TSTP Solution File: GRP183-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP183-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 10:37:41 EDT 2022
% Result : Unsatisfiable 28.43s 28.69s
% Output : CNFRefutation 28.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 100
% Number of leaves : 375
% Syntax : Number of clauses : 1848 ( 958 unt; 0 nHn; 868 RR)
% Number of literals : 3120 (3119 equ;1274 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 3912 ( 66 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X,X) = X ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(prove_p20,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != identity ).
cnf(refute_0_0,plain,
multiply(X_72,greatest_lower_bound(X_73,identity)) = greatest_lower_bound(multiply(X_72,X_73),multiply(X_72,identity)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_72)),bind(Y,$fot(X_73)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(inverse(X_25),X_25),X_26) = multiply(inverse(X_25),multiply(X_25,X_26)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_25))),bind(Y,$fot(X_25)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(X_25),X_25) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_25),X_25),X_26) != multiply(inverse(X_25),multiply(X_25,X_26))
| multiply(inverse(X_25),X_25) != identity
| multiply(identity,X_26) = multiply(inverse(X_25),multiply(X_25,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_25),X_25),X_26),multiply(inverse(X_25),multiply(X_25,X_26))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(inverse(X_25),X_25),X_26) != multiply(inverse(X_25),multiply(X_25,X_26))
| multiply(identity,X_26) = multiply(inverse(X_25),multiply(X_25,X_26)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),X_25),identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_26) = multiply(inverse(X_25),multiply(X_25,X_26)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_25),X_25),X_26),multiply(inverse(X_25),multiply(X_25,X_26))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(identity,X_26) = X_26,
inference(subst,[],[left_identity:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_26) != X_26
| multiply(identity,X_26) != multiply(inverse(X_25),multiply(X_25,X_26))
| X_26 = multiply(inverse(X_25),multiply(X_25,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_26),multiply(inverse(X_25),multiply(X_25,X_26))) ),[0],$fot(X_26)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_26) != multiply(inverse(X_25),multiply(X_25,X_26))
| X_26 = multiply(inverse(X_25),multiply(X_25,X_26)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_26),X_26) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
X_26 = multiply(inverse(X_25),multiply(X_25,X_26)),
inference(resolve,[$cnf( $equal(multiply(identity,X_26),multiply(inverse(X_25),multiply(X_25,X_26))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
X_28 = multiply(inverse(inverse(X_28)),multiply(inverse(X_28),X_28)),
inference(subst,[],[refute_0_9:[bind(X_25,$fot(inverse(X_28))),bind(X_26,$fot(X_28))]]) ).
cnf(refute_0_11,plain,
multiply(inverse(X_28),X_28) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_12,plain,
( X_28 != multiply(inverse(inverse(X_28)),multiply(inverse(X_28),X_28))
| multiply(inverse(X_28),X_28) != identity
| X_28 = multiply(inverse(inverse(X_28)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_28,multiply(inverse(inverse(X_28)),multiply(inverse(X_28),X_28))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_13,plain,
( X_28 != multiply(inverse(inverse(X_28)),multiply(inverse(X_28),X_28))
| X_28 = multiply(inverse(inverse(X_28)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_28),X_28),identity) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
X_28 = multiply(inverse(inverse(X_28)),identity),
inference(resolve,[$cnf( $equal(X_28,multiply(inverse(inverse(X_28)),multiply(inverse(X_28),X_28))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(X_27,X_28) = multiply(inverse(inverse(X_27)),multiply(inverse(X_27),multiply(X_27,X_28))),
inference(subst,[],[refute_0_9:[bind(X_25,$fot(inverse(X_27))),bind(X_26,$fot(multiply(X_27,X_28)))]]) ).
cnf(refute_0_16,plain,
X_28 = multiply(inverse(X_27),multiply(X_27,X_28)),
inference(subst,[],[refute_0_9:[bind(X_25,$fot(X_27)),bind(X_26,$fot(X_28))]]) ).
cnf(refute_0_17,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_18,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_19,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( X_28 != multiply(inverse(X_27),multiply(X_27,X_28))
| multiply(inverse(X_27),multiply(X_27,X_28)) = X_28 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_28)),bind(Y0,$fot(multiply(inverse(X_27),multiply(X_27,X_28))))]]) ).
cnf(refute_0_21,plain,
multiply(inverse(X_27),multiply(X_27,X_28)) = X_28,
inference(resolve,[$cnf( $equal(X_28,multiply(inverse(X_27),multiply(X_27,X_28))) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( multiply(X_27,X_28) != multiply(inverse(inverse(X_27)),multiply(inverse(X_27),multiply(X_27,X_28)))
| multiply(inverse(X_27),multiply(X_27,X_28)) != X_28
| multiply(X_27,X_28) = multiply(inverse(inverse(X_27)),X_28) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_27,X_28),multiply(inverse(inverse(X_27)),multiply(inverse(X_27),multiply(X_27,X_28)))) ),[1,1],$fot(X_28)]]) ).
cnf(refute_0_23,plain,
( multiply(X_27,X_28) != multiply(inverse(inverse(X_27)),multiply(inverse(X_27),multiply(X_27,X_28)))
| multiply(X_27,X_28) = multiply(inverse(inverse(X_27)),X_28) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_27),multiply(X_27,X_28)),X_28) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(X_27,X_28) = multiply(inverse(inverse(X_27)),X_28),
inference(resolve,[$cnf( $equal(multiply(X_27,X_28),multiply(inverse(inverse(X_27)),multiply(inverse(X_27),multiply(X_27,X_28)))) )],[refute_0_15,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(X_27,X_28) != multiply(inverse(inverse(X_27)),X_28)
| multiply(inverse(inverse(X_27)),X_28) = multiply(X_27,X_28) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_27,X_28))),bind(Y0,$fot(multiply(inverse(inverse(X_27)),X_28)))]]) ).
cnf(refute_0_26,plain,
multiply(inverse(inverse(X_27)),X_28) = multiply(X_27,X_28),
inference(resolve,[$cnf( $equal(multiply(X_27,X_28),multiply(inverse(inverse(X_27)),X_28)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(inverse(inverse(X_28)),identity) = multiply(X_28,identity),
inference(subst,[],[refute_0_26:[bind(X_27,$fot(X_28)),bind(X_28,$fot(identity))]]) ).
cnf(refute_0_28,plain,
( X_28 != multiply(inverse(inverse(X_28)),identity)
| multiply(inverse(inverse(X_28)),identity) != multiply(X_28,identity)
| X_28 = multiply(X_28,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_28,multiply(X_28,identity)) ),[0],$fot(multiply(inverse(inverse(X_28)),identity))]]) ).
cnf(refute_0_29,plain,
( X_28 != multiply(inverse(inverse(X_28)),identity)
| X_28 = multiply(X_28,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_28)),identity),multiply(X_28,identity)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
X_28 = multiply(X_28,identity),
inference(resolve,[$cnf( $equal(X_28,multiply(inverse(inverse(X_28)),identity)) )],[refute_0_14,refute_0_29]) ).
cnf(refute_0_31,plain,
X_72 = multiply(X_72,identity),
inference(subst,[],[refute_0_30:[bind(X_28,$fot(X_72))]]) ).
cnf(refute_0_32,plain,
( X_72 != multiply(X_72,identity)
| multiply(X_72,identity) = X_72 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_72)),bind(Y0,$fot(multiply(X_72,identity)))]]) ).
cnf(refute_0_33,plain,
multiply(X_72,identity) = X_72,
inference(resolve,[$cnf( $equal(X_72,multiply(X_72,identity)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( multiply(X_72,greatest_lower_bound(X_73,identity)) != greatest_lower_bound(multiply(X_72,X_73),multiply(X_72,identity))
| multiply(X_72,identity) != X_72
| multiply(X_72,greatest_lower_bound(X_73,identity)) = greatest_lower_bound(multiply(X_72,X_73),X_72) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_72,greatest_lower_bound(X_73,identity)),greatest_lower_bound(multiply(X_72,X_73),multiply(X_72,identity))) ),[1,1],$fot(X_72)]]) ).
cnf(refute_0_35,plain,
( multiply(X_72,greatest_lower_bound(X_73,identity)) != greatest_lower_bound(multiply(X_72,X_73),multiply(X_72,identity))
| multiply(X_72,greatest_lower_bound(X_73,identity)) = greatest_lower_bound(multiply(X_72,X_73),X_72) ),
inference(resolve,[$cnf( $equal(multiply(X_72,identity),X_72) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(X_72,greatest_lower_bound(X_73,identity)) = greatest_lower_bound(multiply(X_72,X_73),X_72),
inference(resolve,[$cnf( $equal(multiply(X_72,greatest_lower_bound(X_73,identity)),greatest_lower_bound(multiply(X_72,X_73),multiply(X_72,identity))) )],[refute_0_0,refute_0_35]) ).
cnf(refute_0_37,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_38,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_37]) ).
cnf(refute_0_39,plain,
greatest_lower_bound(multiply(X_72,X_73),X_72) = greatest_lower_bound(X_72,multiply(X_72,X_73)),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_72)),bind(Y,$fot(multiply(X_72,X_73)))]]) ).
cnf(refute_0_40,plain,
( multiply(X_72,greatest_lower_bound(X_73,identity)) != greatest_lower_bound(multiply(X_72,X_73),X_72)
| greatest_lower_bound(multiply(X_72,X_73),X_72) != greatest_lower_bound(X_72,multiply(X_72,X_73))
| multiply(X_72,greatest_lower_bound(X_73,identity)) = greatest_lower_bound(X_72,multiply(X_72,X_73)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_72,greatest_lower_bound(X_73,identity)),greatest_lower_bound(X_72,multiply(X_72,X_73))) ),[0],$fot(greatest_lower_bound(multiply(X_72,X_73),X_72))]]) ).
cnf(refute_0_41,plain,
( multiply(X_72,greatest_lower_bound(X_73,identity)) != greatest_lower_bound(multiply(X_72,X_73),X_72)
| multiply(X_72,greatest_lower_bound(X_73,identity)) = greatest_lower_bound(X_72,multiply(X_72,X_73)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_72,X_73),X_72),greatest_lower_bound(X_72,multiply(X_72,X_73))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(X_72,greatest_lower_bound(X_73,identity)) = greatest_lower_bound(X_72,multiply(X_72,X_73)),
inference(resolve,[$cnf( $equal(multiply(X_72,greatest_lower_bound(X_73,identity)),greatest_lower_bound(multiply(X_72,X_73),X_72)) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),multiply(inverse(greatest_lower_bound(identity,X_73)),X_73)),
inference(subst,[],[refute_0_42:[bind(X_72,$fot(inverse(greatest_lower_bound(identity,X_73))))]]) ).
cnf(refute_0_44,plain,
X_28 = multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_28)),
inference(subst,[],[refute_0_9:[bind(X_25,$fot(multiply(X,Y))),bind(X_26,$fot(X_28))]]) ).
cnf(refute_0_45,plain,
multiply(multiply(X,Y),X_28) = multiply(X,multiply(Y,X_28)),
inference(subst,[],[associativity:[bind(Z,$fot(X_28))]]) ).
cnf(refute_0_46,plain,
( X_28 != multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_28))
| multiply(multiply(X,Y),X_28) != multiply(X,multiply(Y,X_28))
| X_28 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_28))) ),
introduced(tautology,[equality,[$cnf( $equal(X_28,multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_28))) ),[1,1],$fot(multiply(X,multiply(Y,X_28)))]]) ).
cnf(refute_0_47,plain,
( X_28 != multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_28))
| X_28 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_28))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_28),multiply(X,multiply(Y,X_28))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
X_28 = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,X_28))),
inference(resolve,[$cnf( $equal(X_28,multiply(inverse(multiply(X,Y)),multiply(multiply(X,Y),X_28))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),multiply(X_45,multiply(X_46,inverse(X_46)))),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_45)),bind(Y,$fot(X_46)),bind(X_28,$fot(inverse(X_46)))]]) ).
cnf(refute_0_50,plain,
multiply(inverse(inverse(X_30)),inverse(X_30)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_30)))]]) ).
cnf(refute_0_51,plain,
multiply(X_30,inverse(X_30)) = multiply(inverse(inverse(X_30)),inverse(X_30)),
inference(subst,[],[refute_0_24:[bind(X_27,$fot(X_30)),bind(X_28,$fot(inverse(X_30)))]]) ).
cnf(refute_0_52,plain,
( multiply(X_30,inverse(X_30)) != multiply(inverse(inverse(X_30)),inverse(X_30))
| multiply(inverse(inverse(X_30)),inverse(X_30)) = multiply(X_30,inverse(X_30)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_30,inverse(X_30)))),bind(Y0,$fot(multiply(inverse(inverse(X_30)),inverse(X_30))))]]) ).
cnf(refute_0_53,plain,
multiply(inverse(inverse(X_30)),inverse(X_30)) = multiply(X_30,inverse(X_30)),
inference(resolve,[$cnf( $equal(multiply(X_30,inverse(X_30)),multiply(inverse(inverse(X_30)),inverse(X_30))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( multiply(inverse(inverse(X_30)),inverse(X_30)) != multiply(X_30,inverse(X_30))
| multiply(inverse(inverse(X_30)),inverse(X_30)) != identity
| multiply(X_30,inverse(X_30)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_30)),inverse(X_30)),identity) ),[0],$fot(multiply(X_30,inverse(X_30)))]]) ).
cnf(refute_0_55,plain,
( multiply(inverse(inverse(X_30)),inverse(X_30)) != identity
| multiply(X_30,inverse(X_30)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_30)),inverse(X_30)),multiply(X_30,inverse(X_30))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(X_30,inverse(X_30)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_30)),inverse(X_30)),identity) )],[refute_0_50,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(X_46,inverse(X_46)) = identity,
inference(subst,[],[refute_0_56:[bind(X_30,$fot(X_46))]]) ).
cnf(refute_0_58,plain,
( multiply(X_46,inverse(X_46)) != identity
| inverse(X_46) != multiply(inverse(multiply(X_45,X_46)),multiply(X_45,multiply(X_46,inverse(X_46))))
| inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_46),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,multiply(X_46,inverse(X_46))))) ),[1,1,1],$fot(identity)]]) ).
cnf(refute_0_59,plain,
( inverse(X_46) != multiply(inverse(multiply(X_45,X_46)),multiply(X_45,multiply(X_46,inverse(X_46))))
| inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_46,inverse(X_46)),identity) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)),
inference(resolve,[$cnf( $equal(inverse(X_46),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,multiply(X_46,inverse(X_46))))) )],[refute_0_49,refute_0_59]) ).
cnf(refute_0_61,plain,
( X_28 != multiply(X_28,identity)
| multiply(X_28,identity) = X_28 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_28)),bind(Y0,$fot(multiply(X_28,identity)))]]) ).
cnf(refute_0_62,plain,
multiply(X_28,identity) = X_28,
inference(resolve,[$cnf( $equal(X_28,multiply(X_28,identity)) )],[refute_0_30,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(X_45,identity) = X_45,
inference(subst,[],[refute_0_62:[bind(X_28,$fot(X_45))]]) ).
cnf(refute_0_64,plain,
multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) = multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)))]]) ).
cnf(refute_0_65,plain,
( multiply(X_45,identity) != X_45
| multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) != multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))
| multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) = multiply(inverse(multiply(X_45,X_46)),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))) ),[1,1],$fot(X_45)]]) ).
cnf(refute_0_66,plain,
( multiply(X_45,identity) != X_45
| multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) = multiply(inverse(multiply(X_45,X_46)),X_45) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) = multiply(inverse(multiply(X_45,X_46)),X_45),
inference(resolve,[$cnf( $equal(multiply(X_45,identity),X_45) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
( multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)) != multiply(inverse(multiply(X_45,X_46)),X_45)
| inverse(X_46) != multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))
| inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_46),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))) ),[1],$fot(multiply(inverse(multiply(X_45,X_46)),X_45))]]) ).
cnf(refute_0_69,plain,
( inverse(X_46) != multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))
| inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),X_45) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity)),multiply(inverse(multiply(X_45,X_46)),X_45)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
inverse(X_46) = multiply(inverse(multiply(X_45,X_46)),X_45),
inference(resolve,[$cnf( $equal(inverse(X_46),multiply(inverse(multiply(X_45,X_46)),multiply(X_45,identity))) )],[refute_0_60,refute_0_69]) ).
cnf(refute_0_71,plain,
inverse(multiply(X_25,X_26)) = multiply(inverse(multiply(inverse(X_25),multiply(X_25,X_26))),inverse(X_25)),
inference(subst,[],[refute_0_70:[bind(X_45,$fot(inverse(X_25))),bind(X_46,$fot(multiply(X_25,X_26)))]]) ).
cnf(refute_0_72,plain,
( X_26 != multiply(inverse(X_25),multiply(X_25,X_26))
| multiply(inverse(X_25),multiply(X_25,X_26)) = X_26 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_26)),bind(Y0,$fot(multiply(inverse(X_25),multiply(X_25,X_26))))]]) ).
cnf(refute_0_73,plain,
multiply(inverse(X_25),multiply(X_25,X_26)) = X_26,
inference(resolve,[$cnf( $equal(X_26,multiply(inverse(X_25),multiply(X_25,X_26))) )],[refute_0_9,refute_0_72]) ).
cnf(refute_0_74,plain,
( multiply(inverse(X_25),multiply(X_25,X_26)) != X_26
| inverse(multiply(X_25,X_26)) != multiply(inverse(multiply(inverse(X_25),multiply(X_25,X_26))),inverse(X_25))
| inverse(multiply(X_25,X_26)) = multiply(inverse(X_26),inverse(X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_25,X_26)),multiply(inverse(multiply(inverse(X_25),multiply(X_25,X_26))),inverse(X_25))) ),[1,0,0],$fot(X_26)]]) ).
cnf(refute_0_75,plain,
( inverse(multiply(X_25,X_26)) != multiply(inverse(multiply(inverse(X_25),multiply(X_25,X_26))),inverse(X_25))
| inverse(multiply(X_25,X_26)) = multiply(inverse(X_26),inverse(X_25)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),multiply(X_25,X_26)),X_26) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
inverse(multiply(X_25,X_26)) = multiply(inverse(X_26),inverse(X_25)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_25,X_26)),multiply(inverse(multiply(inverse(X_25),multiply(X_25,X_26))),inverse(X_25))) )],[refute_0_71,refute_0_75]) ).
cnf(refute_0_77,plain,
inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))) = multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))),
inference(subst,[],[refute_0_76:[bind(X_25,$fot(inverse(X_80))),bind(X_26,$fot(greatest_lower_bound(identity,X_80)))]]) ).
cnf(refute_0_78,plain,
multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)) = greatest_lower_bound(multiply(inverse(X_74),X_73),multiply(inverse(X_74),X_74)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_74))),bind(Y,$fot(X_73)),bind(Z,$fot(X_74))]]) ).
cnf(refute_0_79,plain,
multiply(inverse(X_74),X_74) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_74))]]) ).
cnf(refute_0_80,plain,
( multiply(inverse(X_74),X_74) != identity
| multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)) != greatest_lower_bound(multiply(inverse(X_74),X_73),multiply(inverse(X_74),X_74))
| multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)) = greatest_lower_bound(multiply(inverse(X_74),X_73),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)),greatest_lower_bound(multiply(inverse(X_74),X_73),multiply(inverse(X_74),X_74))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_81,plain,
( multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)) != greatest_lower_bound(multiply(inverse(X_74),X_73),multiply(inverse(X_74),X_74))
| multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)) = greatest_lower_bound(multiply(inverse(X_74),X_73),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_74),X_74),identity) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)) = greatest_lower_bound(multiply(inverse(X_74),X_73),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)),greatest_lower_bound(multiply(inverse(X_74),X_73),multiply(inverse(X_74),X_74))) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
greatest_lower_bound(multiply(inverse(X_74),X_73),identity) = greatest_lower_bound(identity,multiply(inverse(X_74),X_73)),
inference(subst,[],[refute_0_38:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_74),X_73)))]]) ).
cnf(refute_0_84,plain,
( multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)) != greatest_lower_bound(multiply(inverse(X_74),X_73),identity)
| greatest_lower_bound(multiply(inverse(X_74),X_73),identity) != greatest_lower_bound(identity,multiply(inverse(X_74),X_73))
| multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)) = greatest_lower_bound(identity,multiply(inverse(X_74),X_73)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)),greatest_lower_bound(identity,multiply(inverse(X_74),X_73))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_74),X_73),identity))]]) ).
cnf(refute_0_85,plain,
( multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)) != greatest_lower_bound(multiply(inverse(X_74),X_73),identity)
| multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)) = greatest_lower_bound(identity,multiply(inverse(X_74),X_73)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_74),X_73),identity),greatest_lower_bound(identity,multiply(inverse(X_74),X_73))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)) = greatest_lower_bound(identity,multiply(inverse(X_74),X_73)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_74),greatest_lower_bound(X_73,X_74)),greatest_lower_bound(multiply(inverse(X_74),X_73),identity)) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(inverse(X_80),greatest_lower_bound(identity,X_80)) = greatest_lower_bound(identity,multiply(inverse(X_80),identity)),
inference(subst,[],[refute_0_86:[bind(X_73,$fot(identity)),bind(X_74,$fot(X_80))]]) ).
cnf(refute_0_88,plain,
inverse(X_80) = multiply(inverse(X_80),identity),
inference(subst,[],[refute_0_30:[bind(X_28,$fot(inverse(X_80)))]]) ).
cnf(refute_0_89,plain,
( inverse(X_80) != multiply(inverse(X_80),identity)
| multiply(inverse(X_80),identity) = inverse(X_80) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(X_80))),bind(Y0,$fot(multiply(inverse(X_80),identity)))]]) ).
cnf(refute_0_90,plain,
multiply(inverse(X_80),identity) = inverse(X_80),
inference(resolve,[$cnf( $equal(inverse(X_80),multiply(inverse(X_80),identity)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( multiply(inverse(X_80),greatest_lower_bound(identity,X_80)) != greatest_lower_bound(identity,multiply(inverse(X_80),identity))
| multiply(inverse(X_80),identity) != inverse(X_80)
| multiply(inverse(X_80),greatest_lower_bound(identity,X_80)) = greatest_lower_bound(identity,inverse(X_80)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_80),greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,multiply(inverse(X_80),identity))) ),[1,1],$fot(inverse(X_80))]]) ).
cnf(refute_0_92,plain,
( multiply(inverse(X_80),greatest_lower_bound(identity,X_80)) != greatest_lower_bound(identity,multiply(inverse(X_80),identity))
| multiply(inverse(X_80),greatest_lower_bound(identity,X_80)) = greatest_lower_bound(identity,inverse(X_80)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),identity),inverse(X_80)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(inverse(X_80),greatest_lower_bound(identity,X_80)) = greatest_lower_bound(identity,inverse(X_80)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,multiply(inverse(X_80),identity))) )],[refute_0_87,refute_0_92]) ).
cnf(refute_0_94,plain,
( multiply(inverse(X_80),greatest_lower_bound(identity,X_80)) != greatest_lower_bound(identity,inverse(X_80))
| inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))) != multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80)))
| inverse(greatest_lower_bound(identity,inverse(X_80))) = multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80)))) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X_80)))]]) ).
cnf(refute_0_95,plain,
( inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))) != multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80)))
| inverse(greatest_lower_bound(identity,inverse(X_80))) = multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,inverse(X_80))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
inverse(greatest_lower_bound(identity,inverse(X_80))) = multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80)))) )],[refute_0_77,refute_0_95]) ).
cnf(refute_0_97,plain,
inverse(multiply(inverse(X_135),X_26)) = multiply(inverse(multiply(X_135,multiply(inverse(X_135),X_26))),X_135),
inference(subst,[],[refute_0_70:[bind(X_45,$fot(X_135)),bind(X_46,$fot(multiply(inverse(X_135),X_26)))]]) ).
cnf(refute_0_98,plain,
X_26 = multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26)),
inference(subst,[],[refute_0_9:[bind(X_25,$fot(inverse(X_30)))]]) ).
cnf(refute_0_99,plain,
multiply(X_30,multiply(inverse(X_30),X_26)) = multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26)),
inference(subst,[],[refute_0_24:[bind(X_27,$fot(X_30)),bind(X_28,$fot(multiply(inverse(X_30),X_26)))]]) ).
cnf(refute_0_100,plain,
( multiply(X_30,multiply(inverse(X_30),X_26)) != multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26))
| multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26)) = multiply(X_30,multiply(inverse(X_30),X_26)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_30,multiply(inverse(X_30),X_26)))),bind(Y0,$fot(multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26))))]]) ).
cnf(refute_0_101,plain,
multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26)) = multiply(X_30,multiply(inverse(X_30),X_26)),
inference(resolve,[$cnf( $equal(multiply(X_30,multiply(inverse(X_30),X_26)),multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
( X_26 != multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26))
| multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26)) != multiply(X_30,multiply(inverse(X_30),X_26))
| X_26 = multiply(X_30,multiply(inverse(X_30),X_26)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_26,multiply(X_30,multiply(inverse(X_30),X_26))) ),[0],$fot(multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26)))]]) ).
cnf(refute_0_103,plain,
( X_26 != multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26))
| X_26 = multiply(X_30,multiply(inverse(X_30),X_26)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26)),multiply(X_30,multiply(inverse(X_30),X_26))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
X_26 = multiply(X_30,multiply(inverse(X_30),X_26)),
inference(resolve,[$cnf( $equal(X_26,multiply(inverse(inverse(X_30)),multiply(inverse(X_30),X_26))) )],[refute_0_98,refute_0_103]) ).
cnf(refute_0_105,plain,
X_26 = multiply(X_135,multiply(inverse(X_135),X_26)),
inference(subst,[],[refute_0_104:[bind(X_30,$fot(X_135))]]) ).
cnf(refute_0_106,plain,
( X_26 != multiply(X_135,multiply(inverse(X_135),X_26))
| multiply(X_135,multiply(inverse(X_135),X_26)) = X_26 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_26)),bind(Y0,$fot(multiply(X_135,multiply(inverse(X_135),X_26))))]]) ).
cnf(refute_0_107,plain,
multiply(X_135,multiply(inverse(X_135),X_26)) = X_26,
inference(resolve,[$cnf( $equal(X_26,multiply(X_135,multiply(inverse(X_135),X_26))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
( multiply(X_135,multiply(inverse(X_135),X_26)) != X_26
| inverse(multiply(inverse(X_135),X_26)) != multiply(inverse(multiply(X_135,multiply(inverse(X_135),X_26))),X_135)
| inverse(multiply(inverse(X_135),X_26)) = multiply(inverse(X_26),X_135) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_135),X_26)),multiply(inverse(multiply(X_135,multiply(inverse(X_135),X_26))),X_135)) ),[1,0,0],$fot(X_26)]]) ).
cnf(refute_0_109,plain,
( inverse(multiply(inverse(X_135),X_26)) != multiply(inverse(multiply(X_135,multiply(inverse(X_135),X_26))),X_135)
| inverse(multiply(inverse(X_135),X_26)) = multiply(inverse(X_26),X_135) ),
inference(resolve,[$cnf( $equal(multiply(X_135,multiply(inverse(X_135),X_26)),X_26) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
inverse(multiply(inverse(X_135),X_26)) = multiply(inverse(X_26),X_135),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_135),X_26)),multiply(inverse(multiply(X_135,multiply(inverse(X_135),X_26))),X_135)) )],[refute_0_97,refute_0_109]) ).
cnf(refute_0_111,plain,
inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))) = multiply(inverse(greatest_lower_bound(identity,X_80)),X_80),
inference(subst,[],[refute_0_110:[bind(X_135,$fot(X_80)),bind(X_26,$fot(greatest_lower_bound(identity,X_80)))]]) ).
cnf(refute_0_112,plain,
( inverse(multiply(X_25,X_26)) != multiply(inverse(X_26),inverse(X_25))
| multiply(inverse(X_26),inverse(X_25)) = inverse(multiply(X_25,X_26)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(multiply(X_25,X_26)))),bind(Y0,$fot(multiply(inverse(X_26),inverse(X_25))))]]) ).
cnf(refute_0_113,plain,
multiply(inverse(X_26),inverse(X_25)) = inverse(multiply(X_25,X_26)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_25,X_26)),multiply(inverse(X_26),inverse(X_25))) )],[refute_0_76,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))) = inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))),
inference(subst,[],[refute_0_113:[bind(X_25,$fot(inverse(X_80))),bind(X_26,$fot(greatest_lower_bound(identity,X_80)))]]) ).
cnf(refute_0_115,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_116,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_19,refute_0_115]) ).
cnf(refute_0_117,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))) != inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80)))
| inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))) != multiply(inverse(greatest_lower_bound(identity,X_80)),X_80)
| multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))) = multiply(inverse(greatest_lower_bound(identity,X_80)),X_80) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))))),bind(Y0,$fot(inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,X_80)),X_80)))]]) ).
cnf(refute_0_118,plain,
( inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))) != multiply(inverse(greatest_lower_bound(identity,X_80)),X_80)
| multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))) = multiply(inverse(greatest_lower_bound(identity,X_80)),X_80) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))),inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80)))) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))) = multiply(inverse(greatest_lower_bound(identity,X_80)),X_80),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(identity,X_80)),X_80)) )],[refute_0_111,refute_0_118]) ).
cnf(refute_0_120,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))) != multiply(inverse(greatest_lower_bound(identity,X_80)),X_80)
| inverse(greatest_lower_bound(identity,inverse(X_80))) != multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80)))
| inverse(greatest_lower_bound(identity,inverse(X_80))) = multiply(inverse(greatest_lower_bound(identity,X_80)),X_80) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_80))),multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(identity,X_80)),X_80))]]) ).
cnf(refute_0_121,plain,
( inverse(greatest_lower_bound(identity,inverse(X_80))) != multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80)))
| inverse(greatest_lower_bound(identity,inverse(X_80))) = multiply(inverse(greatest_lower_bound(identity,X_80)),X_80) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80))),multiply(inverse(greatest_lower_bound(identity,X_80)),X_80)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
inverse(greatest_lower_bound(identity,inverse(X_80))) = multiply(inverse(greatest_lower_bound(identity,X_80)),X_80),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_80))),multiply(inverse(greatest_lower_bound(identity,X_80)),inverse(inverse(X_80)))) )],[refute_0_96,refute_0_121]) ).
cnf(refute_0_123,plain,
inverse(greatest_lower_bound(identity,inverse(X_73))) = multiply(inverse(greatest_lower_bound(identity,X_73)),X_73),
inference(subst,[],[refute_0_122:[bind(X_80,$fot(X_73))]]) ).
cnf(refute_0_124,plain,
( inverse(greatest_lower_bound(identity,inverse(X_73))) != multiply(inverse(greatest_lower_bound(identity,X_73)),X_73)
| multiply(inverse(greatest_lower_bound(identity,X_73)),X_73) = inverse(greatest_lower_bound(identity,inverse(X_73))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_73))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_73)),X_73)))]]) ).
cnf(refute_0_125,plain,
multiply(inverse(greatest_lower_bound(identity,X_73)),X_73) = inverse(greatest_lower_bound(identity,inverse(X_73))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_73))),multiply(inverse(greatest_lower_bound(identity,X_73)),X_73)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
( multiply(inverse(greatest_lower_bound(identity,X_73)),X_73) != inverse(greatest_lower_bound(identity,inverse(X_73)))
| multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),multiply(inverse(greatest_lower_bound(identity,X_73)),X_73))
| multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),multiply(inverse(greatest_lower_bound(identity,X_73)),X_73))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(X_73))))]]) ).
cnf(refute_0_127,plain,
( multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),multiply(inverse(greatest_lower_bound(identity,X_73)),X_73))
| multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_73)),X_73),inverse(greatest_lower_bound(identity,inverse(X_73)))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),multiply(inverse(greatest_lower_bound(identity,X_73)),X_73))) )],[refute_0_43,refute_0_127]) ).
cnf(refute_0_129,plain,
multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79)),
inference(subst,[],[refute_0_86:[bind(X_73,$fot(X_79)),bind(X_74,$fot(greatest_lower_bound(Y,X_79)))]]) ).
cnf(refute_0_130,plain,
greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) = X_12,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_131,plain,
least_upper_bound(X_13,X_12) = least_upper_bound(X_12,X_13),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_132,plain,
( least_upper_bound(X_13,X_12) != least_upper_bound(X_12,X_13)
| least_upper_bound(X_12,X_13) = least_upper_bound(X_13,X_12) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_13,X_12))),bind(Y0,$fot(least_upper_bound(X_12,X_13)))]]) ).
cnf(refute_0_133,plain,
least_upper_bound(X_12,X_13) = least_upper_bound(X_13,X_12),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,X_12),least_upper_bound(X_12,X_13)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
( greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)) != X_12
| least_upper_bound(X_12,X_13) != least_upper_bound(X_13,X_12)
| greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12 ),
introduced(tautology,[equality,[$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_135,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( $equal(least_upper_bound(X_12,X_13),least_upper_bound(X_13,X_12)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
greatest_lower_bound(X_12,least_upper_bound(X_13,X_12)) = X_12,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(X_12,X_13)),X_12) )],[refute_0_130,refute_0_135]) ).
cnf(refute_0_137,plain,
greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))) = greatest_lower_bound(X_17,Y),
inference(subst,[],[refute_0_136:[bind(X_12,$fot(greatest_lower_bound(X_17,Y))),bind(X_13,$fot(X_17))]]) ).
cnf(refute_0_138,plain,
least_upper_bound(X_17,greatest_lower_bound(X_17,Y)) = X_17,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_139,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))) != greatest_lower_bound(X_17,Y)
| least_upper_bound(X_17,greatest_lower_bound(X_17,Y)) != X_17
| greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))),greatest_lower_bound(X_17,Y)) ),[0,1],$fot(X_17)]]) ).
cnf(refute_0_140,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))) != greatest_lower_bound(X_17,Y)
| greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_17,greatest_lower_bound(X_17,Y)),X_17) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),least_upper_bound(X_17,greatest_lower_bound(X_17,Y))),greatest_lower_bound(X_17,Y)) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_143,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_142]) ).
cnf(refute_0_144,plain,
greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) = greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)),
inference(subst,[],[refute_0_143:[bind(X,$fot(X_17)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_145,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) != greatest_lower_bound(X_17,Y)
| greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) != greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)) = greatest_lower_bound(X_17,Y) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17),greatest_lower_bound(X_17,Y)) ),[0],$fot(greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)))]]) ).
cnf(refute_0_146,plain,
( greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17) != greatest_lower_bound(X_17,Y)
| greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)) = greatest_lower_bound(X_17,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17),greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
greatest_lower_bound(X_17,greatest_lower_bound(Y,X_17)) = greatest_lower_bound(X_17,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_17,Y),X_17),greatest_lower_bound(X_17,Y)) )],[refute_0_141,refute_0_146]) ).
cnf(refute_0_148,plain,
greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79)) = greatest_lower_bound(X_79,Y),
inference(subst,[],[refute_0_147:[bind(X_17,$fot(X_79))]]) ).
cnf(refute_0_149,plain,
( multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79))
| greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79)) != greatest_lower_bound(X_79,Y)
| multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79))) ),[0,1],$fot(greatest_lower_bound(X_79,Y))]]) ).
cnf(refute_0_150,plain,
( multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79))) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79))
| multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,greatest_lower_bound(Y,X_79))),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79))) )],[refute_0_129,refute_0_150]) ).
cnf(refute_0_152,plain,
greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_61),X_60))) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_61),X_60)))]]) ).
cnf(refute_0_153,plain,
multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(inverse(X_50),X_49),multiply(inverse(X_50),X_50)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_50))),bind(Y,$fot(X_49)),bind(Z,$fot(X_50))]]) ).
cnf(refute_0_154,plain,
multiply(inverse(X_50),X_50) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_155,plain,
( multiply(inverse(X_50),X_50) != identity
| multiply(inverse(X_50),least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(inverse(X_50),X_49),multiply(inverse(X_50),X_50))
| multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(inverse(X_50),X_49),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_50),least_upper_bound(X_49,X_50)),least_upper_bound(multiply(inverse(X_50),X_49),multiply(inverse(X_50),X_50))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_156,plain,
( multiply(inverse(X_50),least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(inverse(X_50),X_49),multiply(inverse(X_50),X_50))
| multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(inverse(X_50),X_49),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_50),X_50),identity) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(inverse(X_50),X_49),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_50),least_upper_bound(X_49,X_50)),least_upper_bound(multiply(inverse(X_50),X_49),multiply(inverse(X_50),X_50))) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_159,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_158]) ).
cnf(refute_0_160,plain,
least_upper_bound(multiply(inverse(X_50),X_49),identity) = least_upper_bound(identity,multiply(inverse(X_50),X_49)),
inference(subst,[],[refute_0_159:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_50),X_49)))]]) ).
cnf(refute_0_161,plain,
( multiply(inverse(X_50),least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(inverse(X_50),X_49),identity)
| least_upper_bound(multiply(inverse(X_50),X_49),identity) != least_upper_bound(identity,multiply(inverse(X_50),X_49))
| multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(identity,multiply(inverse(X_50),X_49)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_50),least_upper_bound(X_49,X_50)),least_upper_bound(identity,multiply(inverse(X_50),X_49))) ),[0],$fot(least_upper_bound(multiply(inverse(X_50),X_49),identity))]]) ).
cnf(refute_0_162,plain,
( multiply(inverse(X_50),least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(inverse(X_50),X_49),identity)
| multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(identity,multiply(inverse(X_50),X_49)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_50),X_49),identity),least_upper_bound(identity,multiply(inverse(X_50),X_49))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
multiply(inverse(X_50),least_upper_bound(X_49,X_50)) = least_upper_bound(identity,multiply(inverse(X_50),X_49)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_50),least_upper_bound(X_49,X_50)),least_upper_bound(multiply(inverse(X_50),X_49),identity)) )],[refute_0_157,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(inverse(X_61),least_upper_bound(X_60,X_61)) = least_upper_bound(identity,multiply(inverse(X_61),X_60)),
inference(subst,[],[refute_0_163:[bind(X_49,$fot(X_60)),bind(X_50,$fot(X_61))]]) ).
cnf(refute_0_165,plain,
( multiply(inverse(X_61),least_upper_bound(X_60,X_61)) != least_upper_bound(identity,multiply(inverse(X_61),X_60))
| least_upper_bound(identity,multiply(inverse(X_61),X_60)) = multiply(inverse(X_61),least_upper_bound(X_60,X_61)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(inverse(X_61),least_upper_bound(X_60,X_61)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_61),X_60))))]]) ).
cnf(refute_0_166,plain,
least_upper_bound(identity,multiply(inverse(X_61),X_60)) = multiply(inverse(X_61),least_upper_bound(X_60,X_61)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_61),least_upper_bound(X_60,X_61)),least_upper_bound(identity,multiply(inverse(X_61),X_60))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_61),X_60))) != identity
| least_upper_bound(identity,multiply(inverse(X_61),X_60)) != multiply(inverse(X_61),least_upper_bound(X_60,X_61))
| greatest_lower_bound(identity,multiply(inverse(X_61),least_upper_bound(X_60,X_61))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_61),X_60))),identity) ),[0,1],$fot(multiply(inverse(X_61),least_upper_bound(X_60,X_61)))]]) ).
cnf(refute_0_168,plain,
( greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_61),X_60))) != identity
| greatest_lower_bound(identity,multiply(inverse(X_61),least_upper_bound(X_60,X_61))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_61),X_60)),multiply(inverse(X_61),least_upper_bound(X_60,X_61))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
greatest_lower_bound(identity,multiply(inverse(X_61),least_upper_bound(X_60,X_61))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,multiply(inverse(X_61),X_60))),identity) )],[refute_0_152,refute_0_168]) ).
cnf(refute_0_170,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_9,X_100)),least_upper_bound(X_100,greatest_lower_bound(X_9,X_100)))) = identity,
inference(subst,[],[refute_0_169:[bind(X_60,$fot(X_100)),bind(X_61,$fot(greatest_lower_bound(X_9,X_100)))]]) ).
cnf(refute_0_171,plain,
least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) = X_8,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_172,plain,
greatest_lower_bound(X_9,X_8) = greatest_lower_bound(X_8,X_9),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_173,plain,
( greatest_lower_bound(X_9,X_8) != greatest_lower_bound(X_8,X_9)
| greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_9,X_8))),bind(Y0,$fot(greatest_lower_bound(X_8,X_9)))]]) ).
cnf(refute_0_174,plain,
greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,X_8),greatest_lower_bound(X_8,X_9)) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
( greatest_lower_bound(X_8,X_9) != greatest_lower_bound(X_9,X_8)
| least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) ),[0,1],$fot(greatest_lower_bound(X_9,X_8))]]) ).
cnf(refute_0_176,plain,
( least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,X_9),greatest_lower_bound(X_9,X_8)) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) )],[refute_0_171,refute_0_176]) ).
cnf(refute_0_178,plain,
least_upper_bound(X_100,greatest_lower_bound(X_9,X_100)) = X_100,
inference(subst,[],[refute_0_177:[bind(X_8,$fot(X_100))]]) ).
cnf(refute_0_179,plain,
( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_9,X_100)),least_upper_bound(X_100,greatest_lower_bound(X_9,X_100)))) != identity
| least_upper_bound(X_100,greatest_lower_bound(X_9,X_100)) != X_100
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_9,X_100)),X_100)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_9,X_100)),least_upper_bound(X_100,greatest_lower_bound(X_9,X_100)))),identity) ),[0,1,1],$fot(X_100)]]) ).
