound(X_17,X_13)) )],[refute_0_157,refute_0_158]) ).

cnf(refute_0_160,plain,
    greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,X_13)) = least_upper_bound(X_13,X_17),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,least_upper_bound(X_13,X_17))),least_upper_bound(X_13,X_17)) )],[refute_0_156,refute_0_159]) ).

cnf(refute_0_161,plain,
    greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity)) = least_upper_bound(identity,X_32),
    inference(subst,[],[refute_0_160:[bind(X_13,$fot(identity)),bind(X_17,$fot(X_32))]]) ).

cnf(refute_0_162,plain,
    multiply(X_83,least_upper_bound(X_84,identity)) = least_upper_bound(multiply(X_83,X_84),multiply(X_83,identity)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_83)),bind(Y,$fot(X_84)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_163,plain,
    multiply(multiply(inverse(X_45),X_45),X_46) = multiply(inverse(X_45),multiply(X_45,X_46)),
    inference(subst,[],[associativity:[bind(X,$fot(inverse(X_45))),bind(Y,$fot(X_45)),bind(Z,$fot(X_46))]]) ).

cnf(refute_0_164,plain,
    multiply(inverse(X_45),X_45) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_45))]]) ).

cnf(refute_0_165,plain,
    ( multiply(multiply(inverse(X_45),X_45),X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
    | multiply(inverse(X_45),X_45) != identity
    | multiply(identity,X_46) = multiply(inverse(X_45),multiply(X_45,X_46)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_45),X_45),X_46),multiply(inverse(X_45),multiply(X_45,X_46))) ),[0,0],$fot(identity)]]) ).

cnf(refute_0_166,plain,
    ( multiply(multiply(inverse(X_45),X_45),X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
    | multiply(identity,X_46) = multiply(inverse(X_45),multiply(X_45,X_46)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_45),X_45),identity) )],[refute_0_164,refute_0_165]) ).

cnf(refute_0_167,plain,
    multiply(identity,X_46) = multiply(inverse(X_45),multiply(X_45,X_46)),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_45),X_45),X_46),multiply(inverse(X_45),multiply(X_45,X_46))) )],[refute_0_163,refute_0_166]) ).

cnf(refute_0_168,plain,
    multiply(identity,X_46) = X_46,
    inference(subst,[],[left_identity:[bind(X,$fot(X_46))]]) ).

cnf(refute_0_169,plain,
    ( multiply(identity,X_46) != X_46
    | multiply(identity,X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
    | X_46 = multiply(inverse(X_45),multiply(X_45,X_46)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_46),multiply(inverse(X_45),multiply(X_45,X_46))) ),[0],$fot(X_46)]]) ).

cnf(refute_0_170,plain,
    ( multiply(identity,X_46) != multiply(inverse(X_45),multiply(X_45,X_46))
    | X_46 = multiply(inverse(X_45),multiply(X_45,X_46)) ),
    inference(resolve,[$cnf( $equal(multiply(identity,X_46),X_46) )],[refute_0_168,refute_0_169]) ).

cnf(refute_0_171,plain,
    X_46 = multiply(inverse(X_45),multiply(X_45,X_46)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_46),multiply(inverse(X_45),multiply(X_45,X_46))) )],[refute_0_167,refute_0_170]) ).

cnf(refute_0_172,plain,
    X_48 = multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48)),
    inference(subst,[],[refute_0_171:[bind(X_45,$fot(inverse(X_48))),bind(X_46,$fot(X_48))]]) ).

cnf(refute_0_173,plain,
    multiply(inverse(X_48),X_48) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_48))]]) ).

cnf(refute_0_174,plain,
    ( X_48 != multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))
    | multiply(inverse(X_48),X_48) != identity
    | X_48 = multiply(inverse(inverse(X_48)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(X_48,multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_175,plain,
    ( X_48 != multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))
    | X_48 = multiply(inverse(inverse(X_48)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_48),X_48),identity) )],[refute_0_173,refute_0_174]) ).

cnf(refute_0_176,plain,
    X_48 = multiply(inverse(inverse(X_48)),identity),
    inference(resolve,[$cnf( $equal(X_48,multiply(inverse(inverse(X_48)),multiply(inverse(X_48),X_48))) )],[refute_0_172,refute_0_175]) ).

cnf(refute_0_177,plain,
    multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48))),
    inference(subst,[],[refute_0_171:[bind(X_45,$fot(inverse(X_47))),bind(X_46,$fot(multiply(X_47,X_48)))]]) ).

cnf(refute_0_178,plain,
    X_48 = multiply(inverse(X_47),multiply(X_47,X_48)),
    inference(subst,[],[refute_0_171:[bind(X_45,$fot(X_47)),bind(X_46,$fot(X_48))]]) ).

cnf(refute_0_179,plain,
    ( X_48 != multiply(inverse(X_47),multiply(X_47,X_48))
    | multiply(inverse(X_47),multiply(X_47,X_48)) = X_48 ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(X_48)),bind(Y0,$fot(multiply(inverse(X_47),multiply(X_47,X_48))))]]) ).

cnf(refute_0_180,plain,
    multiply(inverse(X_47),multiply(X_47,X_48)) = X_48,
    inference(resolve,[$cnf( $equal(X_48,multiply(inverse(X_47),multiply(X_47,X_48))) )],[refute_0_178,refute_0_179]) ).

cnf(refute_0_181,plain,
    ( multiply(X_47,X_48) != multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))
    | multiply(inverse(X_47),multiply(X_47,X_48)) != X_48
    | multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),X_48) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_47,X_48),multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))) ),[1,1],$fot(X_48)]]) ).

cnf(refute_0_182,plain,
    ( multiply(X_47,X_48) != multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))
    | multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),X_48) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_47),multiply(X_47,X_48)),X_48) )],[refute_0_180,refute_0_181]) ).

cnf(refute_0_183,plain,
    multiply(X_47,X_48) = multiply(inverse(inverse(X_47)),X_48),
    inference(resolve,[$cnf( $equal(multiply(X_47,X_48),multiply(inverse(inverse(X_47)),multiply(inverse(X_47),multiply(X_47,X_48)))) )],[refute_0_177,refute_0_182]) ).