cnf(refute_0_180,plain,
( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_9,X_100)),least_upper_bound(X_100,greatest_lower_bound(X_9,X_100)))) != identity
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_9,X_100)),X_100)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_100,greatest_lower_bound(X_9,X_100)),X_100) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_9,X_100)),X_100)) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_9,X_100)),least_upper_bound(X_100,greatest_lower_bound(X_9,X_100)))),identity) )],[refute_0_170,refute_0_180]) ).
cnf(refute_0_182,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79)) = identity,
inference(subst,[],[refute_0_181:[bind(X_100,$fot(X_79)),bind(X_9,$fot(Y))]]) ).
cnf(refute_0_183,plain,
( multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79))
| greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79)) != identity
| multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)),identity) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79)))]]) ).
cnf(refute_0_184,plain,
( multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)) != greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79))
| multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79)),identity) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(Y,X_79)),greatest_lower_bound(X_79,Y)),greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y,X_79)),X_79))) )],[refute_0_151,refute_0_184]) ).
cnf(refute_0_186,plain,
multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)) = identity,
inference(subst,[],[refute_0_185:[bind(Y,$fot(identity)),bind(X_79,$fot(X_73))]]) ).
cnf(refute_0_187,plain,
( multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73))))
| multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)) != identity
| identity = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73))))) ),[0],$fot(identity)]]) ).
cnf(refute_0_188,plain,
( multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73))))
| identity = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)),identity) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
identity = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_73)),greatest_lower_bound(X_73,identity)),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73))))) )],[refute_0_128,refute_0_188]) ).
cnf(refute_0_190,plain,
multiply(inverse(X_25),greatest_lower_bound(multiply(X_25,X_26),X_74)) = greatest_lower_bound(multiply(inverse(X_25),multiply(X_25,X_26)),multiply(inverse(X_25),X_74)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_25))),bind(Y,$fot(multiply(X_25,X_26))),bind(Z,$fot(X_74))]]) ).
cnf(refute_0_191,plain,
( multiply(inverse(X_25),multiply(X_25,X_26)) != X_26
| multiply(inverse(X_25),greatest_lower_bound(multiply(X_25,X_26),X_74)) != greatest_lower_bound(multiply(inverse(X_25),multiply(X_25,X_26)),multiply(inverse(X_25),X_74))
| multiply(inverse(X_25),greatest_lower_bound(multiply(X_25,X_26),X_74)) = greatest_lower_bound(X_26,multiply(inverse(X_25),X_74)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_25),greatest_lower_bound(multiply(X_25,X_26),X_74)),greatest_lower_bound(multiply(inverse(X_25),multiply(X_25,X_26)),multiply(inverse(X_25),X_74))) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_192,plain,
( multiply(inverse(X_25),greatest_lower_bound(multiply(X_25,X_26),X_74)) != greatest_lower_bound(multiply(inverse(X_25),multiply(X_25,X_26)),multiply(inverse(X_25),X_74))
| multiply(inverse(X_25),greatest_lower_bound(multiply(X_25,X_26),X_74)) = greatest_lower_bound(X_26,multiply(inverse(X_25),X_74)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),multiply(X_25,X_26)),X_26) )],[refute_0_73,refute_0_191]) ).
cnf(refute_0_193,plain,
multiply(inverse(X_25),greatest_lower_bound(multiply(X_25,X_26),X_74)) = greatest_lower_bound(X_26,multiply(inverse(X_25),X_74)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),greatest_lower_bound(multiply(X_25,X_26),X_74)),greatest_lower_bound(multiply(inverse(X_25),multiply(X_25,X_26)),multiply(inverse(X_25),X_74))) )],[refute_0_190,refute_0_192]) ).
cnf(refute_0_194,plain,
multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity)) = greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)),
inference(subst,[],[refute_0_193:[bind(X_25,$fot(greatest_lower_bound(X_419,identity))),bind(X_74,$fot(identity))]]) ).
cnf(refute_0_195,plain,
multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)) = greatest_lower_bound(multiply(inverse(X_52),least_upper_bound(X_52,identity)),multiply(inverse(X_52),X_74)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_52))),bind(Y,$fot(least_upper_bound(X_52,identity))),bind(Z,$fot(X_74))]]) ).
cnf(refute_0_196,plain,
multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(multiply(X_48,X_49),multiply(X_48,identity)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_48)),bind(Y,$fot(X_49)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_197,plain,
X_48 = multiply(X_48,identity),
inference(subst,[],[refute_0_30:[bind(X_28,$fot(X_48))]]) ).
cnf(refute_0_198,plain,
( X_48 != multiply(X_48,identity)
| multiply(X_48,identity) = X_48 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_48)),bind(Y0,$fot(multiply(X_48,identity)))]]) ).
cnf(refute_0_199,plain,
multiply(X_48,identity) = X_48,
inference(resolve,[$cnf( $equal(X_48,multiply(X_48,identity)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
( multiply(X_48,identity) != X_48
| multiply(X_48,least_upper_bound(X_49,identity)) != least_upper_bound(multiply(X_48,X_49),multiply(X_48,identity))
| multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(multiply(X_48,X_49),X_48) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,identity)),least_upper_bound(multiply(X_48,X_49),multiply(X_48,identity))) ),[1,1],$fot(X_48)]]) ).
cnf(refute_0_201,plain,
( multiply(X_48,least_upper_bound(X_49,identity)) != least_upper_bound(multiply(X_48,X_49),multiply(X_48,identity))
| multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(multiply(X_48,X_49),X_48) ),
inference(resolve,[$cnf( $equal(multiply(X_48,identity),X_48) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(multiply(X_48,X_49),X_48),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,identity)),least_upper_bound(multiply(X_48,X_49),multiply(X_48,identity))) )],[refute_0_196,refute_0_201]) ).
cnf(refute_0_203,plain,
least_upper_bound(multiply(X_48,X_49),X_48) = least_upper_bound(X_48,multiply(X_48,X_49)),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_48)),bind(Y,$fot(multiply(X_48,X_49)))]]) ).
cnf(refute_0_204,plain,
( multiply(X_48,least_upper_bound(X_49,identity)) != least_upper_bound(multiply(X_48,X_49),X_48)
| least_upper_bound(multiply(X_48,X_49),X_48) != least_upper_bound(X_48,multiply(X_48,X_49))
| multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(X_48,multiply(X_48,X_49)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_48,least_upper_bound(X_49,identity)),least_upper_bound(X_48,multiply(X_48,X_49))) ),[0],$fot(least_upper_bound(multiply(X_48,X_49),X_48))]]) ).
cnf(refute_0_205,plain,
( multiply(X_48,least_upper_bound(X_49,identity)) != least_upper_bound(multiply(X_48,X_49),X_48)
| multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(X_48,multiply(X_48,X_49)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),X_48),least_upper_bound(X_48,multiply(X_48,X_49))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
multiply(X_48,least_upper_bound(X_49,identity)) = least_upper_bound(X_48,multiply(X_48,X_49)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,identity)),least_upper_bound(multiply(X_48,X_49),X_48)) )],[refute_0_202,refute_0_205]) ).
cnf(refute_0_207,plain,
multiply(inverse(X_52),least_upper_bound(X_52,identity)) = least_upper_bound(inverse(X_52),multiply(inverse(X_52),X_52)),
inference(subst,[],[refute_0_206:[bind(X_48,$fot(inverse(X_52))),bind(X_49,$fot(X_52))]]) ).
cnf(refute_0_208,plain,
multiply(inverse(X_52),X_52) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_52))]]) ).
cnf(refute_0_209,plain,
( multiply(inverse(X_52),X_52) != identity
| multiply(inverse(X_52),least_upper_bound(X_52,identity)) != least_upper_bound(inverse(X_52),multiply(inverse(X_52),X_52))
| multiply(inverse(X_52),least_upper_bound(X_52,identity)) = least_upper_bound(inverse(X_52),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_52),least_upper_bound(X_52,identity)),least_upper_bound(inverse(X_52),multiply(inverse(X_52),X_52))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_210,plain,
( multiply(inverse(X_52),least_upper_bound(X_52,identity)) != least_upper_bound(inverse(X_52),multiply(inverse(X_52),X_52))
| multiply(inverse(X_52),least_upper_bound(X_52,identity)) = least_upper_bound(inverse(X_52),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),X_52),identity) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
multiply(inverse(X_52),least_upper_bound(X_52,identity)) = least_upper_bound(inverse(X_52),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),least_upper_bound(X_52,identity)),least_upper_bound(inverse(X_52),multiply(inverse(X_52),X_52))) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
least_upper_bound(inverse(X_52),identity) = least_upper_bound(identity,inverse(X_52)),
inference(subst,[],[refute_0_159:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_52)))]]) ).
cnf(refute_0_213,plain,
( multiply(inverse(X_52),least_upper_bound(X_52,identity)) != least_upper_bound(inverse(X_52),identity)
| least_upper_bound(inverse(X_52),identity) != least_upper_bound(identity,inverse(X_52))
| multiply(inverse(X_52),least_upper_bound(X_52,identity)) = least_upper_bound(identity,inverse(X_52)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_52),least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52))) ),[0],$fot(least_upper_bound(inverse(X_52),identity))]]) ).
cnf(refute_0_214,plain,
( multiply(inverse(X_52),least_upper_bound(X_52,identity)) != least_upper_bound(inverse(X_52),identity)
| multiply(inverse(X_52),least_upper_bound(X_52,identity)) = least_upper_bound(identity,inverse(X_52)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_52),identity),least_upper_bound(identity,inverse(X_52))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
multiply(inverse(X_52),least_upper_bound(X_52,identity)) = least_upper_bound(identity,inverse(X_52)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),least_upper_bound(X_52,identity)),least_upper_bound(inverse(X_52),identity)) )],[refute_0_211,refute_0_214]) ).
cnf(refute_0_216,plain,
( multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)) != greatest_lower_bound(multiply(inverse(X_52),least_upper_bound(X_52,identity)),multiply(inverse(X_52),X_74))
| multiply(inverse(X_52),least_upper_bound(X_52,identity)) != least_upper_bound(identity,inverse(X_52))
| multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(inverse(X_52),X_74)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)),greatest_lower_bound(multiply(inverse(X_52),least_upper_bound(X_52,identity)),multiply(inverse(X_52),X_74))) ),[1,0],$fot(least_upper_bound(identity,inverse(X_52)))]]) ).
cnf(refute_0_217,plain,
( multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)) != greatest_lower_bound(multiply(inverse(X_52),least_upper_bound(X_52,identity)),multiply(inverse(X_52),X_74))
| multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(inverse(X_52),X_74)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(inverse(X_52),X_74)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)),greatest_lower_bound(multiply(inverse(X_52),least_upper_bound(X_52,identity)),multiply(inverse(X_52),X_74))) )],[refute_0_195,refute_0_217]) ).
cnf(refute_0_219,plain,
multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(identity,X_80)),X_150)),
inference(subst,[],[refute_0_218:[bind(X_52,$fot(greatest_lower_bound(identity,X_80))),bind(X_74,$fot(X_150))]]) ).
cnf(refute_0_220,plain,
inverse(greatest_lower_bound(identity,X_80)) = multiply(inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))),inverse(X_80)),
inference(subst,[],[refute_0_70:[bind(X_45,$fot(inverse(X_80))),bind(X_46,$fot(greatest_lower_bound(identity,X_80)))]]) ).
cnf(refute_0_221,plain,
( multiply(inverse(X_80),greatest_lower_bound(identity,X_80)) != greatest_lower_bound(identity,inverse(X_80))
| inverse(greatest_lower_bound(identity,X_80)) != multiply(inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))),inverse(X_80))
| inverse(greatest_lower_bound(identity,X_80)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))),inverse(X_80))) ),[1,0,0],$fot(greatest_lower_bound(identity,inverse(X_80)))]]) ).
cnf(refute_0_222,plain,
( inverse(greatest_lower_bound(identity,X_80)) != multiply(inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))),inverse(X_80))
| inverse(greatest_lower_bound(identity,X_80)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,inverse(X_80))) )],[refute_0_93,refute_0_221]) ).
cnf(refute_0_223,plain,
inverse(greatest_lower_bound(identity,X_80)) = multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(multiply(inverse(X_80),greatest_lower_bound(identity,X_80))),inverse(X_80))) )],[refute_0_220,refute_0_222]) ).
cnf(refute_0_224,plain,
multiply(greatest_lower_bound(X_80,identity),identity) = greatest_lower_bound(X_80,identity),
inference(subst,[],[refute_0_62:[bind(X_28,$fot(greatest_lower_bound(X_80,identity)))]]) ).
cnf(refute_0_225,plain,
multiply(greatest_lower_bound(X_92,identity),X_91) = greatest_lower_bound(multiply(X_92,X_91),multiply(identity,X_91)),
inference(subst,[],[monotony_glb2:[bind(X,$fot(X_91)),bind(Y,$fot(X_92)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_226,plain,
multiply(identity,X_91) = X_91,
inference(subst,[],[left_identity:[bind(X,$fot(X_91))]]) ).
cnf(refute_0_227,plain,
( multiply(greatest_lower_bound(X_92,identity),X_91) != greatest_lower_bound(multiply(X_92,X_91),multiply(identity,X_91))
| multiply(identity,X_91) != X_91
| multiply(greatest_lower_bound(X_92,identity),X_91) = greatest_lower_bound(multiply(X_92,X_91),X_91) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_92,identity),X_91),greatest_lower_bound(multiply(X_92,X_91),multiply(identity,X_91))) ),[1,1],$fot(X_91)]]) ).
cnf(refute_0_228,plain,
( multiply(greatest_lower_bound(X_92,identity),X_91) != greatest_lower_bound(multiply(X_92,X_91),multiply(identity,X_91))
| multiply(greatest_lower_bound(X_92,identity),X_91) = greatest_lower_bound(multiply(X_92,X_91),X_91) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_91),X_91) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
multiply(greatest_lower_bound(X_92,identity),X_91) = greatest_lower_bound(multiply(X_92,X_91),X_91),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_92,identity),X_91),greatest_lower_bound(multiply(X_92,X_91),multiply(identity,X_91))) )],[refute_0_225,refute_0_228]) ).
cnf(refute_0_230,plain,
greatest_lower_bound(multiply(X_92,X_91),X_91) = greatest_lower_bound(X_91,multiply(X_92,X_91)),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_91)),bind(Y,$fot(multiply(X_92,X_91)))]]) ).
cnf(refute_0_231,plain,
( multiply(greatest_lower_bound(X_92,identity),X_91) != greatest_lower_bound(multiply(X_92,X_91),X_91)
| greatest_lower_bound(multiply(X_92,X_91),X_91) != greatest_lower_bound(X_91,multiply(X_92,X_91))
| multiply(greatest_lower_bound(X_92,identity),X_91) = greatest_lower_bound(X_91,multiply(X_92,X_91)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_92,identity),X_91),greatest_lower_bound(X_91,multiply(X_92,X_91))) ),[0],$fot(greatest_lower_bound(multiply(X_92,X_91),X_91))]]) ).
cnf(refute_0_232,plain,
( multiply(greatest_lower_bound(X_92,identity),X_91) != greatest_lower_bound(multiply(X_92,X_91),X_91)
| multiply(greatest_lower_bound(X_92,identity),X_91) = greatest_lower_bound(X_91,multiply(X_92,X_91)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_92,X_91),X_91),greatest_lower_bound(X_91,multiply(X_92,X_91))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
multiply(greatest_lower_bound(X_92,identity),X_91) = greatest_lower_bound(X_91,multiply(X_92,X_91)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_92,identity),X_91),greatest_lower_bound(multiply(X_92,X_91),X_91)) )],[refute_0_229,refute_0_232]) ).
cnf(refute_0_234,plain,
( multiply(greatest_lower_bound(X_92,identity),X_91) != greatest_lower_bound(X_91,multiply(X_92,X_91))
| greatest_lower_bound(X_91,multiply(X_92,X_91)) = multiply(greatest_lower_bound(X_92,identity),X_91) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(X_92,identity),X_91))),bind(Y0,$fot(greatest_lower_bound(X_91,multiply(X_92,X_91))))]]) ).
cnf(refute_0_235,plain,
greatest_lower_bound(X_91,multiply(X_92,X_91)) = multiply(greatest_lower_bound(X_92,identity),X_91),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_92,identity),X_91),greatest_lower_bound(X_91,multiply(X_92,X_91))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
greatest_lower_bound(identity,multiply(X_80,identity)) = multiply(greatest_lower_bound(X_80,identity),identity),
inference(subst,[],[refute_0_235:[bind(X_91,$fot(identity)),bind(X_92,$fot(X_80))]]) ).
cnf(refute_0_237,plain,
( multiply(greatest_lower_bound(X_80,identity),identity) != greatest_lower_bound(X_80,identity)
| greatest_lower_bound(identity,multiply(X_80,identity)) != multiply(greatest_lower_bound(X_80,identity),identity)
| greatest_lower_bound(identity,multiply(X_80,identity)) = greatest_lower_bound(X_80,identity) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(identity,multiply(X_80,identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(X_80,identity),identity))),bind(Z0,$fot(greatest_lower_bound(X_80,identity)))]]) ).
cnf(refute_0_238,plain,
( multiply(greatest_lower_bound(X_80,identity),identity) != greatest_lower_bound(X_80,identity)
| greatest_lower_bound(identity,multiply(X_80,identity)) = greatest_lower_bound(X_80,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_80,identity)),multiply(greatest_lower_bound(X_80,identity),identity)) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
greatest_lower_bound(identity,multiply(X_80,identity)) = greatest_lower_bound(X_80,identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_80,identity),identity),greatest_lower_bound(X_80,identity)) )],[refute_0_224,refute_0_238]) ).
cnf(refute_0_240,plain,
multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))) = greatest_lower_bound(multiply(X_72,X_73),multiply(X_72,inverse(X_72))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_72)),bind(Y,$fot(X_73)),bind(Z,$fot(inverse(X_72)))]]) ).
cnf(refute_0_241,plain,
multiply(X_72,inverse(X_72)) = identity,
inference(subst,[],[refute_0_56:[bind(X_30,$fot(X_72))]]) ).
cnf(refute_0_242,plain,
( multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))) != greatest_lower_bound(multiply(X_72,X_73),multiply(X_72,inverse(X_72)))
| multiply(X_72,inverse(X_72)) != identity
| multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))) = greatest_lower_bound(multiply(X_72,X_73),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))),greatest_lower_bound(multiply(X_72,X_73),multiply(X_72,inverse(X_72)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_243,plain,
( multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))) != greatest_lower_bound(multiply(X_72,X_73),multiply(X_72,inverse(X_72)))
| multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))) = greatest_lower_bound(multiply(X_72,X_73),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_72,inverse(X_72)),identity) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))) = greatest_lower_bound(multiply(X_72,X_73),identity),
inference(resolve,[$cnf( $equal(multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))),greatest_lower_bound(multiply(X_72,X_73),multiply(X_72,inverse(X_72)))) )],[refute_0_240,refute_0_243]) ).
cnf(refute_0_245,plain,
greatest_lower_bound(multiply(X_72,X_73),identity) = greatest_lower_bound(identity,multiply(X_72,X_73)),
inference(subst,[],[refute_0_38:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_72,X_73)))]]) ).
cnf(refute_0_246,plain,
( multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))) != greatest_lower_bound(multiply(X_72,X_73),identity)
| greatest_lower_bound(multiply(X_72,X_73),identity) != greatest_lower_bound(identity,multiply(X_72,X_73))
| multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))) = greatest_lower_bound(identity,multiply(X_72,X_73)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))),greatest_lower_bound(identity,multiply(X_72,X_73))) ),[0],$fot(greatest_lower_bound(multiply(X_72,X_73),identity))]]) ).
cnf(refute_0_247,plain,
( multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))) != greatest_lower_bound(multiply(X_72,X_73),identity)
| multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))) = greatest_lower_bound(identity,multiply(X_72,X_73)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_72,X_73),identity),greatest_lower_bound(identity,multiply(X_72,X_73))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))) = greatest_lower_bound(identity,multiply(X_72,X_73)),
inference(resolve,[$cnf( $equal(multiply(X_72,greatest_lower_bound(X_73,inverse(X_72))),greatest_lower_bound(multiply(X_72,X_73),identity)) )],[refute_0_244,refute_0_247]) ).
cnf(refute_0_249,plain,
multiply(X_80,greatest_lower_bound(identity,inverse(X_80))) = greatest_lower_bound(identity,multiply(X_80,identity)),
inference(subst,[],[refute_0_248:[bind(X_72,$fot(X_80)),bind(X_73,$fot(identity))]]) ).
cnf(refute_0_250,plain,
( multiply(X_80,greatest_lower_bound(identity,inverse(X_80))) != greatest_lower_bound(identity,multiply(X_80,identity))
| greatest_lower_bound(identity,multiply(X_80,identity)) != greatest_lower_bound(X_80,identity)
| multiply(X_80,greatest_lower_bound(identity,inverse(X_80))) = greatest_lower_bound(X_80,identity) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(X_80,greatest_lower_bound(identity,inverse(X_80))))),bind(Y0,$fot(greatest_lower_bound(identity,multiply(X_80,identity)))),bind(Z0,$fot(greatest_lower_bound(X_80,identity)))]]) ).
cnf(refute_0_251,plain,
( greatest_lower_bound(identity,multiply(X_80,identity)) != greatest_lower_bound(X_80,identity)
| multiply(X_80,greatest_lower_bound(identity,inverse(X_80))) = greatest_lower_bound(X_80,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_80,greatest_lower_bound(identity,inverse(X_80))),greatest_lower_bound(identity,multiply(X_80,identity))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
multiply(X_80,greatest_lower_bound(identity,inverse(X_80))) = greatest_lower_bound(X_80,identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_80,identity)),greatest_lower_bound(X_80,identity)) )],[refute_0_239,refute_0_251]) ).
cnf(refute_0_253,plain,
inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))) = inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))))]]) ).
cnf(refute_0_254,plain,
( multiply(X_80,greatest_lower_bound(identity,inverse(X_80))) != greatest_lower_bound(X_80,identity)
| inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))) != inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80))))
| inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))) = inverse(greatest_lower_bound(X_80,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))),inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80))))) ),[1,0],$fot(greatest_lower_bound(X_80,identity))]]) ).
cnf(refute_0_255,plain,
( multiply(X_80,greatest_lower_bound(identity,inverse(X_80))) != greatest_lower_bound(X_80,identity)
| inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))) = inverse(greatest_lower_bound(X_80,identity)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))),inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80))))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))) = inverse(greatest_lower_bound(X_80,identity)),
inference(resolve,[$cnf( $equal(multiply(X_80,greatest_lower_bound(identity,inverse(X_80))),greatest_lower_bound(X_80,identity)) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)) = inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))),
inference(subst,[],[refute_0_113:[bind(X_25,$fot(X_80)),bind(X_26,$fot(greatest_lower_bound(identity,inverse(X_80))))]]) ).
cnf(refute_0_258,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)) != inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80))))
| inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))) != inverse(greatest_lower_bound(X_80,identity))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)) = inverse(greatest_lower_bound(X_80,identity)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)))),bind(Y0,$fot(inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))))),bind(Z0,$fot(inverse(greatest_lower_bound(X_80,identity))))]]) ).
cnf(refute_0_259,plain,
( inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))) != inverse(greatest_lower_bound(X_80,identity))
| multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)) = inverse(greatest_lower_bound(X_80,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)),inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80))))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)) = inverse(greatest_lower_bound(X_80,identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_80,greatest_lower_bound(identity,inverse(X_80)))),inverse(greatest_lower_bound(X_80,identity))) )],[refute_0_256,refute_0_259]) ).
cnf(refute_0_261,plain,
( multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)) != inverse(greatest_lower_bound(X_80,identity))
| inverse(greatest_lower_bound(identity,X_80)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80))
| inverse(greatest_lower_bound(identity,X_80)) = inverse(greatest_lower_bound(X_80,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80))) ),[1],$fot(inverse(greatest_lower_bound(X_80,identity)))]]) ).
cnf(refute_0_262,plain,
( inverse(greatest_lower_bound(identity,X_80)) != multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80))
| inverse(greatest_lower_bound(identity,X_80)) = inverse(greatest_lower_bound(X_80,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80)),inverse(greatest_lower_bound(X_80,identity))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
inverse(greatest_lower_bound(identity,X_80)) = inverse(greatest_lower_bound(X_80,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(identity,inverse(X_80))),inverse(X_80))) )],[refute_0_223,refute_0_262]) ).
cnf(refute_0_264,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(identity,X_80)),X_150))
| inverse(greatest_lower_bound(identity,X_80)) != inverse(greatest_lower_bound(X_80,identity))
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(identity,X_80)),X_150))) ),[1,1,0],$fot(inverse(greatest_lower_bound(X_80,identity)))]]) ).
cnf(refute_0_265,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(identity,X_80)),X_150))
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_80)),inverse(greatest_lower_bound(X_80,identity))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(identity,X_80)),X_150))) )],[refute_0_219,refute_0_265]) ).
cnf(refute_0_267,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X_80)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_80))]]) ).
cnf(refute_0_268,plain,
greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150) = greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150))]]) ).
cnf(refute_0_269,plain,
( greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150) != greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)
| least_upper_bound(identity,greatest_lower_bound(identity,X_80)) != identity
| greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150) = greatest_lower_bound(identity,X_150) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_270,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_80)) != identity
| greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150) = greatest_lower_bound(identity,X_150) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150) = greatest_lower_bound(identity,X_150),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),identity) )],[refute_0_267,refute_0_270]) ).
cnf(refute_0_272,plain,
multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)) = multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)))]]) ).
cnf(refute_0_273,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)) != multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150))
| greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150) != greatest_lower_bound(identity,X_150)
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)) = multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)),multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150))) ),[1,1],$fot(greatest_lower_bound(identity,X_150))]]) ).
cnf(refute_0_274,plain,
( greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150) != greatest_lower_bound(identity,X_150)
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)) = multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)),multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)) = multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150),greatest_lower_bound(identity,X_150)) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150)),
inference(subst,[],[refute_0_218:[bind(X_52,$fot(X_149)),bind(X_74,$fot(X_150))]]) ).
cnf(refute_0_277,plain,
least_upper_bound(identity,X_149) = least_upper_bound(X_149,identity),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_149))]]) ).
cnf(refute_0_278,plain,
( least_upper_bound(identity,X_149) != least_upper_bound(X_149,identity)
| least_upper_bound(X_149,identity) = least_upper_bound(identity,X_149) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(identity,X_149))),bind(Y0,$fot(least_upper_bound(X_149,identity)))]]) ).
cnf(refute_0_279,plain,
least_upper_bound(X_149,identity) = least_upper_bound(identity,X_149),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_149),least_upper_bound(X_149,identity)) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
( multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150))
| least_upper_bound(X_149,identity) != least_upper_bound(identity,X_149)
| multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150)),greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150))) ),[0,1,0],$fot(least_upper_bound(identity,X_149))]]) ).
cnf(refute_0_281,plain,
( multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150))
| multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_149,identity),least_upper_bound(identity,X_149)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150)),greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150))) )],[refute_0_276,refute_0_281]) ).
cnf(refute_0_283,plain,
( multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(inverse(X_52),X_74))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(inverse(X_52),X_74)) = multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(inverse(X_52),X_74))))]]) ).
cnf(refute_0_284,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(inverse(X_52),X_74)) = multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),greatest_lower_bound(least_upper_bound(X_52,identity),X_74)),greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(inverse(X_52),X_74))) )],[refute_0_218,refute_0_283]) ).
cnf(refute_0_285,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150)) = multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150)),
inference(subst,[],[refute_0_284:[bind(X_52,$fot(X_149)),bind(X_74,$fot(X_150))]]) ).
cnf(refute_0_286,plain,
( multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150)) != multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150))
| multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)) = multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)),multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150)))]]) ).
cnf(refute_0_287,plain,
( multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150))
| multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)) = multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150)),multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)) = multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)),greatest_lower_bound(least_upper_bound(identity,inverse(X_149)),multiply(inverse(X_149),X_150))) )],[refute_0_282,refute_0_287]) ).
cnf(refute_0_289,plain,
( multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)) != multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150))
| multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150)) = multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)))),bind(Y0,$fot(multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150))))]]) ).
cnf(refute_0_290,plain,
multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150)) = multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(identity,X_149),X_150)),multiply(inverse(X_149),greatest_lower_bound(least_upper_bound(X_149,identity),X_150))) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) = multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)),
inference(subst,[],[refute_0_290:[bind(X_149,$fot(greatest_lower_bound(identity,X_80)))]]) ).
cnf(refute_0_292,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) != multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150))
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)) != multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150))
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) = multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150))))]]) ).
cnf(refute_0_293,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)) != multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150))
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) = multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)),multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) = multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,X_80)),X_150)),multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150))) )],[refute_0_275,refute_0_293]) ).
cnf(refute_0_295,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) != multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150))
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))) ),[0],$fot(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)))]]) ).
cnf(refute_0_296,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)),multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))) = greatest_lower_bound(multiply(inverse(X_52),X_73),multiply(inverse(X_52),least_upper_bound(X_52,identity))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_52))),bind(Y,$fot(X_73)),bind(Z,$fot(least_upper_bound(X_52,identity)))]]) ).
cnf(refute_0_298,plain,
( multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))) != greatest_lower_bound(multiply(inverse(X_52),X_73),multiply(inverse(X_52),least_upper_bound(X_52,identity)))
| multiply(inverse(X_52),least_upper_bound(X_52,identity)) != least_upper_bound(identity,inverse(X_52))
| multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))) = greatest_lower_bound(multiply(inverse(X_52),X_73),least_upper_bound(identity,inverse(X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))),greatest_lower_bound(multiply(inverse(X_52),X_73),multiply(inverse(X_52),least_upper_bound(X_52,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_52)))]]) ).
cnf(refute_0_299,plain,
( multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))) != greatest_lower_bound(multiply(inverse(X_52),X_73),multiply(inverse(X_52),least_upper_bound(X_52,identity)))
| multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))) = greatest_lower_bound(multiply(inverse(X_52),X_73),least_upper_bound(identity,inverse(X_52))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52))) )],[refute_0_215,refute_0_298]) ).
cnf(refute_0_300,plain,
multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))) = greatest_lower_bound(multiply(inverse(X_52),X_73),least_upper_bound(identity,inverse(X_52))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))),greatest_lower_bound(multiply(inverse(X_52),X_73),multiply(inverse(X_52),least_upper_bound(X_52,identity)))) )],[refute_0_297,refute_0_299]) ).
cnf(refute_0_301,plain,
multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(X_80,identity)))),
inference(subst,[],[refute_0_300:[bind(X_52,$fot(greatest_lower_bound(X_80,identity))),bind(X_73,$fot(X_148))]]) ).
cnf(refute_0_302,plain,
( inverse(greatest_lower_bound(identity,X_80)) != inverse(greatest_lower_bound(X_80,identity))
| inverse(greatest_lower_bound(X_80,identity)) = inverse(greatest_lower_bound(identity,X_80)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_80)))),bind(Y0,$fot(inverse(greatest_lower_bound(X_80,identity))))]]) ).
cnf(refute_0_303,plain,
inverse(greatest_lower_bound(X_80,identity)) = inverse(greatest_lower_bound(identity,X_80)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_80)),inverse(greatest_lower_bound(X_80,identity))) )],[refute_0_263,refute_0_302]) ).
cnf(refute_0_304,plain,
( multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(X_80,identity))))
| inverse(greatest_lower_bound(X_80,identity)) != inverse(greatest_lower_bound(identity,X_80))
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(X_80,identity))))) ),[1,1,1],$fot(inverse(greatest_lower_bound(identity,X_80)))]]) ).
cnf(refute_0_305,plain,
( multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(X_80,identity))))
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_80,identity)),inverse(greatest_lower_bound(identity,X_80))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(X_80,identity))))) )],[refute_0_301,refute_0_305]) ).
cnf(refute_0_307,plain,
least_upper_bound(identity,greatest_lower_bound(X_80,identity)) = identity,
inference(subst,[],[refute_0_177:[bind(X_8,$fot(identity)),bind(X_9,$fot(X_80))]]) ).
cnf(refute_0_308,plain,
greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))) = greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))))]]) ).
cnf(refute_0_309,plain,
( greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))) != greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))
| least_upper_bound(identity,greatest_lower_bound(X_80,identity)) != identity
| greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))) = greatest_lower_bound(X_148,identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_310,plain,
( least_upper_bound(identity,greatest_lower_bound(X_80,identity)) != identity
| greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))) = greatest_lower_bound(X_148,identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))) = greatest_lower_bound(X_148,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(X_80,identity)),identity) )],[refute_0_307,refute_0_310]) ).
cnf(refute_0_312,plain,
multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))),
introduced(tautology,[refl,[$fot(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))))]]) ).
cnf(refute_0_313,plain,
( multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))) != multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))))
| greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))) != greatest_lower_bound(X_148,identity)
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))),multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))))) ),[1,1],$fot(greatest_lower_bound(X_148,identity))]]) ).
cnf(refute_0_314,plain,
( greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))) != greatest_lower_bound(X_148,identity)
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))),multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))),greatest_lower_bound(X_148,identity)) )],[refute_0_311,refute_0_314]) ).
cnf(refute_0_316,plain,
multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity))) = greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147))),
inference(subst,[],[refute_0_300:[bind(X_52,$fot(X_147)),bind(X_73,$fot(X_148))]]) ).
cnf(refute_0_317,plain,
least_upper_bound(identity,X_147) = least_upper_bound(X_147,identity),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_147))]]) ).
cnf(refute_0_318,plain,
( least_upper_bound(identity,X_147) != least_upper_bound(X_147,identity)
| least_upper_bound(X_147,identity) = least_upper_bound(identity,X_147) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(identity,X_147))),bind(Y0,$fot(least_upper_bound(X_147,identity)))]]) ).
cnf(refute_0_319,plain,
least_upper_bound(X_147,identity) = least_upper_bound(identity,X_147),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_147),least_upper_bound(X_147,identity)) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
( multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity))) != greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147)))
| least_upper_bound(X_147,identity) != least_upper_bound(identity,X_147)
| multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))) = greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity))),greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147)))) ),[0,1,1],$fot(least_upper_bound(identity,X_147))]]) ).
cnf(refute_0_321,plain,
( multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity))) != greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147)))
| multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))) = greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_147,identity),least_upper_bound(identity,X_147)) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))) = greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity))),greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147)))) )],[refute_0_316,refute_0_321]) ).
cnf(refute_0_323,plain,
( multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))) != greatest_lower_bound(multiply(inverse(X_52),X_73),least_upper_bound(identity,inverse(X_52)))
| greatest_lower_bound(multiply(inverse(X_52),X_73),least_upper_bound(identity,inverse(X_52))) = multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(X_52),X_73),least_upper_bound(identity,inverse(X_52)))))]]) ).
cnf(refute_0_324,plain,
greatest_lower_bound(multiply(inverse(X_52),X_73),least_upper_bound(identity,inverse(X_52))) = multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),greatest_lower_bound(X_73,least_upper_bound(X_52,identity))),greatest_lower_bound(multiply(inverse(X_52),X_73),least_upper_bound(identity,inverse(X_52)))) )],[refute_0_300,refute_0_323]) ).
cnf(refute_0_325,plain,
greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147))) = multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity))),
inference(subst,[],[refute_0_324:[bind(X_52,$fot(X_147)),bind(X_73,$fot(X_148))]]) ).
cnf(refute_0_326,plain,
( multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))) != greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147)))
| greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147))) != multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity)))
| multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))) = multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))),multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity)))) ),[0],$fot(greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147))))]]) ).
cnf(refute_0_327,plain,
( multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))) != greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147)))
| multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))) = multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147))),multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity)))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))) = multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))),greatest_lower_bound(multiply(inverse(X_147),X_148),least_upper_bound(identity,inverse(X_147)))) )],[refute_0_322,refute_0_327]) ).
cnf(refute_0_329,plain,
( multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))) != multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity)))
| multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity))) = multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))))),bind(Y0,$fot(multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity)))))]]) ).
cnf(refute_0_330,plain,
multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity))) = multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(identity,X_147))),multiply(inverse(X_147),greatest_lower_bound(X_148,least_upper_bound(X_147,identity)))) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))),
inference(subst,[],[refute_0_330:[bind(X_147,$fot(greatest_lower_bound(X_80,identity)))]]) ).
cnf(refute_0_332,plain,
( multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) != multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))))
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))) != multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity))
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity))))]]) ).
cnf(refute_0_333,plain,
( multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))) != multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity))
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))),multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity))))) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(identity,greatest_lower_bound(X_80,identity)))),multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity))) )],[refute_0_315,refute_0_333]) ).
cnf(refute_0_335,plain,
( multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) != multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity))
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))))
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))))) ),[0],$fot(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)))]]) ).
cnf(refute_0_336,plain,
( multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))))
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))),multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
greatest_lower_bound(X_76,inverse(Y)) = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,greatest_lower_bound(X_76,inverse(Y))))),
inference(subst,[],[refute_0_48:[bind(X_28,$fot(greatest_lower_bound(X_76,inverse(Y))))]]) ).
cnf(refute_0_338,plain,
multiply(Y,greatest_lower_bound(X_76,inverse(Y))) = greatest_lower_bound(identity,multiply(Y,X_76)),
inference(subst,[],[refute_0_248:[bind(X_72,$fot(Y)),bind(X_73,$fot(X_76))]]) ).
cnf(refute_0_339,plain,
( multiply(Y,greatest_lower_bound(X_76,inverse(Y))) != greatest_lower_bound(identity,multiply(Y,X_76))
| greatest_lower_bound(X_76,inverse(Y)) != multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,greatest_lower_bound(X_76,inverse(Y)))))
| greatest_lower_bound(X_76,inverse(Y)) = multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_76,inverse(Y)),multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,greatest_lower_bound(X_76,inverse(Y)))))) ),[1,1,1],$fot(greatest_lower_bound(identity,multiply(Y,X_76)))]]) ).
cnf(refute_0_340,plain,
( greatest_lower_bound(X_76,inverse(Y)) != multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,greatest_lower_bound(X_76,inverse(Y)))))
| greatest_lower_bound(X_76,inverse(Y)) = multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) ),
inference(resolve,[$cnf( $equal(multiply(Y,greatest_lower_bound(X_76,inverse(Y))),greatest_lower_bound(identity,multiply(Y,X_76))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
greatest_lower_bound(X_76,inverse(Y)) = multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_76,inverse(Y)),multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,greatest_lower_bound(X_76,inverse(Y)))))) )],[refute_0_337,refute_0_340]) ).
cnf(refute_0_342,plain,
multiply(inverse(Y),identity) = inverse(Y),
inference(subst,[],[refute_0_62:[bind(X_28,$fot(inverse(Y)))]]) ).
cnf(refute_0_343,plain,
greatest_lower_bound(multiply(inverse(Y),identity),X_76) = greatest_lower_bound(multiply(inverse(Y),identity),X_76),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(inverse(Y),identity),X_76))]]) ).
cnf(refute_0_344,plain,
( multiply(inverse(Y),identity) != inverse(Y)
| greatest_lower_bound(multiply(inverse(Y),identity),X_76) != greatest_lower_bound(multiply(inverse(Y),identity),X_76)
| greatest_lower_bound(multiply(inverse(Y),identity),X_76) = greatest_lower_bound(inverse(Y),X_76) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(Y),identity),X_76),greatest_lower_bound(multiply(inverse(Y),identity),X_76)) ),[1,0],$fot(inverse(Y))]]) ).
cnf(refute_0_345,plain,
( multiply(inverse(Y),identity) != inverse(Y)
| greatest_lower_bound(multiply(inverse(Y),identity),X_76) = greatest_lower_bound(inverse(Y),X_76) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(Y),identity),X_76),greatest_lower_bound(multiply(inverse(Y),identity),X_76)) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
greatest_lower_bound(multiply(inverse(Y),identity),X_76) = greatest_lower_bound(inverse(Y),X_76),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),identity),inverse(Y)) )],[refute_0_342,refute_0_345]) ).
cnf(refute_0_347,plain,
multiply(inverse(X_25),greatest_lower_bound(X_73,multiply(X_25,X_26))) = greatest_lower_bound(multiply(inverse(X_25),X_73),multiply(inverse(X_25),multiply(X_25,X_26))),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_25))),bind(Y,$fot(X_73)),bind(Z,$fot(multiply(X_25,X_26)))]]) ).
cnf(refute_0_348,plain,
( multiply(inverse(X_25),multiply(X_25,X_26)) != X_26
| multiply(inverse(X_25),greatest_lower_bound(X_73,multiply(X_25,X_26))) != greatest_lower_bound(multiply(inverse(X_25),X_73),multiply(inverse(X_25),multiply(X_25,X_26)))
| multiply(inverse(X_25),greatest_lower_bound(X_73,multiply(X_25,X_26))) = greatest_lower_bound(multiply(inverse(X_25),X_73),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_25),greatest_lower_bound(X_73,multiply(X_25,X_26))),greatest_lower_bound(multiply(inverse(X_25),X_73),multiply(inverse(X_25),multiply(X_25,X_26)))) ),[1,1],$fot(X_26)]]) ).
cnf(refute_0_349,plain,
( multiply(inverse(X_25),greatest_lower_bound(X_73,multiply(X_25,X_26))) != greatest_lower_bound(multiply(inverse(X_25),X_73),multiply(inverse(X_25),multiply(X_25,X_26)))
| multiply(inverse(X_25),greatest_lower_bound(X_73,multiply(X_25,X_26))) = greatest_lower_bound(multiply(inverse(X_25),X_73),X_26) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),multiply(X_25,X_26)),X_26) )],[refute_0_73,refute_0_348]) ).
cnf(refute_0_350,plain,
multiply(inverse(X_25),greatest_lower_bound(X_73,multiply(X_25,X_26))) = greatest_lower_bound(multiply(inverse(X_25),X_73),X_26),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),greatest_lower_bound(X_73,multiply(X_25,X_26))),greatest_lower_bound(multiply(inverse(X_25),X_73),multiply(inverse(X_25),multiply(X_25,X_26)))) )],[refute_0_347,refute_0_349]) ).
cnf(refute_0_351,plain,
multiply(inverse(Y),greatest_lower_bound(identity,multiply(Y,X_76))) = greatest_lower_bound(multiply(inverse(Y),identity),X_76),
inference(subst,[],[refute_0_350:[bind(X_25,$fot(Y)),bind(X_26,$fot(X_76)),bind(X_73,$fot(identity))]]) ).
cnf(refute_0_352,plain,
multiply(inverse(Y),X_98) = multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(inverse(Y),X_98)))),
inference(subst,[],[refute_0_48:[bind(X_28,$fot(multiply(inverse(Y),X_98)))]]) ).
cnf(refute_0_353,plain,
X_98 = multiply(Y,multiply(inverse(Y),X_98)),
inference(subst,[],[refute_0_104:[bind(X_26,$fot(X_98)),bind(X_30,$fot(Y))]]) ).
cnf(refute_0_354,plain,
( X_98 != multiply(Y,multiply(inverse(Y),X_98))
| multiply(Y,multiply(inverse(Y),X_98)) = X_98 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_98)),bind(Y0,$fot(multiply(Y,multiply(inverse(Y),X_98))))]]) ).
cnf(refute_0_355,plain,
multiply(Y,multiply(inverse(Y),X_98)) = X_98,
inference(resolve,[$cnf( $equal(X_98,multiply(Y,multiply(inverse(Y),X_98))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
( multiply(Y,multiply(inverse(Y),X_98)) != X_98
| multiply(inverse(Y),X_98) != multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(inverse(Y),X_98))))
| multiply(inverse(Y),X_98) = multiply(inverse(multiply(X,Y)),multiply(X,X_98)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(Y),X_98),multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(inverse(Y),X_98))))) ),[1,1,1],$fot(X_98)]]) ).
cnf(refute_0_357,plain,
( multiply(inverse(Y),X_98) != multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(inverse(Y),X_98))))
| multiply(inverse(Y),X_98) = multiply(inverse(multiply(X,Y)),multiply(X,X_98)) ),
inference(resolve,[$cnf( $equal(multiply(Y,multiply(inverse(Y),X_98)),X_98) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
multiply(inverse(Y),X_98) = multiply(inverse(multiply(X,Y)),multiply(X,X_98)),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),X_98),multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,multiply(inverse(Y),X_98))))) )],[refute_0_352,refute_0_357]) ).
cnf(refute_0_359,plain,
( multiply(inverse(Y),X_98) != multiply(inverse(multiply(X,Y)),multiply(X,X_98))
| multiply(inverse(multiply(X,Y)),multiply(X,X_98)) = multiply(inverse(Y),X_98) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(inverse(Y),X_98))),bind(Y0,$fot(multiply(inverse(multiply(X,Y)),multiply(X,X_98))))]]) ).
cnf(refute_0_360,plain,
multiply(inverse(multiply(X,Y)),multiply(X,X_98)) = multiply(inverse(Y),X_98),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),X_98),multiply(inverse(multiply(X,Y)),multiply(X,X_98))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) = multiply(inverse(Y),greatest_lower_bound(identity,multiply(Y,X_76))),
inference(subst,[],[refute_0_360:[bind(X_98,$fot(greatest_lower_bound(identity,multiply(Y,X_76))))]]) ).
cnf(refute_0_362,plain,
( multiply(inverse(Y),greatest_lower_bound(identity,multiply(Y,X_76))) != greatest_lower_bound(multiply(inverse(Y),identity),X_76)
| multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) != multiply(inverse(Y),greatest_lower_bound(identity,multiply(Y,X_76)))
| multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) = greatest_lower_bound(multiply(inverse(Y),identity),X_76) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))))),bind(Y0,$fot(multiply(inverse(Y),greatest_lower_bound(identity,multiply(Y,X_76))))),bind(Z0,$fot(greatest_lower_bound(multiply(inverse(Y),identity),X_76)))]]) ).
cnf(refute_0_363,plain,
( multiply(inverse(Y),greatest_lower_bound(identity,multiply(Y,X_76))) != greatest_lower_bound(multiply(inverse(Y),identity),X_76)
| multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) = greatest_lower_bound(multiply(inverse(Y),identity),X_76) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))),multiply(inverse(Y),greatest_lower_bound(identity,multiply(Y,X_76)))) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) = greatest_lower_bound(multiply(inverse(Y),identity),X_76),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),greatest_lower_bound(identity,multiply(Y,X_76))),greatest_lower_bound(multiply(inverse(Y),identity),X_76)) )],[refute_0_351,refute_0_363]) ).
cnf(refute_0_365,plain,
( multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) != greatest_lower_bound(multiply(inverse(Y),identity),X_76)
| greatest_lower_bound(multiply(inverse(Y),identity),X_76) != greatest_lower_bound(inverse(Y),X_76)
| multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) = greatest_lower_bound(inverse(Y),X_76) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(Y),identity),X_76))),bind(Z0,$fot(greatest_lower_bound(inverse(Y),X_76)))]]) ).
cnf(refute_0_366,plain,
( greatest_lower_bound(multiply(inverse(Y),identity),X_76) != greatest_lower_bound(inverse(Y),X_76)
| multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) = greatest_lower_bound(inverse(Y),X_76) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))),greatest_lower_bound(multiply(inverse(Y),identity),X_76)) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) = greatest_lower_bound(inverse(Y),X_76),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(Y),identity),X_76),greatest_lower_bound(inverse(Y),X_76)) )],[refute_0_346,refute_0_366]) ).
cnf(refute_0_368,plain,
( multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))) != greatest_lower_bound(inverse(Y),X_76)
| greatest_lower_bound(X_76,inverse(Y)) != multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76))))
| greatest_lower_bound(X_76,inverse(Y)) = greatest_lower_bound(inverse(Y),X_76) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_76,inverse(Y)),multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76))))) ),[1],$fot(greatest_lower_bound(inverse(Y),X_76))]]) ).
cnf(refute_0_369,plain,
( greatest_lower_bound(X_76,inverse(Y)) != multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76))))
| greatest_lower_bound(X_76,inverse(Y)) = greatest_lower_bound(inverse(Y),X_76) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76)))),greatest_lower_bound(inverse(Y),X_76)) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
greatest_lower_bound(X_76,inverse(Y)) = greatest_lower_bound(inverse(Y),X_76),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_76,inverse(Y)),multiply(inverse(multiply(X,Y)),multiply(X,greatest_lower_bound(identity,multiply(Y,X_76))))) )],[refute_0_341,refute_0_369]) ).
cnf(refute_0_371,plain,
greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),inverse(greatest_lower_bound(identity,X_80))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148)),
inference(subst,[],[refute_0_370:[bind(Y,$fot(greatest_lower_bound(identity,X_80))),bind(X_76,$fot(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148)))]]) ).
cnf(refute_0_372,plain,
multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) = least_upper_bound(inverse(X_59),multiply(inverse(X_59),least_upper_bound(X_59,identity))),
inference(subst,[],[refute_0_206:[bind(X_48,$fot(inverse(X_59))),bind(X_49,$fot(least_upper_bound(X_59,identity)))]]) ).
cnf(refute_0_373,plain,
multiply(inverse(X_59),least_upper_bound(X_59,identity)) = least_upper_bound(identity,inverse(X_59)),
inference(subst,[],[refute_0_215:[bind(X_52,$fot(X_59))]]) ).
cnf(refute_0_374,plain,
( multiply(inverse(X_59),least_upper_bound(X_59,identity)) != least_upper_bound(identity,inverse(X_59))
| multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) != least_upper_bound(inverse(X_59),multiply(inverse(X_59),least_upper_bound(X_59,identity)))
| multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) = least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)),least_upper_bound(inverse(X_59),multiply(inverse(X_59),least_upper_bound(X_59,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_59)))]]) ).
cnf(refute_0_375,plain,
( multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) != least_upper_bound(inverse(X_59),multiply(inverse(X_59),least_upper_bound(X_59,identity)))
| multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) = least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(X_59,identity)),least_upper_bound(identity,inverse(X_59))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) = least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)),least_upper_bound(inverse(X_59),multiply(inverse(X_59),least_upper_bound(X_59,identity)))) )],[refute_0_372,refute_0_375]) ).
cnf(refute_0_377,plain,
least_upper_bound(least_upper_bound(X_9,X_13),greatest_lower_bound(X_9,least_upper_bound(X_9,X_13))) = least_upper_bound(X_9,X_13),
inference(subst,[],[refute_0_177:[bind(X_8,$fot(least_upper_bound(X_9,X_13)))]]) ).
cnf(refute_0_378,plain,
greatest_lower_bound(X_9,least_upper_bound(X_9,X_13)) = X_9,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_9)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_379,plain,
( greatest_lower_bound(X_9,least_upper_bound(X_9,X_13)) != X_9
| least_upper_bound(least_upper_bound(X_9,X_13),greatest_lower_bound(X_9,least_upper_bound(X_9,X_13))) != least_upper_bound(X_9,X_13)
| least_upper_bound(least_upper_bound(X_9,X_13),X_9) = least_upper_bound(X_9,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_9,X_13),greatest_lower_bound(X_9,least_upper_bound(X_9,X_13))),least_upper_bound(X_9,X_13)) ),[0,1],$fot(X_9)]]) ).
cnf(refute_0_380,plain,
( least_upper_bound(least_upper_bound(X_9,X_13),greatest_lower_bound(X_9,least_upper_bound(X_9,X_13))) != least_upper_bound(X_9,X_13)
| least_upper_bound(least_upper_bound(X_9,X_13),X_9) = least_upper_bound(X_9,X_13) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,least_upper_bound(X_9,X_13)),X_9) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
least_upper_bound(least_upper_bound(X_9,X_13),X_9) = least_upper_bound(X_9,X_13),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_9,X_13),greatest_lower_bound(X_9,least_upper_bound(X_9,X_13))),least_upper_bound(X_9,X_13)) )],[refute_0_377,refute_0_380]) ).
cnf(refute_0_382,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_383,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_382]) ).
cnf(refute_0_384,plain,
least_upper_bound(least_upper_bound(X_9,X_13),X_9) = least_upper_bound(X_9,least_upper_bound(X_13,X_9)),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_9)),bind(Y,$fot(X_13)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_385,plain,
( least_upper_bound(least_upper_bound(X_9,X_13),X_9) != least_upper_bound(X_9,X_13)
| least_upper_bound(least_upper_bound(X_9,X_13),X_9) != least_upper_bound(X_9,least_upper_bound(X_13,X_9))
| least_upper_bound(X_9,least_upper_bound(X_13,X_9)) = least_upper_bound(X_9,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_9,X_13),X_9),least_upper_bound(X_9,X_13)) ),[0],$fot(least_upper_bound(X_9,least_upper_bound(X_13,X_9)))]]) ).
cnf(refute_0_386,plain,
( least_upper_bound(least_upper_bound(X_9,X_13),X_9) != least_upper_bound(X_9,X_13)
| least_upper_bound(X_9,least_upper_bound(X_13,X_9)) = least_upper_bound(X_9,X_13) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_9,X_13),X_9),least_upper_bound(X_9,least_upper_bound(X_13,X_9))) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
least_upper_bound(X_9,least_upper_bound(X_13,X_9)) = least_upper_bound(X_9,X_13),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_9,X_13),X_9),least_upper_bound(X_9,X_13)) )],[refute_0_381,refute_0_386]) ).
cnf(refute_0_388,plain,
least_upper_bound(identity,least_upper_bound(X_59,identity)) = least_upper_bound(identity,X_59),
inference(subst,[],[refute_0_387:[bind(X_13,$fot(X_59)),bind(X_9,$fot(identity))]]) ).
cnf(refute_0_389,plain,
multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))) = multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))))]]) ).
cnf(refute_0_390,plain,
( multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))) != multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity)))
| least_upper_bound(identity,least_upper_bound(X_59,identity)) != least_upper_bound(identity,X_59)
| multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))) = multiply(inverse(X_59),least_upper_bound(identity,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))),multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_59))]]) ).
cnf(refute_0_391,plain,
( least_upper_bound(identity,least_upper_bound(X_59,identity)) != least_upper_bound(identity,X_59)
| multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))) = multiply(inverse(X_59),least_upper_bound(identity,X_59)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))),multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity)))) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))) = multiply(inverse(X_59),least_upper_bound(identity,X_59)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_59,identity)),least_upper_bound(identity,X_59)) )],[refute_0_388,refute_0_391]) ).
cnf(refute_0_393,plain,
least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),greatest_lower_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity)))) = multiply(X_9,least_upper_bound(X_58,identity)),
inference(subst,[],[refute_0_177:[bind(X_8,$fot(multiply(X_9,least_upper_bound(X_58,identity))))]]) ).
cnf(refute_0_394,plain,
greatest_lower_bound(X,least_upper_bound(X,multiply(X,X_52))) = X,
inference(subst,[],[glb_absorbtion:[bind(Y,$fot(multiply(X,X_52)))]]) ).
cnf(refute_0_395,plain,
multiply(X,least_upper_bound(X_52,identity)) = least_upper_bound(X,multiply(X,X_52)),
inference(subst,[],[refute_0_206:[bind(X_48,$fot(X)),bind(X_49,$fot(X_52))]]) ).
cnf(refute_0_396,plain,
( multiply(X,least_upper_bound(X_52,identity)) != least_upper_bound(X,multiply(X,X_52))
| least_upper_bound(X,multiply(X,X_52)) = multiply(X,least_upper_bound(X_52,identity)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X,least_upper_bound(X_52,identity)))),bind(Y0,$fot(least_upper_bound(X,multiply(X,X_52))))]]) ).
cnf(refute_0_397,plain,
least_upper_bound(X,multiply(X,X_52)) = multiply(X,least_upper_bound(X_52,identity)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(X_52,identity)),least_upper_bound(X,multiply(X,X_52))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
( greatest_lower_bound(X,least_upper_bound(X,multiply(X,X_52))) != X
| least_upper_bound(X,multiply(X,X_52)) != multiply(X,least_upper_bound(X_52,identity))
| greatest_lower_bound(X,multiply(X,least_upper_bound(X_52,identity))) = X ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,multiply(X,X_52))),X) ),[0,1],$fot(multiply(X,least_upper_bound(X_52,identity)))]]) ).
cnf(refute_0_399,plain,
( greatest_lower_bound(X,least_upper_bound(X,multiply(X,X_52))) != X
| greatest_lower_bound(X,multiply(X,least_upper_bound(X_52,identity))) = X ),
inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(X,X_52)),multiply(X,least_upper_bound(X_52,identity))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
greatest_lower_bound(X,multiply(X,least_upper_bound(X_52,identity))) = X,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,least_upper_bound(X,multiply(X,X_52))),X) )],[refute_0_394,refute_0_399]) ).
cnf(refute_0_401,plain,
greatest_lower_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))) = X_9,
inference(subst,[],[refute_0_400:[bind(X,$fot(X_9)),bind(X_52,$fot(X_58))]]) ).
cnf(refute_0_402,plain,
( greatest_lower_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))) != X_9
| least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),greatest_lower_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity)))) != multiply(X_9,least_upper_bound(X_58,identity))
| least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) = multiply(X_9,least_upper_bound(X_58,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),greatest_lower_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity)))),multiply(X_9,least_upper_bound(X_58,identity))) ),[0,1],$fot(X_9)]]) ).
cnf(refute_0_403,plain,
( least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),greatest_lower_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity)))) != multiply(X_9,least_upper_bound(X_58,identity))
| least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) = multiply(X_9,least_upper_bound(X_58,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))),X_9) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) = multiply(X_9,least_upper_bound(X_58,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),greatest_lower_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity)))),multiply(X_9,least_upper_bound(X_58,identity))) )],[refute_0_393,refute_0_403]) ).
cnf(refute_0_405,plain,
least_upper_bound(identity,least_upper_bound(X_58,identity)) = least_upper_bound(identity,X_58),
inference(subst,[],[refute_0_387:[bind(X_13,$fot(X_58)),bind(X_9,$fot(identity))]]) ).
cnf(refute_0_406,plain,
multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))) = multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))),
introduced(tautology,[refl,[$fot(multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))))]]) ).
cnf(refute_0_407,plain,
( multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))) != multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))
| least_upper_bound(identity,least_upper_bound(X_58,identity)) != least_upper_bound(identity,X_58)
| multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))) = multiply(X_9,least_upper_bound(identity,X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))),multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_58))]]) ).
cnf(refute_0_408,plain,
( least_upper_bound(identity,least_upper_bound(X_58,identity)) != least_upper_bound(identity,X_58)
| multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))) = multiply(X_9,least_upper_bound(identity,X_58)) ),
inference(resolve,[$cnf( $equal(multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))),multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))) = multiply(X_9,least_upper_bound(identity,X_58)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_58,identity)),least_upper_bound(identity,X_58)) )],[refute_0_405,refute_0_408]) ).
cnf(refute_0_410,plain,
least_upper_bound(X_15,least_upper_bound(X_14,X_15)) = least_upper_bound(X_15,X_14),
inference(subst,[],[refute_0_387:[bind(X_13,$fot(X_14)),bind(X_9,$fot(X_15))]]) ).
cnf(refute_0_411,plain,
least_upper_bound(X_15,X_14) = least_upper_bound(X_14,X_15),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_15)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_412,plain,
( least_upper_bound(X_15,X_14) != least_upper_bound(X_14,X_15)
| least_upper_bound(X_14,X_15) = least_upper_bound(X_15,X_14) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_15,X_14))),bind(Y0,$fot(least_upper_bound(X_14,X_15)))]]) ).
cnf(refute_0_413,plain,
least_upper_bound(X_14,X_15) = least_upper_bound(X_15,X_14),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,X_14),least_upper_bound(X_14,X_15)) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
( least_upper_bound(X_14,X_15) != least_upper_bound(X_15,X_14)
| least_upper_bound(X_15,least_upper_bound(X_14,X_15)) != least_upper_bound(X_15,X_14)
| least_upper_bound(X_15,least_upper_bound(X_15,X_14)) = least_upper_bound(X_15,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_14,X_15)),least_upper_bound(X_15,X_14)) ),[0,1],$fot(least_upper_bound(X_15,X_14))]]) ).
cnf(refute_0_415,plain,
( least_upper_bound(X_15,least_upper_bound(X_14,X_15)) != least_upper_bound(X_15,X_14)
| least_upper_bound(X_15,least_upper_bound(X_15,X_14)) = least_upper_bound(X_15,X_14) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_14,X_15),least_upper_bound(X_15,X_14)) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
least_upper_bound(X_15,least_upper_bound(X_15,X_14)) = least_upper_bound(X_15,X_14),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_14,X_15)),least_upper_bound(X_15,X_14)) )],[refute_0_410,refute_0_415]) ).
cnf(refute_0_417,plain,
least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) = least_upper_bound(X_15,multiply(X_15,X_52)),
inference(subst,[],[refute_0_416:[bind(X_14,$fot(multiply(X_15,X_52)))]]) ).
cnf(refute_0_418,plain,
multiply(X_15,least_upper_bound(X_52,identity)) = least_upper_bound(X_15,multiply(X_15,X_52)),
inference(subst,[],[refute_0_206:[bind(X_48,$fot(X_15)),bind(X_49,$fot(X_52))]]) ).
cnf(refute_0_419,plain,
( multiply(X_15,least_upper_bound(X_52,identity)) != least_upper_bound(X_15,multiply(X_15,X_52))
| least_upper_bound(X_15,multiply(X_15,X_52)) = multiply(X_15,least_upper_bound(X_52,identity)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_15,least_upper_bound(X_52,identity)))),bind(Y0,$fot(least_upper_bound(X_15,multiply(X_15,X_52))))]]) ).
cnf(refute_0_420,plain,
least_upper_bound(X_15,multiply(X_15,X_52)) = multiply(X_15,least_upper_bound(X_52,identity)),
inference(resolve,[$cnf( $equal(multiply(X_15,least_upper_bound(X_52,identity)),least_upper_bound(X_15,multiply(X_15,X_52))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
( least_upper_bound(X_15,multiply(X_15,X_52)) != multiply(X_15,least_upper_bound(X_52,identity))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) != least_upper_bound(X_15,multiply(X_15,X_52))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) = multiply(X_15,least_upper_bound(X_52,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))),least_upper_bound(X_15,multiply(X_15,X_52))) ),[1],$fot(multiply(X_15,least_upper_bound(X_52,identity)))]]) ).
cnf(refute_0_422,plain,
( least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) != least_upper_bound(X_15,multiply(X_15,X_52))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) = multiply(X_15,least_upper_bound(X_52,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_15,X_52)),multiply(X_15,least_upper_bound(X_52,identity))) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) = multiply(X_15,least_upper_bound(X_52,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))),least_upper_bound(X_15,multiply(X_15,X_52))) )],[refute_0_417,refute_0_422]) ).
cnf(refute_0_424,plain,
least_upper_bound(identity,least_upper_bound(X_52,identity)) = least_upper_bound(identity,X_52),
inference(subst,[],[refute_0_387:[bind(X_13,$fot(X_52)),bind(X_9,$fot(identity))]]) ).
cnf(refute_0_425,plain,
multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))),
introduced(tautology,[refl,[$fot(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))))]]) ).
cnf(refute_0_426,plain,
( multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))
| least_upper_bound(identity,least_upper_bound(X_52,identity)) != least_upper_bound(identity,X_52)
| multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))) = multiply(X_15,least_upper_bound(identity,X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))),multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_52))]]) ).
cnf(refute_0_427,plain,
( least_upper_bound(identity,least_upper_bound(X_52,identity)) != least_upper_bound(identity,X_52)
| multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))) = multiply(X_15,least_upper_bound(identity,X_52)) ),
inference(resolve,[$cnf( $equal(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))),multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))) = multiply(X_15,least_upper_bound(identity,X_52)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_52,identity)),least_upper_bound(identity,X_52)) )],[refute_0_424,refute_0_427]) ).
cnf(refute_0_429,plain,
least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)),
inference(subst,[],[refute_0_416:[bind(X_14,$fot(multiply(X_48,X_50))),bind(X_15,$fot(multiply(X_48,X_49)))]]) ).
cnf(refute_0_430,plain,
multiply(X_48,least_upper_bound(X_49,X_50)) = least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_48)),bind(Y,$fot(X_49)),bind(Z,$fot(X_50))]]) ).
cnf(refute_0_431,plain,
( multiply(X_48,least_upper_bound(X_49,X_50)) != least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))
| least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_48,least_upper_bound(X_49,X_50)))),bind(Y0,$fot(least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))))]]) ).
cnf(refute_0_432,plain,
least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)) = multiply(X_48,least_upper_bound(X_49,X_50)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,X_50)),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
( least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)) != multiply(X_48,least_upper_bound(X_49,X_50))
| least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) != least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))
| least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) ),[1],$fot(multiply(X_48,least_upper_bound(X_49,X_50)))]]) ).
cnf(refute_0_434,plain,
( least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) != least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))
| least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)),multiply(X_48,least_upper_bound(X_49,X_50))) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = multiply(X_48,least_upper_bound(X_49,X_50)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) )],[refute_0_429,refute_0_434]) ).
cnf(refute_0_436,plain,
least_upper_bound(X_49,X_49) = X_49,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_437,plain,
least_upper_bound(X_50,least_upper_bound(X_49,X_49)) = least_upper_bound(X_50,least_upper_bound(X_49,X_49)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_50,least_upper_bound(X_49,X_49)))]]) ).
cnf(refute_0_438,plain,
( least_upper_bound(X_49,X_49) != X_49
| least_upper_bound(X_50,least_upper_bound(X_49,X_49)) != least_upper_bound(X_50,least_upper_bound(X_49,X_49))
| least_upper_bound(X_50,least_upper_bound(X_49,X_49)) = least_upper_bound(X_50,X_49) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_49,X_49)),least_upper_bound(X_50,least_upper_bound(X_49,X_49))) ),[1,1],$fot(X_49)]]) ).
cnf(refute_0_439,plain,
( least_upper_bound(X_49,X_49) != X_49
| least_upper_bound(X_50,least_upper_bound(X_49,X_49)) = least_upper_bound(X_50,X_49) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_49,X_49)),least_upper_bound(X_50,least_upper_bound(X_49,X_49))) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
least_upper_bound(X_50,least_upper_bound(X_49,X_49)) = least_upper_bound(X_50,X_49),
inference(resolve,[$cnf( $equal(least_upper_bound(X_49,X_49),X_49) )],[refute_0_436,refute_0_439]) ).
cnf(refute_0_441,plain,
multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))) = multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))),
introduced(tautology,[refl,[$fot(multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))))]]) ).
cnf(refute_0_442,plain,
( multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))) != multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49)))
| least_upper_bound(X_50,least_upper_bound(X_49,X_49)) != least_upper_bound(X_50,X_49)
| multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))) = multiply(X_48,least_upper_bound(X_50,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))),multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49)))) ),[1,1],$fot(least_upper_bound(X_50,X_49))]]) ).
cnf(refute_0_443,plain,
( least_upper_bound(X_50,least_upper_bound(X_49,X_49)) != least_upper_bound(X_50,X_49)
| multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))) = multiply(X_48,least_upper_bound(X_50,X_49)) ),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))),multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49)))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))) = multiply(X_48,least_upper_bound(X_50,X_49)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_49,X_49)),least_upper_bound(X_50,X_49)) )],[refute_0_440,refute_0_443]) ).
cnf(refute_0_445,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_446,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_445]) ).
cnf(refute_0_447,plain,
least_upper_bound(multiply(X_48,X_50),multiply(X_48,least_upper_bound(X_49,X_49))) = multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))),
inference(subst,[],[refute_0_446:[bind(X,$fot(X_48)),bind(Y,$fot(X_50)),bind(Z,$fot(least_upper_bound(X_49,X_49)))]]) ).
cnf(refute_0_448,plain,
least_upper_bound(X,least_upper_bound(X_39,X_40)) = least_upper_bound(least_upper_bound(X_39,X_40),X),
inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_39,X_40)))]]) ).
cnf(refute_0_449,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X)) = least_upper_bound(least_upper_bound(X_39,X_40),X),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(X))]]) ).
cnf(refute_0_450,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,X)) != least_upper_bound(least_upper_bound(X_39,X_40),X)
| least_upper_bound(least_upper_bound(X_39,X_40),X) = least_upper_bound(X_39,least_upper_bound(X_40,X)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_39,X_40),X)))]]) ).
cnf(refute_0_451,plain,
least_upper_bound(least_upper_bound(X_39,X_40),X) = least_upper_bound(X_39,least_upper_bound(X_40,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,X)),least_upper_bound(least_upper_bound(X_39,X_40),X)) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
( least_upper_bound(X,least_upper_bound(X_39,X_40)) != least_upper_bound(least_upper_bound(X_39,X_40),X)
| least_upper_bound(least_upper_bound(X_39,X_40),X) != least_upper_bound(X_39,least_upper_bound(X_40,X))
| least_upper_bound(X,least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_39,X_40),X))]]) ).
cnf(refute_0_453,plain,
( least_upper_bound(X,least_upper_bound(X_39,X_40)) != least_upper_bound(least_upper_bound(X_39,X_40),X)
| least_upper_bound(X,least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),X),least_upper_bound(X_39,least_upper_bound(X_40,X))) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
least_upper_bound(X,least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_39,X_40)),least_upper_bound(least_upper_bound(X_39,X_40),X)) )],[refute_0_448,refute_0_453]) ).
cnf(refute_0_455,plain,
least_upper_bound(X,least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X)),
inference(subst,[],[refute_0_454:[bind(X_39,$fot(multiply(X_48,X_49))),bind(X_40,$fot(multiply(X_48,X_50)))]]) ).
cnf(refute_0_456,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) != least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X))
| least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)) != multiply(X_48,least_upper_bound(X_49,X_50))
| least_upper_bound(X,multiply(X_48,least_upper_bound(X_49,X_50))) = least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))),least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X))) ),[0,1],$fot(multiply(X_48,least_upper_bound(X_49,X_50)))]]) ).
cnf(refute_0_457,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) != least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X))
| least_upper_bound(X,multiply(X_48,least_upper_bound(X_49,X_50))) = least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50)),multiply(X_48,least_upper_bound(X_49,X_50))) )],[refute_0_432,refute_0_456]) ).
cnf(refute_0_458,plain,
least_upper_bound(X,multiply(X_48,least_upper_bound(X_49,X_50))) = least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))),least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X))) )],[refute_0_455,refute_0_457]) ).
cnf(refute_0_459,plain,
( least_upper_bound(X,multiply(X_48,least_upper_bound(X_49,X_50))) != least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X))
| least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X)) = least_upper_bound(X,multiply(X_48,least_upper_bound(X_49,X_50))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,multiply(X_48,least_upper_bound(X_49,X_50))))),bind(Y0,$fot(least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X))))]]) ).
cnf(refute_0_460,plain,
least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X)) = least_upper_bound(X,multiply(X_48,least_upper_bound(X_49,X_50))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(X_48,least_upper_bound(X_49,X_50))),least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_50),X))) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = least_upper_bound(multiply(X_48,X_50),multiply(X_48,least_upper_bound(X_49,X_49))),
inference(subst,[],[refute_0_460:[bind(X,$fot(multiply(X_48,X_50))),bind(X_50,$fot(X_49))]]) ).
cnf(refute_0_462,plain,
( least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) != least_upper_bound(multiply(X_48,X_50),multiply(X_48,least_upper_bound(X_49,X_49)))
| least_upper_bound(multiply(X_48,X_50),multiply(X_48,least_upper_bound(X_49,X_49))) != multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49)))
| least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))))),bind(Y0,$fot(least_upper_bound(multiply(X_48,X_50),multiply(X_48,least_upper_bound(X_49,X_49))))),bind(Z0,$fot(multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49)))))]]) ).
cnf(refute_0_463,plain,
( least_upper_bound(multiply(X_48,X_50),multiply(X_48,least_upper_bound(X_49,X_49))) != multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49)))
| least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))),least_upper_bound(multiply(X_48,X_50),multiply(X_48,least_upper_bound(X_49,X_49)))) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_50),multiply(X_48,least_upper_bound(X_49,X_49))),multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49)))) )],[refute_0_447,refute_0_463]) ).
cnf(refute_0_465,plain,
( multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))) != multiply(X_48,least_upper_bound(X_50,X_49))
| least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) != multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49)))
| least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = multiply(X_48,least_upper_bound(X_50,X_49)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))))),bind(Y0,$fot(multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))))),bind(Z0,$fot(multiply(X_48,least_upper_bound(X_50,X_49))))]]) ).
cnf(refute_0_466,plain,
( multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))) != multiply(X_48,least_upper_bound(X_50,X_49))
| least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = multiply(X_48,least_upper_bound(X_50,X_49)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))),multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49)))) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) = multiply(X_48,least_upper_bound(X_50,X_49)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_50,least_upper_bound(X_49,X_49))),multiply(X_48,least_upper_bound(X_50,X_49))) )],[refute_0_444,refute_0_466]) ).
cnf(refute_0_468,plain,
( least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) != multiply(X_48,least_upper_bound(X_49,X_50))
| least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) != multiply(X_48,least_upper_bound(X_50,X_49))
| multiply(X_48,least_upper_bound(X_50,X_49)) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))),multiply(X_48,least_upper_bound(X_49,X_50))) ),[0],$fot(multiply(X_48,least_upper_bound(X_50,X_49)))]]) ).
cnf(refute_0_469,plain,
( least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))) != multiply(X_48,least_upper_bound(X_49,X_50))
| multiply(X_48,least_upper_bound(X_50,X_49)) = multiply(X_48,least_upper_bound(X_49,X_50)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))),multiply(X_48,least_upper_bound(X_50,X_49))) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
multiply(X_48,least_upper_bound(X_50,X_49)) = multiply(X_48,least_upper_bound(X_49,X_50)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_48,X_49),least_upper_bound(multiply(X_48,X_49),multiply(X_48,X_50))),multiply(X_48,least_upper_bound(X_49,X_50))) )],[refute_0_435,refute_0_469]) ).
cnf(refute_0_471,plain,
( multiply(X_48,least_upper_bound(X_50,X_49)) != multiply(X_48,least_upper_bound(X_49,X_50))
| multiply(X_48,least_upper_bound(X_49,X_50)) = multiply(X_48,least_upper_bound(X_50,X_49)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_48,least_upper_bound(X_50,X_49)))),bind(Y0,$fot(multiply(X_48,least_upper_bound(X_49,X_50))))]]) ).
cnf(refute_0_472,plain,
multiply(X_48,least_upper_bound(X_49,X_50)) = multiply(X_48,least_upper_bound(X_50,X_49)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_50,X_49)),multiply(X_48,least_upper_bound(X_49,X_50))) )],[refute_0_470,refute_0_471]) ).
cnf(refute_0_473,plain,
multiply(X_15,least_upper_bound(least_upper_bound(X_52,identity),identity)) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))),
inference(subst,[],[refute_0_472:[bind(X_48,$fot(X_15)),bind(X_49,$fot(least_upper_bound(X_52,identity))),bind(X_50,$fot(identity))]]) ).
cnf(refute_0_474,plain,
( multiply(X_48,least_upper_bound(X_49,identity)) != least_upper_bound(X_48,multiply(X_48,X_49))
| least_upper_bound(X_48,multiply(X_48,X_49)) = multiply(X_48,least_upper_bound(X_49,identity)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_48,least_upper_bound(X_49,identity)))),bind(Y0,$fot(least_upper_bound(X_48,multiply(X_48,X_49))))]]) ).
cnf(refute_0_475,plain,
least_upper_bound(X_48,multiply(X_48,X_49)) = multiply(X_48,least_upper_bound(X_49,identity)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(X_49,identity)),least_upper_bound(X_48,multiply(X_48,X_49))) )],[refute_0_206,refute_0_474]) ).
cnf(refute_0_476,plain,
least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))) = multiply(X_15,least_upper_bound(least_upper_bound(X_52,identity),identity)),
inference(subst,[],[refute_0_475:[bind(X_48,$fot(X_15)),bind(X_49,$fot(least_upper_bound(X_52,identity)))]]) ).
cnf(refute_0_477,plain,
( multiply(X_15,least_upper_bound(least_upper_bound(X_52,identity),identity)) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))
| least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))) != multiply(X_15,least_upper_bound(least_upper_bound(X_52,identity),identity))
| least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))))),bind(Y0,$fot(multiply(X_15,least_upper_bound(least_upper_bound(X_52,identity),identity)))),bind(Z0,$fot(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))))]]) ).
cnf(refute_0_478,plain,
( multiply(X_15,least_upper_bound(least_upper_bound(X_52,identity),identity)) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))
| least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))),multiply(X_15,least_upper_bound(least_upper_bound(X_52,identity),identity))) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))),
inference(resolve,[$cnf( $equal(multiply(X_15,least_upper_bound(least_upper_bound(X_52,identity),identity)),multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))) )],[refute_0_473,refute_0_478]) ).
cnf(refute_0_480,plain,
least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,multiply(X_40,X_52))),
inference(subst,[],[refute_0_454:[bind(X,$fot(multiply(X_40,X_52)))]]) ).
cnf(refute_0_481,plain,
multiply(X_40,least_upper_bound(X_52,identity)) = least_upper_bound(X_40,multiply(X_40,X_52)),
inference(subst,[],[refute_0_206:[bind(X_48,$fot(X_40)),bind(X_49,$fot(X_52))]]) ).
cnf(refute_0_482,plain,
( multiply(X_40,least_upper_bound(X_52,identity)) != least_upper_bound(X_40,multiply(X_40,X_52))
| least_upper_bound(X_40,multiply(X_40,X_52)) = multiply(X_40,least_upper_bound(X_52,identity)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_40,least_upper_bound(X_52,identity)))),bind(Y0,$fot(least_upper_bound(X_40,multiply(X_40,X_52))))]]) ).
cnf(refute_0_483,plain,
least_upper_bound(X_40,multiply(X_40,X_52)) = multiply(X_40,least_upper_bound(X_52,identity)),
inference(resolve,[$cnf( $equal(multiply(X_40,least_upper_bound(X_52,identity)),least_upper_bound(X_40,multiply(X_40,X_52))) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
( least_upper_bound(X_40,multiply(X_40,X_52)) != multiply(X_40,least_upper_bound(X_52,identity))
| least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,multiply(X_40,X_52)))
| least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,multiply(X_40,least_upper_bound(X_52,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,multiply(X_40,X_52)))) ),[1,1],$fot(multiply(X_40,least_upper_bound(X_52,identity)))]]) ).
cnf(refute_0_485,plain,
( least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,multiply(X_40,X_52)))
| least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,multiply(X_40,least_upper_bound(X_52,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,multiply(X_40,X_52)),multiply(X_40,least_upper_bound(X_52,identity))) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,multiply(X_40,least_upper_bound(X_52,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,multiply(X_40,X_52)))) )],[refute_0_480,refute_0_485]) ).
cnf(refute_0_487,plain,
least_upper_bound(X_42,least_upper_bound(X_43,least_upper_bound(X_13,X_43))) = least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)),
inference(subst,[],[refute_0_454:[bind(X,$fot(X_42)),bind(X_39,$fot(X_43)),bind(X_40,$fot(least_upper_bound(X_13,X_43)))]]) ).
cnf(refute_0_488,plain,
least_upper_bound(X_43,least_upper_bound(X_13,X_43)) = least_upper_bound(X_43,X_13),
inference(subst,[],[refute_0_387:[bind(X_9,$fot(X_43))]]) ).
cnf(refute_0_489,plain,
( least_upper_bound(X_42,least_upper_bound(X_43,least_upper_bound(X_13,X_43))) != least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42))
| least_upper_bound(X_43,least_upper_bound(X_13,X_43)) != least_upper_bound(X_43,X_13)
| least_upper_bound(X_42,least_upper_bound(X_43,X_13)) = least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(X_43,least_upper_bound(X_13,X_43))),least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42))) ),[0,1],$fot(least_upper_bound(X_43,X_13))]]) ).
cnf(refute_0_490,plain,
( least_upper_bound(X_42,least_upper_bound(X_43,least_upper_bound(X_13,X_43))) != least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42))
| least_upper_bound(X_42,least_upper_bound(X_43,X_13)) = least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_13,X_43)),least_upper_bound(X_43,X_13)) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
least_upper_bound(X_42,least_upper_bound(X_43,X_13)) = least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(X_43,least_upper_bound(X_13,X_43))),least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42))) )],[refute_0_487,refute_0_490]) ).
cnf(refute_0_492,plain,
least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_13,X_40))) = least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(least_upper_bound(X_13,X_40)))]]) ).
cnf(refute_0_493,plain,
least_upper_bound(X_40,least_upper_bound(X_13,X_40)) = least_upper_bound(X_40,X_13),
inference(subst,[],[refute_0_387:[bind(X_9,$fot(X_40))]]) ).
cnf(refute_0_494,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_13,X_40))) != least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40))
| least_upper_bound(X_40,least_upper_bound(X_13,X_40)) != least_upper_bound(X_40,X_13)
| least_upper_bound(X_39,least_upper_bound(X_40,X_13)) = least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_13,X_40))),least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40))) ),[0,1],$fot(least_upper_bound(X_40,X_13))]]) ).
cnf(refute_0_495,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_13,X_40))) != least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40))
| least_upper_bound(X_39,least_upper_bound(X_40,X_13)) = least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,least_upper_bound(X_13,X_40)),least_upper_bound(X_40,X_13)) )],[refute_0_493,refute_0_494]) ).
cnf(refute_0_496,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X_13)) = least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_13,X_40))),least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40))) )],[refute_0_492,refute_0_495]) ).
cnf(refute_0_497,plain,
least_upper_bound(least_upper_bound(X_39,X_40),X_13) = least_upper_bound(X_39,least_upper_bound(X_40,X_13)),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_498,plain,
least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)) = least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)))]]) ).
cnf(refute_0_499,plain,
( least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)) != least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13))
| least_upper_bound(least_upper_bound(X_39,X_40),X_13) != least_upper_bound(X_39,least_upper_bound(X_40,X_13))
| least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)),least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13))) ),[1,1],$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_13)))]]) ).