cnf(refute_0_184,plain,
    ( multiply(X_47,X_48) != multiply(inverse(inverse(X_47)),X_48)
    | multiply(inverse(inverse(X_47)),X_48) = multiply(X_47,X_48) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(X_47,X_48))),bind(Y0,$fot(multiply(inverse(inverse(X_47)),X_48)))]]) ).

cnf(refute_0_185,plain,
    multiply(inverse(inverse(X_47)),X_48) = multiply(X_47,X_48),
    inference(resolve,[$cnf( $equal(multiply(X_47,X_48),multiply(inverse(inverse(X_47)),X_48)) )],[refute_0_183,refute_0_184]) ).

cnf(refute_0_186,plain,
    multiply(inverse(inverse(X_48)),identity) = multiply(X_48,identity),
    inference(subst,[],[refute_0_185:[bind(X_47,$fot(X_48)),bind(X_48,$fot(identity))]]) ).

cnf(refute_0_187,plain,
    ( X_48 != multiply(inverse(inverse(X_48)),identity)
    | multiply(inverse(inverse(X_48)),identity) != multiply(X_48,identity)
    | X_48 = multiply(X_48,identity) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_48,multiply(X_48,identity)) ),[0],$fot(multiply(inverse(inverse(X_48)),identity))]]) ).

cnf(refute_0_188,plain,
    ( X_48 != multiply(inverse(inverse(X_48)),identity)
    | X_48 = multiply(X_48,identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_48)),identity),multiply(X_48,identity)) )],[refute_0_186,refute_0_187]) ).

cnf(refute_0_189,plain,
    X_48 = multiply(X_48,identity),
    inference(resolve,[$cnf( $equal(X_48,multiply(inverse(inverse(X_48)),identity)) )],[refute_0_176,refute_0_188]) ).

cnf(refute_0_190,plain,
    X_83 = multiply(X_83,identity),
    inference(subst,[],[refute_0_189:[bind(X_48,$fot(X_83))]]) ).

cnf(refute_0_191,plain,
    ( X_83 != multiply(X_83,identity)
    | multiply(X_83,identity) = X_83 ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(X_83)),bind(Y0,$fot(multiply(X_83,identity)))]]) ).

cnf(refute_0_192,plain,
    multiply(X_83,identity) = X_83,
    inference(resolve,[$cnf( $equal(X_83,multiply(X_83,identity)) )],[refute_0_190,refute_0_191]) ).

cnf(refute_0_193,plain,
    ( multiply(X_83,identity) != X_83
    | multiply(X_83,least_upper_bound(X_84,identity)) != least_upper_bound(multiply(X_83,X_84),multiply(X_83,identity))
    | multiply(X_83,least_upper_bound(X_84,identity)) = least_upper_bound(multiply(X_83,X_84),X_83) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_83,least_upper_bound(X_84,identity)),least_upper_bound(multiply(X_83,X_84),multiply(X_83,identity))) ),[1,1],$fot(X_83)]]) ).

cnf(refute_0_194,plain,
    ( multiply(X_83,least_upper_bound(X_84,identity)) != least_upper_bound(multiply(X_83,X_84),multiply(X_83,identity))
    | multiply(X_83,least_upper_bound(X_84,identity)) = least_upper_bound(multiply(X_83,X_84),X_83) ),
    inference(resolve,[$cnf( $equal(multiply(X_83,identity),X_83) )],[refute_0_192,refute_0_193]) ).

cnf(refute_0_195,plain,
    multiply(X_83,least_upper_bound(X_84,identity)) = least_upper_bound(multiply(X_83,X_84),X_83),
    inference(resolve,[$cnf( $equal(multiply(X_83,least_upper_bound(X_84,identity)),least_upper_bound(multiply(X_83,X_84),multiply(X_83,identity))) )],[refute_0_162,refute_0_194]) ).

cnf(refute_0_196,plain,
    least_upper_bound(multiply(X_83,X_84),X_83) = least_upper_bound(X_83,multiply(X_83,X_84)),
    inference(subst,[],[refute_0_17:[bind(X,$fot(X_83)),bind(Y,$fot(multiply(X_83,X_84)))]]) ).

cnf(refute_0_197,plain,
    ( multiply(X_83,least_upper_bound(X_84,identity)) != least_upper_bound(multiply(X_83,X_84),X_83)
    | least_upper_bound(multiply(X_83,X_84),X_83) != least_upper_bound(X_83,multiply(X_83,X_84))
    | multiply(X_83,least_upper_bound(X_84,identity)) = least_upper_bound(X_83,multiply(X_83,X_84)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_83,least_upper_bound(X_84,identity)),least_upper_bound(X_83,multiply(X_83,X_84))) ),[0],$fot(least_upper_bound(multiply(X_83,X_84),X_83))]]) ).

cnf(refute_0_198,plain,
    ( multiply(X_83,least_upper_bound(X_84,identity)) != least_upper_bound(multiply(X_83,X_84),X_83)
    | multiply(X_83,least_upper_bound(X_84,identity)) = least_upper_bound(X_83,multiply(X_83,X_84)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_83,X_84),X_83),least_upper_bound(X_83,multiply(X_83,X_84))) )],[refute_0_196,refute_0_197]) ).

cnf(refute_0_199,plain,
    multiply(X_83,least_upper_bound(X_84,identity)) = least_upper_bound(X_83,multiply(X_83,X_84)),
    inference(resolve,[$cnf( $equal(multiply(X_83,least_upper_bound(X_84,identity)),least_upper_bound(multiply(X_83,X_84),X_83)) )],[refute_0_195,refute_0_198]) ).

cnf(refute_0_200,plain,
    multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(inverse(X_87),multiply(inverse(X_87),X_87)),
    inference(subst,[],[refute_0_199:[bind(X_83,$fot(inverse(X_87))),bind(X_84,$fot(X_87))]]) ).