cnf(refute_0_500,plain,
( least_upper_bound(least_upper_bound(X_39,X_40),X_13) != least_upper_bound(X_39,least_upper_bound(X_40,X_13))
| least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)),least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13))) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),X_13),least_upper_bound(X_39,least_upper_bound(X_40,X_13))) )],[refute_0_497,refute_0_500]) ).
cnf(refute_0_502,plain,
( least_upper_bound(X,least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,X))
| least_upper_bound(X_39,least_upper_bound(X_40,X)) = least_upper_bound(X,least_upper_bound(X_39,X_40)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_39,X_40)))),bind(Y0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X))))]]) ).
cnf(refute_0_503,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X)) = least_upper_bound(X,least_upper_bound(X_39,X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,X))) )],[refute_0_454,refute_0_502]) ).
cnf(refute_0_504,plain,
least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)) = least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)),
inference(subst,[],[refute_0_503:[bind(X,$fot(X_40)),bind(X_39,$fot(least_upper_bound(X_39,X_40))),bind(X_40,$fot(X_13))]]) ).
cnf(refute_0_505,plain,
( least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13)))
| least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)) != least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13))
| least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)))),bind(Y0,$fot(least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)))),bind(Z0,$fot(least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13)))))]]) ).
cnf(refute_0_506,plain,
( least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13)))
| least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)),least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13))) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,least_upper_bound(least_upper_bound(X_39,X_40),X_13)),least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13)))) )],[refute_0_501,refute_0_506]) ).
cnf(refute_0_508,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,X_13)) != least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40))
| least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13)))
| least_upper_bound(X_39,least_upper_bound(X_40,X_13)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_39,least_upper_bound(X_40,X_13)),least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)))]]) ).
cnf(refute_0_509,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,X_13)) != least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40))
| least_upper_bound(X_39,least_upper_bound(X_40,X_13)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40)),least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13)))) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X_13)) = least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,X_13)),least_upper_bound(least_upper_bound(X_39,X_40),least_upper_bound(X_13,X_40))) )],[refute_0_496,refute_0_509]) ).
cnf(refute_0_511,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,X_13)) != least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13)))
| least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13))) = least_upper_bound(X_39,least_upper_bound(X_40,X_13)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_13)))),bind(Y0,$fot(least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13)))))]]) ).
cnf(refute_0_512,plain,
least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13))) = least_upper_bound(X_39,least_upper_bound(X_40,X_13)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,X_13)),least_upper_bound(X_40,least_upper_bound(X_39,least_upper_bound(X_40,X_13)))) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
least_upper_bound(X_43,least_upper_bound(X_13,least_upper_bound(X_43,X_42))) = least_upper_bound(X_13,least_upper_bound(X_43,X_42)),
inference(subst,[],[refute_0_512:[bind(X_13,$fot(X_42)),bind(X_39,$fot(X_13)),bind(X_40,$fot(X_43))]]) ).
cnf(refute_0_514,plain,
least_upper_bound(least_upper_bound(X_13,X_43),X_42) = least_upper_bound(X_13,least_upper_bound(X_43,X_42)),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_13)),bind(Y,$fot(X_43)),bind(Z,$fot(X_42))]]) ).
cnf(refute_0_515,plain,
least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) = least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)))]]) ).
cnf(refute_0_516,plain,
( least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) != least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42))
| least_upper_bound(least_upper_bound(X_13,X_43),X_42) != least_upper_bound(X_13,least_upper_bound(X_43,X_42))
| least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) = least_upper_bound(X_43,least_upper_bound(X_13,least_upper_bound(X_43,X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)),least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42))) ),[1,1],$fot(least_upper_bound(X_13,least_upper_bound(X_43,X_42)))]]) ).
cnf(refute_0_517,plain,
( least_upper_bound(least_upper_bound(X_13,X_43),X_42) != least_upper_bound(X_13,least_upper_bound(X_43,X_42))
| least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) = least_upper_bound(X_43,least_upper_bound(X_13,least_upper_bound(X_43,X_42))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)),least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42))) )],[refute_0_515,refute_0_516]) ).
cnf(refute_0_518,plain,
least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) = least_upper_bound(X_43,least_upper_bound(X_13,least_upper_bound(X_43,X_42))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,X_43),X_42),least_upper_bound(X_13,least_upper_bound(X_43,X_42))) )],[refute_0_514,refute_0_517]) ).
cnf(refute_0_519,plain,
( least_upper_bound(X_43,least_upper_bound(X_13,least_upper_bound(X_43,X_42))) != least_upper_bound(X_13,least_upper_bound(X_43,X_42))
| least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) != least_upper_bound(X_43,least_upper_bound(X_13,least_upper_bound(X_43,X_42)))
| least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) = least_upper_bound(X_13,least_upper_bound(X_43,X_42)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)))),bind(Y0,$fot(least_upper_bound(X_43,least_upper_bound(X_13,least_upper_bound(X_43,X_42))))),bind(Z0,$fot(least_upper_bound(X_13,least_upper_bound(X_43,X_42))))]]) ).
cnf(refute_0_520,plain,
( least_upper_bound(X_43,least_upper_bound(X_13,least_upper_bound(X_43,X_42))) != least_upper_bound(X_13,least_upper_bound(X_43,X_42))
| least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) = least_upper_bound(X_13,least_upper_bound(X_43,X_42)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)),least_upper_bound(X_43,least_upper_bound(X_13,least_upper_bound(X_43,X_42)))) )],[refute_0_518,refute_0_519]) ).
cnf(refute_0_521,plain,
least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) = least_upper_bound(X_13,least_upper_bound(X_43,X_42)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(X_13,least_upper_bound(X_43,X_42))),least_upper_bound(X_13,least_upper_bound(X_43,X_42))) )],[refute_0_513,refute_0_520]) ).
cnf(refute_0_522,plain,
( least_upper_bound(X_42,least_upper_bound(X_43,X_13)) != least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42))
| least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)) != least_upper_bound(X_13,least_upper_bound(X_43,X_42))
| least_upper_bound(X_42,least_upper_bound(X_43,X_13)) = least_upper_bound(X_13,least_upper_bound(X_43,X_42)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_42,least_upper_bound(X_43,X_13)),least_upper_bound(X_13,least_upper_bound(X_43,X_42))) ),[0],$fot(least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)))]]) ).
cnf(refute_0_523,plain,
( least_upper_bound(X_42,least_upper_bound(X_43,X_13)) != least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42))
| least_upper_bound(X_42,least_upper_bound(X_43,X_13)) = least_upper_bound(X_13,least_upper_bound(X_43,X_42)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42)),least_upper_bound(X_13,least_upper_bound(X_43,X_42))) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
least_upper_bound(X_42,least_upper_bound(X_43,X_13)) = least_upper_bound(X_13,least_upper_bound(X_43,X_42)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(X_43,X_13)),least_upper_bound(X_43,least_upper_bound(least_upper_bound(X_13,X_43),X_42))) )],[refute_0_491,refute_0_523]) ).
cnf(refute_0_525,plain,
( least_upper_bound(X_42,least_upper_bound(X_43,X_13)) != least_upper_bound(X_13,least_upper_bound(X_43,X_42))
| least_upper_bound(X_13,least_upper_bound(X_43,X_42)) = least_upper_bound(X_42,least_upper_bound(X_43,X_13)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_42,least_upper_bound(X_43,X_13)))),bind(Y0,$fot(least_upper_bound(X_13,least_upper_bound(X_43,X_42))))]]) ).
cnf(refute_0_526,plain,
least_upper_bound(X_13,least_upper_bound(X_43,X_42)) = least_upper_bound(X_42,least_upper_bound(X_43,X_13)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_42,least_upper_bound(X_43,X_13)),least_upper_bound(X_13,least_upper_bound(X_43,X_42))) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)) = least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_40,X_52))),
inference(subst,[],[refute_0_526:[bind(X_13,$fot(multiply(X_40,X_52))),bind(X_42,$fot(X_40)),bind(X_43,$fot(X_39))]]) ).
cnf(refute_0_528,plain,
( least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,multiply(X_40,least_upper_bound(X_52,identity)))
| least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)) != least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_40,X_52)))
| least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_40,X_52))) = least_upper_bound(X_39,multiply(X_40,least_upper_bound(X_52,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,multiply(X_40,least_upper_bound(X_52,identity)))) ),[0],$fot(least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_40,X_52))))]]) ).
cnf(refute_0_529,plain,
( least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,multiply(X_40,least_upper_bound(X_52,identity)))
| least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_40,X_52))) = least_upper_bound(X_39,multiply(X_40,least_upper_bound(X_52,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)),least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_40,X_52)))) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_40,X_52))) = least_upper_bound(X_39,multiply(X_40,least_upper_bound(X_52,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_40,X_52),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,multiply(X_40,least_upper_bound(X_52,identity)))) )],[refute_0_486,refute_0_529]) ).
cnf(refute_0_531,plain,
least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) = least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))),
inference(subst,[],[refute_0_530:[bind(X_39,$fot(X_15)),bind(X_40,$fot(X_15))]]) ).
cnf(refute_0_532,plain,
( least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) != least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity)))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))))),bind(Y0,$fot(least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))))),bind(Z0,$fot(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))))]]) ).
cnf(refute_0_533,plain,
( least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))),least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity)))) )],[refute_0_531,refute_0_532]) ).
cnf(refute_0_534,plain,
least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) = multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_15,least_upper_bound(X_52,identity))),multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))) )],[refute_0_479,refute_0_533]) ).
cnf(refute_0_535,plain,
( multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))) != multiply(X_15,least_upper_bound(identity,X_52))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) != multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) = multiply(X_15,least_upper_bound(identity,X_52)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))))),bind(Y0,$fot(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))))),bind(Z0,$fot(multiply(X_15,least_upper_bound(identity,X_52))))]]) ).
cnf(refute_0_536,plain,
( multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))) != multiply(X_15,least_upper_bound(identity,X_52))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) = multiply(X_15,least_upper_bound(identity,X_52)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))),multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity)))) )],[refute_0_534,refute_0_535]) ).
cnf(refute_0_537,plain,
least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) = multiply(X_15,least_upper_bound(identity,X_52)),
inference(resolve,[$cnf( $equal(multiply(X_15,least_upper_bound(identity,least_upper_bound(X_52,identity))),multiply(X_15,least_upper_bound(identity,X_52))) )],[refute_0_428,refute_0_536]) ).
cnf(refute_0_538,plain,
( least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) != multiply(X_15,least_upper_bound(X_52,identity))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) != multiply(X_15,least_upper_bound(identity,X_52))
| multiply(X_15,least_upper_bound(identity,X_52)) = multiply(X_15,least_upper_bound(X_52,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))),multiply(X_15,least_upper_bound(X_52,identity))) ),[0],$fot(multiply(X_15,least_upper_bound(identity,X_52)))]]) ).
cnf(refute_0_539,plain,
( least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))) != multiply(X_15,least_upper_bound(X_52,identity))
| multiply(X_15,least_upper_bound(identity,X_52)) = multiply(X_15,least_upper_bound(X_52,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))),multiply(X_15,least_upper_bound(identity,X_52))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
multiply(X_15,least_upper_bound(identity,X_52)) = multiply(X_15,least_upper_bound(X_52,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_15,X_52))),multiply(X_15,least_upper_bound(X_52,identity))) )],[refute_0_423,refute_0_539]) ).
cnf(refute_0_541,plain,
( multiply(X_15,least_upper_bound(identity,X_52)) != multiply(X_15,least_upper_bound(X_52,identity))
| multiply(X_15,least_upper_bound(X_52,identity)) = multiply(X_15,least_upper_bound(identity,X_52)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_15,least_upper_bound(identity,X_52)))),bind(Y0,$fot(multiply(X_15,least_upper_bound(X_52,identity))))]]) ).
cnf(refute_0_542,plain,
multiply(X_15,least_upper_bound(X_52,identity)) = multiply(X_15,least_upper_bound(identity,X_52)),
inference(resolve,[$cnf( $equal(multiply(X_15,least_upper_bound(identity,X_52)),multiply(X_15,least_upper_bound(X_52,identity))) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
multiply(X_9,least_upper_bound(least_upper_bound(X_58,identity),identity)) = multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))),
inference(subst,[],[refute_0_542:[bind(X_15,$fot(X_9)),bind(X_52,$fot(least_upper_bound(X_58,identity)))]]) ).
cnf(refute_0_544,plain,
least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))) = multiply(X_9,least_upper_bound(least_upper_bound(X_58,identity),identity)),
inference(subst,[],[refute_0_475:[bind(X_48,$fot(X_9)),bind(X_49,$fot(least_upper_bound(X_58,identity)))]]) ).
cnf(refute_0_545,plain,
( multiply(X_9,least_upper_bound(least_upper_bound(X_58,identity),identity)) != multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))
| least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))) != multiply(X_9,least_upper_bound(least_upper_bound(X_58,identity),identity))
| least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))) = multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))))),bind(Y0,$fot(multiply(X_9,least_upper_bound(least_upper_bound(X_58,identity),identity)))),bind(Z0,$fot(multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))))]]) ).
cnf(refute_0_546,plain,
( multiply(X_9,least_upper_bound(least_upper_bound(X_58,identity),identity)) != multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))
| least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))) = multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))),multiply(X_9,least_upper_bound(least_upper_bound(X_58,identity),identity))) )],[refute_0_544,refute_0_545]) ).
cnf(refute_0_547,plain,
least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))) = multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))),
inference(resolve,[$cnf( $equal(multiply(X_9,least_upper_bound(least_upper_bound(X_58,identity),identity)),multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))) )],[refute_0_543,refute_0_546]) ).
cnf(refute_0_548,plain,
least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) = least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_9)),bind(Y,$fot(multiply(X_9,least_upper_bound(X_58,identity))))]]) ).
cnf(refute_0_549,plain,
( least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))) != multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))
| least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) != least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity)))
| least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) = multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9))),bind(Y0,$fot(least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))))),bind(Z0,$fot(multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))))]]) ).
cnf(refute_0_550,plain,
( least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))) != multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))
| least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) = multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9),least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity)))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) = multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,multiply(X_9,least_upper_bound(X_58,identity))),multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))) )],[refute_0_547,refute_0_550]) ).
cnf(refute_0_552,plain,
( multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))) != multiply(X_9,least_upper_bound(identity,X_58))
| least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) != multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))
| least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) = multiply(X_9,least_upper_bound(identity,X_58)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9))),bind(Y0,$fot(multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))))),bind(Z0,$fot(multiply(X_9,least_upper_bound(identity,X_58))))]]) ).
cnf(refute_0_553,plain,
( multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))) != multiply(X_9,least_upper_bound(identity,X_58))
| least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) = multiply(X_9,least_upper_bound(identity,X_58)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9),multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity)))) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) = multiply(X_9,least_upper_bound(identity,X_58)),
inference(resolve,[$cnf( $equal(multiply(X_9,least_upper_bound(identity,least_upper_bound(X_58,identity))),multiply(X_9,least_upper_bound(identity,X_58))) )],[refute_0_409,refute_0_553]) ).
cnf(refute_0_555,plain,
( least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) != multiply(X_9,least_upper_bound(X_58,identity))
| least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) != multiply(X_9,least_upper_bound(identity,X_58))
| multiply(X_9,least_upper_bound(identity,X_58)) = multiply(X_9,least_upper_bound(X_58,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9),multiply(X_9,least_upper_bound(X_58,identity))) ),[0],$fot(multiply(X_9,least_upper_bound(identity,X_58)))]]) ).
cnf(refute_0_556,plain,
( least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9) != multiply(X_9,least_upper_bound(X_58,identity))
| multiply(X_9,least_upper_bound(identity,X_58)) = multiply(X_9,least_upper_bound(X_58,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9),multiply(X_9,least_upper_bound(identity,X_58))) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
multiply(X_9,least_upper_bound(identity,X_58)) = multiply(X_9,least_upper_bound(X_58,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_9,least_upper_bound(X_58,identity)),X_9),multiply(X_9,least_upper_bound(X_58,identity))) )],[refute_0_404,refute_0_556]) ).
cnf(refute_0_558,plain,
( multiply(X_9,least_upper_bound(identity,X_58)) != multiply(X_9,least_upper_bound(X_58,identity))
| multiply(X_9,least_upper_bound(X_58,identity)) = multiply(X_9,least_upper_bound(identity,X_58)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_9,least_upper_bound(identity,X_58)))),bind(Y0,$fot(multiply(X_9,least_upper_bound(X_58,identity))))]]) ).
cnf(refute_0_559,plain,
multiply(X_9,least_upper_bound(X_58,identity)) = multiply(X_9,least_upper_bound(identity,X_58)),
inference(resolve,[$cnf( $equal(multiply(X_9,least_upper_bound(identity,X_58)),multiply(X_9,least_upper_bound(X_58,identity))) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) = multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))),
inference(subst,[],[refute_0_559:[bind(X_58,$fot(least_upper_bound(X_59,identity))),bind(X_9,$fot(inverse(X_59)))]]) ).
cnf(refute_0_561,plain,
( multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))) != multiply(inverse(X_59),least_upper_bound(identity,X_59))
| multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) != multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity)))
| multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) = multiply(inverse(X_59),least_upper_bound(identity,X_59)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)))),bind(Y0,$fot(multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))))),bind(Z0,$fot(multiply(inverse(X_59),least_upper_bound(identity,X_59))))]]) ).
cnf(refute_0_562,plain,
( multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))) != multiply(inverse(X_59),least_upper_bound(identity,X_59))
| multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) = multiply(inverse(X_59),least_upper_bound(identity,X_59)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)),multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity)))) )],[refute_0_560,refute_0_561]) ).
cnf(refute_0_563,plain,
multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) = multiply(inverse(X_59),least_upper_bound(identity,X_59)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(identity,least_upper_bound(X_59,identity))),multiply(inverse(X_59),least_upper_bound(identity,X_59))) )],[refute_0_392,refute_0_562]) ).
cnf(refute_0_564,plain,
( multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) != multiply(inverse(X_59),least_upper_bound(identity,X_59))
| multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) != least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59)))
| multiply(inverse(X_59),least_upper_bound(identity,X_59)) = least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)),least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59)))) ),[0],$fot(multiply(inverse(X_59),least_upper_bound(identity,X_59)))]]) ).
cnf(refute_0_565,plain,
( multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) != least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59)))
| multiply(inverse(X_59),least_upper_bound(identity,X_59)) = least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)),multiply(inverse(X_59),least_upper_bound(identity,X_59))) )],[refute_0_563,refute_0_564]) ).
cnf(refute_0_566,plain,
least_upper_bound(inverse(X_59),inverse(X_59)) = inverse(X_59),
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(inverse(X_59)))]]) ).
cnf(refute_0_567,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))) = least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))))]]) ).
cnf(refute_0_568,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))) != least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59)))
| least_upper_bound(inverse(X_59),inverse(X_59)) != inverse(X_59)
| least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))) = least_upper_bound(identity,inverse(X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))),least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59)))) ),[1,1],$fot(inverse(X_59))]]) ).
cnf(refute_0_569,plain,
( least_upper_bound(inverse(X_59),inverse(X_59)) != inverse(X_59)
| least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))) = least_upper_bound(identity,inverse(X_59)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))),least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59)))) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))) = least_upper_bound(identity,inverse(X_59)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_59),inverse(X_59)),inverse(X_59)) )],[refute_0_566,refute_0_569]) ).
cnf(refute_0_571,plain,
least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,least_upper_bound(X_13,X_44))),
inference(subst,[],[refute_0_454:[bind(X,$fot(least_upper_bound(X_13,X_44))),bind(X_39,$fot(X_43)),bind(X_40,$fot(X_44))]]) ).
cnf(refute_0_572,plain,
least_upper_bound(X_44,least_upper_bound(X_13,X_44)) = least_upper_bound(X_44,X_13),
inference(subst,[],[refute_0_387:[bind(X_9,$fot(X_44))]]) ).
cnf(refute_0_573,plain,
( least_upper_bound(X_44,least_upper_bound(X_13,X_44)) != least_upper_bound(X_44,X_13)
| least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) != least_upper_bound(X_43,least_upper_bound(X_44,least_upper_bound(X_13,X_44)))
| least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)),least_upper_bound(X_43,least_upper_bound(X_44,least_upper_bound(X_13,X_44)))) ),[1,1],$fot(least_upper_bound(X_44,X_13))]]) ).
cnf(refute_0_574,plain,
( least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) != least_upper_bound(X_43,least_upper_bound(X_44,least_upper_bound(X_13,X_44)))
| least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,X_13)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_13,X_44)),least_upper_bound(X_44,X_13)) )],[refute_0_572,refute_0_573]) ).
cnf(refute_0_575,plain,
least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,X_13)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)),least_upper_bound(X_43,least_upper_bound(X_44,least_upper_bound(X_13,X_44)))) )],[refute_0_571,refute_0_574]) ).
cnf(refute_0_576,plain,
least_upper_bound(X_9,least_upper_bound(least_upper_bound(X_39,X_40),X_9)) = least_upper_bound(X_9,least_upper_bound(X_39,X_40)),
inference(subst,[],[refute_0_387:[bind(X_13,$fot(least_upper_bound(X_39,X_40)))]]) ).
cnf(refute_0_577,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X_9)) = least_upper_bound(least_upper_bound(X_39,X_40),X_9),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_578,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,X_9)) != least_upper_bound(least_upper_bound(X_39,X_40),X_9)
| least_upper_bound(least_upper_bound(X_39,X_40),X_9) = least_upper_bound(X_39,least_upper_bound(X_40,X_9)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_9)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_39,X_40),X_9)))]]) ).
cnf(refute_0_579,plain,
least_upper_bound(least_upper_bound(X_39,X_40),X_9) = least_upper_bound(X_39,least_upper_bound(X_40,X_9)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,X_9)),least_upper_bound(least_upper_bound(X_39,X_40),X_9)) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
( least_upper_bound(X_9,least_upper_bound(least_upper_bound(X_39,X_40),X_9)) != least_upper_bound(X_9,least_upper_bound(X_39,X_40))
| least_upper_bound(least_upper_bound(X_39,X_40),X_9) != least_upper_bound(X_39,least_upper_bound(X_40,X_9))
| least_upper_bound(X_9,least_upper_bound(X_39,least_upper_bound(X_40,X_9))) = least_upper_bound(X_9,least_upper_bound(X_39,X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_9,least_upper_bound(least_upper_bound(X_39,X_40),X_9)),least_upper_bound(X_9,least_upper_bound(X_39,X_40))) ),[0,1],$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_9)))]]) ).
cnf(refute_0_581,plain,
( least_upper_bound(X_9,least_upper_bound(least_upper_bound(X_39,X_40),X_9)) != least_upper_bound(X_9,least_upper_bound(X_39,X_40))
| least_upper_bound(X_9,least_upper_bound(X_39,least_upper_bound(X_40,X_9))) = least_upper_bound(X_9,least_upper_bound(X_39,X_40)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),X_9),least_upper_bound(X_39,least_upper_bound(X_40,X_9))) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
least_upper_bound(X_9,least_upper_bound(X_39,least_upper_bound(X_40,X_9))) = least_upper_bound(X_9,least_upper_bound(X_39,X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,least_upper_bound(least_upper_bound(X_39,X_40),X_9)),least_upper_bound(X_9,least_upper_bound(X_39,X_40))) )],[refute_0_576,refute_0_581]) ).
cnf(refute_0_583,plain,
least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_13,X_44))) = least_upper_bound(X_44,least_upper_bound(X_43,X_13)),
inference(subst,[],[refute_0_582:[bind(X_39,$fot(X_43)),bind(X_40,$fot(X_13)),bind(X_9,$fot(X_44))]]) ).
cnf(refute_0_584,plain,
least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) = least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_13,X_44))),
inference(subst,[],[refute_0_526:[bind(X_13,$fot(least_upper_bound(X_13,X_44))),bind(X_42,$fot(X_44))]]) ).
cnf(refute_0_585,plain,
( least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_13,X_44))) != least_upper_bound(X_44,least_upper_bound(X_43,X_13))
| least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) != least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_13,X_44)))
| least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) = least_upper_bound(X_44,least_upper_bound(X_43,X_13)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)))),bind(Y0,$fot(least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_13,X_44))))),bind(Z0,$fot(least_upper_bound(X_44,least_upper_bound(X_43,X_13))))]]) ).
cnf(refute_0_586,plain,
( least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_13,X_44))) != least_upper_bound(X_44,least_upper_bound(X_43,X_13))
| least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) = least_upper_bound(X_44,least_upper_bound(X_43,X_13)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)),least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_13,X_44)))) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) = least_upper_bound(X_44,least_upper_bound(X_43,X_13)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_43,least_upper_bound(X_13,X_44))),least_upper_bound(X_44,least_upper_bound(X_43,X_13))) )],[refute_0_583,refute_0_586]) ).
cnf(refute_0_588,plain,
( least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) != least_upper_bound(X_43,least_upper_bound(X_44,X_13))
| least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) != least_upper_bound(X_44,least_upper_bound(X_43,X_13))
| least_upper_bound(X_44,least_upper_bound(X_43,X_13)) = least_upper_bound(X_43,least_upper_bound(X_44,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)),least_upper_bound(X_43,least_upper_bound(X_44,X_13))) ),[0],$fot(least_upper_bound(X_44,least_upper_bound(X_43,X_13)))]]) ).
cnf(refute_0_589,plain,
( least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)) != least_upper_bound(X_43,least_upper_bound(X_44,X_13))
| least_upper_bound(X_44,least_upper_bound(X_43,X_13)) = least_upper_bound(X_43,least_upper_bound(X_44,X_13)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)),least_upper_bound(X_44,least_upper_bound(X_43,X_13))) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
least_upper_bound(X_44,least_upper_bound(X_43,X_13)) = least_upper_bound(X_43,least_upper_bound(X_44,X_13)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,X_44),least_upper_bound(X_43,X_44)),least_upper_bound(X_43,least_upper_bound(X_44,X_13))) )],[refute_0_575,refute_0_589]) ).
cnf(refute_0_591,plain,
( least_upper_bound(X_44,least_upper_bound(X_43,X_13)) != least_upper_bound(X_43,least_upper_bound(X_44,X_13))
| least_upper_bound(X_43,least_upper_bound(X_44,X_13)) = least_upper_bound(X_44,least_upper_bound(X_43,X_13)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_44,least_upper_bound(X_43,X_13)))),bind(Y0,$fot(least_upper_bound(X_43,least_upper_bound(X_44,X_13))))]]) ).
cnf(refute_0_592,plain,
least_upper_bound(X_43,least_upper_bound(X_44,X_13)) = least_upper_bound(X_44,least_upper_bound(X_43,X_13)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_44,least_upper_bound(X_43,X_13)),least_upper_bound(X_43,least_upper_bound(X_44,X_13))) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))) = least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))),
inference(subst,[],[refute_0_592:[bind(X_13,$fot(inverse(X_59))),bind(X_43,$fot(inverse(X_59))),bind(X_44,$fot(identity))]]) ).
cnf(refute_0_594,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))) != least_upper_bound(identity,inverse(X_59))
| least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))) != least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59)))
| least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))) = least_upper_bound(identity,inverse(X_59)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_59))))]]) ).
cnf(refute_0_595,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))) != least_upper_bound(identity,inverse(X_59))
| least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))) = least_upper_bound(identity,inverse(X_59)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))),least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59)))) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))) = least_upper_bound(identity,inverse(X_59)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_59),inverse(X_59))),least_upper_bound(identity,inverse(X_59))) )],[refute_0_570,refute_0_595]) ).
cnf(refute_0_597,plain,
( multiply(inverse(X_59),least_upper_bound(identity,X_59)) != least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59)))
| least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))) != least_upper_bound(identity,inverse(X_59))
| multiply(inverse(X_59),least_upper_bound(identity,X_59)) = least_upper_bound(identity,inverse(X_59)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_59),least_upper_bound(identity,X_59)),least_upper_bound(identity,inverse(X_59))) ),[0],$fot(least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))))]]) ).
cnf(refute_0_598,plain,
( multiply(inverse(X_59),least_upper_bound(identity,X_59)) != least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59)))
| multiply(inverse(X_59),least_upper_bound(identity,X_59)) = least_upper_bound(identity,inverse(X_59)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59))),least_upper_bound(identity,inverse(X_59))) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
( multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)) != least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59)))
| multiply(inverse(X_59),least_upper_bound(identity,X_59)) = least_upper_bound(identity,inverse(X_59)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(identity,X_59)),least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59)))) )],[refute_0_565,refute_0_598]) ).
cnf(refute_0_600,plain,
multiply(inverse(X_59),least_upper_bound(identity,X_59)) = least_upper_bound(identity,inverse(X_59)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(least_upper_bound(X_59,identity),identity)),least_upper_bound(inverse(X_59),least_upper_bound(identity,inverse(X_59)))) )],[refute_0_376,refute_0_599]) ).
cnf(refute_0_601,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(subst,[],[refute_0_600:[bind(X_59,$fot(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_602,plain,
least_upper_bound(identity,greatest_lower_bound(identity,Y)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity))]]) ).
cnf(refute_0_603,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| least_upper_bound(identity,greatest_lower_bound(identity,Y)) != identity
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_604,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,Y)),identity) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,greatest_lower_bound(identity,Y))),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_601,refute_0_604]) ).
cnf(refute_0_606,plain,
multiply(inverse(greatest_lower_bound(identity,Y)),identity) = inverse(greatest_lower_bound(identity,Y)),
inference(subst,[],[refute_0_62:[bind(X_28,$fot(inverse(greatest_lower_bound(identity,Y))))]]) ).
cnf(refute_0_607,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),identity) != inverse(greatest_lower_bound(identity,Y))
| multiply(inverse(greatest_lower_bound(identity,Y)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) ),[0],$fot(inverse(greatest_lower_bound(identity,Y)))]]) ).
cnf(refute_0_608,plain,
( multiply(inverse(greatest_lower_bound(identity,Y)),identity) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),inverse(greatest_lower_bound(identity,Y))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
inverse(greatest_lower_bound(identity,Y)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,Y)),identity),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_605,refute_0_608]) ).
cnf(refute_0_610,plain,
( inverse(greatest_lower_bound(identity,Y)) != least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) = inverse(greatest_lower_bound(identity,Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(greatest_lower_bound(identity,Y)))),bind(Y0,$fot(least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))))]]) ).
cnf(refute_0_611,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y))) = inverse(greatest_lower_bound(identity,Y)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,Y)),least_upper_bound(identity,inverse(greatest_lower_bound(identity,Y)))) )],[refute_0_609,refute_0_610]) ).
cnf(refute_0_612,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))) = inverse(greatest_lower_bound(identity,X_80)),
inference(subst,[],[refute_0_611:[bind(Y,$fot(X_80))]]) ).
cnf(refute_0_613,plain,
greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))))]]) ).
cnf(refute_0_614,plain,
( greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))) != inverse(greatest_lower_bound(identity,X_80))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),inverse(greatest_lower_bound(identity,X_80))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,X_80)))]]) ).
cnf(refute_0_615,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))) != inverse(greatest_lower_bound(identity,X_80))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),inverse(greatest_lower_bound(identity,X_80))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))))) )],[refute_0_613,refute_0_614]) ).
cnf(refute_0_616,plain,
greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),inverse(greatest_lower_bound(identity,X_80))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),inverse(greatest_lower_bound(identity,X_80))) )],[refute_0_612,refute_0_615]) ).
cnf(refute_0_617,plain,
( greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),inverse(greatest_lower_bound(identity,X_80))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),inverse(greatest_lower_bound(identity,X_80)))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),inverse(greatest_lower_bound(identity,X_80))))),bind(Z0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148))))]]) ).
cnf(refute_0_618,plain,
( greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),inverse(greatest_lower_bound(identity,X_80))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),inverse(greatest_lower_bound(identity,X_80)))) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),inverse(greatest_lower_bound(identity,X_80))),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148))) )],[refute_0_371,refute_0_618]) ).
cnf(refute_0_620,plain,
( multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148))
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148))) ),[0],$fot(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))))]]) ).
cnf(refute_0_621,plain,
( multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))))
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80)))),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148))) )],[refute_0_619,refute_0_620]) ).
cnf(refute_0_622,plain,
( multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))))
| multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))))) )],[refute_0_336,refute_0_621]) ).
cnf(refute_0_623,plain,
multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,least_upper_bound(greatest_lower_bound(X_80,identity),identity))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_80,identity)),X_148),least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))))) )],[refute_0_306,refute_0_622]) ).
cnf(refute_0_624,plain,
( multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148)) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148))))]]) ).
cnf(refute_0_625,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148)) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_148,identity)),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_148))) )],[refute_0_623,refute_0_624]) ).
cnf(refute_0_626,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity)),
inference(subst,[],[refute_0_625:[bind(X_148,$fot(X_150))]]) ).
cnf(refute_0_627,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) = greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)))]]) ).
cnf(refute_0_628,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))
| least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))) != inverse(greatest_lower_bound(identity,X_80))
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))) ),[1,0],$fot(inverse(greatest_lower_bound(identity,X_80)))]]) ).
cnf(refute_0_629,plain,
( least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))) != inverse(greatest_lower_bound(identity,X_80))
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))) )],[refute_0_627,refute_0_628]) ).
cnf(refute_0_630,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),inverse(greatest_lower_bound(identity,X_80))) )],[refute_0_612,refute_0_629]) ).
cnf(refute_0_631,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) != multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity))))]]) ).
cnf(refute_0_632,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) != multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))) )],[refute_0_630,refute_0_631]) ).
cnf(refute_0_633,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_80)),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)),multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity))) )],[refute_0_626,refute_0_632]) ).
cnf(refute_0_634,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))
| greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)) != multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity))
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)),multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)))]]) ).
cnf(refute_0_635,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150)),multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity))) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
( multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)) != greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))
| multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))) )],[refute_0_296,refute_0_635]) ).
cnf(refute_0_637,plain,
multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,X_150)) = multiply(inverse(greatest_lower_bound(X_80,identity)),greatest_lower_bound(X_150,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_80)),greatest_lower_bound(least_upper_bound(greatest_lower_bound(identity,X_80),identity),X_150)),greatest_lower_bound(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X_80))),multiply(inverse(greatest_lower_bound(X_80,identity)),X_150))) )],[refute_0_266,refute_0_636]) ).
cnf(refute_0_638,plain,
multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) = multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity)),
inference(subst,[],[refute_0_637:[bind(X_150,$fot(multiply(greatest_lower_bound(X_419,identity),X_26))),bind(X_80,$fot(X_419))]]) ).
cnf(refute_0_639,plain,
( multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) != multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity))
| multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity)) = multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity))))]]) ).
cnf(refute_0_640,plain,
multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity)) = multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))),multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity))) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
( multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity)) != multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26)))
| multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity)) != greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))
| multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) = greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity)),greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))) ),[0],$fot(multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))))]]) ).
cnf(refute_0_642,plain,
( multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity)) != greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))
| multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) = greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity)),multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26)))) )],[refute_0_640,refute_0_641]) ).
cnf(refute_0_643,plain,
multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) = greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_419,identity)),greatest_lower_bound(multiply(greatest_lower_bound(X_419,identity),X_26),identity)),greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))) )],[refute_0_194,refute_0_642]) ).
cnf(refute_0_644,plain,
multiply(inverse(greatest_lower_bound(identity,X_419)),identity) = inverse(greatest_lower_bound(identity,X_419)),
inference(subst,[],[refute_0_62:[bind(X_28,$fot(inverse(greatest_lower_bound(identity,X_419))))]]) ).
cnf(refute_0_645,plain,
greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26))]]) ).
cnf(refute_0_646,plain,
( multiply(inverse(greatest_lower_bound(identity,X_419)),identity) != inverse(greatest_lower_bound(identity,X_419))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26)
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26),greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26)) ),[1,0],$fot(inverse(greatest_lower_bound(identity,X_419)))]]) ).
cnf(refute_0_647,plain,
( multiply(inverse(greatest_lower_bound(identity,X_419)),identity) != inverse(greatest_lower_bound(identity,X_419))
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26),greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26)) )],[refute_0_645,refute_0_646]) ).
cnf(refute_0_648,plain,
greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),inverse(greatest_lower_bound(identity,X_419))) )],[refute_0_644,refute_0_647]) ).
cnf(refute_0_649,plain,
multiply(inverse(greatest_lower_bound(X_330,X_332)),greatest_lower_bound(X_73,multiply(greatest_lower_bound(X_330,X_332),X_26))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_330,X_332)),X_73),X_26),
inference(subst,[],[refute_0_350:[bind(X_25,$fot(greatest_lower_bound(X_330,X_332)))]]) ).
cnf(refute_0_650,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_136:[bind(X_12,$fot(least_upper_bound(X_13,X_17))),bind(X_13,$fot(X_17))]]) ).
cnf(refute_0_651,plain,
least_upper_bound(X_17,least_upper_bound(X_13,X_17)) = least_upper_bound(X_17,X_13),
inference(subst,[],[refute_0_387:[bind(X_9,$fot(X_17))]]) ).
cnf(refute_0_652,plain,
( greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,least_upper_bound(X_13,X_17))) != least_upper_bound(X_13,X_17)
| least_upper_bound(X_17,least_upper_bound(X_13,X_17)) != least_upper_bound(X_17,X_13)
| greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,X_13)) = least_upper_bound(X_13,X_17) ),
introduced(tautology,[equality,[$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_653,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( $equal(least_upper_bound(X_17,least_upper_bound(X_13,X_17)),least_upper_bound(X_17,X_13)) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,X_13)) = least_upper_bound(X_13,X_17),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_13,X_17),least_upper_bound(X_17,least_upper_bound(X_13,X_17))),least_upper_bound(X_13,X_17)) )],[refute_0_650,refute_0_653]) ).
cnf(refute_0_655,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
inference(subst,[],[refute_0_654:[bind(X_13,$fot(multiply(Z,X))),bind(X_17,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_656,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_657,plain,
least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_656]) ).
cnf(refute_0_658,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(multiply(Y,X),multiply(Z,X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) ),[0,1],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).
cnf(refute_0_659,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),multiply(Z,X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_657,refute_0_658]) ).
cnf(refute_0_660,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = least_upper_bound(multiply(Z,X),multiply(Y,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),least_upper_bound(multiply(Y,X),multiply(Z,X))),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_655,refute_0_659]) ).
cnf(refute_0_661,plain,
greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) = least_upper_bound(Y,Z),
inference(subst,[],[refute_0_654:[bind(X_13,$fot(Y)),bind(X_17,$fot(Z))]]) ).
cnf(refute_0_662,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))]]) ).
cnf(refute_0_663,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
| greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) ),[1,0],$fot(least_upper_bound(Y,Z))]]) ).
cnf(refute_0_664,plain,
( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_661,refute_0_664]) ).
cnf(refute_0_666,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_667,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_666]) ).
cnf(refute_0_668,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),
inference(subst,[],[refute_0_667:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_669,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)))),bind(Y0,$fot(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_670,plain,
( multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X)) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),X),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_665,refute_0_670]) ).
cnf(refute_0_672,plain,
least_upper_bound(multiply(Z,X),multiply(Y,X)) = multiply(least_upper_bound(Z,Y),X),
inference(subst,[],[refute_0_657:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_673,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_674,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
| least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) ),[1,1],$fot(multiply(least_upper_bound(Z,Y),X))]]) ).
cnf(refute_0_675,plain,
( least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_673,refute_0_674]) ).
cnf(refute_0_676,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_672,refute_0_675]) ).
cnf(refute_0_677,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_678,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X))) )],[refute_0_676,refute_0_677]) ).
cnf(refute_0_679,plain,
greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_671,refute_0_678]) ).
cnf(refute_0_680,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),
inference(subst,[],[refute_0_38:[bind(X,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y,$fot(least_upper_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_681,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)))),bind(Y0,$fot(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))))),bind(Z0,$fot(multiply(least_upper_bound(Y,Z),X)))]]) ).
cnf(refute_0_682,plain,
( greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) = multiply(least_upper_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_679,refute_0_682]) ).
cnf(refute_0_684,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != multiply(least_upper_bound(Y,Z),X)
| greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) ),[0],$fot(multiply(least_upper_bound(Y,Z),X))]]) ).
cnf(refute_0_685,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),multiply(least_upper_bound(Y,Z),X)) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(multiply(Z,X),multiply(Y,X)) != multiply(least_upper_bound(Z,Y),X)
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,Z),X),multiply(least_upper_bound(Z,Y),X)) ),[0],$fot(least_upper_bound(multiply(Z,X),multiply(Y,X)))]]) ).
cnf(refute_0_687,plain,
( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Z,Y),X)) )],[refute_0_672,refute_0_686]) ).
cnf(refute_0_688,plain,
( greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)) != least_upper_bound(multiply(Z,X),multiply(Y,X))
| multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_685,refute_0_687]) ).
cnf(refute_0_689,plain,
multiply(least_upper_bound(Y,Z),X) = multiply(least_upper_bound(Z,Y),X),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(Z,X),multiply(Y,X)),multiply(least_upper_bound(Y,Z),X)),least_upper_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_660,refute_0_688]) ).
cnf(refute_0_690,plain,
multiply(least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,X_18)),X_241) = multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241),
inference(subst,[],[refute_0_689:[bind(X,$fot(X_241)),bind(Y,$fot(greatest_lower_bound(X_18,X_9))),bind(Z,$fot(greatest_lower_bound(X_9,X_18)))]]) ).
cnf(refute_0_691,plain,
least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_18,X_9))) = greatest_lower_bound(X_18,X_9),
inference(subst,[],[refute_0_177:[bind(X_8,$fot(greatest_lower_bound(X_18,X_9)))]]) ).
cnf(refute_0_692,plain,
greatest_lower_bound(X_9,greatest_lower_bound(X_18,X_9)) = greatest_lower_bound(X_9,X_18),
inference(subst,[],[refute_0_147:[bind(Y,$fot(X_18)),bind(X_17,$fot(X_9))]]) ).
cnf(refute_0_693,plain,
( greatest_lower_bound(X_9,greatest_lower_bound(X_18,X_9)) != greatest_lower_bound(X_9,X_18)
| least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_18,X_9))) != greatest_lower_bound(X_18,X_9)
| least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,X_18)) = greatest_lower_bound(X_18,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_18,X_9))),greatest_lower_bound(X_18,X_9)) ),[0,1],$fot(greatest_lower_bound(X_9,X_18))]]) ).
cnf(refute_0_694,plain,
( least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_18,X_9))) != greatest_lower_bound(X_18,X_9)
| least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,X_18)) = greatest_lower_bound(X_18,X_9) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,greatest_lower_bound(X_18,X_9)),greatest_lower_bound(X_9,X_18)) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,X_18)) = greatest_lower_bound(X_18,X_9),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,greatest_lower_bound(X_18,X_9))),greatest_lower_bound(X_18,X_9)) )],[refute_0_691,refute_0_694]) ).
cnf(refute_0_696,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,X_18)),X_241) != multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241)
| least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,X_18)) != greatest_lower_bound(X_18,X_9)
| multiply(greatest_lower_bound(X_18,X_9),X_241) = multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,X_18)),X_241),multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241)) ),[0,0],$fot(greatest_lower_bound(X_18,X_9))]]) ).
cnf(refute_0_697,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,X_18)),X_241) != multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241)
| multiply(greatest_lower_bound(X_18,X_9),X_241) = multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,X_18)),greatest_lower_bound(X_18,X_9)) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
multiply(greatest_lower_bound(X_18,X_9),X_241) = multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_18,X_9),greatest_lower_bound(X_9,X_18)),X_241),multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241)) )],[refute_0_690,refute_0_697]) ).
cnf(refute_0_699,plain,
least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)) = greatest_lower_bound(X_9,X_18),
inference(subst,[],[refute_0_695:[bind(X_18,$fot(X_9)),bind(X_9,$fot(X_18))]]) ).
cnf(refute_0_700,plain,
multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241) = multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241))]]) ).
cnf(refute_0_701,plain,
( multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241) != multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241)
| least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)) != greatest_lower_bound(X_9,X_18)
| multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241) = multiply(greatest_lower_bound(X_9,X_18),X_241) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241),multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241)) ),[1,0],$fot(greatest_lower_bound(X_9,X_18))]]) ).
cnf(refute_0_702,plain,
( least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)) != greatest_lower_bound(X_9,X_18)
| multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241) = multiply(greatest_lower_bound(X_9,X_18),X_241) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241),multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241)) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241) = multiply(greatest_lower_bound(X_9,X_18),X_241),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),greatest_lower_bound(X_9,X_18)) )],[refute_0_699,refute_0_702]) ).
cnf(refute_0_704,plain,
( multiply(greatest_lower_bound(X_18,X_9),X_241) != multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241)
| multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241) != multiply(greatest_lower_bound(X_9,X_18),X_241)
| multiply(greatest_lower_bound(X_18,X_9),X_241) = multiply(greatest_lower_bound(X_9,X_18),X_241) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_18,X_9),X_241),multiply(greatest_lower_bound(X_9,X_18),X_241)) ),[0],$fot(multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241))]]) ).
cnf(refute_0_705,plain,
( multiply(greatest_lower_bound(X_18,X_9),X_241) != multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241)
| multiply(greatest_lower_bound(X_18,X_9),X_241) = multiply(greatest_lower_bound(X_9,X_18),X_241) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241),multiply(greatest_lower_bound(X_9,X_18),X_241)) )],[refute_0_703,refute_0_704]) ).
cnf(refute_0_706,plain,
multiply(greatest_lower_bound(X_18,X_9),X_241) = multiply(greatest_lower_bound(X_9,X_18),X_241),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_18,X_9),X_241),multiply(least_upper_bound(greatest_lower_bound(X_9,X_18),greatest_lower_bound(X_18,X_9)),X_241)) )],[refute_0_698,refute_0_705]) ).
cnf(refute_0_707,plain,
multiply(greatest_lower_bound(X_330,X_332),X_26) = multiply(greatest_lower_bound(X_332,X_330),X_26),
inference(subst,[],[refute_0_706:[bind(X_18,$fot(X_330)),bind(X_241,$fot(X_26)),bind(X_9,$fot(X_332))]]) ).
cnf(refute_0_708,plain,
( multiply(greatest_lower_bound(X_330,X_332),X_26) != multiply(greatest_lower_bound(X_332,X_330),X_26)
| multiply(inverse(greatest_lower_bound(X_330,X_332)),greatest_lower_bound(X_73,multiply(greatest_lower_bound(X_330,X_332),X_26))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_330,X_332)),X_73),X_26)
| multiply(inverse(greatest_lower_bound(X_330,X_332)),greatest_lower_bound(X_73,multiply(greatest_lower_bound(X_332,X_330),X_26))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_330,X_332)),X_73),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_330,X_332)),greatest_lower_bound(X_73,multiply(greatest_lower_bound(X_330,X_332),X_26))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_330,X_332)),X_73),X_26)) ),[0,1,1],$fot(multiply(greatest_lower_bound(X_332,X_330),X_26))]]) ).
cnf(refute_0_709,plain,
( multiply(inverse(greatest_lower_bound(X_330,X_332)),greatest_lower_bound(X_73,multiply(greatest_lower_bound(X_330,X_332),X_26))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_330,X_332)),X_73),X_26)
| multiply(inverse(greatest_lower_bound(X_330,X_332)),greatest_lower_bound(X_73,multiply(greatest_lower_bound(X_332,X_330),X_26))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_330,X_332)),X_73),X_26) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_330,X_332),X_26),multiply(greatest_lower_bound(X_332,X_330),X_26)) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
multiply(inverse(greatest_lower_bound(X_330,X_332)),greatest_lower_bound(X_73,multiply(greatest_lower_bound(X_332,X_330),X_26))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_330,X_332)),X_73),X_26),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_330,X_332)),greatest_lower_bound(X_73,multiply(greatest_lower_bound(X_330,X_332),X_26))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(X_330,X_332)),X_73),X_26)) )],[refute_0_649,refute_0_709]) ).
cnf(refute_0_711,plain,
multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) = greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26),
inference(subst,[],[refute_0_710:[bind(X_330,$fot(identity)),bind(X_332,$fot(X_419)),bind(X_73,$fot(identity))]]) ).
cnf(refute_0_712,plain,
( multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) != greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26)
| greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26)
| multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))))),bind(Y0,$fot(greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26))),bind(Z0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26)))]]) ).
cnf(refute_0_713,plain,
( greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26)
| multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))),greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26)) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(inverse(greatest_lower_bound(identity,X_419)),identity),X_26),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26)) )],[refute_0_648,refute_0_713]) ).
cnf(refute_0_715,plain,
( multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) != greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))
| multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26)
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) = greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))),greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))) ),[0],$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26))]]) ).
cnf(refute_0_716,plain,
( multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) != greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) = greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26)) )],[refute_0_714,refute_0_715]) ).
cnf(refute_0_717,plain,
multiply(inverse(greatest_lower_bound(X_419,identity)),identity) = inverse(greatest_lower_bound(X_419,identity)),
inference(subst,[],[refute_0_62:[bind(X_28,$fot(inverse(greatest_lower_bound(X_419,identity))))]]) ).
cnf(refute_0_718,plain,
greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)) = greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)))]]) ).
cnf(refute_0_719,plain,
( multiply(inverse(greatest_lower_bound(X_419,identity)),identity) != inverse(greatest_lower_bound(X_419,identity))
| greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)) != greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))
| greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)) = greatest_lower_bound(X_26,inverse(greatest_lower_bound(X_419,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)),greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))) ),[1,1],$fot(inverse(greatest_lower_bound(X_419,identity)))]]) ).
cnf(refute_0_720,plain,
( multiply(inverse(greatest_lower_bound(X_419,identity)),identity) != inverse(greatest_lower_bound(X_419,identity))
| greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)) = greatest_lower_bound(X_26,inverse(greatest_lower_bound(X_419,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)),greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))) )],[refute_0_718,refute_0_719]) ).
cnf(refute_0_721,plain,
greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)) = greatest_lower_bound(X_26,inverse(greatest_lower_bound(X_419,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_419,identity)),identity),inverse(greatest_lower_bound(X_419,identity))) )],[refute_0_717,refute_0_720]) ).
cnf(refute_0_722,plain,
( greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)) != greatest_lower_bound(X_26,inverse(greatest_lower_bound(X_419,identity)))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) != greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) = greatest_lower_bound(X_26,inverse(greatest_lower_bound(X_419,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26),greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))) ),[1],$fot(greatest_lower_bound(X_26,inverse(greatest_lower_bound(X_419,identity))))]]) ).
cnf(refute_0_723,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) != greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) = greatest_lower_bound(X_26,inverse(greatest_lower_bound(X_419,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity)),greatest_lower_bound(X_26,inverse(greatest_lower_bound(X_419,identity)))) )],[refute_0_721,refute_0_722]) ).
cnf(refute_0_724,plain,
( multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))) != greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) = greatest_lower_bound(X_26,inverse(greatest_lower_bound(X_419,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26),greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))) )],[refute_0_716,refute_0_723]) ).
cnf(refute_0_725,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,X_419)),X_26) = greatest_lower_bound(X_26,inverse(greatest_lower_bound(X_419,identity))),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,X_419)),greatest_lower_bound(identity,multiply(greatest_lower_bound(X_419,identity),X_26))),greatest_lower_bound(X_26,multiply(inverse(greatest_lower_bound(X_419,identity)),identity))) )],[refute_0_643,refute_0_724]) ).
cnf(refute_0_726,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),least_upper_bound(X_73,identity)) = greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity))),
inference(subst,[],[refute_0_725:[bind(X_26,$fot(least_upper_bound(X_73,identity))),bind(X_419,$fot(X_73))]]) ).
cnf(refute_0_727,plain,
inverse(inverse(X_30)) = multiply(inverse(inverse(X_30)),identity),
inference(subst,[],[refute_0_30:[bind(X_28,$fot(inverse(inverse(X_30))))]]) ).
cnf(refute_0_728,plain,
multiply(X_30,identity) = multiply(inverse(inverse(X_30)),identity),
inference(subst,[],[refute_0_24:[bind(X_27,$fot(X_30)),bind(X_28,$fot(identity))]]) ).
cnf(refute_0_729,plain,
( multiply(X_30,identity) != multiply(inverse(inverse(X_30)),identity)
| multiply(inverse(inverse(X_30)),identity) = multiply(X_30,identity) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_30,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_30)),identity)))]]) ).
cnf(refute_0_730,plain,
multiply(inverse(inverse(X_30)),identity) = multiply(X_30,identity),
inference(resolve,[$cnf( $equal(multiply(X_30,identity),multiply(inverse(inverse(X_30)),identity)) )],[refute_0_728,refute_0_729]) ).
cnf(refute_0_731,plain,
( multiply(inverse(inverse(X_30)),identity) != multiply(X_30,identity)
| inverse(inverse(X_30)) != multiply(inverse(inverse(X_30)),identity)
| inverse(inverse(X_30)) = multiply(X_30,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_30)),multiply(inverse(inverse(X_30)),identity)) ),[1],$fot(multiply(X_30,identity))]]) ).
cnf(refute_0_732,plain,
( inverse(inverse(X_30)) != multiply(inverse(inverse(X_30)),identity)
| inverse(inverse(X_30)) = multiply(X_30,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_30)),identity),multiply(X_30,identity)) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
inverse(inverse(X_30)) = multiply(X_30,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_30)),multiply(inverse(inverse(X_30)),identity)) )],[refute_0_727,refute_0_732]) ).
cnf(refute_0_734,plain,
multiply(X_30,identity) = X_30,
inference(subst,[],[refute_0_62:[bind(X_28,$fot(X_30))]]) ).
cnf(refute_0_735,plain,
( multiply(X_30,identity) != X_30
| inverse(inverse(X_30)) != multiply(X_30,identity)
| inverse(inverse(X_30)) = X_30 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_30)),multiply(X_30,identity)) ),[1],$fot(X_30)]]) ).
cnf(refute_0_736,plain,
( inverse(inverse(X_30)) != multiply(X_30,identity)
| inverse(inverse(X_30)) = X_30 ),
inference(resolve,[$cnf( $equal(multiply(X_30,identity),X_30) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
inverse(inverse(X_30)) = X_30,
inference(resolve,[$cnf( $equal(inverse(inverse(X_30)),multiply(X_30,identity)) )],[refute_0_733,refute_0_736]) ).
cnf(refute_0_738,plain,
inverse(inverse(least_upper_bound(X_73,identity))) = least_upper_bound(X_73,identity),
inference(subst,[],[refute_0_737:[bind(X_30,$fot(least_upper_bound(X_73,identity)))]]) ).
cnf(refute_0_739,plain,
multiply(inverse(X_73),greatest_lower_bound(X_73,X_74)) = greatest_lower_bound(multiply(inverse(X_73),X_73),multiply(inverse(X_73),X_74)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_73))),bind(Y,$fot(X_73)),bind(Z,$fot(X_74))]]) ).
cnf(refute_0_740,plain,
multiply(inverse(X_73),X_73) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_73))]]) ).
cnf(refute_0_741,plain,
( multiply(inverse(X_73),X_73) != identity
| multiply(inverse(X_73),greatest_lower_bound(X_73,X_74)) != greatest_lower_bound(multiply(inverse(X_73),X_73),multiply(inverse(X_73),X_74))
| multiply(inverse(X_73),greatest_lower_bound(X_73,X_74)) = greatest_lower_bound(identity,multiply(inverse(X_73),X_74)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_73),greatest_lower_bound(X_73,X_74)),greatest_lower_bound(multiply(inverse(X_73),X_73),multiply(inverse(X_73),X_74))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_742,plain,
( multiply(inverse(X_73),greatest_lower_bound(X_73,X_74)) != greatest_lower_bound(multiply(inverse(X_73),X_73),multiply(inverse(X_73),X_74))
| multiply(inverse(X_73),greatest_lower_bound(X_73,X_74)) = greatest_lower_bound(identity,multiply(inverse(X_73),X_74)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_73),X_73),identity) )],[refute_0_740,refute_0_741]) ).
cnf(refute_0_743,plain,
multiply(inverse(X_73),greatest_lower_bound(X_73,X_74)) = greatest_lower_bound(identity,multiply(inverse(X_73),X_74)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_73),greatest_lower_bound(X_73,X_74)),greatest_lower_bound(multiply(inverse(X_73),X_73),multiply(inverse(X_73),X_74))) )],[refute_0_739,refute_0_742]) ).
cnf(refute_0_744,plain,
multiply(inverse(least_upper_bound(X_223,identity)),greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))),
inference(subst,[],[refute_0_743:[bind(X_73,$fot(least_upper_bound(X_223,identity))),bind(X_74,$fot(least_upper_bound(identity,inverse(X_223))))]]) ).
cnf(refute_0_745,plain,
multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)) = greatest_lower_bound(least_upper_bound(X_88,identity),multiply(least_upper_bound(X_88,identity),inverse(X_88))),
inference(subst,[],[refute_0_42:[bind(X_72,$fot(least_upper_bound(X_88,identity))),bind(X_73,$fot(inverse(X_88)))]]) ).
cnf(refute_0_746,plain,
multiply(least_upper_bound(X_85,identity),X_84) = least_upper_bound(multiply(X_85,X_84),multiply(identity,X_84)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_84)),bind(Y,$fot(X_85)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_747,plain,
multiply(identity,X_84) = X_84,
inference(subst,[],[left_identity:[bind(X,$fot(X_84))]]) ).
cnf(refute_0_748,plain,
( multiply(identity,X_84) != X_84
| multiply(least_upper_bound(X_85,identity),X_84) != least_upper_bound(multiply(X_85,X_84),multiply(identity,X_84))
| multiply(least_upper_bound(X_85,identity),X_84) = least_upper_bound(multiply(X_85,X_84),X_84) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_85,identity),X_84),least_upper_bound(multiply(X_85,X_84),multiply(identity,X_84))) ),[1,1],$fot(X_84)]]) ).
cnf(refute_0_749,plain,
( multiply(least_upper_bound(X_85,identity),X_84) != least_upper_bound(multiply(X_85,X_84),multiply(identity,X_84))
| multiply(least_upper_bound(X_85,identity),X_84) = least_upper_bound(multiply(X_85,X_84),X_84) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_84),X_84) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
multiply(least_upper_bound(X_85,identity),X_84) = least_upper_bound(multiply(X_85,X_84),X_84),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,identity),X_84),least_upper_bound(multiply(X_85,X_84),multiply(identity,X_84))) )],[refute_0_746,refute_0_749]) ).
cnf(refute_0_751,plain,
least_upper_bound(multiply(X_85,X_84),X_84) = least_upper_bound(X_84,multiply(X_85,X_84)),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_84)),bind(Y,$fot(multiply(X_85,X_84)))]]) ).
cnf(refute_0_752,plain,
( multiply(least_upper_bound(X_85,identity),X_84) != least_upper_bound(multiply(X_85,X_84),X_84)
| least_upper_bound(multiply(X_85,X_84),X_84) != least_upper_bound(X_84,multiply(X_85,X_84))
| multiply(least_upper_bound(X_85,identity),X_84) = least_upper_bound(X_84,multiply(X_85,X_84)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_85,identity),X_84),least_upper_bound(X_84,multiply(X_85,X_84))) ),[0],$fot(least_upper_bound(multiply(X_85,X_84),X_84))]]) ).
cnf(refute_0_753,plain,
( multiply(least_upper_bound(X_85,identity),X_84) != least_upper_bound(multiply(X_85,X_84),X_84)
| multiply(least_upper_bound(X_85,identity),X_84) = least_upper_bound(X_84,multiply(X_85,X_84)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,X_84),X_84),least_upper_bound(X_84,multiply(X_85,X_84))) )],[refute_0_751,refute_0_752]) ).
cnf(refute_0_754,plain,
multiply(least_upper_bound(X_85,identity),X_84) = least_upper_bound(X_84,multiply(X_85,X_84)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,identity),X_84),least_upper_bound(multiply(X_85,X_84),X_84)) )],[refute_0_750,refute_0_753]) ).
cnf(refute_0_755,plain,
multiply(least_upper_bound(X_88,identity),inverse(X_88)) = least_upper_bound(inverse(X_88),multiply(X_88,inverse(X_88))),
inference(subst,[],[refute_0_754:[bind(X_84,$fot(inverse(X_88))),bind(X_85,$fot(X_88))]]) ).
cnf(refute_0_756,plain,
multiply(X_88,inverse(X_88)) = identity,
inference(subst,[],[refute_0_56:[bind(X_30,$fot(X_88))]]) ).
cnf(refute_0_757,plain,
( multiply(X_88,inverse(X_88)) != identity
| multiply(least_upper_bound(X_88,identity),inverse(X_88)) != least_upper_bound(inverse(X_88),multiply(X_88,inverse(X_88)))
| multiply(least_upper_bound(X_88,identity),inverse(X_88)) = least_upper_bound(inverse(X_88),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),inverse(X_88)),least_upper_bound(inverse(X_88),multiply(X_88,inverse(X_88)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_758,plain,
( multiply(least_upper_bound(X_88,identity),inverse(X_88)) != least_upper_bound(inverse(X_88),multiply(X_88,inverse(X_88)))
| multiply(least_upper_bound(X_88,identity),inverse(X_88)) = least_upper_bound(inverse(X_88),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_88,inverse(X_88)),identity) )],[refute_0_756,refute_0_757]) ).
cnf(refute_0_759,plain,
multiply(least_upper_bound(X_88,identity),inverse(X_88)) = least_upper_bound(inverse(X_88),identity),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),inverse(X_88)),least_upper_bound(inverse(X_88),multiply(X_88,inverse(X_88)))) )],[refute_0_755,refute_0_758]) ).
cnf(refute_0_760,plain,
least_upper_bound(X,least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)))) = least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)),
inference(subst,[],[refute_0_454:[bind(X_39,$fot(identity)),bind(X_40,$fot(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66))))]]) ).
cnf(refute_0_761,plain,
multiply(X_48,least_upper_bound(inverse(X_48),X_50)) = least_upper_bound(multiply(X_48,inverse(X_48)),multiply(X_48,X_50)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_48)),bind(Y,$fot(inverse(X_48))),bind(Z,$fot(X_50))]]) ).
cnf(refute_0_762,plain,
multiply(X_48,inverse(X_48)) = identity,
inference(subst,[],[refute_0_56:[bind(X_30,$fot(X_48))]]) ).
cnf(refute_0_763,plain,
( multiply(X_48,inverse(X_48)) != identity
| multiply(X_48,least_upper_bound(inverse(X_48),X_50)) != least_upper_bound(multiply(X_48,inverse(X_48)),multiply(X_48,X_50))
| multiply(X_48,least_upper_bound(inverse(X_48),X_50)) = least_upper_bound(identity,multiply(X_48,X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_48,least_upper_bound(inverse(X_48),X_50)),least_upper_bound(multiply(X_48,inverse(X_48)),multiply(X_48,X_50))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_764,plain,
( multiply(X_48,least_upper_bound(inverse(X_48),X_50)) != least_upper_bound(multiply(X_48,inverse(X_48)),multiply(X_48,X_50))
| multiply(X_48,least_upper_bound(inverse(X_48),X_50)) = least_upper_bound(identity,multiply(X_48,X_50)) ),
inference(resolve,[$cnf( $equal(multiply(X_48,inverse(X_48)),identity) )],[refute_0_762,refute_0_763]) ).
cnf(refute_0_765,plain,
multiply(X_48,least_upper_bound(inverse(X_48),X_50)) = least_upper_bound(identity,multiply(X_48,X_50)),
inference(resolve,[$cnf( $equal(multiply(X_48,least_upper_bound(inverse(X_48),X_50)),least_upper_bound(multiply(X_48,inverse(X_48)),multiply(X_48,X_50))) )],[refute_0_761,refute_0_764]) ).
cnf(refute_0_766,plain,
multiply(X_55,least_upper_bound(inverse(X_55),greatest_lower_bound(inverse(X_55),Y))) = least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y))),
inference(subst,[],[refute_0_765:[bind(X_48,$fot(X_55)),bind(X_50,$fot(greatest_lower_bound(inverse(X_55),Y)))]]) ).
cnf(refute_0_767,plain,
least_upper_bound(inverse(X_55),greatest_lower_bound(inverse(X_55),Y)) = inverse(X_55),
inference(subst,[],[lub_absorbtion:[bind(X,$fot(inverse(X_55)))]]) ).
cnf(refute_0_768,plain,
( multiply(X_55,least_upper_bound(inverse(X_55),greatest_lower_bound(inverse(X_55),Y))) != least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y)))
| least_upper_bound(inverse(X_55),greatest_lower_bound(inverse(X_55),Y)) != inverse(X_55)
| multiply(X_55,inverse(X_55)) = least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,least_upper_bound(inverse(X_55),greatest_lower_bound(inverse(X_55),Y))),least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y)))) ),[0,1],$fot(inverse(X_55))]]) ).
cnf(refute_0_769,plain,
( multiply(X_55,least_upper_bound(inverse(X_55),greatest_lower_bound(inverse(X_55),Y))) != least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y)))
| multiply(X_55,inverse(X_55)) = least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_55),greatest_lower_bound(inverse(X_55),Y)),inverse(X_55)) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
multiply(X_55,inverse(X_55)) = least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y))),
inference(resolve,[$cnf( $equal(multiply(X_55,least_upper_bound(inverse(X_55),greatest_lower_bound(inverse(X_55),Y))),least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y)))) )],[refute_0_766,refute_0_769]) ).
cnf(refute_0_771,plain,
multiply(X_55,inverse(X_55)) = identity,
inference(subst,[],[refute_0_56:[bind(X_30,$fot(X_55))]]) ).
cnf(refute_0_772,plain,
( multiply(X_55,inverse(X_55)) != identity
| multiply(X_55,inverse(X_55)) != least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y)))
| identity = least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_55,inverse(X_55)),least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_773,plain,
( multiply(X_55,inverse(X_55)) != least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y)))
| identity = least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y))) ),
inference(resolve,[$cnf( $equal(multiply(X_55,inverse(X_55)),identity) )],[refute_0_771,refute_0_772]) ).
cnf(refute_0_774,plain,
identity = least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y))),
inference(resolve,[$cnf( $equal(multiply(X_55,inverse(X_55)),least_upper_bound(identity,multiply(X_55,greatest_lower_bound(inverse(X_55),Y)))) )],[refute_0_770,refute_0_773]) ).
cnf(refute_0_775,plain,
identity = least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66))),
inference(subst,[],[refute_0_774:[bind(Y,$fot(X_66)),bind(X_55,$fot(X_67))]]) ).
cnf(refute_0_776,plain,
( identity != least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)))
| least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66))) = identity ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)))))]]) ).
cnf(refute_0_777,plain,
least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66))) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)))) )],[refute_0_775,refute_0_776]) ).
cnf(refute_0_778,plain,
( least_upper_bound(X,least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)))) != least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X))
| least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66))) != identity
| least_upper_bound(X,identity) = least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)))),least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_779,plain,
( least_upper_bound(X,least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)))) != least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X))
| least_upper_bound(X,identity) = least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66))),identity) )],[refute_0_777,refute_0_778]) ).
cnf(refute_0_780,plain,
least_upper_bound(X,identity) = least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(identity,multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)))),least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X))) )],[refute_0_760,refute_0_779]) ).
cnf(refute_0_781,plain,
least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_39,Y),X_41)) = least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_39,Y)),X_41),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(greatest_lower_bound(X_39,Y))),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_782,plain,
least_upper_bound(X_39,greatest_lower_bound(X_39,Y)) = X_39,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_39))]]) ).
cnf(refute_0_783,plain,
( least_upper_bound(X_39,greatest_lower_bound(X_39,Y)) != X_39
| least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_39,Y),X_41)) != least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_39,Y)),X_41)
| least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_39,Y),X_41)) = least_upper_bound(X_39,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_39,Y),X_41)),least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_39,Y)),X_41)) ),[1,0],$fot(X_39)]]) ).
cnf(refute_0_784,plain,
( least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_39,Y),X_41)) != least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_39,Y)),X_41)
| least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_39,Y),X_41)) = least_upper_bound(X_39,X_41) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,greatest_lower_bound(X_39,Y)),X_39) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_39,Y),X_41)) = least_upper_bound(X_39,X_41),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_39,Y),X_41)),least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_39,Y)),X_41)) )],[refute_0_781,refute_0_784]) ).
cnf(refute_0_786,plain,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X)) = least_upper_bound(identity,X),
inference(subst,[],[refute_0_785:[bind(Y,$fot(multiply(X_67,X_66))),bind(X_39,$fot(identity)),bind(X_41,$fot(X))]]) ).
cnf(refute_0_787,plain,
multiply(X_72,greatest_lower_bound(inverse(X_72),X_74)) = greatest_lower_bound(multiply(X_72,inverse(X_72)),multiply(X_72,X_74)),
inference(subst,[],[monotony_glb1:[bind(X,$fot(X_72)),bind(Y,$fot(inverse(X_72))),bind(Z,$fot(X_74))]]) ).
cnf(refute_0_788,plain,
( multiply(X_72,greatest_lower_bound(inverse(X_72),X_74)) != greatest_lower_bound(multiply(X_72,inverse(X_72)),multiply(X_72,X_74))
| multiply(X_72,inverse(X_72)) != identity
| multiply(X_72,greatest_lower_bound(inverse(X_72),X_74)) = greatest_lower_bound(identity,multiply(X_72,X_74)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_72,greatest_lower_bound(inverse(X_72),X_74)),greatest_lower_bound(multiply(X_72,inverse(X_72)),multiply(X_72,X_74))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_789,plain,
( multiply(X_72,greatest_lower_bound(inverse(X_72),X_74)) != greatest_lower_bound(multiply(X_72,inverse(X_72)),multiply(X_72,X_74))
| multiply(X_72,greatest_lower_bound(inverse(X_72),X_74)) = greatest_lower_bound(identity,multiply(X_72,X_74)) ),
inference(resolve,[$cnf( $equal(multiply(X_72,inverse(X_72)),identity) )],[refute_0_241,refute_0_788]) ).
cnf(refute_0_790,plain,
multiply(X_72,greatest_lower_bound(inverse(X_72),X_74)) = greatest_lower_bound(identity,multiply(X_72,X_74)),
inference(resolve,[$cnf( $equal(multiply(X_72,greatest_lower_bound(inverse(X_72),X_74)),greatest_lower_bound(multiply(X_72,inverse(X_72)),multiply(X_72,X_74))) )],[refute_0_787,refute_0_789]) ).
cnf(refute_0_791,plain,
multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)) = greatest_lower_bound(identity,multiply(X_67,X_66)),
inference(subst,[],[refute_0_790:[bind(X_72,$fot(X_67)),bind(X_74,$fot(X_66))]]) ).
cnf(refute_0_792,plain,
least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X) = least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X))]]) ).
cnf(refute_0_793,plain,
( multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)) != greatest_lower_bound(identity,multiply(X_67,X_66))
| least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X) != least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)
| least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X) = least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X),least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) ),[1,0],$fot(greatest_lower_bound(identity,multiply(X_67,X_66)))]]) ).
cnf(refute_0_794,plain,
( multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)) != greatest_lower_bound(identity,multiply(X_67,X_66))
| least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X) = least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X),least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) )],[refute_0_792,refute_0_793]) ).
cnf(refute_0_795,plain,
least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X) = least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X),
inference(resolve,[$cnf( $equal(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),greatest_lower_bound(identity,multiply(X_67,X_66))) )],[refute_0_791,refute_0_794]) ).
cnf(refute_0_796,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) = least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)))]]) ).
cnf(refute_0_797,plain,
( least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X) != least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X)
| least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) != least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X))
| least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)),least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X))) ),[1,1],$fot(least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X))]]) ).
cnf(refute_0_798,plain,
( least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X) != least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X)
| least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)),least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X))) )],[refute_0_796,refute_0_797]) ).
cnf(refute_0_799,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X),least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X)) )],[refute_0_795,refute_0_798]) ).
cnf(refute_0_800,plain,
( least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) != least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X))
| least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X)) != least_upper_bound(identity,X)
| least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) = least_upper_bound(identity,X) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X)))),bind(Z0,$fot(least_upper_bound(identity,X)))]]) ).
cnf(refute_0_801,plain,
( least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X)) != least_upper_bound(identity,X)
| least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) = least_upper_bound(identity,X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X))) )],[refute_0_799,refute_0_800]) ).
cnf(refute_0_802,plain,
least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) = least_upper_bound(identity,X),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,multiply(X_67,X_66)),X)),least_upper_bound(identity,X)) )],[refute_0_786,refute_0_801]) ).
cnf(refute_0_803,plain,
( least_upper_bound(X,identity) != least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X))
| least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)) != least_upper_bound(identity,X)
| least_upper_bound(X,identity) = least_upper_bound(identity,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,identity),least_upper_bound(identity,X)) ),[0],$fot(least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)))]]) ).
cnf(refute_0_804,plain,
( least_upper_bound(X,identity) != least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X))
| least_upper_bound(X,identity) = least_upper_bound(identity,X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X)),least_upper_bound(identity,X)) )],[refute_0_802,refute_0_803]) ).
cnf(refute_0_805,plain,
least_upper_bound(X,identity) = least_upper_bound(identity,X),
inference(resolve,[$cnf( $equal(least_upper_bound(X,identity),least_upper_bound(identity,least_upper_bound(multiply(X_67,greatest_lower_bound(inverse(X_67),X_66)),X))) )],[refute_0_780,refute_0_804]) ).
cnf(refute_0_806,plain,
least_upper_bound(inverse(X_88),identity) = least_upper_bound(identity,inverse(X_88)),
inference(subst,[],[refute_0_805:[bind(X,$fot(inverse(X_88)))]]) ).
cnf(refute_0_807,plain,
( multiply(least_upper_bound(X_88,identity),inverse(X_88)) != least_upper_bound(inverse(X_88),identity)
| least_upper_bound(inverse(X_88),identity) != least_upper_bound(identity,inverse(X_88))
| multiply(least_upper_bound(X_88,identity),inverse(X_88)) = least_upper_bound(identity,inverse(X_88)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_88,identity),inverse(X_88)),least_upper_bound(identity,inverse(X_88))) ),[0],$fot(least_upper_bound(inverse(X_88),identity))]]) ).
cnf(refute_0_808,plain,
( multiply(least_upper_bound(X_88,identity),inverse(X_88)) != least_upper_bound(inverse(X_88),identity)
| multiply(least_upper_bound(X_88,identity),inverse(X_88)) = least_upper_bound(identity,inverse(X_88)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_88),identity),least_upper_bound(identity,inverse(X_88))) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
multiply(least_upper_bound(X_88,identity),inverse(X_88)) = least_upper_bound(identity,inverse(X_88)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),inverse(X_88)),least_upper_bound(inverse(X_88),identity)) )],[refute_0_759,refute_0_808]) ).
cnf(refute_0_810,plain,
( multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)) != greatest_lower_bound(least_upper_bound(X_88,identity),multiply(least_upper_bound(X_88,identity),inverse(X_88)))
| multiply(least_upper_bound(X_88,identity),inverse(X_88)) != least_upper_bound(identity,inverse(X_88))
| multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)) = greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)),greatest_lower_bound(least_upper_bound(X_88,identity),multiply(least_upper_bound(X_88,identity),inverse(X_88)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_88)))]]) ).
cnf(refute_0_811,plain,
( multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)) != greatest_lower_bound(least_upper_bound(X_88,identity),multiply(least_upper_bound(X_88,identity),inverse(X_88)))
| multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)) = greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),inverse(X_88)),least_upper_bound(identity,inverse(X_88))) )],[refute_0_809,refute_0_810]) ).
cnf(refute_0_812,plain,
multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)) = greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)),greatest_lower_bound(least_upper_bound(X_88,identity),multiply(least_upper_bound(X_88,identity),inverse(X_88)))) )],[refute_0_745,refute_0_811]) ).
cnf(refute_0_813,plain,
greatest_lower_bound(X_19,greatest_lower_bound(X_18,X_19)) = greatest_lower_bound(X_19,X_18),
inference(subst,[],[refute_0_147:[bind(Y,$fot(X_18)),bind(X_17,$fot(X_19))]]) ).
cnf(refute_0_814,plain,
greatest_lower_bound(X_19,X_18) = greatest_lower_bound(X_18,X_19),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_19)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_815,plain,
( greatest_lower_bound(X_19,X_18) != greatest_lower_bound(X_18,X_19)
| greatest_lower_bound(X_18,X_19) = greatest_lower_bound(X_19,X_18) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_19,X_18))),bind(Y0,$fot(greatest_lower_bound(X_18,X_19)))]]) ).
cnf(refute_0_816,plain,
greatest_lower_bound(X_18,X_19) = greatest_lower_bound(X_19,X_18),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,X_18),greatest_lower_bound(X_18,X_19)) )],[refute_0_814,refute_0_815]) ).
cnf(refute_0_817,plain,
( greatest_lower_bound(X_18,X_19) != greatest_lower_bound(X_19,X_18)
| greatest_lower_bound(X_19,greatest_lower_bound(X_18,X_19)) != greatest_lower_bound(X_19,X_18)
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_18)) = greatest_lower_bound(X_19,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_18,X_19)),greatest_lower_bound(X_19,X_18)) ),[0,1],$fot(greatest_lower_bound(X_19,X_18))]]) ).
cnf(refute_0_818,plain,
( greatest_lower_bound(X_19,greatest_lower_bound(X_18,X_19)) != greatest_lower_bound(X_19,X_18)
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_18)) = greatest_lower_bound(X_19,X_18) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_18,X_19),greatest_lower_bound(X_19,X_18)) )],[refute_0_816,refute_0_817]) ).
cnf(refute_0_819,plain,
greatest_lower_bound(X_19,greatest_lower_bound(X_19,X_18)) = greatest_lower_bound(X_19,X_18),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_18,X_19)),greatest_lower_bound(X_19,X_18)) )],[refute_0_813,refute_0_818]) ).
cnf(refute_0_820,plain,
greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_119))) = greatest_lower_bound(X_19,multiply(X_19,X_119)),
inference(subst,[],[refute_0_819:[bind(X_18,$fot(multiply(X_19,X_119)))]]) ).
cnf(refute_0_821,plain,
multiply(X_19,greatest_lower_bound(X_119,identity)) = greatest_lower_bound(X_19,multiply(X_19,X_119)),
inference(subst,[],[refute_0_42:[bind(X_72,$fot(X_19)),bind(X_73,$fot(X_119))]]) ).
cnf(refute_0_822,plain,
( multiply(X_19,greatest_lower_bound(X_119,identity)) != greatest_lower_bound(X_19,multiply(X_19,X_119))
| greatest_lower_bound(X_19,multiply(X_19,X_119)) = multiply(X_19,greatest_lower_bound(X_119,identity)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_19,greatest_lower_bound(X_119,identity)))),bind(Y0,$fot(greatest_lower_bound(X_19,multiply(X_19,X_119))))]]) ).
cnf(refute_0_823,plain,
greatest_lower_bound(X_19,multiply(X_19,X_119)) = multiply(X_19,greatest_lower_bound(X_119,identity)),
inference(resolve,[$cnf( $equal(multiply(X_19,greatest_lower_bound(X_119,identity)),greatest_lower_bound(X_19,multiply(X_19,X_119))) )],[refute_0_821,refute_0_822]) ).
cnf(refute_0_824,plain,
( greatest_lower_bound(X_19,multiply(X_19,X_119)) != multiply(X_19,greatest_lower_bound(X_119,identity))
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_119))) != greatest_lower_bound(X_19,multiply(X_19,X_119))
| greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) = greatest_lower_bound(X_19,multiply(X_19,X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_119))),greatest_lower_bound(X_19,multiply(X_19,X_119))) ),[0,1],$fot(multiply(X_19,greatest_lower_bound(X_119,identity)))]]) ).
cnf(refute_0_825,plain,
( greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_119))) != greatest_lower_bound(X_19,multiply(X_19,X_119))
| greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) = greatest_lower_bound(X_19,multiply(X_19,X_119)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(X_19,X_119)),multiply(X_19,greatest_lower_bound(X_119,identity))) )],[refute_0_823,refute_0_824]) ).
cnf(refute_0_826,plain,
greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) = greatest_lower_bound(X_19,multiply(X_19,X_119)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_19,X_119))),greatest_lower_bound(X_19,multiply(X_19,X_119))) )],[refute_0_820,refute_0_825]) ).
cnf(refute_0_827,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)) = greatest_lower_bound(identity,X_119),
inference(subst,[],[refute_0_147:[bind(Y,$fot(X_119)),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_828,plain,
multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))),
introduced(tautology,[refl,[$fot(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))))]]) ).
cnf(refute_0_829,plain,
( multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))) != multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)))
| greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)) != greatest_lower_bound(identity,X_119)
| multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))) = multiply(X_19,greatest_lower_bound(identity,X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))),multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)))) ),[1,1],$fot(greatest_lower_bound(identity,X_119))]]) ).
cnf(refute_0_830,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)) != greatest_lower_bound(identity,X_119)
| multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))) = multiply(X_19,greatest_lower_bound(identity,X_119)) ),
inference(resolve,[$cnf( $equal(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))),multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)))) )],[refute_0_828,refute_0_829]) ).
cnf(refute_0_831,plain,
multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))) = multiply(X_19,greatest_lower_bound(identity,X_119)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)),greatest_lower_bound(identity,X_119)) )],[refute_0_827,refute_0_830]) ).
cnf(refute_0_832,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)),
inference(subst,[],[refute_0_695:[bind(X_18,$fot(multiply(X,Z))),bind(X_9,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_833,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Y),multiply(X,Z))
| greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_834,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_glb1,refute_0_833]) ).
cnf(refute_0_835,plain,
( greatest_lower_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_836,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Y),multiply(X,Z)),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_834,refute_0_835]) ).
cnf(refute_0_837,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_832,refute_0_836]) ).
cnf(refute_0_838,plain,
least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) = greatest_lower_bound(Y,Z),
inference(subst,[],[refute_0_695:[bind(X_18,$fot(Y)),bind(X_9,$fot(Z))]]) ).
cnf(refute_0_839,plain,
multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_840,plain,
( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))
| least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
| multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) ),[1,1],$fot(greatest_lower_bound(Y,Z))]]) ).
cnf(refute_0_841,plain,
( least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
| multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),greatest_lower_bound(Y,Z)) )],[refute_0_838,refute_0_841]) ).