cnf(refute_0_201,plain,
    multiply(inverse(X_87),X_87) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_87))]]) ).

cnf(refute_0_202,plain,
    ( multiply(inverse(X_87),X_87) != identity
    | multiply(inverse(X_87),least_upper_bound(X_87,identity)) != least_upper_bound(inverse(X_87),multiply(inverse(X_87),X_87))
    | multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(inverse(X_87),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_87),least_upper_bound(X_87,identity)),least_upper_bound(inverse(X_87),multiply(inverse(X_87),X_87))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_203,plain,
    ( multiply(inverse(X_87),least_upper_bound(X_87,identity)) != least_upper_bound(inverse(X_87),multiply(inverse(X_87),X_87))
    | multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(inverse(X_87),identity) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_87),X_87),identity) )],[refute_0_201,refute_0_202]) ).

cnf(refute_0_204,plain,
    multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(inverse(X_87),identity),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_87),least_upper_bound(X_87,identity)),least_upper_bound(inverse(X_87),multiply(inverse(X_87),X_87))) )],[refute_0_200,refute_0_203]) ).

cnf(refute_0_205,plain,
    least_upper_bound(inverse(X_87),identity) = least_upper_bound(identity,inverse(X_87)),
    inference(subst,[],[refute_0_17:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_87)))]]) ).

cnf(refute_0_206,plain,
    ( multiply(inverse(X_87),least_upper_bound(X_87,identity)) != least_upper_bound(inverse(X_87),identity)
    | least_upper_bound(inverse(X_87),identity) != least_upper_bound(identity,inverse(X_87))
    | multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(identity,inverse(X_87)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_87),least_upper_bound(X_87,identity)),least_upper_bound(identity,inverse(X_87))) ),[0],$fot(least_upper_bound(inverse(X_87),identity))]]) ).

cnf(refute_0_207,plain,
    ( multiply(inverse(X_87),least_upper_bound(X_87,identity)) != least_upper_bound(inverse(X_87),identity)
    | multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(identity,inverse(X_87)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_87),identity),least_upper_bound(identity,inverse(X_87))) )],[refute_0_205,refute_0_206]) ).

cnf(refute_0_208,plain,
    multiply(inverse(X_87),least_upper_bound(X_87,identity)) = least_upper_bound(identity,inverse(X_87)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_87),least_upper_bound(X_87,identity)),least_upper_bound(inverse(X_87),identity)) )],[refute_0_204,refute_0_207]) ).

cnf(refute_0_209,plain,
    multiply(inverse(a),least_upper_bound(a,identity)) = least_upper_bound(identity,inverse(a)),
    inference(subst,[],[refute_0_208:[bind(X_87,$fot(a))]]) ).

cnf(refute_0_210,plain,
    ( multiply(inverse(a),least_upper_bound(a,identity)) != least_upper_bound(identity,inverse(a))
    | least_upper_bound(a,identity) != identity
    | multiply(inverse(a),identity) = least_upper_bound(identity,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,identity)),least_upper_bound(identity,inverse(a))) ),[0,1],$fot(identity)]]) ).

cnf(refute_0_211,plain,
    ( multiply(inverse(a),least_upper_bound(a,identity)) != least_upper_bound(identity,inverse(a))
    | multiply(inverse(a),identity) = least_upper_bound(identity,inverse(a)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),identity) )],[refute_0_21,refute_0_210]) ).

cnf(refute_0_212,plain,
    multiply(inverse(a),identity) = least_upper_bound(identity,inverse(a)),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,identity)),least_upper_bound(identity,inverse(a))) )],[refute_0_209,refute_0_211]) ).

cnf(refute_0_213,plain,
    ( X_48 != multiply(X_48,identity)
    | multiply(X_48,identity) = X_48 ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(X_48)),bind(Y0,$fot(multiply(X_48,identity)))]]) ).

cnf(refute_0_214,plain,
    multiply(X_48,identity) = X_48,
    inference(resolve,[$cnf( $equal(X_48,multiply(X_48,identity)) )],[refute_0_189,refute_0_213]) ).

cnf(refute_0_215,plain,
    multiply(inverse(a),identity) = inverse(a),
    inference(subst,[],[refute_0_214:[bind(X_48,$fot(inverse(a)))]]) ).

cnf(refute_0_216,plain,
    ( multiply(inverse(a),identity) != inverse(a)
    | multiply(inverse(a),identity) != least_upper_bound(identity,inverse(a))
    | inverse(a) = least_upper_bound(identity,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),identity),least_upper_bound(identity,inverse(a))) ),[0],$fot(inverse(a))]]) ).

cnf(refute_0_217,plain,
    ( multiply(inverse(a),identity) != least_upper_bound(identity,inverse(a))
    | inverse(a) = least_upper_bound(identity,inverse(a)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),inverse(a)) )],[refute_0_215,refute_0_216]) ).

cnf(refute_0_218,plain,
    ( inverse(a) != least_upper_bound(identity,inverse(a))
    | least_upper_bound(identity,inverse(a)) != identity
    | inverse(a) = identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(a),identity) ),[0],$fot(least_upper_bound(identity,inverse(a)))]]) ).

cnf(refute_0_219,plain,
    ( inverse(a) != least_upper_bound(identity,inverse(a))
    | inverse(a) = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),identity) )],[refute_0_47,refute_0_218]) ).

cnf(refute_0_220,plain,
    ( multiply(inverse(a),identity) != least_upper_bound(identity,inverse(a))
    | inverse(a) = identity ),
    inference(resolve,[$cnf( $equal(inverse(a),least_upper_bound(identity,inverse(a))) )],[refute_0_217,refute_0_219]) ).

cnf(refute_0_221,plain,
    inverse(a) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),least_upper_bound(identity,inverse(a))) )],[refute_0_212,refute_0_220]) ).

cnf(refute_0_222,plain,
    least_upper_bound(X_32,inverse(a)) = least_upper_bound(X_32,inverse(a)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_32,inverse(a)))]]) ).