cnf(refute_0_843,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),
inference(subst,[],[refute_0_446:[bind(Y,$fot(greatest_lower_bound(Y,Z))),bind(Z,$fot(greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_844,plain,
( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))))),bind(Y0,$fot(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_845,plain,
( multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)))) )],[refute_0_843,refute_0_844]) ).
cnf(refute_0_846,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_842,refute_0_845]) ).
cnf(refute_0_847,plain,
greatest_lower_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(subst,[],[refute_0_834:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_848,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_849,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_850,plain,
( greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_848,refute_0_849]) ).
cnf(refute_0_851,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_847,refute_0_850]) ).
cnf(refute_0_852,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y)))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_853,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y)))) )],[refute_0_851,refute_0_852]) ).
cnf(refute_0_854,plain,
least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_846,refute_0_853]) ).
cnf(refute_0_855,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_159:[bind(X,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y,$fot(greatest_lower_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_856,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))))),bind(Y0,$fot(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,greatest_lower_bound(Y,Z))))]]) ).
cnf(refute_0_857,plain,
( least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_855,refute_0_856]) ).
cnf(refute_0_858,plain,
least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_854,refute_0_857]) ).
cnf(refute_0_859,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != multiply(X,greatest_lower_bound(Y,Z))
| least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,greatest_lower_bound(Y,Z)))]]) ).
cnf(refute_0_860,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),multiply(X,greatest_lower_bound(Y,Z))) )],[refute_0_858,refute_0_859]) ).
cnf(refute_0_861,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| greatest_lower_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,greatest_lower_bound(Z,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) ),[0],$fot(greatest_lower_bound(multiply(X,Z),multiply(X,Y)))]]) ).
cnf(refute_0_862,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_847,refute_0_861]) ).
cnf(refute_0_863,plain,
( least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))) != greatest_lower_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_860,refute_0_862]) ).
cnf(refute_0_864,plain,
multiply(X,greatest_lower_bound(Y,Z)) = multiply(X,greatest_lower_bound(Z,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(X,Z),multiply(X,Y)),multiply(X,greatest_lower_bound(Y,Z))),greatest_lower_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_837,refute_0_863]) ).
cnf(refute_0_865,plain,
( multiply(X,greatest_lower_bound(Y,Z)) != multiply(X,greatest_lower_bound(Z,Y))
| multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(multiply(X,greatest_lower_bound(Z,Y))))]]) ).
cnf(refute_0_866,plain,
multiply(X,greatest_lower_bound(Z,Y)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(Y,Z)),multiply(X,greatest_lower_bound(Z,Y))) )],[refute_0_864,refute_0_865]) ).
cnf(refute_0_867,plain,
multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_119,identity),identity)) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))),
inference(subst,[],[refute_0_866:[bind(X,$fot(X_19)),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(X_119,identity)))]]) ).
cnf(refute_0_868,plain,
( multiply(X_72,greatest_lower_bound(X_73,identity)) != greatest_lower_bound(X_72,multiply(X_72,X_73))
| greatest_lower_bound(X_72,multiply(X_72,X_73)) = multiply(X_72,greatest_lower_bound(X_73,identity)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_72,greatest_lower_bound(X_73,identity)))),bind(Y0,$fot(greatest_lower_bound(X_72,multiply(X_72,X_73))))]]) ).
cnf(refute_0_869,plain,
greatest_lower_bound(X_72,multiply(X_72,X_73)) = multiply(X_72,greatest_lower_bound(X_73,identity)),
inference(resolve,[$cnf( $equal(multiply(X_72,greatest_lower_bound(X_73,identity)),greatest_lower_bound(X_72,multiply(X_72,X_73))) )],[refute_0_42,refute_0_868]) ).
cnf(refute_0_870,plain,
greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) = multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_119,identity),identity)),
inference(subst,[],[refute_0_869:[bind(X_72,$fot(X_19)),bind(X_73,$fot(greatest_lower_bound(X_119,identity)))]]) ).
cnf(refute_0_871,plain,
( multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_119,identity),identity)) != multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)))
| greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) != multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_119,identity),identity))
| greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))))),bind(Y0,$fot(multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_119,identity),identity)))),bind(Z0,$fot(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)))))]]) ).
cnf(refute_0_872,plain,
( multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_119,identity),identity)) != multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)))
| greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))),multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_119,identity),identity))) )],[refute_0_870,refute_0_871]) ).
cnf(refute_0_873,plain,
greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) = multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))),
inference(resolve,[$cnf( $equal(multiply(X_19,greatest_lower_bound(greatest_lower_bound(X_119,identity),identity)),multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)))) )],[refute_0_867,refute_0_872]) ).
cnf(refute_0_874,plain,
( multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))) != multiply(X_19,greatest_lower_bound(identity,X_119))
| greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) != multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)))
| greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) = multiply(X_19,greatest_lower_bound(identity,X_119)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))))),bind(Y0,$fot(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))))),bind(Z0,$fot(multiply(X_19,greatest_lower_bound(identity,X_119))))]]) ).
cnf(refute_0_875,plain,
( multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))) != multiply(X_19,greatest_lower_bound(identity,X_119))
| greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) = multiply(X_19,greatest_lower_bound(identity,X_119)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))),multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity)))) )],[refute_0_873,refute_0_874]) ).
cnf(refute_0_876,plain,
greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) = multiply(X_19,greatest_lower_bound(identity,X_119)),
inference(resolve,[$cnf( $equal(multiply(X_19,greatest_lower_bound(identity,greatest_lower_bound(X_119,identity))),multiply(X_19,greatest_lower_bound(identity,X_119))) )],[refute_0_831,refute_0_875]) ).
cnf(refute_0_877,plain,
( greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) != multiply(X_19,greatest_lower_bound(identity,X_119))
| greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) != greatest_lower_bound(X_19,multiply(X_19,X_119))
| multiply(X_19,greatest_lower_bound(identity,X_119)) = greatest_lower_bound(X_19,multiply(X_19,X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))),greatest_lower_bound(X_19,multiply(X_19,X_119))) ),[0],$fot(multiply(X_19,greatest_lower_bound(identity,X_119)))]]) ).
cnf(refute_0_878,plain,
( greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) != greatest_lower_bound(X_19,multiply(X_19,X_119))
| multiply(X_19,greatest_lower_bound(identity,X_119)) = greatest_lower_bound(X_19,multiply(X_19,X_119)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))),multiply(X_19,greatest_lower_bound(identity,X_119))) )],[refute_0_876,refute_0_877]) ).
cnf(refute_0_879,plain,
( multiply(X_19,greatest_lower_bound(identity,X_119)) != greatest_lower_bound(X_19,multiply(X_19,X_119))
| greatest_lower_bound(X_19,multiply(X_19,X_119)) != multiply(X_19,greatest_lower_bound(X_119,identity))
| multiply(X_19,greatest_lower_bound(identity,X_119)) = multiply(X_19,greatest_lower_bound(X_119,identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_19,greatest_lower_bound(identity,X_119)),multiply(X_19,greatest_lower_bound(X_119,identity))) ),[0],$fot(greatest_lower_bound(X_19,multiply(X_19,X_119)))]]) ).
cnf(refute_0_880,plain,
( multiply(X_19,greatest_lower_bound(identity,X_119)) != greatest_lower_bound(X_19,multiply(X_19,X_119))
| multiply(X_19,greatest_lower_bound(identity,X_119)) = multiply(X_19,greatest_lower_bound(X_119,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(X_19,X_119)),multiply(X_19,greatest_lower_bound(X_119,identity))) )],[refute_0_823,refute_0_879]) ).
cnf(refute_0_881,plain,
( greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))) != greatest_lower_bound(X_19,multiply(X_19,X_119))
| multiply(X_19,greatest_lower_bound(identity,X_119)) = multiply(X_19,greatest_lower_bound(X_119,identity)) ),
inference(resolve,[$cnf( $equal(multiply(X_19,greatest_lower_bound(identity,X_119)),greatest_lower_bound(X_19,multiply(X_19,X_119))) )],[refute_0_878,refute_0_880]) ).
cnf(refute_0_882,plain,
multiply(X_19,greatest_lower_bound(identity,X_119)) = multiply(X_19,greatest_lower_bound(X_119,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(X_19,greatest_lower_bound(X_119,identity))),greatest_lower_bound(X_19,multiply(X_19,X_119))) )],[refute_0_826,refute_0_881]) ).
cnf(refute_0_883,plain,
( multiply(X_19,greatest_lower_bound(identity,X_119)) != multiply(X_19,greatest_lower_bound(X_119,identity))
| multiply(X_19,greatest_lower_bound(X_119,identity)) = multiply(X_19,greatest_lower_bound(identity,X_119)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X_19,greatest_lower_bound(identity,X_119)))),bind(Y0,$fot(multiply(X_19,greatest_lower_bound(X_119,identity))))]]) ).
cnf(refute_0_884,plain,
multiply(X_19,greatest_lower_bound(X_119,identity)) = multiply(X_19,greatest_lower_bound(identity,X_119)),
inference(resolve,[$cnf( $equal(multiply(X_19,greatest_lower_bound(identity,X_119)),multiply(X_19,greatest_lower_bound(X_119,identity))) )],[refute_0_882,refute_0_883]) ).
cnf(refute_0_885,plain,
multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)) = multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))),
inference(subst,[],[refute_0_884:[bind(X_119,$fot(inverse(X_88))),bind(X_19,$fot(least_upper_bound(X_88,identity)))]]) ).
cnf(refute_0_886,plain,
( multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)) != multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88)))
| multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)) != greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88)))
| multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))) = greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)),greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88)))) ),[0],$fot(multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))))]]) ).
cnf(refute_0_887,plain,
( multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)) != greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88)))
| multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))) = greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)),multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88)))) )],[refute_0_885,refute_0_886]) ).
cnf(refute_0_888,plain,
multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))) = greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),greatest_lower_bound(inverse(X_88),identity)),greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88)))) )],[refute_0_812,refute_0_887]) ).
cnf(refute_0_889,plain,
multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)) = least_upper_bound(multiply(inverse(X_85),X_98),multiply(X_85,multiply(inverse(X_85),X_98))),
inference(subst,[],[refute_0_754:[bind(X_84,$fot(multiply(inverse(X_85),X_98)))]]) ).
cnf(refute_0_890,plain,
X_98 = multiply(X_85,multiply(inverse(X_85),X_98)),
inference(subst,[],[refute_0_104:[bind(X_26,$fot(X_98)),bind(X_30,$fot(X_85))]]) ).
cnf(refute_0_891,plain,
( X_98 != multiply(X_85,multiply(inverse(X_85),X_98))
| multiply(X_85,multiply(inverse(X_85),X_98)) = X_98 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_98)),bind(Y0,$fot(multiply(X_85,multiply(inverse(X_85),X_98))))]]) ).
cnf(refute_0_892,plain,
multiply(X_85,multiply(inverse(X_85),X_98)) = X_98,
inference(resolve,[$cnf( $equal(X_98,multiply(X_85,multiply(inverse(X_85),X_98))) )],[refute_0_890,refute_0_891]) ).
cnf(refute_0_893,plain,
( multiply(X_85,multiply(inverse(X_85),X_98)) != X_98
| multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)) != least_upper_bound(multiply(inverse(X_85),X_98),multiply(X_85,multiply(inverse(X_85),X_98)))
| multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)) = least_upper_bound(multiply(inverse(X_85),X_98),X_98) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)),least_upper_bound(multiply(inverse(X_85),X_98),multiply(X_85,multiply(inverse(X_85),X_98)))) ),[1,1],$fot(X_98)]]) ).
cnf(refute_0_894,plain,
( multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)) != least_upper_bound(multiply(inverse(X_85),X_98),multiply(X_85,multiply(inverse(X_85),X_98)))
| multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)) = least_upper_bound(multiply(inverse(X_85),X_98),X_98) ),
inference(resolve,[$cnf( $equal(multiply(X_85,multiply(inverse(X_85),X_98)),X_98) )],[refute_0_892,refute_0_893]) ).
cnf(refute_0_895,plain,
multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)) = least_upper_bound(multiply(inverse(X_85),X_98),X_98),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)),least_upper_bound(multiply(inverse(X_85),X_98),multiply(X_85,multiply(inverse(X_85),X_98)))) )],[refute_0_889,refute_0_894]) ).
cnf(refute_0_896,plain,
least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) = least_upper_bound(X_15,multiply(X_88,X_15)),
inference(subst,[],[refute_0_416:[bind(X_14,$fot(multiply(X_88,X_15)))]]) ).
cnf(refute_0_897,plain,
multiply(least_upper_bound(X_88,identity),X_15) = least_upper_bound(X_15,multiply(X_88,X_15)),
inference(subst,[],[refute_0_754:[bind(X_84,$fot(X_15)),bind(X_85,$fot(X_88))]]) ).
cnf(refute_0_898,plain,
( multiply(least_upper_bound(X_88,identity),X_15) != least_upper_bound(X_15,multiply(X_88,X_15))
| least_upper_bound(X_15,multiply(X_88,X_15)) = multiply(least_upper_bound(X_88,identity),X_15) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(least_upper_bound(X_88,identity),X_15))),bind(Y0,$fot(least_upper_bound(X_15,multiply(X_88,X_15))))]]) ).
cnf(refute_0_899,plain,
least_upper_bound(X_15,multiply(X_88,X_15)) = multiply(least_upper_bound(X_88,identity),X_15),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),X_15),least_upper_bound(X_15,multiply(X_88,X_15))) )],[refute_0_897,refute_0_898]) ).
cnf(refute_0_900,plain,
( least_upper_bound(X_15,multiply(X_88,X_15)) != multiply(least_upper_bound(X_88,identity),X_15)
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) != least_upper_bound(X_15,multiply(X_88,X_15))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) = multiply(least_upper_bound(X_88,identity),X_15) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))),least_upper_bound(X_15,multiply(X_88,X_15))) ),[1],$fot(multiply(least_upper_bound(X_88,identity),X_15))]]) ).
cnf(refute_0_901,plain,
( least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) != least_upper_bound(X_15,multiply(X_88,X_15))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) = multiply(least_upper_bound(X_88,identity),X_15) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(X_88,X_15)),multiply(least_upper_bound(X_88,identity),X_15)) )],[refute_0_899,refute_0_900]) ).
cnf(refute_0_902,plain,
least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) = multiply(least_upper_bound(X_88,identity),X_15),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))),least_upper_bound(X_15,multiply(X_88,X_15))) )],[refute_0_896,refute_0_901]) ).
cnf(refute_0_903,plain,
least_upper_bound(identity,least_upper_bound(X_88,identity)) = least_upper_bound(identity,X_88),
inference(subst,[],[refute_0_387:[bind(X_13,$fot(X_88)),bind(X_9,$fot(identity))]]) ).
cnf(refute_0_904,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15) = multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15))]]) ).
cnf(refute_0_905,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15) != multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)
| least_upper_bound(identity,least_upper_bound(X_88,identity)) != least_upper_bound(identity,X_88)
| multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15) = multiply(least_upper_bound(identity,X_88),X_15) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15),multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)) ),[1,0],$fot(least_upper_bound(identity,X_88))]]) ).
cnf(refute_0_906,plain,
( least_upper_bound(identity,least_upper_bound(X_88,identity)) != least_upper_bound(identity,X_88)
| multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15) = multiply(least_upper_bound(identity,X_88),X_15) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15),multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)) )],[refute_0_904,refute_0_905]) ).
cnf(refute_0_907,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15) = multiply(least_upper_bound(identity,X_88),X_15),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_88,identity)),least_upper_bound(identity,X_88)) )],[refute_0_903,refute_0_906]) ).
cnf(refute_0_908,plain,
least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84)),
inference(subst,[],[refute_0_416:[bind(X_14,$fot(multiply(X_86,X_84))),bind(X_15,$fot(multiply(X_85,X_84)))]]) ).
cnf(refute_0_909,plain,
multiply(least_upper_bound(X_85,X_86),X_84) = least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_84)),bind(Y,$fot(X_85)),bind(Z,$fot(X_86))]]) ).
cnf(refute_0_910,plain,
( multiply(least_upper_bound(X_85,X_86),X_84) != least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))
| least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84)) = multiply(least_upper_bound(X_85,X_86),X_84) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(least_upper_bound(X_85,X_86),X_84))),bind(Y0,$fot(least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))))]]) ).
cnf(refute_0_911,plain,
least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84)) = multiply(least_upper_bound(X_85,X_86),X_84),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,X_86),X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) )],[refute_0_909,refute_0_910]) ).
cnf(refute_0_912,plain,
( least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84)) != multiply(least_upper_bound(X_85,X_86),X_84)
| least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))
| least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(least_upper_bound(X_85,X_86),X_84) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) ),[1],$fot(multiply(least_upper_bound(X_85,X_86),X_84))]]) ).
cnf(refute_0_913,plain,
( least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))
| least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(least_upper_bound(X_85,X_86),X_84) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84)),multiply(least_upper_bound(X_85,X_86),X_84)) )],[refute_0_911,refute_0_912]) ).
cnf(refute_0_914,plain,
least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(least_upper_bound(X_85,X_86),X_84),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) )],[refute_0_908,refute_0_913]) ).
cnf(refute_0_915,plain,
least_upper_bound(X_85,X_85) = X_85,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_85))]]) ).
cnf(refute_0_916,plain,
least_upper_bound(X_86,least_upper_bound(X_85,X_85)) = least_upper_bound(X_86,least_upper_bound(X_85,X_85)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_86,least_upper_bound(X_85,X_85)))]]) ).
cnf(refute_0_917,plain,
( least_upper_bound(X_85,X_85) != X_85
| least_upper_bound(X_86,least_upper_bound(X_85,X_85)) != least_upper_bound(X_86,least_upper_bound(X_85,X_85))
| least_upper_bound(X_86,least_upper_bound(X_85,X_85)) = least_upper_bound(X_86,X_85) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),least_upper_bound(X_86,least_upper_bound(X_85,X_85))) ),[1,1],$fot(X_85)]]) ).
cnf(refute_0_918,plain,
( least_upper_bound(X_85,X_85) != X_85
| least_upper_bound(X_86,least_upper_bound(X_85,X_85)) = least_upper_bound(X_86,X_85) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),least_upper_bound(X_86,least_upper_bound(X_85,X_85))) )],[refute_0_916,refute_0_917]) ).
cnf(refute_0_919,plain,
least_upper_bound(X_86,least_upper_bound(X_85,X_85)) = least_upper_bound(X_86,X_85),
inference(resolve,[$cnf( $equal(least_upper_bound(X_85,X_85),X_85) )],[refute_0_915,refute_0_918]) ).
cnf(refute_0_920,plain,
multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84) = multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84))]]) ).
cnf(refute_0_921,plain,
( multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84) != multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84)
| least_upper_bound(X_86,least_upper_bound(X_85,X_85)) != least_upper_bound(X_86,X_85)
| multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84) = multiply(least_upper_bound(X_86,X_85),X_84) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84),multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84)) ),[1,0],$fot(least_upper_bound(X_86,X_85))]]) ).
cnf(refute_0_922,plain,
( least_upper_bound(X_86,least_upper_bound(X_85,X_85)) != least_upper_bound(X_86,X_85)
| multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84) = multiply(least_upper_bound(X_86,X_85),X_84) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84),multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84)) )],[refute_0_920,refute_0_921]) ).
cnf(refute_0_923,plain,
multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84) = multiply(least_upper_bound(X_86,X_85),X_84),
inference(resolve,[$cnf( $equal(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),least_upper_bound(X_86,X_85)) )],[refute_0_919,refute_0_922]) ).
cnf(refute_0_924,plain,
least_upper_bound(multiply(X_86,X_84),multiply(least_upper_bound(X_85,X_85),X_84)) = multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84),
inference(subst,[],[refute_0_657:[bind(X,$fot(X_84)),bind(Y,$fot(X_86)),bind(Z,$fot(least_upper_bound(X_85,X_85)))]]) ).
cnf(refute_0_925,plain,
least_upper_bound(X,least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X)),
inference(subst,[],[refute_0_454:[bind(X_39,$fot(multiply(X_85,X_84))),bind(X_40,$fot(multiply(X_86,X_84)))]]) ).
cnf(refute_0_926,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X))
| least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84)) != multiply(least_upper_bound(X_85,X_86),X_84)
| least_upper_bound(X,multiply(least_upper_bound(X_85,X_86),X_84)) = least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))),least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X))) ),[0,1],$fot(multiply(least_upper_bound(X_85,X_86),X_84))]]) ).
cnf(refute_0_927,plain,
( least_upper_bound(X,least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X))
| least_upper_bound(X,multiply(least_upper_bound(X_85,X_86),X_84)) = least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84)),multiply(least_upper_bound(X_85,X_86),X_84)) )],[refute_0_911,refute_0_926]) ).
cnf(refute_0_928,plain,
least_upper_bound(X,multiply(least_upper_bound(X_85,X_86),X_84)) = least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))),least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X))) )],[refute_0_925,refute_0_927]) ).
cnf(refute_0_929,plain,
( least_upper_bound(X,multiply(least_upper_bound(X_85,X_86),X_84)) != least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X))
| least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X)) = least_upper_bound(X,multiply(least_upper_bound(X_85,X_86),X_84)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X,multiply(least_upper_bound(X_85,X_86),X_84)))),bind(Y0,$fot(least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X))))]]) ).
cnf(refute_0_930,plain,
least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X)) = least_upper_bound(X,multiply(least_upper_bound(X_85,X_86),X_84)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(least_upper_bound(X_85,X_86),X_84)),least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_86,X_84),X))) )],[refute_0_928,refute_0_929]) ).
cnf(refute_0_931,plain,
least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = least_upper_bound(multiply(X_86,X_84),multiply(least_upper_bound(X_85,X_85),X_84)),
inference(subst,[],[refute_0_930:[bind(X,$fot(multiply(X_86,X_84))),bind(X_86,$fot(X_85))]]) ).
cnf(refute_0_932,plain,
( least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != least_upper_bound(multiply(X_86,X_84),multiply(least_upper_bound(X_85,X_85),X_84))
| least_upper_bound(multiply(X_86,X_84),multiply(least_upper_bound(X_85,X_85),X_84)) != multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84)
| least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))))),bind(Y0,$fot(least_upper_bound(multiply(X_86,X_84),multiply(least_upper_bound(X_85,X_85),X_84)))),bind(Z0,$fot(multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84)))]]) ).
cnf(refute_0_933,plain,
( least_upper_bound(multiply(X_86,X_84),multiply(least_upper_bound(X_85,X_85),X_84)) != multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84)
| least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))),least_upper_bound(multiply(X_86,X_84),multiply(least_upper_bound(X_85,X_85),X_84))) )],[refute_0_931,refute_0_932]) ).
cnf(refute_0_934,plain,
least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_86,X_84),multiply(least_upper_bound(X_85,X_85),X_84)),multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84)) )],[refute_0_924,refute_0_933]) ).
cnf(refute_0_935,plain,
( multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84) != multiply(least_upper_bound(X_86,X_85),X_84)
| least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84)
| least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(least_upper_bound(X_86,X_85),X_84) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))))),bind(Y0,$fot(multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84))),bind(Z0,$fot(multiply(least_upper_bound(X_86,X_85),X_84)))]]) ).
cnf(refute_0_936,plain,
( multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84) != multiply(least_upper_bound(X_86,X_85),X_84)
| least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(least_upper_bound(X_86,X_85),X_84) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))),multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84)) )],[refute_0_934,refute_0_935]) ).
cnf(refute_0_937,plain,
least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) = multiply(least_upper_bound(X_86,X_85),X_84),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,least_upper_bound(X_85,X_85)),X_84),multiply(least_upper_bound(X_86,X_85),X_84)) )],[refute_0_923,refute_0_936]) ).
cnf(refute_0_938,plain,
( least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != multiply(least_upper_bound(X_85,X_86),X_84)
| least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != multiply(least_upper_bound(X_86,X_85),X_84)
| multiply(least_upper_bound(X_86,X_85),X_84) = multiply(least_upper_bound(X_85,X_86),X_84) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))),multiply(least_upper_bound(X_85,X_86),X_84)) ),[0],$fot(multiply(least_upper_bound(X_86,X_85),X_84))]]) ).
cnf(refute_0_939,plain,
( least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))) != multiply(least_upper_bound(X_85,X_86),X_84)
| multiply(least_upper_bound(X_86,X_85),X_84) = multiply(least_upper_bound(X_85,X_86),X_84) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))),multiply(least_upper_bound(X_86,X_85),X_84)) )],[refute_0_937,refute_0_938]) ).
cnf(refute_0_940,plain,
multiply(least_upper_bound(X_86,X_85),X_84) = multiply(least_upper_bound(X_85,X_86),X_84),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,X_84),least_upper_bound(multiply(X_85,X_84),multiply(X_86,X_84))),multiply(least_upper_bound(X_85,X_86),X_84)) )],[refute_0_914,refute_0_939]) ).
cnf(refute_0_941,plain,
( multiply(least_upper_bound(X_86,X_85),X_84) != multiply(least_upper_bound(X_85,X_86),X_84)
| multiply(least_upper_bound(X_85,X_86),X_84) = multiply(least_upper_bound(X_86,X_85),X_84) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(least_upper_bound(X_86,X_85),X_84))),bind(Y0,$fot(multiply(least_upper_bound(X_85,X_86),X_84)))]]) ).
cnf(refute_0_942,plain,
multiply(least_upper_bound(X_85,X_86),X_84) = multiply(least_upper_bound(X_86,X_85),X_84),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,X_85),X_84),multiply(least_upper_bound(X_85,X_86),X_84)) )],[refute_0_940,refute_0_941]) ).
cnf(refute_0_943,plain,
multiply(least_upper_bound(least_upper_bound(X_88,identity),identity),X_15) = multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15),
inference(subst,[],[refute_0_942:[bind(X_84,$fot(X_15)),bind(X_85,$fot(least_upper_bound(X_88,identity))),bind(X_86,$fot(identity))]]) ).
cnf(refute_0_944,plain,
( multiply(least_upper_bound(X_85,identity),X_84) != least_upper_bound(X_84,multiply(X_85,X_84))
| least_upper_bound(X_84,multiply(X_85,X_84)) = multiply(least_upper_bound(X_85,identity),X_84) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(least_upper_bound(X_85,identity),X_84))),bind(Y0,$fot(least_upper_bound(X_84,multiply(X_85,X_84))))]]) ).
cnf(refute_0_945,plain,
least_upper_bound(X_84,multiply(X_85,X_84)) = multiply(least_upper_bound(X_85,identity),X_84),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,identity),X_84),least_upper_bound(X_84,multiply(X_85,X_84))) )],[refute_0_754,refute_0_944]) ).
cnf(refute_0_946,plain,
least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)) = multiply(least_upper_bound(least_upper_bound(X_88,identity),identity),X_15),
inference(subst,[],[refute_0_945:[bind(X_84,$fot(X_15)),bind(X_85,$fot(least_upper_bound(X_88,identity)))]]) ).
cnf(refute_0_947,plain,
( multiply(least_upper_bound(least_upper_bound(X_88,identity),identity),X_15) != multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)
| least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)) != multiply(least_upper_bound(least_upper_bound(X_88,identity),identity),X_15)
| least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)) = multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)))),bind(Y0,$fot(multiply(least_upper_bound(least_upper_bound(X_88,identity),identity),X_15))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)))]]) ).
cnf(refute_0_948,plain,
( multiply(least_upper_bound(least_upper_bound(X_88,identity),identity),X_15) != multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)
| least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)) = multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)),multiply(least_upper_bound(least_upper_bound(X_88,identity),identity),X_15)) )],[refute_0_946,refute_0_947]) ).
cnf(refute_0_949,plain,
least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)) = multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_88,identity),identity),X_15),multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)) )],[refute_0_943,refute_0_948]) ).
cnf(refute_0_950,plain,
least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,multiply(X_88,X_40))),
inference(subst,[],[refute_0_454:[bind(X,$fot(multiply(X_88,X_40)))]]) ).
cnf(refute_0_951,plain,
multiply(least_upper_bound(X_88,identity),X_40) = least_upper_bound(X_40,multiply(X_88,X_40)),
inference(subst,[],[refute_0_754:[bind(X_84,$fot(X_40)),bind(X_85,$fot(X_88))]]) ).
cnf(refute_0_952,plain,
( multiply(least_upper_bound(X_88,identity),X_40) != least_upper_bound(X_40,multiply(X_88,X_40))
| least_upper_bound(X_40,multiply(X_88,X_40)) = multiply(least_upper_bound(X_88,identity),X_40) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(least_upper_bound(X_88,identity),X_40))),bind(Y0,$fot(least_upper_bound(X_40,multiply(X_88,X_40))))]]) ).
cnf(refute_0_953,plain,
least_upper_bound(X_40,multiply(X_88,X_40)) = multiply(least_upper_bound(X_88,identity),X_40),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),X_40),least_upper_bound(X_40,multiply(X_88,X_40))) )],[refute_0_951,refute_0_952]) ).
cnf(refute_0_954,plain,
( least_upper_bound(X_40,multiply(X_88,X_40)) != multiply(least_upper_bound(X_88,identity),X_40)
| least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,multiply(X_88,X_40)))
| least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,multiply(least_upper_bound(X_88,identity),X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,multiply(X_88,X_40)))) ),[1,1],$fot(multiply(least_upper_bound(X_88,identity),X_40))]]) ).
cnf(refute_0_955,plain,
( least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,multiply(X_88,X_40)))
| least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,multiply(least_upper_bound(X_88,identity),X_40)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_40,multiply(X_88,X_40)),multiply(least_upper_bound(X_88,identity),X_40)) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,multiply(least_upper_bound(X_88,identity),X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,multiply(X_88,X_40)))) )],[refute_0_950,refute_0_955]) ).
cnf(refute_0_957,plain,
least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)) = least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_88,X_40))),
inference(subst,[],[refute_0_526:[bind(X_13,$fot(multiply(X_88,X_40))),bind(X_42,$fot(X_40)),bind(X_43,$fot(X_39))]]) ).
cnf(refute_0_958,plain,
( least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,multiply(least_upper_bound(X_88,identity),X_40))
| least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)) != least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_88,X_40)))
| least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_88,X_40))) = least_upper_bound(X_39,multiply(least_upper_bound(X_88,identity),X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,multiply(least_upper_bound(X_88,identity),X_40))) ),[0],$fot(least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_88,X_40))))]]) ).
cnf(refute_0_959,plain,
( least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,multiply(least_upper_bound(X_88,identity),X_40))
| least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_88,X_40))) = least_upper_bound(X_39,multiply(least_upper_bound(X_88,identity),X_40)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)),least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_88,X_40)))) )],[refute_0_957,refute_0_958]) ).
cnf(refute_0_960,plain,
least_upper_bound(X_40,least_upper_bound(X_39,multiply(X_88,X_40))) = least_upper_bound(X_39,multiply(least_upper_bound(X_88,identity),X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_88,X_40),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,multiply(least_upper_bound(X_88,identity),X_40))) )],[refute_0_956,refute_0_959]) ).
cnf(refute_0_961,plain,
least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) = least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)),
inference(subst,[],[refute_0_960:[bind(X_39,$fot(X_15)),bind(X_40,$fot(X_15))]]) ).
cnf(refute_0_962,plain,
( least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)) != multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) != least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15))
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) = multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))))),bind(Y0,$fot(least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)))),bind(Z0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)))]]) ).
cnf(refute_0_963,plain,
( least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)) != multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) = multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))),least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15))) )],[refute_0_961,refute_0_962]) ).
cnf(refute_0_964,plain,
least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) = multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,multiply(least_upper_bound(X_88,identity),X_15)),multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)) )],[refute_0_949,refute_0_963]) ).
cnf(refute_0_965,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15) != multiply(least_upper_bound(identity,X_88),X_15)
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) != multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) = multiply(least_upper_bound(identity,X_88),X_15) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_88),X_15)))]]) ).
cnf(refute_0_966,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15) != multiply(least_upper_bound(identity,X_88),X_15)
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) = multiply(least_upper_bound(identity,X_88),X_15) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))),multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15)) )],[refute_0_964,refute_0_965]) ).
cnf(refute_0_967,plain,
least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) = multiply(least_upper_bound(identity,X_88),X_15),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_88,identity)),X_15),multiply(least_upper_bound(identity,X_88),X_15)) )],[refute_0_907,refute_0_966]) ).
cnf(refute_0_968,plain,
( least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) != multiply(least_upper_bound(X_88,identity),X_15)
| least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) != multiply(least_upper_bound(identity,X_88),X_15)
| multiply(least_upper_bound(identity,X_88),X_15) = multiply(least_upper_bound(X_88,identity),X_15) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))),multiply(least_upper_bound(X_88,identity),X_15)) ),[0],$fot(multiply(least_upper_bound(identity,X_88),X_15))]]) ).
cnf(refute_0_969,plain,
( least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))) != multiply(least_upper_bound(X_88,identity),X_15)
| multiply(least_upper_bound(identity,X_88),X_15) = multiply(least_upper_bound(X_88,identity),X_15) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))),multiply(least_upper_bound(identity,X_88),X_15)) )],[refute_0_967,refute_0_968]) ).
cnf(refute_0_970,plain,
multiply(least_upper_bound(identity,X_88),X_15) = multiply(least_upper_bound(X_88,identity),X_15),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,multiply(X_88,X_15))),multiply(least_upper_bound(X_88,identity),X_15)) )],[refute_0_902,refute_0_969]) ).
cnf(refute_0_971,plain,
( multiply(least_upper_bound(identity,X_88),X_15) != multiply(least_upper_bound(X_88,identity),X_15)
| multiply(least_upper_bound(X_88,identity),X_15) = multiply(least_upper_bound(identity,X_88),X_15) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(least_upper_bound(identity,X_88),X_15))),bind(Y0,$fot(multiply(least_upper_bound(X_88,identity),X_15)))]]) ).
cnf(refute_0_972,plain,
multiply(least_upper_bound(X_88,identity),X_15) = multiply(least_upper_bound(identity,X_88),X_15),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_88),X_15),multiply(least_upper_bound(X_88,identity),X_15)) )],[refute_0_970,refute_0_971]) ).
cnf(refute_0_973,plain,
multiply(least_upper_bound(inverse(X_85),identity),X_98) = multiply(least_upper_bound(identity,inverse(X_85)),X_98),
inference(subst,[],[refute_0_972:[bind(X_15,$fot(X_98)),bind(X_88,$fot(inverse(X_85)))]]) ).
cnf(refute_0_974,plain,
least_upper_bound(X_98,multiply(inverse(X_85),X_98)) = multiply(least_upper_bound(inverse(X_85),identity),X_98),
inference(subst,[],[refute_0_945:[bind(X_84,$fot(X_98)),bind(X_85,$fot(inverse(X_85)))]]) ).
cnf(refute_0_975,plain,
( multiply(least_upper_bound(inverse(X_85),identity),X_98) != multiply(least_upper_bound(identity,inverse(X_85)),X_98)
| least_upper_bound(X_98,multiply(inverse(X_85),X_98)) != multiply(least_upper_bound(inverse(X_85),identity),X_98)
| least_upper_bound(X_98,multiply(inverse(X_85),X_98)) = multiply(least_upper_bound(identity,inverse(X_85)),X_98) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_98,multiply(inverse(X_85),X_98)))),bind(Y0,$fot(multiply(least_upper_bound(inverse(X_85),identity),X_98))),bind(Z0,$fot(multiply(least_upper_bound(identity,inverse(X_85)),X_98)))]]) ).
cnf(refute_0_976,plain,
( multiply(least_upper_bound(inverse(X_85),identity),X_98) != multiply(least_upper_bound(identity,inverse(X_85)),X_98)
| least_upper_bound(X_98,multiply(inverse(X_85),X_98)) = multiply(least_upper_bound(identity,inverse(X_85)),X_98) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_98,multiply(inverse(X_85),X_98)),multiply(least_upper_bound(inverse(X_85),identity),X_98)) )],[refute_0_974,refute_0_975]) ).
cnf(refute_0_977,plain,
least_upper_bound(X_98,multiply(inverse(X_85),X_98)) = multiply(least_upper_bound(identity,inverse(X_85)),X_98),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_85),identity),X_98),multiply(least_upper_bound(identity,inverse(X_85)),X_98)) )],[refute_0_973,refute_0_976]) ).
cnf(refute_0_978,plain,
least_upper_bound(multiply(inverse(X_85),X_98),X_98) = least_upper_bound(X_98,multiply(inverse(X_85),X_98)),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_98)),bind(Y,$fot(multiply(inverse(X_85),X_98)))]]) ).
cnf(refute_0_979,plain,
( least_upper_bound(X_98,multiply(inverse(X_85),X_98)) != multiply(least_upper_bound(identity,inverse(X_85)),X_98)
| least_upper_bound(multiply(inverse(X_85),X_98),X_98) != least_upper_bound(X_98,multiply(inverse(X_85),X_98))
| least_upper_bound(multiply(inverse(X_85),X_98),X_98) = multiply(least_upper_bound(identity,inverse(X_85)),X_98) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(inverse(X_85),X_98),X_98))),bind(Y0,$fot(least_upper_bound(X_98,multiply(inverse(X_85),X_98)))),bind(Z0,$fot(multiply(least_upper_bound(identity,inverse(X_85)),X_98)))]]) ).
cnf(refute_0_980,plain,
( least_upper_bound(X_98,multiply(inverse(X_85),X_98)) != multiply(least_upper_bound(identity,inverse(X_85)),X_98)
| least_upper_bound(multiply(inverse(X_85),X_98),X_98) = multiply(least_upper_bound(identity,inverse(X_85)),X_98) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_85),X_98),X_98),least_upper_bound(X_98,multiply(inverse(X_85),X_98))) )],[refute_0_978,refute_0_979]) ).
cnf(refute_0_981,plain,
least_upper_bound(multiply(inverse(X_85),X_98),X_98) = multiply(least_upper_bound(identity,inverse(X_85)),X_98),
inference(resolve,[$cnf( $equal(least_upper_bound(X_98,multiply(inverse(X_85),X_98)),multiply(least_upper_bound(identity,inverse(X_85)),X_98)) )],[refute_0_977,refute_0_980]) ).
cnf(refute_0_982,plain,
( multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)) != least_upper_bound(multiply(inverse(X_85),X_98),X_98)
| least_upper_bound(multiply(inverse(X_85),X_98),X_98) != multiply(least_upper_bound(identity,inverse(X_85)),X_98)
| multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)) = multiply(least_upper_bound(identity,inverse(X_85)),X_98) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)),multiply(least_upper_bound(identity,inverse(X_85)),X_98)) ),[0],$fot(least_upper_bound(multiply(inverse(X_85),X_98),X_98))]]) ).
cnf(refute_0_983,plain,
( multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)) != least_upper_bound(multiply(inverse(X_85),X_98),X_98)
| multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)) = multiply(least_upper_bound(identity,inverse(X_85)),X_98) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_85),X_98),X_98),multiply(least_upper_bound(identity,inverse(X_85)),X_98)) )],[refute_0_981,refute_0_982]) ).
cnf(refute_0_984,plain,
multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)) = multiply(least_upper_bound(identity,inverse(X_85)),X_98),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,identity),multiply(inverse(X_85),X_98)),least_upper_bound(multiply(inverse(X_85),X_98),X_98)) )],[refute_0_895,refute_0_983]) ).
cnf(refute_0_985,plain,
multiply(least_upper_bound(X_171,identity),multiply(inverse(X_171),greatest_lower_bound(identity,X_171))) = multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171)),
inference(subst,[],[refute_0_984:[bind(X_85,$fot(X_171)),bind(X_98,$fot(greatest_lower_bound(identity,X_171)))]]) ).
cnf(refute_0_986,plain,
multiply(inverse(X_171),greatest_lower_bound(identity,X_171)) = greatest_lower_bound(identity,inverse(X_171)),
inference(subst,[],[refute_0_93:[bind(X_80,$fot(X_171))]]) ).
cnf(refute_0_987,plain,
( multiply(inverse(X_171),greatest_lower_bound(identity,X_171)) != greatest_lower_bound(identity,inverse(X_171))
| multiply(least_upper_bound(X_171,identity),multiply(inverse(X_171),greatest_lower_bound(identity,X_171))) != multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171))
| multiply(least_upper_bound(X_171,identity),greatest_lower_bound(identity,inverse(X_171))) = multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_171,identity),multiply(inverse(X_171),greatest_lower_bound(identity,X_171))),multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171))) ),[0,1],$fot(greatest_lower_bound(identity,inverse(X_171)))]]) ).
cnf(refute_0_988,plain,
( multiply(least_upper_bound(X_171,identity),multiply(inverse(X_171),greatest_lower_bound(identity,X_171))) != multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171))
| multiply(least_upper_bound(X_171,identity),greatest_lower_bound(identity,inverse(X_171))) = multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_171),greatest_lower_bound(identity,X_171)),greatest_lower_bound(identity,inverse(X_171))) )],[refute_0_986,refute_0_987]) ).
cnf(refute_0_989,plain,
multiply(least_upper_bound(X_171,identity),greatest_lower_bound(identity,inverse(X_171))) = multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_171,identity),multiply(inverse(X_171),greatest_lower_bound(identity,X_171))),multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171))) )],[refute_0_985,refute_0_988]) ).