cnf(refute_0_223,plain,
    ( inverse(a) != identity
    | least_upper_bound(X_32,inverse(a)) != least_upper_bound(X_32,inverse(a))
    | least_upper_bound(X_32,inverse(a)) = least_upper_bound(X_32,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_32,inverse(a)),least_upper_bound(X_32,inverse(a))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_224,plain,
    ( inverse(a) != identity
    | least_upper_bound(X_32,inverse(a)) = least_upper_bound(X_32,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_32,inverse(a)),least_upper_bound(X_32,inverse(a))) )],[refute_0_222,refute_0_223]) ).

cnf(refute_0_225,plain,
    least_upper_bound(X_32,inverse(a)) = least_upper_bound(X_32,identity),
    inference(resolve,[$cnf( $equal(inverse(a),identity) )],[refute_0_221,refute_0_224]) ).

cnf(refute_0_226,plain,
    greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) = greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))))]]) ).

cnf(refute_0_227,plain,
    ( greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) != greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a)))
    | least_upper_bound(X_32,inverse(a)) != least_upper_bound(X_32,identity)
    | greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) = greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))),greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a)))) ),[1,1],$fot(least_upper_bound(X_32,identity))]]) ).

cnf(refute_0_228,plain,
    ( least_upper_bound(X_32,inverse(a)) != least_upper_bound(X_32,identity)
    | greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) = greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))),greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a)))) )],[refute_0_226,refute_0_227]) ).

cnf(refute_0_229,plain,
    greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) = greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_32,inverse(a)),least_upper_bound(X_32,identity)) )],[refute_0_225,refute_0_228]) ).

cnf(refute_0_230,plain,
    ( greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity)) != least_upper_bound(identity,X_32)
    | greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) != greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity))
    | greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) = least_upper_bound(identity,X_32) ),
    inference(subst,[],[refute_0_100:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity)))),bind(Z0,$fot(least_upper_bound(identity,X_32)))]]) ).

cnf(refute_0_231,plain,
    ( greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity)) != least_upper_bound(identity,X_32)
    | greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) = least_upper_bound(identity,X_32) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))),greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity))) )],[refute_0_229,refute_0_230]) ).

cnf(refute_0_232,plain,
    greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) = least_upper_bound(identity,X_32),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity)),least_upper_bound(identity,X_32)) )],[refute_0_161,refute_0_231]) ).

cnf(refute_0_233,plain,
    ( greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) != least_upper_bound(X_32,inverse(a))
    | greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) != least_upper_bound(identity,X_32)
    | least_upper_bound(identity,X_32) = least_upper_bound(X_32,inverse(a)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))),least_upper_bound(X_32,inverse(a))) ),[0],$fot(least_upper_bound(identity,X_32))]]) ).

cnf(refute_0_234,plain,
    ( greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) != least_upper_bound(X_32,inverse(a))
    | least_upper_bound(identity,X_32) = least_upper_bound(X_32,inverse(a)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))),least_upper_bound(identity,X_32)) )],[refute_0_232,refute_0_233]) ).

cnf(refute_0_235,plain,
    ( least_upper_bound(X_32,inverse(a)) != least_upper_bound(X_32,identity)
    | least_upper_bound(identity,X_32) != least_upper_bound(X_32,inverse(a))
    | least_upper_bound(identity,X_32) = least_upper_bound(X_32,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) ),[1],$fot(least_upper_bound(X_32,identity))]]) ).

cnf(refute_0_236,plain,
    ( least_upper_bound(identity,X_32) != least_upper_bound(X_32,inverse(a))
    | least_upper_bound(identity,X_32) = least_upper_bound(X_32,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_32,inverse(a)),least_upper_bound(X_32,identity)) )],[refute_0_225,refute_0_235]) ).

cnf(refute_0_237,plain,
    ( greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) != least_upper_bound(X_32,inverse(a))
    | least_upper_bound(identity,X_32) = least_upper_bound(X_32,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))) )],[refute_0_234,refute_0_236]) ).

cnf(refute_0_238,plain,
    least_upper_bound(identity,X_32) = least_upper_bound(X_32,identity),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_32),least_upper_bound(X_32,inverse(a))),least_upper_bound(X_32,inverse(a))) )],[refute_0_155,refute_0_237]) ).

cnf(refute_0_239,plain,
    least_upper_bound(identity,least_upper_bound(inverse(a),multiply(inverse(a),X_87))) = least_upper_bound(identity,multiply(inverse(a),X_87)),
    inference(subst,[],[refute_0_50:[bind(X_24,$fot(multiply(inverse(a),X_87)))]]) ).

cnf(refute_0_240,plain,
    multiply(inverse(a),least_upper_bound(X_87,identity)) = least_upper_bound(inverse(a),multiply(inverse(a),X_87)),
    inference(subst,[],[refute_0_199:[bind(X_83,$fot(inverse(a))),bind(X_84,$fot(X_87))]]) ).

cnf(refute_0_241,plain,
    ( multiply(inverse(a),least_upper_bound(X_87,identity)) != least_upper_bound(inverse(a),multiply(inverse(a),X_87))
    | least_upper_bound(inverse(a),multiply(inverse(a),X_87)) = multiply(inverse(a),least_upper_bound(X_87,identity)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(inverse(a),least_upper_bound(X_87,identity)))),bind(Y0,$fot(least_upper_bound(inverse(a),multiply(inverse(a),X_87))))]]) ).

cnf(refute_0_242,plain,
    least_upper_bound(inverse(a),multiply(inverse(a),X_87)) = multiply(inverse(a),least_upper_bound(X_87,identity)),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(X_87,identity)),least_upper_bound(inverse(a),multiply(inverse(a),X_87))) )],[refute_0_240,refute_0_241]) ).