cnf(refute_0_990,plain,
multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)) = least_upper_bound(greatest_lower_bound(identity,X_132),multiply(greatest_lower_bound(identity,X_132),inverse(X_132))),
inference(subst,[],[refute_0_206:[bind(X_48,$fot(greatest_lower_bound(identity,X_132))),bind(X_49,$fot(inverse(X_132)))]]) ).
cnf(refute_0_991,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) = greatest_lower_bound(inverse(X_131),multiply(greatest_lower_bound(X_131,identity),inverse(X_131))),
inference(subst,[],[refute_0_233:[bind(X_91,$fot(inverse(X_131))),bind(X_92,$fot(greatest_lower_bound(X_131,identity)))]]) ).
cnf(refute_0_992,plain,
multiply(greatest_lower_bound(X_130,identity),inverse(X_130)) = greatest_lower_bound(inverse(X_130),multiply(X_130,inverse(X_130))),
inference(subst,[],[refute_0_233:[bind(X_91,$fot(inverse(X_130))),bind(X_92,$fot(X_130))]]) ).
cnf(refute_0_993,plain,
multiply(X_130,inverse(X_130)) = identity,
inference(subst,[],[refute_0_56:[bind(X_30,$fot(X_130))]]) ).
cnf(refute_0_994,plain,
( multiply(X_130,inverse(X_130)) != identity
| multiply(greatest_lower_bound(X_130,identity),inverse(X_130)) != greatest_lower_bound(inverse(X_130),multiply(X_130,inverse(X_130)))
| multiply(greatest_lower_bound(X_130,identity),inverse(X_130)) = greatest_lower_bound(inverse(X_130),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_130,identity),inverse(X_130)),greatest_lower_bound(inverse(X_130),multiply(X_130,inverse(X_130)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_995,plain,
( multiply(greatest_lower_bound(X_130,identity),inverse(X_130)) != greatest_lower_bound(inverse(X_130),multiply(X_130,inverse(X_130)))
| multiply(greatest_lower_bound(X_130,identity),inverse(X_130)) = greatest_lower_bound(inverse(X_130),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_130,inverse(X_130)),identity) )],[refute_0_993,refute_0_994]) ).
cnf(refute_0_996,plain,
multiply(greatest_lower_bound(X_130,identity),inverse(X_130)) = greatest_lower_bound(inverse(X_130),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_130,identity),inverse(X_130)),greatest_lower_bound(inverse(X_130),multiply(X_130,inverse(X_130)))) )],[refute_0_992,refute_0_995]) ).
cnf(refute_0_997,plain,
( greatest_lower_bound(X_76,inverse(Y)) != greatest_lower_bound(inverse(Y),X_76)
| greatest_lower_bound(inverse(Y),X_76) = greatest_lower_bound(X_76,inverse(Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_76,inverse(Y)))),bind(Y0,$fot(greatest_lower_bound(inverse(Y),X_76)))]]) ).
cnf(refute_0_998,plain,
greatest_lower_bound(inverse(Y),X_76) = greatest_lower_bound(X_76,inverse(Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_76,inverse(Y)),greatest_lower_bound(inverse(Y),X_76)) )],[refute_0_370,refute_0_997]) ).
cnf(refute_0_999,plain,
greatest_lower_bound(inverse(X_130),identity) = greatest_lower_bound(identity,inverse(X_130)),
inference(subst,[],[refute_0_998:[bind(Y,$fot(X_130)),bind(X_76,$fot(identity))]]) ).
cnf(refute_0_1000,plain,
( multiply(greatest_lower_bound(X_130,identity),inverse(X_130)) != greatest_lower_bound(inverse(X_130),identity)
| greatest_lower_bound(inverse(X_130),identity) != greatest_lower_bound(identity,inverse(X_130))
| multiply(greatest_lower_bound(X_130,identity),inverse(X_130)) = greatest_lower_bound(identity,inverse(X_130)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_130,identity),inverse(X_130)),greatest_lower_bound(identity,inverse(X_130))) ),[0],$fot(greatest_lower_bound(inverse(X_130),identity))]]) ).
cnf(refute_0_1001,plain,
( multiply(greatest_lower_bound(X_130,identity),inverse(X_130)) != greatest_lower_bound(inverse(X_130),identity)
| multiply(greatest_lower_bound(X_130,identity),inverse(X_130)) = greatest_lower_bound(identity,inverse(X_130)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_130),identity),greatest_lower_bound(identity,inverse(X_130))) )],[refute_0_999,refute_0_1000]) ).
cnf(refute_0_1002,plain,
multiply(greatest_lower_bound(X_130,identity),inverse(X_130)) = greatest_lower_bound(identity,inverse(X_130)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_130,identity),inverse(X_130)),greatest_lower_bound(inverse(X_130),identity)) )],[refute_0_996,refute_0_1001]) ).
cnf(refute_0_1003,plain,
multiply(greatest_lower_bound(X_131,identity),inverse(X_131)) = greatest_lower_bound(identity,inverse(X_131)),
inference(subst,[],[refute_0_1002:[bind(X_130,$fot(X_131))]]) ).
cnf(refute_0_1004,plain,
( multiply(greatest_lower_bound(X_131,identity),inverse(X_131)) != greatest_lower_bound(identity,inverse(X_131))
| multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) != greatest_lower_bound(inverse(X_131),multiply(greatest_lower_bound(X_131,identity),inverse(X_131)))
| multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) = greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)),greatest_lower_bound(inverse(X_131),multiply(greatest_lower_bound(X_131,identity),inverse(X_131)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_131)))]]) ).
cnf(refute_0_1005,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) != greatest_lower_bound(inverse(X_131),multiply(greatest_lower_bound(X_131,identity),inverse(X_131)))
| multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) = greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_131,identity),inverse(X_131)),greatest_lower_bound(identity,inverse(X_131))) )],[refute_0_1003,refute_0_1004]) ).
cnf(refute_0_1006,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) = greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)),greatest_lower_bound(inverse(X_131),multiply(greatest_lower_bound(X_131,identity),inverse(X_131)))) )],[refute_0_991,refute_0_1005]) ).
cnf(refute_0_1007,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)) = greatest_lower_bound(identity,X_131),
inference(subst,[],[refute_0_147:[bind(Y,$fot(X_131)),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1008,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)))]]) ).
cnf(refute_0_1009,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131))
| greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)) != greatest_lower_bound(identity,X_131)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)) = multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131))) ),[1,0],$fot(greatest_lower_bound(identity,X_131))]]) ).
cnf(refute_0_1010,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)) != greatest_lower_bound(identity,X_131)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)) = multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131))) )],[refute_0_1008,refute_0_1009]) ).
cnf(refute_0_1011,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)) = multiply(greatest_lower_bound(identity,X_131),inverse(X_131)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),greatest_lower_bound(identity,X_131)) )],[refute_0_1007,refute_0_1010]) ).
cnf(refute_0_1012,plain,
greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) = greatest_lower_bound(X_19,multiply(X_130,X_19)),
inference(subst,[],[refute_0_819:[bind(X_18,$fot(multiply(X_130,X_19)))]]) ).
cnf(refute_0_1013,plain,
multiply(greatest_lower_bound(X_130,identity),X_19) = greatest_lower_bound(X_19,multiply(X_130,X_19)),
inference(subst,[],[refute_0_233:[bind(X_91,$fot(X_19)),bind(X_92,$fot(X_130))]]) ).
cnf(refute_0_1014,plain,
( multiply(greatest_lower_bound(X_130,identity),X_19) != greatest_lower_bound(X_19,multiply(X_130,X_19))
| greatest_lower_bound(X_19,multiply(X_130,X_19)) = multiply(greatest_lower_bound(X_130,identity),X_19) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(X_130,identity),X_19))),bind(Y0,$fot(greatest_lower_bound(X_19,multiply(X_130,X_19))))]]) ).
cnf(refute_0_1015,plain,
greatest_lower_bound(X_19,multiply(X_130,X_19)) = multiply(greatest_lower_bound(X_130,identity),X_19),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_130,identity),X_19),greatest_lower_bound(X_19,multiply(X_130,X_19))) )],[refute_0_1013,refute_0_1014]) ).
cnf(refute_0_1016,plain,
( greatest_lower_bound(X_19,multiply(X_130,X_19)) != multiply(greatest_lower_bound(X_130,identity),X_19)
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) != greatest_lower_bound(X_19,multiply(X_130,X_19))
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) = multiply(greatest_lower_bound(X_130,identity),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))),greatest_lower_bound(X_19,multiply(X_130,X_19))) ),[1],$fot(multiply(greatest_lower_bound(X_130,identity),X_19))]]) ).
cnf(refute_0_1017,plain,
( greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) != greatest_lower_bound(X_19,multiply(X_130,X_19))
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) = multiply(greatest_lower_bound(X_130,identity),X_19) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(X_130,X_19)),multiply(greatest_lower_bound(X_130,identity),X_19)) )],[refute_0_1015,refute_0_1016]) ).
cnf(refute_0_1018,plain,
greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) = multiply(greatest_lower_bound(X_130,identity),X_19),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))),greatest_lower_bound(X_19,multiply(X_130,X_19))) )],[refute_0_1012,refute_0_1017]) ).
cnf(refute_0_1019,plain,
greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)) = greatest_lower_bound(identity,X_130),
inference(subst,[],[refute_0_147:[bind(Y,$fot(X_130)),bind(X_17,$fot(identity))]]) ).
cnf(refute_0_1020,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19))]]) ).
cnf(refute_0_1021,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)
| greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)) != greatest_lower_bound(identity,X_130)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19) = multiply(greatest_lower_bound(identity,X_130),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)) ),[1,0],$fot(greatest_lower_bound(identity,X_130))]]) ).
cnf(refute_0_1022,plain,
( greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)) != greatest_lower_bound(identity,X_130)
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19) = multiply(greatest_lower_bound(identity,X_130),X_19) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)) )],[refute_0_1020,refute_0_1021]) ).
cnf(refute_0_1023,plain,
multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19) = multiply(greatest_lower_bound(identity,X_130),X_19),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),greatest_lower_bound(identity,X_130)) )],[refute_0_1019,refute_0_1022]) ).
cnf(refute_0_1024,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)),
inference(subst,[],[refute_0_695:[bind(X_18,$fot(multiply(Z,X))),bind(X_9,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_1025,plain,
( greatest_lower_bound(multiply(Y,X),multiply(Z,X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) ),[0,1],$fot(multiply(greatest_lower_bound(Y,Z),X))]]) ).
cnf(refute_0_1026,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Y,X),multiply(Z,X)),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_667,refute_0_1025]) ).
cnf(refute_0_1027,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),greatest_lower_bound(multiply(Y,X),multiply(Z,X))),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_1024,refute_0_1026]) ).
cnf(refute_0_1028,plain,
multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X))]]) ).
cnf(refute_0_1029,plain,
( multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) != multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)
| least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
| multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(greatest_lower_bound(Y,Z),X) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)) ),[1,0],$fot(greatest_lower_bound(Y,Z))]]) ).
cnf(refute_0_1030,plain,
( least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)) != greatest_lower_bound(Y,Z)
| multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)) )],[refute_0_1028,refute_0_1029]) ).
cnf(refute_0_1031,plain,
multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),greatest_lower_bound(Y,Z)) )],[refute_0_838,refute_0_1030]) ).
cnf(refute_0_1032,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),
inference(subst,[],[refute_0_657:[bind(Y,$fot(greatest_lower_bound(Y,Z))),bind(Z,$fot(greatest_lower_bound(Z,Y)))]]) ).
cnf(refute_0_1033,plain,
( multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) != multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)))),bind(Y0,$fot(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X))),bind(Z0,$fot(multiply(greatest_lower_bound(Y,Z),X)))]]) ).
cnf(refute_0_1034,plain,
( multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)),multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X)) )],[refute_0_1032,refute_0_1033]) ).
cnf(refute_0_1035,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(greatest_lower_bound(Y,Z),greatest_lower_bound(Z,Y)),X),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_1031,refute_0_1034]) ).
cnf(refute_0_1036,plain,
greatest_lower_bound(multiply(Z,X),multiply(Y,X)) = multiply(greatest_lower_bound(Z,Y),X),
inference(subst,[],[refute_0_667:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1037,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_1038,plain,
( greatest_lower_bound(multiply(Z,X),multiply(Y,X)) != multiply(greatest_lower_bound(Z,Y),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))) ),[1,1],$fot(multiply(greatest_lower_bound(Z,Y),X))]]) ).
cnf(refute_0_1039,plain,
( greatest_lower_bound(multiply(Z,X),multiply(Y,X)) != multiply(greatest_lower_bound(Z,Y),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_1037,refute_0_1038]) ).
cnf(refute_0_1040,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Z,Y),X)) )],[refute_0_1036,refute_0_1039]) ).
cnf(refute_0_1041,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X))
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)))),bind(Z0,$fot(multiply(greatest_lower_bound(Y,Z),X)))]]) ).
cnf(refute_0_1042,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X))) )],[refute_0_1040,refute_0_1041]) ).
cnf(refute_0_1043,plain,
least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_1035,refute_0_1042]) ).
cnf(refute_0_1044,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),
inference(subst,[],[refute_0_159:[bind(X,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y,$fot(greatest_lower_bound(multiply(Z,X),multiply(Y,X))))]]) ).
cnf(refute_0_1045,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))))),bind(Z0,$fot(multiply(greatest_lower_bound(Y,Z),X)))]]) ).
cnf(refute_0_1046,plain,
( least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X)))) )],[refute_0_1044,refute_0_1045]) ).
cnf(refute_0_1047,plain,
least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_1043,refute_0_1046]) ).
cnf(refute_0_1048,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != multiply(greatest_lower_bound(Y,Z),X)
| least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) ),[0],$fot(multiply(greatest_lower_bound(Y,Z),X))]]) ).
cnf(refute_0_1049,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Z,X),multiply(Y,X)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),multiply(greatest_lower_bound(Y,Z),X)) )],[refute_0_1047,refute_0_1048]) ).
cnf(refute_0_1050,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| greatest_lower_bound(multiply(Z,X),multiply(Y,X)) != multiply(greatest_lower_bound(Z,Y),X)
| multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) ),[0],$fot(greatest_lower_bound(multiply(Z,X),multiply(Y,X)))]]) ).
cnf(refute_0_1051,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Z,Y),X)) )],[refute_0_1036,refute_0_1050]) ).
cnf(refute_0_1052,plain,
( least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)) != greatest_lower_bound(multiply(Z,X),multiply(Y,X))
| multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_1049,refute_0_1051]) ).
cnf(refute_0_1053,plain,
multiply(greatest_lower_bound(Y,Z),X) = multiply(greatest_lower_bound(Z,Y),X),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(multiply(Z,X),multiply(Y,X)),multiply(greatest_lower_bound(Y,Z),X)),greatest_lower_bound(multiply(Z,X),multiply(Y,X))) )],[refute_0_1027,refute_0_1052]) ).
cnf(refute_0_1054,plain,
( multiply(greatest_lower_bound(Y,Z),X) != multiply(greatest_lower_bound(Z,Y),X)
| multiply(greatest_lower_bound(Z,Y),X) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(multiply(greatest_lower_bound(Z,Y),X)))]]) ).
cnf(refute_0_1055,plain,
multiply(greatest_lower_bound(Z,Y),X) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),multiply(greatest_lower_bound(Z,Y),X)) )],[refute_0_1053,refute_0_1054]) ).
cnf(refute_0_1056,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_130,identity),identity),X_19) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19),
inference(subst,[],[refute_0_1055:[bind(X,$fot(X_19)),bind(Y,$fot(identity)),bind(Z,$fot(greatest_lower_bound(X_130,identity)))]]) ).
cnf(refute_0_1057,plain,
greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)) = multiply(greatest_lower_bound(greatest_lower_bound(X_130,identity),identity),X_19),
inference(subst,[],[refute_0_235:[bind(X_91,$fot(X_19)),bind(X_92,$fot(greatest_lower_bound(X_130,identity)))]]) ).
cnf(refute_0_1058,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_130,identity),identity),X_19) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)
| greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)) != multiply(greatest_lower_bound(greatest_lower_bound(X_130,identity),identity),X_19)
| greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)))),bind(Y0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(X_130,identity),identity),X_19))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)))]]) ).
cnf(refute_0_1059,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_130,identity),identity),X_19) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)
| greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)),multiply(greatest_lower_bound(greatest_lower_bound(X_130,identity),identity),X_19)) )],[refute_0_1057,refute_0_1058]) ).
cnf(refute_0_1060,plain,
greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_130,identity),identity),X_19),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)) )],[refute_0_1056,refute_0_1059]) ).
cnf(refute_0_1061,plain,
greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X),
inference(subst,[],[symmetry_of_glb:[bind(Y,$fot(greatest_lower_bound(X_36,X_37)))]]) ).
cnf(refute_0_1062,plain,
greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X))]]) ).
cnf(refute_0_1063,plain,
( greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)
| greatest_lower_bound(greatest_lower_bound(X_36,X_37),X) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)))]]) ).
cnf(refute_0_1064,plain,
greatest_lower_bound(greatest_lower_bound(X_36,X_37),X) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)) )],[refute_0_1062,refute_0_1063]) ).
cnf(refute_0_1065,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)
| greatest_lower_bound(greatest_lower_bound(X_36,X_37),X) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))
| greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X))]]) ).
cnf(refute_0_1066,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)
| greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))) )],[refute_0_1064,refute_0_1065]) ).
cnf(refute_0_1067,plain,
greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X)) )],[refute_0_1061,refute_0_1066]) ).
cnf(refute_0_1068,plain,
greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,multiply(X_130,X_37))),
inference(subst,[],[refute_0_1067:[bind(X,$fot(multiply(X_130,X_37)))]]) ).
cnf(refute_0_1069,plain,
multiply(greatest_lower_bound(X_130,identity),X_37) = greatest_lower_bound(X_37,multiply(X_130,X_37)),
inference(subst,[],[refute_0_233:[bind(X_91,$fot(X_37)),bind(X_92,$fot(X_130))]]) ).
cnf(refute_0_1070,plain,
( multiply(greatest_lower_bound(X_130,identity),X_37) != greatest_lower_bound(X_37,multiply(X_130,X_37))
| greatest_lower_bound(X_37,multiply(X_130,X_37)) = multiply(greatest_lower_bound(X_130,identity),X_37) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(X_130,identity),X_37))),bind(Y0,$fot(greatest_lower_bound(X_37,multiply(X_130,X_37))))]]) ).
cnf(refute_0_1071,plain,
greatest_lower_bound(X_37,multiply(X_130,X_37)) = multiply(greatest_lower_bound(X_130,identity),X_37),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_130,identity),X_37),greatest_lower_bound(X_37,multiply(X_130,X_37))) )],[refute_0_1069,refute_0_1070]) ).
cnf(refute_0_1072,plain,
( greatest_lower_bound(X_37,multiply(X_130,X_37)) != multiply(greatest_lower_bound(X_130,identity),X_37)
| greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,multiply(X_130,X_37)))
| greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,multiply(greatest_lower_bound(X_130,identity),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,greatest_lower_bound(X_37,multiply(X_130,X_37)))) ),[1,1],$fot(multiply(greatest_lower_bound(X_130,identity),X_37))]]) ).
cnf(refute_0_1073,plain,
( greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,multiply(X_130,X_37)))
| greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,multiply(greatest_lower_bound(X_130,identity),X_37)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,multiply(X_130,X_37)),multiply(greatest_lower_bound(X_130,identity),X_37)) )],[refute_0_1071,refute_0_1072]) ).
cnf(refute_0_1074,plain,
greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_36,multiply(greatest_lower_bound(X_130,identity),X_37)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,greatest_lower_bound(X_37,multiply(X_130,X_37)))) )],[refute_0_1068,refute_0_1073]) ).
cnf(refute_0_1075,plain,
greatest_lower_bound(X_120,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_121))) = greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)),
inference(subst,[],[refute_0_1067:[bind(X,$fot(X_120)),bind(X_36,$fot(X_121)),bind(X_37,$fot(greatest_lower_bound(Y,X_121)))]]) ).
cnf(refute_0_1076,plain,
greatest_lower_bound(X_121,greatest_lower_bound(Y,X_121)) = greatest_lower_bound(X_121,Y),
inference(subst,[],[refute_0_147:[bind(X_17,$fot(X_121))]]) ).
cnf(refute_0_1077,plain,
( greatest_lower_bound(X_120,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_121))) != greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120))
| greatest_lower_bound(X_121,greatest_lower_bound(Y,X_121)) != greatest_lower_bound(X_121,Y)
| greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)) = greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_120,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_121))),greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120))) ),[0,1],$fot(greatest_lower_bound(X_121,Y))]]) ).
cnf(refute_0_1078,plain,
( greatest_lower_bound(X_120,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_121))) != greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120))
| greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)) = greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_121,greatest_lower_bound(Y,X_121)),greatest_lower_bound(X_121,Y)) )],[refute_0_1076,refute_0_1077]) ).
cnf(refute_0_1079,plain,
greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)) = greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_120,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_121))),greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120))) )],[refute_0_1075,refute_0_1078]) ).
cnf(refute_0_1080,plain,
greatest_lower_bound(X_36,greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(greatest_lower_bound(Y,X_37)))]]) ).
cnf(refute_0_1081,plain,
greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37)) = greatest_lower_bound(X_37,Y),
inference(subst,[],[refute_0_147:[bind(X_17,$fot(X_37))]]) ).
cnf(refute_0_1082,plain,
( greatest_lower_bound(X_36,greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))
| greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37)) != greatest_lower_bound(X_37,Y)
| greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))),greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))) ),[0,1],$fot(greatest_lower_bound(X_37,Y))]]) ).
cnf(refute_0_1083,plain,
( greatest_lower_bound(X_36,greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))
| greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,Y)) )],[refute_0_1081,refute_0_1082]) ).
cnf(refute_0_1084,plain,
greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,greatest_lower_bound(Y,X_37))),greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))) )],[refute_0_1080,refute_0_1083]) ).
cnf(refute_0_1085,plain,
greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)),
inference(subst,[],[refute_0_143:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1086,plain,
greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) = greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)))]]) ).
cnf(refute_0_1087,plain,
( greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) != greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y))
| greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))
| greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y))) ),[1,1],$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))]]) ).
cnf(refute_0_1088,plain,
( greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))
| greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y))) )],[refute_0_1086,refute_0_1087]) ).
cnf(refute_0_1089,plain,
greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y),greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) )],[refute_0_1085,refute_0_1088]) ).
cnf(refute_0_1090,plain,
( greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))
| greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) = greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)))),bind(Y0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))))]]) ).
cnf(refute_0_1091,plain,
greatest_lower_bound(X_36,greatest_lower_bound(X_37,X)) = greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X))) )],[refute_0_1067,refute_0_1090]) ).
cnf(refute_0_1092,plain,
greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),
inference(subst,[],[refute_0_1091:[bind(X,$fot(X_37)),bind(X_36,$fot(greatest_lower_bound(X_36,X_37))),bind(X_37,$fot(Y))]]) ).
cnf(refute_0_1093,plain,
( greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))
| greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) != greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y))
| greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)))),bind(Y0,$fot(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)))),bind(Z0,$fot(greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))))]]) ).
cnf(refute_0_1094,plain,
( greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))
| greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y))) )],[refute_0_1092,refute_0_1093]) ).
cnf(refute_0_1095,plain,
greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_37,greatest_lower_bound(greatest_lower_bound(X_36,X_37),Y)),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))) )],[refute_0_1089,refute_0_1094]) ).
cnf(refute_0_1096,plain,
( greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))
| greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))
| greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))) ),[0],$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)))]]) ).
cnf(refute_0_1097,plain,
( greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))
| greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))) )],[refute_0_1095,refute_0_1096]) ).
cnf(refute_0_1098,plain,
greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),greatest_lower_bound(Y,X_37))) )],[refute_0_1084,refute_0_1097]) ).
cnf(refute_0_1099,plain,
( greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))
| greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))),bind(Y0,$fot(greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))))]]) ).
cnf(refute_0_1100,plain,
greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y))) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)),greatest_lower_bound(X_37,greatest_lower_bound(X_36,greatest_lower_bound(X_37,Y)))) )],[refute_0_1098,refute_0_1099]) ).
cnf(refute_0_1101,plain,
greatest_lower_bound(X_121,greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))) = greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)),
inference(subst,[],[refute_0_1100:[bind(Y,$fot(X_120)),bind(X_36,$fot(Y)),bind(X_37,$fot(X_121))]]) ).
cnf(refute_0_1102,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120) = greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)),
inference(subst,[],[refute_0_143:[bind(X,$fot(Y)),bind(Y,$fot(X_121)),bind(Z,$fot(X_120))]]) ).
cnf(refute_0_1103,plain,
greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) = greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)))]]) ).
cnf(refute_0_1104,plain,
( greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) != greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120))
| greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120) != greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))
| greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) = greatest_lower_bound(X_121,greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)),greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120))) ),[1,1],$fot(greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)))]]) ).
cnf(refute_0_1105,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120) != greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))
| greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) = greatest_lower_bound(X_121,greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)),greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120))) )],[refute_0_1103,refute_0_1104]) ).
cnf(refute_0_1106,plain,
greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) = greatest_lower_bound(X_121,greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120),greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))) )],[refute_0_1102,refute_0_1105]) ).
cnf(refute_0_1107,plain,
( greatest_lower_bound(X_121,greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))) != greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))
| greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) != greatest_lower_bound(X_121,greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)))
| greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) = greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)))),bind(Y0,$fot(greatest_lower_bound(X_121,greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))))),bind(Z0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))))]]) ).
cnf(refute_0_1108,plain,
( greatest_lower_bound(X_121,greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))) != greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))
| greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) = greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)),greatest_lower_bound(X_121,greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)))) )],[refute_0_1106,refute_0_1107]) ).
cnf(refute_0_1109,plain,
greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) = greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_121,greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))),greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))) )],[refute_0_1101,refute_0_1108]) ).
cnf(refute_0_1110,plain,
( greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)) != greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120))
| greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)) != greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))
| greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))) ),[0],$fot(greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)))]]) ).
cnf(refute_0_1111,plain,
( greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)) != greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120))
| greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120)),greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))) )],[refute_0_1109,refute_0_1110]) ).
cnf(refute_0_1112,plain,
greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)) = greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)),greatest_lower_bound(X_121,greatest_lower_bound(greatest_lower_bound(Y,X_121),X_120))) )],[refute_0_1079,refute_0_1111]) ).
cnf(refute_0_1113,plain,
( greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)) != greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))
| greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)) = greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)))),bind(Y0,$fot(greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))))]]) ).
cnf(refute_0_1114,plain,
greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120)) = greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_120,greatest_lower_bound(X_121,Y)),greatest_lower_bound(Y,greatest_lower_bound(X_121,X_120))) )],[refute_0_1112,refute_0_1113]) ).
cnf(refute_0_1115,plain,
greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)) = greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_130,X_37))),
inference(subst,[],[refute_0_1114:[bind(Y,$fot(multiply(X_130,X_37))),bind(X_120,$fot(X_37)),bind(X_121,$fot(X_36))]]) ).
cnf(refute_0_1116,plain,
( greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,multiply(greatest_lower_bound(X_130,identity),X_37))
| greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_130,X_37)))
| greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_130,X_37))) = greatest_lower_bound(X_36,multiply(greatest_lower_bound(X_130,identity),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,multiply(greatest_lower_bound(X_130,identity),X_37))) ),[0],$fot(greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_130,X_37))))]]) ).
cnf(refute_0_1117,plain,
( greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)) != greatest_lower_bound(X_36,multiply(greatest_lower_bound(X_130,identity),X_37))
| greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_130,X_37))) = greatest_lower_bound(X_36,multiply(greatest_lower_bound(X_130,identity),X_37)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_130,X_37)))) )],[refute_0_1115,refute_0_1116]) ).
cnf(refute_0_1118,plain,
greatest_lower_bound(X_37,greatest_lower_bound(X_36,multiply(X_130,X_37))) = greatest_lower_bound(X_36,multiply(greatest_lower_bound(X_130,identity),X_37)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_130,X_37),greatest_lower_bound(X_36,X_37)),greatest_lower_bound(X_36,multiply(greatest_lower_bound(X_130,identity),X_37))) )],[refute_0_1074,refute_0_1117]) ).
cnf(refute_0_1119,plain,
greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) = greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)),
inference(subst,[],[refute_0_1118:[bind(X_36,$fot(X_19)),bind(X_37,$fot(X_19))]]) ).
cnf(refute_0_1120,plain,
( greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) != greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19))
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))))),bind(Y0,$fot(greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)))]]) ).
cnf(refute_0_1121,plain,
( greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))),greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19))) )],[refute_0_1119,refute_0_1120]) ).
cnf(refute_0_1122,plain,
greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,multiply(greatest_lower_bound(X_130,identity),X_19)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)) )],[refute_0_1060,refute_0_1121]) ).
cnf(refute_0_1123,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19) != multiply(greatest_lower_bound(identity,X_130),X_19)
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) = multiply(greatest_lower_bound(identity,X_130),X_19) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_130),X_19)))]]) ).
cnf(refute_0_1124,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19) != multiply(greatest_lower_bound(identity,X_130),X_19)
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) = multiply(greatest_lower_bound(identity,X_130),X_19) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19)) )],[refute_0_1122,refute_0_1123]) ).
cnf(refute_0_1125,plain,
greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) = multiply(greatest_lower_bound(identity,X_130),X_19),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_130,identity)),X_19),multiply(greatest_lower_bound(identity,X_130),X_19)) )],[refute_0_1023,refute_0_1124]) ).
cnf(refute_0_1126,plain,
( greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) != multiply(greatest_lower_bound(X_130,identity),X_19)
| greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) != multiply(greatest_lower_bound(identity,X_130),X_19)
| multiply(greatest_lower_bound(identity,X_130),X_19) = multiply(greatest_lower_bound(X_130,identity),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))),multiply(greatest_lower_bound(X_130,identity),X_19)) ),[0],$fot(multiply(greatest_lower_bound(identity,X_130),X_19))]]) ).
cnf(refute_0_1127,plain,
( greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))) != multiply(greatest_lower_bound(X_130,identity),X_19)
| multiply(greatest_lower_bound(identity,X_130),X_19) = multiply(greatest_lower_bound(X_130,identity),X_19) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))),multiply(greatest_lower_bound(identity,X_130),X_19)) )],[refute_0_1125,refute_0_1126]) ).
cnf(refute_0_1128,plain,
multiply(greatest_lower_bound(identity,X_130),X_19) = multiply(greatest_lower_bound(X_130,identity),X_19),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_19,greatest_lower_bound(X_19,multiply(X_130,X_19))),multiply(greatest_lower_bound(X_130,identity),X_19)) )],[refute_0_1018,refute_0_1127]) ).
cnf(refute_0_1129,plain,
( multiply(greatest_lower_bound(identity,X_130),X_19) != multiply(greatest_lower_bound(X_130,identity),X_19)
| multiply(greatest_lower_bound(X_130,identity),X_19) = multiply(greatest_lower_bound(identity,X_130),X_19) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_130),X_19))),bind(Y0,$fot(multiply(greatest_lower_bound(X_130,identity),X_19)))]]) ).
cnf(refute_0_1130,plain,
multiply(greatest_lower_bound(X_130,identity),X_19) = multiply(greatest_lower_bound(identity,X_130),X_19),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_130),X_19),multiply(greatest_lower_bound(X_130,identity),X_19)) )],[refute_0_1128,refute_0_1129]) ).
cnf(refute_0_1131,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)),
inference(subst,[],[refute_0_1130:[bind(X_130,$fot(greatest_lower_bound(X_131,identity))),bind(X_19,$fot(inverse(X_131)))]]) ).
cnf(refute_0_1132,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) != multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131))
| multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)) != multiply(greatest_lower_bound(identity,X_131),inverse(X_131))
| multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) = multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_131),inverse(X_131))))]]) ).
cnf(refute_0_1133,plain,
( multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)) != multiply(greatest_lower_bound(identity,X_131),inverse(X_131))
| multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) = multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)),multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131))) )],[refute_0_1131,refute_0_1132]) ).
cnf(refute_0_1134,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) = multiply(greatest_lower_bound(identity,X_131),inverse(X_131)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,greatest_lower_bound(X_131,identity)),inverse(X_131)),multiply(greatest_lower_bound(identity,X_131),inverse(X_131))) )],[refute_0_1011,refute_0_1133]) ).
cnf(refute_0_1135,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) != multiply(greatest_lower_bound(identity,X_131),inverse(X_131))
| multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) != greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131)))
| multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) = greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)),greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_131),inverse(X_131)))]]) ).
cnf(refute_0_1136,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) != greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131)))
| multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) = greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)),multiply(greatest_lower_bound(identity,X_131),inverse(X_131))) )],[refute_0_1134,refute_0_1135]) ).
cnf(refute_0_1137,plain,
greatest_lower_bound(inverse(X_131),inverse(X_131)) = inverse(X_131),
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(inverse(X_131)))]]) ).
cnf(refute_0_1138,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))))]]) ).
cnf(refute_0_1139,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131)))
| greatest_lower_bound(inverse(X_131),inverse(X_131)) != inverse(X_131)
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))) = greatest_lower_bound(identity,inverse(X_131)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131)))) ),[1,1],$fot(inverse(X_131))]]) ).
cnf(refute_0_1140,plain,
( greatest_lower_bound(inverse(X_131),inverse(X_131)) != inverse(X_131)
| greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))) = greatest_lower_bound(identity,inverse(X_131)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131)))) )],[refute_0_1138,refute_0_1139]) ).
cnf(refute_0_1141,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))) = greatest_lower_bound(identity,inverse(X_131)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_131),inverse(X_131)),inverse(X_131)) )],[refute_0_1137,refute_0_1140]) ).
cnf(refute_0_1142,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) = greatest_lower_bound(X_121,greatest_lower_bound(X_122,greatest_lower_bound(Y,X_122))),
inference(subst,[],[refute_0_1067:[bind(X,$fot(greatest_lower_bound(Y,X_122))),bind(X_36,$fot(X_121)),bind(X_37,$fot(X_122))]]) ).
cnf(refute_0_1143,plain,
greatest_lower_bound(X_122,greatest_lower_bound(Y,X_122)) = greatest_lower_bound(X_122,Y),
inference(subst,[],[refute_0_147:[bind(X_17,$fot(X_122))]]) ).
cnf(refute_0_1144,plain,
( greatest_lower_bound(X_122,greatest_lower_bound(Y,X_122)) != greatest_lower_bound(X_122,Y)
| greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) != greatest_lower_bound(X_121,greatest_lower_bound(X_122,greatest_lower_bound(Y,X_122)))
| greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) = greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)),greatest_lower_bound(X_121,greatest_lower_bound(X_122,greatest_lower_bound(Y,X_122)))) ),[1,1],$fot(greatest_lower_bound(X_122,Y))]]) ).
cnf(refute_0_1145,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) != greatest_lower_bound(X_121,greatest_lower_bound(X_122,greatest_lower_bound(Y,X_122)))
| greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) = greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_122,greatest_lower_bound(Y,X_122)),greatest_lower_bound(X_122,Y)) )],[refute_0_1143,refute_0_1144]) ).
cnf(refute_0_1146,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) = greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)),greatest_lower_bound(X_121,greatest_lower_bound(X_122,greatest_lower_bound(Y,X_122)))) )],[refute_0_1142,refute_0_1145]) ).
cnf(refute_0_1147,plain,
greatest_lower_bound(X_17,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17)) = greatest_lower_bound(X_17,greatest_lower_bound(X_36,X_37)),
inference(subst,[],[refute_0_147:[bind(Y,$fot(greatest_lower_bound(X_36,X_37)))]]) ).
cnf(refute_0_1148,plain,
greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_1149,plain,
( greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17)
| greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17)))]]) ).
cnf(refute_0_1150,plain,
greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17)) )],[refute_0_1148,refute_0_1149]) ).
cnf(refute_0_1151,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17)) != greatest_lower_bound(X_17,greatest_lower_bound(X_36,X_37))
| greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17))
| greatest_lower_bound(X_17,greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17))) = greatest_lower_bound(X_17,greatest_lower_bound(X_36,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17)),greatest_lower_bound(X_17,greatest_lower_bound(X_36,X_37))) ),[0,1],$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17)))]]) ).
cnf(refute_0_1152,plain,
( greatest_lower_bound(X_17,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17)) != greatest_lower_bound(X_17,greatest_lower_bound(X_36,X_37))
| greatest_lower_bound(X_17,greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17))) = greatest_lower_bound(X_17,greatest_lower_bound(X_36,X_37)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17))) )],[refute_0_1150,refute_0_1151]) ).
cnf(refute_0_1153,plain,
greatest_lower_bound(X_17,greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_17))) = greatest_lower_bound(X_17,greatest_lower_bound(X_36,X_37)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_17,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_17)),greatest_lower_bound(X_17,greatest_lower_bound(X_36,X_37))) )],[refute_0_1147,refute_0_1152]) ).
cnf(refute_0_1154,plain,
greatest_lower_bound(X_122,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_122))) = greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)),
inference(subst,[],[refute_0_1153:[bind(X_17,$fot(X_122)),bind(X_36,$fot(X_121)),bind(X_37,$fot(Y))]]) ).
cnf(refute_0_1155,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) = greatest_lower_bound(X_122,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_122))),
inference(subst,[],[refute_0_1114:[bind(Y,$fot(greatest_lower_bound(Y,X_122))),bind(X_120,$fot(X_122))]]) ).
cnf(refute_0_1156,plain,
( greatest_lower_bound(X_122,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_122))) != greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) != greatest_lower_bound(X_122,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_122)))
| greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) = greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)))),bind(Y0,$fot(greatest_lower_bound(X_122,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_122))))),bind(Z0,$fot(greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y))))]]) ).
cnf(refute_0_1157,plain,
( greatest_lower_bound(X_122,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_122))) != greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) = greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)),greatest_lower_bound(X_122,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_122)))) )],[refute_0_1155,refute_0_1156]) ).
cnf(refute_0_1158,plain,
greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) = greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_122,greatest_lower_bound(X_121,greatest_lower_bound(Y,X_122))),greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y))) )],[refute_0_1154,refute_0_1157]) ).
cnf(refute_0_1159,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) != greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y))
| greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) != greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y))
| greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)) = greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)),greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y))) ),[0],$fot(greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)))]]) ).
cnf(refute_0_1160,plain,
( greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)) != greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y))
| greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)) = greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)),greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y))) )],[refute_0_1158,refute_0_1159]) ).
cnf(refute_0_1161,plain,
greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)) = greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(Y,X_122),greatest_lower_bound(X_121,X_122)),greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y))) )],[refute_0_1146,refute_0_1160]) ).
cnf(refute_0_1162,plain,
( greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)) != greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y))
| greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y)) = greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)))),bind(Y0,$fot(greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y))))]]) ).
cnf(refute_0_1163,plain,
greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y)) = greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_122,greatest_lower_bound(X_121,Y)),greatest_lower_bound(X_121,greatest_lower_bound(X_122,Y))) )],[refute_0_1161,refute_0_1162]) ).
cnf(refute_0_1164,plain,
greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))),
inference(subst,[],[refute_0_1163:[bind(Y,$fot(inverse(X_131))),bind(X_121,$fot(inverse(X_131))),bind(X_122,$fot(identity))]]) ).
cnf(refute_0_1165,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))) != greatest_lower_bound(identity,inverse(X_131))
| greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))) != greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131)))
| greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))) = greatest_lower_bound(identity,inverse(X_131)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))))),bind(Y0,$fot(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(X_131))))]]) ).
cnf(refute_0_1166,plain,
( greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))) != greatest_lower_bound(identity,inverse(X_131))
| greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))) = greatest_lower_bound(identity,inverse(X_131)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))),greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131)))) )],[refute_0_1164,refute_0_1165]) ).
cnf(refute_0_1167,plain,
greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))) = greatest_lower_bound(identity,inverse(X_131)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(inverse(X_131),inverse(X_131))),greatest_lower_bound(identity,inverse(X_131))) )],[refute_0_1141,refute_0_1166]) ).
cnf(refute_0_1168,plain,
( multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) != greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131)))
| greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))) != greatest_lower_bound(identity,inverse(X_131))
| multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) = greatest_lower_bound(identity,inverse(X_131)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_131),inverse(X_131)),greatest_lower_bound(identity,inverse(X_131))) ),[0],$fot(greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))))]]) ).
cnf(refute_0_1169,plain,
( multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) != greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131)))
| multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) = greatest_lower_bound(identity,inverse(X_131)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131))),greatest_lower_bound(identity,inverse(X_131))) )],[refute_0_1167,refute_0_1168]) ).