cnf(refute_0_243,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(a),multiply(inverse(a),X_87))) != least_upper_bound(identity,multiply(inverse(a),X_87))
    | least_upper_bound(inverse(a),multiply(inverse(a),X_87)) != multiply(inverse(a),least_upper_bound(X_87,identity))
    | least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) = least_upper_bound(identity,multiply(inverse(a),X_87)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(a),multiply(inverse(a),X_87))),least_upper_bound(identity,multiply(inverse(a),X_87))) ),[0,1],$fot(multiply(inverse(a),least_upper_bound(X_87,identity)))]]) ).

cnf(refute_0_244,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(a),multiply(inverse(a),X_87))) != least_upper_bound(identity,multiply(inverse(a),X_87))
    | least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) = least_upper_bound(identity,multiply(inverse(a),X_87)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),multiply(inverse(a),X_87)),multiply(inverse(a),least_upper_bound(X_87,identity))) )],[refute_0_242,refute_0_243]) ).

cnf(refute_0_245,plain,
    least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) = least_upper_bound(identity,multiply(inverse(a),X_87)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(a),multiply(inverse(a),X_87))),least_upper_bound(identity,multiply(inverse(a),X_87))) )],[refute_0_239,refute_0_244]) ).

cnf(refute_0_246,plain,
    least_upper_bound(a,least_upper_bound(identity,X_24)) = least_upper_bound(least_upper_bound(a,identity),X_24),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(a)),bind(Y,$fot(identity)),bind(Z,$fot(X_24))]]) ).

cnf(refute_0_247,plain,
    ( least_upper_bound(a,identity) != identity
    | least_upper_bound(a,least_upper_bound(identity,X_24)) != least_upper_bound(least_upper_bound(a,identity),X_24)
    | least_upper_bound(a,least_upper_bound(identity,X_24)) = least_upper_bound(identity,X_24) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,X_24)),least_upper_bound(least_upper_bound(a,identity),X_24)) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_248,plain,
    ( least_upper_bound(a,least_upper_bound(identity,X_24)) != least_upper_bound(least_upper_bound(a,identity),X_24)
    | least_upper_bound(a,least_upper_bound(identity,X_24)) = least_upper_bound(identity,X_24) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),identity) )],[refute_0_21,refute_0_247]) ).

cnf(refute_0_249,plain,
    least_upper_bound(a,least_upper_bound(identity,X_24)) = least_upper_bound(identity,X_24),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,X_24)),least_upper_bound(least_upper_bound(a,identity),X_24)) )],[refute_0_246,refute_0_248]) ).

cnf(refute_0_250,plain,
    least_upper_bound(a,least_upper_bound(identity,X_25)) = least_upper_bound(identity,X_25),
    inference(subst,[],[refute_0_249:[bind(X_24,$fot(X_25))]]) ).

cnf(refute_0_251,plain,
    least_upper_bound(X_25,identity) = least_upper_bound(identity,X_25),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_25)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_252,plain,
    ( least_upper_bound(X_25,identity) != least_upper_bound(identity,X_25)
    | least_upper_bound(identity,X_25) = least_upper_bound(X_25,identity) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_25,identity))),bind(Y0,$fot(least_upper_bound(identity,X_25)))]]) ).

cnf(refute_0_253,plain,
    least_upper_bound(identity,X_25) = least_upper_bound(X_25,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_25,identity),least_upper_bound(identity,X_25)) )],[refute_0_251,refute_0_252]) ).

cnf(refute_0_254,plain,
    ( least_upper_bound(a,least_upper_bound(identity,X_25)) != least_upper_bound(identity,X_25)
    | least_upper_bound(identity,X_25) != least_upper_bound(X_25,identity)
    | least_upper_bound(a,least_upper_bound(X_25,identity)) = least_upper_bound(identity,X_25) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,X_25)),least_upper_bound(identity,X_25)) ),[0,1],$fot(least_upper_bound(X_25,identity))]]) ).

cnf(refute_0_255,plain,
    ( least_upper_bound(a,least_upper_bound(identity,X_25)) != least_upper_bound(identity,X_25)
    | least_upper_bound(a,least_upper_bound(X_25,identity)) = least_upper_bound(identity,X_25) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_25),least_upper_bound(X_25,identity)) )],[refute_0_253,refute_0_254]) ).

cnf(refute_0_256,plain,
    least_upper_bound(a,least_upper_bound(X_25,identity)) = least_upper_bound(identity,X_25),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,X_25)),least_upper_bound(identity,X_25)) )],[refute_0_250,refute_0_255]) ).

cnf(refute_0_257,plain,
    least_upper_bound(a,least_upper_bound(X_87,identity)) = least_upper_bound(identity,X_87),
    inference(subst,[],[refute_0_256:[bind(X_25,$fot(X_87))]]) ).

cnf(refute_0_258,plain,
    multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))) = multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))),
    introduced(tautology,[refl,[$fot(multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))))]]) ).

cnf(refute_0_259,plain,
    ( multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))) != multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity)))
    | least_upper_bound(a,least_upper_bound(X_87,identity)) != least_upper_bound(identity,X_87)
    | multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))) = multiply(inverse(a),least_upper_bound(identity,X_87)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))),multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_87))]]) ).

cnf(refute_0_260,plain,
    ( least_upper_bound(a,least_upper_bound(X_87,identity)) != least_upper_bound(identity,X_87)
    | multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))) = multiply(inverse(a),least_upper_bound(identity,X_87)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))),multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity)))) )],[refute_0_258,refute_0_259]) ).

cnf(refute_0_261,plain,
    multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))) = multiply(inverse(a),least_upper_bound(identity,X_87)),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(X_87,identity)),least_upper_bound(identity,X_87)) )],[refute_0_257,refute_0_260]) ).

cnf(refute_0_262,plain,
    multiply(inverse(X_84),least_upper_bound(X_84,X_85)) = least_upper_bound(multiply(inverse(X_84),X_84),multiply(inverse(X_84),X_85)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_84))),bind(Y,$fot(X_84)),bind(Z,$fot(X_85))]]) ).

cnf(refute_0_263,plain,
    multiply(inverse(X_84),X_84) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_84))]]) ).

cnf(refute_0_264,plain,
    ( multiply(inverse(X_84),X_84) != identity
    | multiply(inverse(X_84),least_upper_bound(X_84,X_85)) != least_upper_bound(multiply(inverse(X_84),X_84),multiply(inverse(X_84),X_85))
    | multiply(inverse(X_84),least_upper_bound(X_84,X_85)) = least_upper_bound(identity,multiply(inverse(X_84),X_85)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,X_85)),least_upper_bound(multiply(inverse(X_84),X_84),multiply(inverse(X_84),X_85))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_265,plain,
    ( multiply(inverse(X_84),least_upper_bound(X_84,X_85)) != least_upper_bound(multiply(inverse(X_84),X_84),multiply(inverse(X_84),X_85))
    | multiply(inverse(X_84),least_upper_bound(X_84,X_85)) = least_upper_bound(identity,multiply(inverse(X_84),X_85)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_84),X_84),identity) )],[refute_0_263,refute_0_264]) ).

cnf(refute_0_266,plain,
    multiply(inverse(X_84),least_upper_bound(X_84,X_85)) = least_upper_bound(identity,multiply(inverse(X_84),X_85)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,X_85)),least_upper_bound(multiply(inverse(X_84),X_84),multiply(inverse(X_84),X_85))) )],[refute_0_262,refute_0_265]) ).

cnf(refute_0_267,plain,
    ( multiply(inverse(X_84),least_upper_bound(X_84,X_85)) != least_upper_bound(identity,multiply(inverse(X_84),X_85))
    | least_upper_bound(identity,multiply(inverse(X_84),X_85)) = multiply(inverse(X_84),least_upper_bound(X_84,X_85)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(inverse(X_84),least_upper_bound(X_84,X_85)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_84),X_85))))]]) ).

cnf(refute_0_268,plain,
    least_upper_bound(identity,multiply(inverse(X_84),X_85)) = multiply(inverse(X_84),least_upper_bound(X_84,X_85)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_84),least_upper_bound(X_84,X_85)),least_upper_bound(identity,multiply(inverse(X_84),X_85))) )],[refute_0_266,refute_0_267]) ).

cnf(refute_0_269,plain,
    least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) = multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))),
    inference(subst,[],[refute_0_268:[bind(X_84,$fot(a)),bind(X_85,$fot(least_upper_bound(X_87,identity)))]]) ).

cnf(refute_0_270,plain,
    ( multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))) != multiply(inverse(a),least_upper_bound(identity,X_87))
    | least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) != multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity)))
    | least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) = multiply(inverse(a),least_upper_bound(identity,X_87)) ),
    inference(subst,[],[refute_0_100:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))))),bind(Y0,$fot(multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))))),bind(Z0,$fot(multiply(inverse(a),least_upper_bound(identity,X_87))))]]) ).

cnf(refute_0_271,plain,
    ( multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))) != multiply(inverse(a),least_upper_bound(identity,X_87))
    | least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) = multiply(inverse(a),least_upper_bound(identity,X_87)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))),multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity)))) )],[refute_0_269,refute_0_270]) ).

cnf(refute_0_272,plain,
    least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) = multiply(inverse(a),least_upper_bound(identity,X_87)),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,least_upper_bound(X_87,identity))),multiply(inverse(a),least_upper_bound(identity,X_87))) )],[refute_0_261,refute_0_271]) ).

cnf(refute_0_273,plain,
    ( least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) != multiply(inverse(a),least_upper_bound(identity,X_87))
    | least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) != least_upper_bound(identity,multiply(inverse(a),X_87))
    | multiply(inverse(a),least_upper_bound(identity,X_87)) = least_upper_bound(identity,multiply(inverse(a),X_87)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))),least_upper_bound(identity,multiply(inverse(a),X_87))) ),[0],$fot(multiply(inverse(a),least_upper_bound(identity,X_87)))]]) ).

cnf(refute_0_274,plain,
    ( least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) != least_upper_bound(identity,multiply(inverse(a),X_87))
    | multiply(inverse(a),least_upper_bound(identity,X_87)) = least_upper_bound(identity,multiply(inverse(a),X_87)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))),multiply(inverse(a),least_upper_bound(identity,X_87))) )],[refute_0_272,refute_0_273]) ).

cnf(refute_0_275,plain,
    least_upper_bound(identity,multiply(inverse(a),X_87)) = multiply(inverse(a),least_upper_bound(a,X_87)),
    inference(subst,[],[refute_0_268:[bind(X_84,$fot(a)),bind(X_85,$fot(X_87))]]) ).

cnf(refute_0_276,plain,
    ( multiply(inverse(a),least_upper_bound(identity,X_87)) != least_upper_bound(identity,multiply(inverse(a),X_87))
    | least_upper_bound(identity,multiply(inverse(a),X_87)) != multiply(inverse(a),least_upper_bound(a,X_87))
    | multiply(inverse(a),least_upper_bound(identity,X_87)) = multiply(inverse(a),least_upper_bound(a,X_87)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a),least_upper_bound(identity,X_87)),multiply(inverse(a),least_upper_bound(a,X_87))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(a),X_87)))]]) ).

cnf(refute_0_277,plain,
    ( multiply(inverse(a),least_upper_bound(identity,X_87)) != least_upper_bound(identity,multiply(inverse(a),X_87))
    | multiply(inverse(a),least_upper_bound(identity,X_87)) = multiply(inverse(a),least_upper_bound(a,X_87)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(a),X_87)),multiply(inverse(a),least_upper_bound(a,X_87))) )],[refute_0_275,refute_0_276]) ).

cnf(refute_0_278,plain,
    ( least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))) != least_upper_bound(identity,multiply(inverse(a),X_87))
    | multiply(inverse(a),least_upper_bound(identity,X_87)) = multiply(inverse(a),least_upper_bound(a,X_87)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,X_87)),least_upper_bound(identity,multiply(inverse(a),X_87))) )],[refute_0_274,refute_0_277]) ).

cnf(refute_0_279,plain,
    multiply(inverse(a),least_upper_bound(identity,X_87)) = multiply(inverse(a),least_upper_bound(a,X_87)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(a),least_upper_bound(X_87,identity))),least_upper_bound(identity,multiply(inverse(a),X_87))) )],[refute_0_245,refute_0_278]) ).

cnf(refute_0_280,plain,
    multiply(identity,least_upper_bound(identity,X_87)) = least_upper_bound(identity,X_87),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(identity,X_87)))]]) ).

cnf(refute_0_281,plain,
    multiply(inverse(a),least_upper_bound(identity,X_87)) = multiply(inverse(a),least_upper_bound(identity,X_87)),
    introduced(tautology,[refl,[$fot(multiply(inverse(a),least_upper_bound(identity,X_87)))]]) ).

cnf(refute_0_282,plain,
    ( multiply(inverse(a),least_upper_bound(identity,X_87)) != multiply(inverse(a),least_upper_bound(identity,X_87))
    | inverse(a) != identity
    | multiply(inverse(a),least_upper_bound(identity,X_87)) = multiply(identity,least_upper_bound(identity,X_87)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,X_87)),multiply(inverse(a),least_upper_bound(identity,X_87))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_283,plain,
    ( inverse(a) != identity
    | multiply(inverse(a),least_upper_bound(identity,X_87)) = multiply(identity,least_upper_bound(identity,X_87)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,X_87)),multiply(inverse(a),least_upper_bound(identity,X_87))) )],[refute_0_281,refute_0_282]) ).

cnf(refute_0_284,plain,
    multiply(inverse(a),least_upper_bound(identity,X_87)) = multiply(identity,least_upper_bound(identity,X_87)),
    inference(resolve,[$cnf( $equal(inverse(a),identity) )],[refute_0_221,refute_0_283]) ).

cnf(refute_0_285,plain,
    ( multiply(identity,least_upper_bound(identity,X_87)) != least_upper_bound(identity,X_87)
    | multiply(inverse(a),least_upper_bound(identity,X_87)) != multiply(identity,least_upper_bound(identity,X_87))
    | multiply(inverse(a),least_upper_bound(identity,X_87)) = least_upper_bound(identity,X_87) ),
    inference(subst,[],[refute_0_100:[bind(X0,$fot(multiply(inverse(a),least_upper_bound(identity,X_87)))),bind(Y0,$fot(multiply(identity,least_upper_bound(identity,X_87)))),bind(Z0,$fot(least_upper_bound(identity,X_87)))]]) ).

cnf(refute_0_286,plain,
    ( multiply(identity,least_upper_bound(identity,X_87)) != least_upper_bound(identity,X_87)
    | multiply(inverse(a),least_upper_bound(identity,X_87)) = least_upper_bound(identity,X_87) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,X_87)),multiply(identity,least_upper_bound(identity,X_87))) )],[refute_0_284,refute_0_285]) ).

cnf(refute_0_287,plain,
    multiply(inverse(a),least_upper_bound(identity,X_87)) = least_upper_bound(identity,X_87),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(identity,X_87)),least_upper_bound(identity,X_87)) )],[refute_0_280,refute_0_286]) ).

cnf(refute_0_288,plain,
    ( multiply(inverse(a),least_upper_bound(identity,X_87)) != multiply(inverse(a),least_upper_bound(a,X_87))
    | multiply(inverse(a),least_upper_bound(identity,X_87)) != least_upper_bound(identity,X_87)
    | least_upper_bound(identity,X_87) = multiply(inverse(a),least_upper_bound(a,X_87)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,X_87)),multiply(inverse(a),least_upper_bound(a,X_87))) ),[0],$fot(least_upper_bound(identity,X_87))]]) ).

cnf(refute_0_289,plain,
    ( multiply(inverse(a),least_upper_bound(identity,X_87)) != multiply(inverse(a),least_upper_bound(a,X_87))
    | least_upper_bound(identity,X_87) = multiply(inverse(a),least_upper_bound(a,X_87)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,X_87)),least_upper_bound(identity,X_87)) )],[refute_0_287,refute_0_288]) ).

cnf(refute_0_290,plain,
    multiply(identity,least_upper_bound(a,X_87)) = least_upper_bound(a,X_87),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(a,X_87)))]]) ).

cnf(refute_0_291,plain,
    multiply(inverse(a),least_upper_bound(a,X_87)) = multiply(inverse(a),least_upper_bound(a,X_87)),
    introduced(tautology,[refl,[$fot(multiply(inverse(a),least_upper_bound(a,X_87)))]]) ).

cnf(refute_0_292,plain,
    ( multiply(inverse(a),least_upper_bound(a,X_87)) != multiply(inverse(a),least_upper_bound(a,X_87))
    | inverse(a) != identity
    | multiply(inverse(a),least_upper_bound(a,X_87)) = multiply(identity,least_upper_bound(a,X_87)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,X_87)),multiply(inverse(a),least_upper_bound(a,X_87))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_293,plain,
    ( inverse(a) != identity
    | multiply(inverse(a),least_upper_bound(a,X_87)) = multiply(identity,least_upper_bound(a,X_87)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,X_87)),multiply(inverse(a),least_upper_bound(a,X_87))) )],[refute_0_291,refute_0_292]) ).

cnf(refute_0_294,plain,
    multiply(inverse(a),least_upper_bound(a,X_87)) = multiply(identity,least_upper_bound(a,X_87)),
    inference(resolve,[$cnf( $equal(inverse(a),identity) )],[refute_0_221,refute_0_293]) ).

cnf(refute_0_295,plain,
    ( multiply(identity,least_upper_bound(a,X_87)) != least_upper_bound(a,X_87)
    | multiply(inverse(a),least_upper_bound(a,X_87)) != multiply(identity,least_upper_bound(a,X_87))
    | multiply(inverse(a),least_upper_bound(a,X_87)) = least_upper_bound(a,X_87) ),
    inference(subst,[],[refute_0_100:[bind(X0,$fot(multiply(inverse(a),least_upper_bound(a,X_87)))),bind(Y0,$fot(multiply(identity,least_upper_bound(a,X_87)))),bind(Z0,$fot(least_upper_bound(a,X_87)))]]) ).

cnf(refute_0_296,plain,
    ( multiply(identity,least_upper_bound(a,X_87)) != least_upper_bound(a,X_87)
    | multiply(inverse(a),least_upper_bound(a,X_87)) = least_upper_bound(a,X_87) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,X_87)),multiply(identity,least_upper_bound(a,X_87))) )],[refute_0_294,refute_0_295]) ).

cnf(refute_0_297,plain,
    multiply(inverse(a),least_upper_bound(a,X_87)) = least_upper_bound(a,X_87),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(a,X_87)),least_upper_bound(a,X_87)) )],[refute_0_290,refute_0_296]) ).

cnf(refute_0_298,plain,
    ( multiply(inverse(a),least_upper_bound(a,X_87)) != least_upper_bound(a,X_87)
    | least_upper_bound(identity,X_87) != multiply(inverse(a),least_upper_bound(a,X_87))
    | least_upper_bound(identity,X_87) = least_upper_bound(a,X_87) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,X_87),multiply(inverse(a),least_upper_bound(a,X_87))) ),[1],$fot(least_upper_bound(a,X_87))]]) ).

cnf(refute_0_299,plain,
    ( least_upper_bound(identity,X_87) != multiply(inverse(a),least_upper_bound(a,X_87))
    | least_upper_bound(identity,X_87) = least_upper_bound(a,X_87) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,X_87)),least_upper_bound(a,X_87)) )],[refute_0_297,refute_0_298]) ).

cnf(refute_0_300,plain,
    ( multiply(inverse(a),least_upper_bound(identity,X_87)) != multiply(inverse(a),least_upper_bound(a,X_87))
    | least_upper_bound(identity,X_87) = least_upper_bound(a,X_87) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_87),multiply(inverse(a),least_upper_bound(a,X_87))) )],[refute_0_289,refute_0_299]) ).

cnf(refute_0_301,plain,
    least_upper_bound(identity,X_87) = least_upper_bound(a,X_87),
    inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(identity,X_87)),multiply(inverse(a),least_upper_bound(a,X_87))) )],[refute_0_279,refute_0_300]) ).

cnf(refute_0_302,plain,
    least_upper_bound(identity,X_32) = least_upper_bound(a,X_32),
    inference(subst,[],[refute_0_301:[bind(X_87,$fot(X_32))]]) ).

cnf(refute_0_303,plain,
    ( least_upper_bound(identity,X_32) != least_upper_bound(X_32,identity)
    | least_upper_bound(identity,X_32) != least_upper_bound(a,X_32)
    | least_upper_bound(a,X_32) = least_upper_bound(X_32,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity)) ),[0],$fot(least_upper_bound(a,X_32))]]) ).

cnf(refute_0_304,plain,
    ( least_upper_bound(identity,X_32) != least_upper_bound(X_32,identity)
    | least_upper_bound(a,X_32) = least_upper_bound(X_32,identity) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_32),least_upper_bound(a,X_32)) )],[refute_0_302,refute_0_303]) ).

cnf(refute_0_305,plain,
    least_upper_bound(a,X_32) = least_upper_bound(X_32,identity),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_32),least_upper_bound(X_32,identity)) )],[refute_0_238,refute_0_304]) ).

cnf(refute_0_306,plain,
    ( least_upper_bound(a,X_32) != least_upper_bound(X_32,identity)
    | least_upper_bound(X_32,identity) = least_upper_bound(a,X_32) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(a,X_32))),bind(Y0,$fot(least_upper_bound(X_32,identity)))]]) ).

cnf(refute_0_307,plain,
    least_upper_bound(X_32,identity) = least_upper_bound(a,X_32),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,X_32),least_upper_bound(X_32,identity)) )],[refute_0_305,refute_0_306]) ).

cnf(refute_0_308,plain,
    least_upper_bound(a,identity) = least_upper_bound(a,a),
    inference(subst,[],[refute_0_307:[bind(X_32,$fot(a))]]) ).

cnf(refute_0_309,plain,
    ( least_upper_bound(a,a) != a
    | least_upper_bound(a,identity) != least_upper_bound(a,a)
    | least_upper_bound(a,identity) = a ),
    inference(subst,[],[refute_0_100:[bind(X0,$fot(least_upper_bound(a,identity))),bind(Y0,$fot(least_upper_bound(a,a))),bind(Z0,$fot(a))]]) ).

cnf(refute_0_310,plain,
    ( least_upper_bound(a,a) != a
    | least_upper_bound(a,identity) = a ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),least_upper_bound(a,a)) )],[refute_0_308,refute_0_309]) ).

cnf(refute_0_311,plain,
    least_upper_bound(a,identity) = a,
    inference(resolve,[$cnf( $equal(least_upper_bound(a,a),a) )],[refute_0_22,refute_0_310]) ).

cnf(refute_0_312,plain,
    ( least_upper_bound(a,identity) != a
    | least_upper_bound(a,identity) != identity
    | a = identity ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,identity),identity) ),[0],$fot(a)]]) ).

cnf(refute_0_313,plain,
    ( least_upper_bound(a,identity) != identity
    | a = identity ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),a) )],[refute_0_311,refute_0_312]) ).

cnf(refute_0_314,plain,
    a = identity,
    inference(resolve,[$cnf( $equal(least_upper_bound(a,identity),identity) )],[refute_0_21,refute_0_313]) ).

cnf(refute_0_315,plain,
    ( a != identity
    | identity = a ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(a)),bind(Y0,$fot(identity))]]) ).

cnf(refute_0_316,plain,
    a != identity,
    inference(resolve,[$cnf( $equal(identity,a) )],[refute_0_315,prove_p05b]) ).

cnf(refute_0_317,plain,
    $false,
    inference(resolve,[$cnf( $equal(a,identity) )],[refute_0_314,refute_0_316]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP174-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n008.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Tue Jun 14 08:10:52 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.52/0.73  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.73  
% 0.52/0.73  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.60/0.77  
%------------------------------------------------------------------------------