cnf(refute_0_1170,plain,
( multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)) != greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131)))
| multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) = greatest_lower_bound(identity,inverse(X_131)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_131),inverse(X_131)),greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131)))) )],[refute_0_1136,refute_0_1169]) ).
cnf(refute_0_1171,plain,
multiply(greatest_lower_bound(identity,X_131),inverse(X_131)) = greatest_lower_bound(identity,inverse(X_131)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(greatest_lower_bound(X_131,identity),identity),inverse(X_131)),greatest_lower_bound(inverse(X_131),greatest_lower_bound(identity,inverse(X_131)))) )],[refute_0_1006,refute_0_1170]) ).
cnf(refute_0_1172,plain,
multiply(greatest_lower_bound(identity,X_132),inverse(X_132)) = greatest_lower_bound(identity,inverse(X_132)),
inference(subst,[],[refute_0_1171:[bind(X_131,$fot(X_132))]]) ).
cnf(refute_0_1173,plain,
( multiply(greatest_lower_bound(identity,X_132),inverse(X_132)) != greatest_lower_bound(identity,inverse(X_132))
| multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)) != least_upper_bound(greatest_lower_bound(identity,X_132),multiply(greatest_lower_bound(identity,X_132),inverse(X_132)))
| multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)) = least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)),least_upper_bound(greatest_lower_bound(identity,X_132),multiply(greatest_lower_bound(identity,X_132),inverse(X_132)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_132)))]]) ).
cnf(refute_0_1174,plain,
( multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)) != least_upper_bound(greatest_lower_bound(identity,X_132),multiply(greatest_lower_bound(identity,X_132),inverse(X_132)))
| multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)) = least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_132),inverse(X_132)),greatest_lower_bound(identity,inverse(X_132))) )],[refute_0_1172,refute_0_1173]) ).
cnf(refute_0_1175,plain,
multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)) = least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)),least_upper_bound(greatest_lower_bound(identity,X_132),multiply(greatest_lower_bound(identity,X_132),inverse(X_132)))) )],[refute_0_990,refute_0_1174]) ).
cnf(refute_0_1176,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(subst,[],[refute_0_654:[bind(X_13,$fot(multiply(X,Z))),bind(X_17,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_1177,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Y),multiply(X,Z)) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0,1],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_1178,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Y),multiply(X,Z)),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_446,refute_0_1177]) ).
cnf(refute_0_1179,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = least_upper_bound(multiply(X,Z),multiply(X,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),least_upper_bound(multiply(X,Y),multiply(X,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_1176,refute_0_1178]) ).
cnf(refute_0_1180,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
introduced(tautology,[refl,[$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_1181,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) ),[1,1],$fot(least_upper_bound(Y,Z))]]) ).
cnf(refute_0_1182,plain,
( greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)) != least_upper_bound(Y,Z)
| multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_1180,refute_0_1181]) ).
cnf(refute_0_1183,plain,
multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)),least_upper_bound(Y,Z)) )],[refute_0_661,refute_0_1182]) ).
cnf(refute_0_1184,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),
inference(subst,[],[refute_0_834:[bind(Y,$fot(least_upper_bound(Y,Z))),bind(Z,$fot(least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_1185,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Y0,$fot(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_1186,plain,
( multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y)))) )],[refute_0_1184,refute_0_1185]) ).
cnf(refute_0_1187,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_1183,refute_0_1186]) ).
cnf(refute_0_1188,plain,
least_upper_bound(multiply(X,Z),multiply(X,Y)) = multiply(X,least_upper_bound(Z,Y)),
inference(subst,[],[refute_0_446:[bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1189,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_1190,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) ),[1,1],$fot(multiply(X,least_upper_bound(Z,Y)))]]) ).
cnf(refute_0_1191,plain,
( least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_1189,refute_0_1190]) ).
cnf(refute_0_1192,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_1188,refute_0_1191]) ).
cnf(refute_0_1193,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_1194,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y)))) )],[refute_0_1192,refute_0_1193]) ).
cnf(refute_0_1195,plain,
greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_1187,refute_0_1194]) ).
cnf(refute_0_1196,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),
inference(subst,[],[refute_0_38:[bind(X,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y,$fot(least_upper_bound(multiply(X,Z),multiply(X,Y))))]]) ).
cnf(refute_0_1197,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))))),bind(Y0,$fot(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))))),bind(Z0,$fot(multiply(X,least_upper_bound(Y,Z))))]]) ).
cnf(refute_0_1198,plain,
( greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y)))) )],[refute_0_1196,refute_0_1197]) ).
cnf(refute_0_1199,plain,
greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_1195,refute_0_1198]) ).
cnf(refute_0_1200,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != multiply(X,least_upper_bound(Y,Z))
| greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) ),[0],$fot(multiply(X,least_upper_bound(Y,Z)))]]) ).
cnf(refute_0_1201,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Z),multiply(X,Y)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),multiply(X,least_upper_bound(Y,Z))) )],[refute_0_1199,refute_0_1200]) ).
cnf(refute_0_1202,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| least_upper_bound(multiply(X,Z),multiply(X,Y)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) ),[0],$fot(least_upper_bound(multiply(X,Z),multiply(X,Y)))]]) ).
cnf(refute_0_1203,plain,
( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_1188,refute_0_1202]) ).
cnf(refute_0_1204,plain,
( greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))) != least_upper_bound(multiply(X,Z),multiply(X,Y))
| multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)) ),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_1201,refute_0_1203]) ).
cnf(refute_0_1205,plain,
multiply(X,least_upper_bound(Y,Z)) = multiply(X,least_upper_bound(Z,Y)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(multiply(X,Z),multiply(X,Y)),multiply(X,least_upper_bound(Y,Z))),least_upper_bound(multiply(X,Z),multiply(X,Y))) )],[refute_0_1179,refute_0_1204]) ).
cnf(refute_0_1206,plain,
( multiply(X,least_upper_bound(Y,Z)) != multiply(X,least_upper_bound(Z,Y))
| multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(multiply(X,least_upper_bound(Z,Y))))]]) ).
cnf(refute_0_1207,plain,
multiply(X,least_upper_bound(Z,Y)) = multiply(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),multiply(X,least_upper_bound(Z,Y))) )],[refute_0_1205,refute_0_1206]) ).
cnf(refute_0_1208,plain,
multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)) = multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))),
inference(subst,[],[refute_0_1207:[bind(X,$fot(greatest_lower_bound(identity,X_132))),bind(Y,$fot(identity)),bind(Z,$fot(inverse(X_132)))]]) ).
cnf(refute_0_1209,plain,
( multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)) != multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132)))
| multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)) != least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132)))
| multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))) = least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)),least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))))]]) ).
cnf(refute_0_1210,plain,
( multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)) != least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132)))
| multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))) = least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)),multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132)))) )],[refute_0_1208,refute_0_1209]) ).
cnf(refute_0_1211,plain,
multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)) = least_upper_bound(greatest_lower_bound(identity,X_80),multiply(inverse(X_80),greatest_lower_bound(identity,X_80))),
inference(subst,[],[refute_0_754:[bind(X_84,$fot(greatest_lower_bound(identity,X_80))),bind(X_85,$fot(inverse(X_80)))]]) ).
cnf(refute_0_1212,plain,
( multiply(inverse(X_80),greatest_lower_bound(identity,X_80)) != greatest_lower_bound(identity,inverse(X_80))
| multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)) != least_upper_bound(greatest_lower_bound(identity,X_80),multiply(inverse(X_80),greatest_lower_bound(identity,X_80)))
| multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)) = least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)),least_upper_bound(greatest_lower_bound(identity,X_80),multiply(inverse(X_80),greatest_lower_bound(identity,X_80)))) ),[1,1],$fot(greatest_lower_bound(identity,inverse(X_80)))]]) ).
cnf(refute_0_1213,plain,
( multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)) != least_upper_bound(greatest_lower_bound(identity,X_80),multiply(inverse(X_80),greatest_lower_bound(identity,X_80)))
| multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)) = least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_80),greatest_lower_bound(identity,X_80)),greatest_lower_bound(identity,inverse(X_80))) )],[refute_0_93,refute_0_1212]) ).
cnf(refute_0_1214,plain,
multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)) = least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)),least_upper_bound(greatest_lower_bound(identity,X_80),multiply(inverse(X_80),greatest_lower_bound(identity,X_80)))) )],[refute_0_1211,refute_0_1213]) ).
cnf(refute_0_1215,plain,
multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)) = multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)),
inference(subst,[],[refute_0_972:[bind(X_15,$fot(greatest_lower_bound(identity,X_80))),bind(X_88,$fot(inverse(X_80)))]]) ).
cnf(refute_0_1216,plain,
( multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)) != multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80))
| multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)) != least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80)))
| multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)) = least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)),least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)))]]) ).
cnf(refute_0_1217,plain,
( multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)) != least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80)))
| multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)) = least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)),multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80))) )],[refute_0_1215,refute_0_1216]) ).
cnf(refute_0_1218,plain,
multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)) = least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_80),identity),greatest_lower_bound(identity,X_80)),least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80)))) )],[refute_0_1214,refute_0_1217]) ).
cnf(refute_0_1219,plain,
( multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)) != least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80)))
| least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80))) = multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80)))))]]) ).
cnf(refute_0_1220,plain,
least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80))) = multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)),least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80)))) )],[refute_0_1218,refute_0_1219]) ).
cnf(refute_0_1221,plain,
least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132))) = multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132)),
inference(subst,[],[refute_0_1220:[bind(X_80,$fot(X_132))]]) ).
cnf(refute_0_1222,plain,
( multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))) != least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132)))
| least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132))) != multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132))
| multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))) = multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))),multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132))) ),[0],$fot(least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132))))]]) ).
cnf(refute_0_1223,plain,
( multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))) != least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132)))
| multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))) = multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132))),multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132))) )],[refute_0_1221,refute_0_1222]) ).
cnf(refute_0_1224,plain,
( multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)) != least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132)))
| multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))) = multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))),least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132)))) )],[refute_0_1210,refute_0_1223]) ).
cnf(refute_0_1225,plain,
multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))) = multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_132),least_upper_bound(inverse(X_132),identity)),least_upper_bound(greatest_lower_bound(identity,X_132),greatest_lower_bound(identity,inverse(X_132)))) )],[refute_0_1175,refute_0_1224]) ).
cnf(refute_0_1226,plain,
( multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))) != multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132))
| multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132)) = multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))))),bind(Y0,$fot(multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132))))]]) ).
cnf(refute_0_1227,plain,
multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132)) = multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_132),least_upper_bound(identity,inverse(X_132))),multiply(least_upper_bound(identity,inverse(X_132)),greatest_lower_bound(identity,X_132))) )],[refute_0_1225,refute_0_1226]) ).
cnf(refute_0_1228,plain,
multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171)) = multiply(greatest_lower_bound(identity,X_171),least_upper_bound(identity,inverse(X_171))),
inference(subst,[],[refute_0_1227:[bind(X_132,$fot(X_171))]]) ).
cnf(refute_0_1229,plain,
( multiply(least_upper_bound(X_171,identity),greatest_lower_bound(identity,inverse(X_171))) != multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171))
| multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171)) != multiply(greatest_lower_bound(identity,X_171),least_upper_bound(identity,inverse(X_171)))
| multiply(least_upper_bound(X_171,identity),greatest_lower_bound(identity,inverse(X_171))) = multiply(greatest_lower_bound(identity,X_171),least_upper_bound(identity,inverse(X_171))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_171,identity),greatest_lower_bound(identity,inverse(X_171))),multiply(greatest_lower_bound(identity,X_171),least_upper_bound(identity,inverse(X_171)))) ),[0],$fot(multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171)))]]) ).
cnf(refute_0_1230,plain,
( multiply(least_upper_bound(X_171,identity),greatest_lower_bound(identity,inverse(X_171))) != multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171))
| multiply(least_upper_bound(X_171,identity),greatest_lower_bound(identity,inverse(X_171))) = multiply(greatest_lower_bound(identity,X_171),least_upper_bound(identity,inverse(X_171))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171)),multiply(greatest_lower_bound(identity,X_171),least_upper_bound(identity,inverse(X_171)))) )],[refute_0_1228,refute_0_1229]) ).
cnf(refute_0_1231,plain,
multiply(least_upper_bound(X_171,identity),greatest_lower_bound(identity,inverse(X_171))) = multiply(greatest_lower_bound(identity,X_171),least_upper_bound(identity,inverse(X_171))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_171,identity),greatest_lower_bound(identity,inverse(X_171))),multiply(least_upper_bound(identity,inverse(X_171)),greatest_lower_bound(identity,X_171))) )],[refute_0_989,refute_0_1230]) ).
cnf(refute_0_1232,plain,
multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))) = multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88))),
inference(subst,[],[refute_0_1231:[bind(X_171,$fot(X_88))]]) ).
cnf(refute_0_1233,plain,
( multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))) != multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88)))
| multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))) != greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88)))
| multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88))) = greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))),greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88))))]]) ).
cnf(refute_0_1234,plain,
( multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))) != greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88)))
| multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88))) = greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))),multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88)))) )],[refute_0_1232,refute_0_1233]) ).
cnf(refute_0_1235,plain,
multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88))) = greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_88,identity),greatest_lower_bound(identity,inverse(X_88))),greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88)))) )],[refute_0_888,refute_0_1234]) ).
cnf(refute_0_1236,plain,
multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))) = greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223))),
inference(subst,[],[refute_0_1235:[bind(X_88,$fot(X_223))]]) ).
cnf(refute_0_1237,plain,
( multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))) != greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223)))
| greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223))) = multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223)))))]]) ).
cnf(refute_0_1238,plain,
greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223))) = multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))),greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223)))) )],[refute_0_1236,refute_0_1237]) ).
cnf(refute_0_1239,plain,
( multiply(inverse(least_upper_bound(X_223,identity)),greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))))
| greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223))) != multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))
| multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_223,identity)),greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))))) ),[0,1],$fot(multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))))]]) ).
cnf(refute_0_1240,plain,
( multiply(inverse(least_upper_bound(X_223,identity)),greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))))
| multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223))),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) )],[refute_0_1238,refute_0_1239]) ).
cnf(refute_0_1241,plain,
multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_223,identity)),greatest_lower_bound(least_upper_bound(X_223,identity),least_upper_bound(identity,inverse(X_223)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))))) )],[refute_0_744,refute_0_1240]) ).
cnf(refute_0_1242,plain,
inverse(X_110) = multiply(inverse(least_upper_bound(X_110,identity)),multiply(least_upper_bound(X_110,identity),inverse(X_110))),
inference(subst,[],[refute_0_9:[bind(X_25,$fot(least_upper_bound(X_110,identity))),bind(X_26,$fot(inverse(X_110)))]]) ).
cnf(refute_0_1243,plain,
multiply(least_upper_bound(X_110,identity),inverse(X_110)) = least_upper_bound(identity,inverse(X_110)),
inference(subst,[],[refute_0_809:[bind(X_88,$fot(X_110))]]) ).
cnf(refute_0_1244,plain,
( multiply(least_upper_bound(X_110,identity),inverse(X_110)) != least_upper_bound(identity,inverse(X_110))
| inverse(X_110) != multiply(inverse(least_upper_bound(X_110,identity)),multiply(least_upper_bound(X_110,identity),inverse(X_110)))
| inverse(X_110) = multiply(inverse(least_upper_bound(X_110,identity)),least_upper_bound(identity,inverse(X_110))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_110),multiply(inverse(least_upper_bound(X_110,identity)),multiply(least_upper_bound(X_110,identity),inverse(X_110)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_110)))]]) ).
cnf(refute_0_1245,plain,
( inverse(X_110) != multiply(inverse(least_upper_bound(X_110,identity)),multiply(least_upper_bound(X_110,identity),inverse(X_110)))
| inverse(X_110) = multiply(inverse(least_upper_bound(X_110,identity)),least_upper_bound(identity,inverse(X_110))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_110,identity),inverse(X_110)),least_upper_bound(identity,inverse(X_110))) )],[refute_0_1243,refute_0_1244]) ).
cnf(refute_0_1246,plain,
inverse(X_110) = multiply(inverse(least_upper_bound(X_110,identity)),least_upper_bound(identity,inverse(X_110))),
inference(resolve,[$cnf( $equal(inverse(X_110),multiply(inverse(least_upper_bound(X_110,identity)),multiply(least_upper_bound(X_110,identity),inverse(X_110)))) )],[refute_0_1242,refute_0_1245]) ).
cnf(refute_0_1247,plain,
( inverse(X_110) != multiply(inverse(least_upper_bound(X_110,identity)),least_upper_bound(identity,inverse(X_110)))
| multiply(inverse(least_upper_bound(X_110,identity)),least_upper_bound(identity,inverse(X_110))) = inverse(X_110) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(X_110))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_110,identity)),least_upper_bound(identity,inverse(X_110)))))]]) ).
cnf(refute_0_1248,plain,
multiply(inverse(least_upper_bound(X_110,identity)),least_upper_bound(identity,inverse(X_110))) = inverse(X_110),
inference(resolve,[$cnf( $equal(inverse(X_110),multiply(inverse(least_upper_bound(X_110,identity)),least_upper_bound(identity,inverse(X_110)))) )],[refute_0_1246,refute_0_1247]) ).
cnf(refute_0_1249,plain,
multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))) = inverse(X_223),
inference(subst,[],[refute_0_1248:[bind(X_110,$fot(X_223))]]) ).
cnf(refute_0_1250,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))) = greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))))]]) ).
cnf(refute_0_1251,plain,
( multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))) != inverse(X_223)
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))) = greatest_lower_bound(identity,inverse(X_223)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))))) ),[1,1],$fot(inverse(X_223))]]) ).
cnf(refute_0_1252,plain,
( multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))) != inverse(X_223)
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))) = greatest_lower_bound(identity,inverse(X_223)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))))) )],[refute_0_1250,refute_0_1251]) ).
cnf(refute_0_1253,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))) = greatest_lower_bound(identity,inverse(X_223)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))),inverse(X_223)) )],[refute_0_1249,refute_0_1252]) ).
cnf(refute_0_1254,plain,
( multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))))
| greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))) != greatest_lower_bound(identity,inverse(X_223))
| multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = greatest_lower_bound(identity,inverse(X_223)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))),greatest_lower_bound(identity,inverse(X_223))) ),[0],$fot(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))))]]) ).
cnf(refute_0_1255,plain,
( multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) != greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))))
| multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = greatest_lower_bound(identity,inverse(X_223)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223)))),greatest_lower_bound(identity,inverse(X_223))) )],[refute_0_1253,refute_0_1254]) ).
cnf(refute_0_1256,plain,
multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = greatest_lower_bound(identity,inverse(X_223)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))),greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X_223,identity)),least_upper_bound(identity,inverse(X_223))))) )],[refute_0_1241,refute_0_1255]) ).
cnf(refute_0_1257,plain,
multiply(inverse(least_upper_bound(X_223,identity)),identity) = inverse(least_upper_bound(X_223,identity)),
inference(subst,[],[refute_0_62:[bind(X_28,$fot(inverse(least_upper_bound(X_223,identity))))]]) ).
cnf(refute_0_1258,plain,
least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8)) = X_8,
inference(subst,[],[refute_0_177:[bind(X_9,$fot(greatest_lower_bound(X_36,X_37)))]]) ).
cnf(refute_0_1259,plain,
greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8)) = greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_1260,plain,
( greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8)) != greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8)
| greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8)))]]) ).
cnf(refute_0_1261,plain,
greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8) = greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8)),greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8)) )],[refute_0_1259,refute_0_1260]) ).
cnf(refute_0_1262,plain,
( greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8) != greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8))
| least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8)),X_8) ),[0,1],$fot(greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8)))]]) ).
cnf(refute_0_1263,plain,
( least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8))) = X_8 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8),greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8))) )],[refute_0_1261,refute_0_1262]) ).
cnf(refute_0_1264,plain,
least_upper_bound(X_8,greatest_lower_bound(X_36,greatest_lower_bound(X_37,X_8))) = X_8,
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(greatest_lower_bound(X_36,X_37),X_8)),X_8) )],[refute_0_1258,refute_0_1263]) ).
cnf(refute_0_1265,plain,
least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))))) = multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),
inference(subst,[],[refute_0_1264:[bind(X_37,$fot(identity)),bind(X_8,$fot(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))))]]) ).
cnf(refute_0_1266,plain,
greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) = greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_38),
inference(subst,[],[associativity_of_glb:[bind(X,$fot(X_36)),bind(Y,$fot(least_upper_bound(X_36,Y))),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_1267,plain,
greatest_lower_bound(X_36,least_upper_bound(X_36,Y)) = X_36,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_1268,plain,
( greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_38)
| greatest_lower_bound(X_36,least_upper_bound(X_36,Y)) != X_36
| greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) = greatest_lower_bound(X_36,X_38) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)),greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_38)) ),[1,0],$fot(X_36)]]) ).
cnf(refute_0_1269,plain,
( greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) != greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_38)
| greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) = greatest_lower_bound(X_36,X_38) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_36) )],[refute_0_1267,refute_0_1268]) ).
cnf(refute_0_1270,plain,
greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)) = greatest_lower_bound(X_36,X_38),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_36,greatest_lower_bound(least_upper_bound(X_36,Y),X_38)),greatest_lower_bound(greatest_lower_bound(X_36,least_upper_bound(X_36,Y)),X_38)) )],[refute_0_1266,refute_0_1269]) ).
cnf(refute_0_1271,plain,
greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) = greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y))),
inference(subst,[],[refute_0_1270:[bind(X_36,$fot(identity)),bind(X_38,$fot(least_upper_bound(identity,inverse(Y))))]]) ).
cnf(refute_0_1272,plain,
multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)) = greatest_lower_bound(least_upper_bound(identity,X_59),multiply(inverse(X_59),least_upper_bound(identity,X_59))),
inference(subst,[],[refute_0_233:[bind(X_91,$fot(least_upper_bound(identity,X_59))),bind(X_92,$fot(inverse(X_59)))]]) ).
cnf(refute_0_1273,plain,
( multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)) != greatest_lower_bound(least_upper_bound(identity,X_59),multiply(inverse(X_59),least_upper_bound(identity,X_59)))
| multiply(inverse(X_59),least_upper_bound(identity,X_59)) != least_upper_bound(identity,inverse(X_59))
| multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)),greatest_lower_bound(least_upper_bound(identity,X_59),multiply(inverse(X_59),least_upper_bound(identity,X_59)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_59)))]]) ).
cnf(refute_0_1274,plain,
( multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)) != greatest_lower_bound(least_upper_bound(identity,X_59),multiply(inverse(X_59),least_upper_bound(identity,X_59)))
| multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_59),least_upper_bound(identity,X_59)),least_upper_bound(identity,inverse(X_59))) )],[refute_0_600,refute_0_1273]) ).
cnf(refute_0_1275,plain,
multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)),greatest_lower_bound(least_upper_bound(identity,X_59),multiply(inverse(X_59),least_upper_bound(identity,X_59)))) )],[refute_0_1272,refute_0_1274]) ).
cnf(refute_0_1276,plain,
multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)) = multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)),
inference(subst,[],[refute_0_1130:[bind(X_130,$fot(inverse(X_59))),bind(X_19,$fot(least_upper_bound(identity,X_59)))]]) ).
cnf(refute_0_1277,plain,
( multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)) != multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59))
| multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)) != greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))
| multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)),greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) ),[0],$fot(multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)))]]) ).
cnf(refute_0_1278,plain,
( multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)) != greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))
| multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)),multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59))) )],[refute_0_1276,refute_0_1277]) ).
cnf(refute_0_1279,plain,
multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_59),identity),least_upper_bound(identity,X_59)),greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) )],[refute_0_1275,refute_0_1278]) ).
cnf(refute_0_1280,plain,
multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) = greatest_lower_bound(least_upper_bound(identity,X_157),multiply(least_upper_bound(identity,X_157),inverse(X_157))),
inference(subst,[],[refute_0_42:[bind(X_72,$fot(least_upper_bound(identity,X_157))),bind(X_73,$fot(inverse(X_157)))]]) ).
cnf(refute_0_1281,plain,
multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) = least_upper_bound(inverse(X_110),multiply(least_upper_bound(X_110,identity),inverse(X_110))),
inference(subst,[],[refute_0_754:[bind(X_84,$fot(inverse(X_110))),bind(X_85,$fot(least_upper_bound(X_110,identity)))]]) ).
cnf(refute_0_1282,plain,
( multiply(least_upper_bound(X_110,identity),inverse(X_110)) != least_upper_bound(identity,inverse(X_110))
| multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) != least_upper_bound(inverse(X_110),multiply(least_upper_bound(X_110,identity),inverse(X_110)))
| multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) = least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)),least_upper_bound(inverse(X_110),multiply(least_upper_bound(X_110,identity),inverse(X_110)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_110)))]]) ).
cnf(refute_0_1283,plain,
( multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) != least_upper_bound(inverse(X_110),multiply(least_upper_bound(X_110,identity),inverse(X_110)))
| multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) = least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_110,identity),inverse(X_110)),least_upper_bound(identity,inverse(X_110))) )],[refute_0_1243,refute_0_1282]) ).
cnf(refute_0_1284,plain,
multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) = least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)),least_upper_bound(inverse(X_110),multiply(least_upper_bound(X_110,identity),inverse(X_110)))) )],[refute_0_1281,refute_0_1283]) ).
cnf(refute_0_1285,plain,
least_upper_bound(identity,least_upper_bound(X_110,identity)) = least_upper_bound(identity,X_110),
inference(subst,[],[refute_0_387:[bind(X_13,$fot(X_110)),bind(X_9,$fot(identity))]]) ).
cnf(refute_0_1286,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)) = multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)))]]) ).
cnf(refute_0_1287,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)) != multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110))
| least_upper_bound(identity,least_upper_bound(X_110,identity)) != least_upper_bound(identity,X_110)
| multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)) = multiply(least_upper_bound(identity,X_110),inverse(X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)),multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110))) ),[1,0],$fot(least_upper_bound(identity,X_110))]]) ).
cnf(refute_0_1288,plain,
( least_upper_bound(identity,least_upper_bound(X_110,identity)) != least_upper_bound(identity,X_110)
| multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)) = multiply(least_upper_bound(identity,X_110),inverse(X_110)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)),multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110))) )],[refute_0_1286,refute_0_1287]) ).
cnf(refute_0_1289,plain,
multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)) = multiply(least_upper_bound(identity,X_110),inverse(X_110)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_110,identity)),least_upper_bound(identity,X_110)) )],[refute_0_1285,refute_0_1288]) ).
cnf(refute_0_1290,plain,
multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) = multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)),
inference(subst,[],[refute_0_972:[bind(X_15,$fot(inverse(X_110))),bind(X_88,$fot(least_upper_bound(X_110,identity)))]]) ).
cnf(refute_0_1291,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)) != multiply(least_upper_bound(identity,X_110),inverse(X_110))
| multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) != multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110))
| multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) = multiply(least_upper_bound(identity,X_110),inverse(X_110)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)))),bind(Y0,$fot(multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_110),inverse(X_110))))]]) ).
cnf(refute_0_1292,plain,
( multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)) != multiply(least_upper_bound(identity,X_110),inverse(X_110))
| multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) = multiply(least_upper_bound(identity,X_110),inverse(X_110)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)),multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110))) )],[refute_0_1290,refute_0_1291]) ).
cnf(refute_0_1293,plain,
multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) = multiply(least_upper_bound(identity,X_110),inverse(X_110)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_110,identity)),inverse(X_110)),multiply(least_upper_bound(identity,X_110),inverse(X_110))) )],[refute_0_1289,refute_0_1292]) ).
cnf(refute_0_1294,plain,
( multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) != multiply(least_upper_bound(identity,X_110),inverse(X_110))
| multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) != least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110)))
| multiply(least_upper_bound(identity,X_110),inverse(X_110)) = least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)),least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110)))) ),[0],$fot(multiply(least_upper_bound(identity,X_110),inverse(X_110)))]]) ).
cnf(refute_0_1295,plain,
( multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) != least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110)))
| multiply(least_upper_bound(identity,X_110),inverse(X_110)) = least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)),multiply(least_upper_bound(identity,X_110),inverse(X_110))) )],[refute_0_1293,refute_0_1294]) ).
cnf(refute_0_1296,plain,
least_upper_bound(inverse(X_110),inverse(X_110)) = inverse(X_110),
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(inverse(X_110)))]]) ).
cnf(refute_0_1297,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))) = least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))),
introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))))]]) ).
cnf(refute_0_1298,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))) != least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110)))
| least_upper_bound(inverse(X_110),inverse(X_110)) != inverse(X_110)
| least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))) = least_upper_bound(identity,inverse(X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))),least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110)))) ),[1,1],$fot(inverse(X_110))]]) ).
cnf(refute_0_1299,plain,
( least_upper_bound(inverse(X_110),inverse(X_110)) != inverse(X_110)
| least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))) = least_upper_bound(identity,inverse(X_110)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))),least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110)))) )],[refute_0_1297,refute_0_1298]) ).
cnf(refute_0_1300,plain,
least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))) = least_upper_bound(identity,inverse(X_110)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_110),inverse(X_110)),inverse(X_110)) )],[refute_0_1296,refute_0_1299]) ).
cnf(refute_0_1301,plain,
least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))) = least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))),
inference(subst,[],[refute_0_592:[bind(X_13,$fot(inverse(X_110))),bind(X_43,$fot(inverse(X_110))),bind(X_44,$fot(identity))]]) ).
cnf(refute_0_1302,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))) != least_upper_bound(identity,inverse(X_110))
| least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))) != least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110)))
| least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))) = least_upper_bound(identity,inverse(X_110)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))))),bind(Z0,$fot(least_upper_bound(identity,inverse(X_110))))]]) ).
cnf(refute_0_1303,plain,
( least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))) != least_upper_bound(identity,inverse(X_110))
| least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))) = least_upper_bound(identity,inverse(X_110)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))),least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110)))) )],[refute_0_1301,refute_0_1302]) ).
cnf(refute_0_1304,plain,
least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))) = least_upper_bound(identity,inverse(X_110)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_110),inverse(X_110))),least_upper_bound(identity,inverse(X_110))) )],[refute_0_1300,refute_0_1303]) ).
cnf(refute_0_1305,plain,
( multiply(least_upper_bound(identity,X_110),inverse(X_110)) != least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110)))
| least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))) != least_upper_bound(identity,inverse(X_110))
| multiply(least_upper_bound(identity,X_110),inverse(X_110)) = least_upper_bound(identity,inverse(X_110)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_110),inverse(X_110)),least_upper_bound(identity,inverse(X_110))) ),[0],$fot(least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))))]]) ).
cnf(refute_0_1306,plain,
( multiply(least_upper_bound(identity,X_110),inverse(X_110)) != least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110)))
| multiply(least_upper_bound(identity,X_110),inverse(X_110)) = least_upper_bound(identity,inverse(X_110)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110))),least_upper_bound(identity,inverse(X_110))) )],[refute_0_1304,refute_0_1305]) ).
cnf(refute_0_1307,plain,
( multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)) != least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110)))
| multiply(least_upper_bound(identity,X_110),inverse(X_110)) = least_upper_bound(identity,inverse(X_110)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_110),inverse(X_110)),least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110)))) )],[refute_0_1295,refute_0_1306]) ).
cnf(refute_0_1308,plain,
multiply(least_upper_bound(identity,X_110),inverse(X_110)) = least_upper_bound(identity,inverse(X_110)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(least_upper_bound(X_110,identity),identity),inverse(X_110)),least_upper_bound(inverse(X_110),least_upper_bound(identity,inverse(X_110)))) )],[refute_0_1284,refute_0_1307]) ).
cnf(refute_0_1309,plain,
multiply(least_upper_bound(identity,X_157),inverse(X_157)) = least_upper_bound(identity,inverse(X_157)),
inference(subst,[],[refute_0_1308:[bind(X_110,$fot(X_157))]]) ).
cnf(refute_0_1310,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != greatest_lower_bound(least_upper_bound(identity,X_157),multiply(least_upper_bound(identity,X_157),inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),inverse(X_157)) != least_upper_bound(identity,inverse(X_157))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) = greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)),greatest_lower_bound(least_upper_bound(identity,X_157),multiply(least_upper_bound(identity,X_157),inverse(X_157)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_157)))]]) ).
cnf(refute_0_1311,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != greatest_lower_bound(least_upper_bound(identity,X_157),multiply(least_upper_bound(identity,X_157),inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) = greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),inverse(X_157)),least_upper_bound(identity,inverse(X_157))) )],[refute_0_1309,refute_0_1310]) ).
cnf(refute_0_1312,plain,
multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) = greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)),greatest_lower_bound(least_upper_bound(identity,X_157),multiply(least_upper_bound(identity,X_157),inverse(X_157)))) )],[refute_0_1280,refute_0_1311]) ).
cnf(refute_0_1313,plain,
multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) = multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),
inference(subst,[],[refute_0_884:[bind(X_119,$fot(inverse(X_157))),bind(X_19,$fot(least_upper_bound(identity,X_157)))]]) ).
cnf(refute_0_1314,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)),greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))) ),[0],$fot(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))))]]) ).
cnf(refute_0_1315,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)),multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157)))) )],[refute_0_1313,refute_0_1314]) ).
cnf(refute_0_1316,plain,
( multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)) != greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))
| greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) = multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))))]]) ).
cnf(refute_0_1317,plain,
greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) = multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)),greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) )],[refute_0_1279,refute_0_1316]) ).
cnf(refute_0_1318,plain,
greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)),
inference(subst,[],[refute_0_1317:[bind(X_59,$fot(X_157))]]) ).
cnf(refute_0_1319,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) != greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))
| greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))) != multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))))]]) ).
cnf(refute_0_1320,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) != greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157))),multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))) )],[refute_0_1318,refute_0_1319]) ).
cnf(refute_0_1321,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)) != greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))
| multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))) )],[refute_0_1315,refute_0_1320]) ).
cnf(refute_0_1322,plain,
multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) = multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(inverse(X_157),identity)),greatest_lower_bound(least_upper_bound(identity,X_157),least_upper_bound(identity,inverse(X_157)))) )],[refute_0_1312,refute_0_1321]) ).
cnf(refute_0_1323,plain,
( multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) != multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))
| multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) = multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))))]]) ).
cnf(refute_0_1324,plain,
multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157)) = multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_157),greatest_lower_bound(identity,inverse(X_157))),multiply(greatest_lower_bound(identity,inverse(X_157)),least_upper_bound(identity,X_157))) )],[refute_0_1322,refute_0_1323]) ).
cnf(refute_0_1325,plain,
multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)) = multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))),
inference(subst,[],[refute_0_1324:[bind(X_157,$fot(X_59))]]) ).
cnf(refute_0_1326,plain,
( multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)) != multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59)))
| multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)) != greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))
| multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)),greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) ),[0],$fot(multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))))]]) ).
cnf(refute_0_1327,plain,
( multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)) != greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))
| multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)),multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59)))) )],[refute_0_1325,refute_0_1326]) ).
cnf(refute_0_1328,plain,
multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_59)),least_upper_bound(identity,X_59)),greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) )],[refute_0_1279,refute_0_1327]) ).
cnf(refute_0_1329,plain,
multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)) = greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),multiply(inverse(X_52),least_upper_bound(X_52,identity))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(least_upper_bound(X_52,identity))),bind(Y,$fot(X_92)),bind(Z,$fot(inverse(X_52)))]]) ).
cnf(refute_0_1330,plain,
( multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)) != greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),multiply(inverse(X_52),least_upper_bound(X_52,identity)))
| multiply(inverse(X_52),least_upper_bound(X_52,identity)) != least_upper_bound(identity,inverse(X_52))
| multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)) = greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)),greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),multiply(inverse(X_52),least_upper_bound(X_52,identity)))) ),[1,1],$fot(least_upper_bound(identity,inverse(X_52)))]]) ).
cnf(refute_0_1331,plain,
( multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)) != greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),multiply(inverse(X_52),least_upper_bound(X_52,identity)))
| multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)) = greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_52),least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52))) )],[refute_0_215,refute_0_1330]) ).
cnf(refute_0_1332,plain,
multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)) = greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)),greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),multiply(inverse(X_52),least_upper_bound(X_52,identity)))) )],[refute_0_1329,refute_0_1331]) ).
cnf(refute_0_1333,plain,
greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(X_92,least_upper_bound(X_52,identity))),
inference(subst,[],[refute_0_38:[bind(X,$fot(least_upper_bound(identity,inverse(X_52)))),bind(Y,$fot(multiply(X_92,least_upper_bound(X_52,identity))))]]) ).
cnf(refute_0_1334,plain,
( multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)) != greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52)))
| greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(X_92,least_upper_bound(X_52,identity)))
| multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(X_92,least_upper_bound(X_52,identity))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(X_92,least_upper_bound(X_52,identity)))) ),[0],$fot(greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52))))]]) ).
cnf(refute_0_1335,plain,
( multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)) != greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52)))
| multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(X_92,least_upper_bound(X_52,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52))),greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(X_92,least_upper_bound(X_52,identity)))) )],[refute_0_1333,refute_0_1334]) ).
cnf(refute_0_1336,plain,
multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_52)),multiply(X_92,least_upper_bound(X_52,identity))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_92,inverse(X_52)),least_upper_bound(X_52,identity)),greatest_lower_bound(multiply(X_92,least_upper_bound(X_52,identity)),least_upper_bound(identity,inverse(X_52)))) )],[refute_0_1332,refute_0_1335]) ).
cnf(refute_0_1337,plain,
multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity))),
inference(subst,[],[refute_0_1336:[bind(X_52,$fot(X_197)),bind(X_92,$fot(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))))]]) ).
cnf(refute_0_1338,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) = multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity)),
inference(subst,[],[refute_0_122:[bind(X_80,$fot(least_upper_bound(X_197,identity)))]]) ).
cnf(refute_0_1339,plain,
( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) != multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity))
| multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity)) = inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity))))]]) ).
cnf(refute_0_1340,plain,
multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity)) = inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity))) )],[refute_0_1338,refute_0_1339]) ).
cnf(refute_0_1341,plain,
( multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity)))
| multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity)) != inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))
| multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity)))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))]]) ).
cnf(refute_0_1342,plain,
( multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity)))
| multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) )],[refute_0_1340,refute_0_1341]) ).
cnf(refute_0_1343,plain,
multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity)))) )],[refute_0_1337,refute_0_1342]) ).
cnf(refute_0_1344,plain,
multiply(greatest_lower_bound(identity,inverse(X_197)),least_upper_bound(identity,X_197)) = multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))),
inference(subst,[],[refute_0_1324:[bind(X_157,$fot(X_197))]]) ).
cnf(refute_0_1345,plain,
greatest_lower_bound(inverse(X_197),identity) = greatest_lower_bound(identity,inverse(X_197)),
inference(subst,[],[refute_0_998:[bind(Y,$fot(X_197)),bind(X_76,$fot(identity))]]) ).
cnf(refute_0_1346,plain,
multiply(inverse(identity),identity) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(identity))]]) ).
cnf(refute_0_1347,plain,
inverse(identity) = multiply(inverse(identity),identity),
inference(subst,[],[refute_0_30:[bind(X_28,$fot(inverse(identity)))]]) ).
cnf(refute_0_1348,plain,
( inverse(identity) != multiply(inverse(identity),identity)
| multiply(inverse(identity),identity) = inverse(identity) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(identity))),bind(Y0,$fot(multiply(inverse(identity),identity)))]]) ).
cnf(refute_0_1349,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),multiply(inverse(identity),identity)) )],[refute_0_1347,refute_0_1348]) ).
cnf(refute_0_1350,plain,
( multiply(inverse(identity),identity) != identity
| multiply(inverse(identity),identity) != inverse(identity)
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),identity),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_1351,plain,
( multiply(inverse(identity),identity) != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_1349,refute_0_1350]) ).
cnf(refute_0_1352,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),identity) )],[refute_0_1346,refute_0_1351]) ).
cnf(refute_0_1353,plain,
greatest_lower_bound(identity,least_upper_bound(X_197,identity)) = identity,
inference(subst,[],[refute_0_136:[bind(X_12,$fot(identity)),bind(X_13,$fot(X_197))]]) ).
cnf(refute_0_1354,plain,
inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))) = inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))))]]) ).
cnf(refute_0_1355,plain,
( greatest_lower_bound(identity,least_upper_bound(X_197,identity)) != identity
| inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))) != inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))
| inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1356,plain,
( greatest_lower_bound(identity,least_upper_bound(X_197,identity)) != identity
| inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) )],[refute_0_1354,refute_0_1355]) ).
cnf(refute_0_1357,plain,
inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))) = inverse(identity),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_197,identity)),identity) )],[refute_0_1353,refute_0_1356]) ).
cnf(refute_0_1358,plain,
( inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))) != inverse(identity)
| inverse(identity) != identity
| inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))) = identity ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1359,plain,
( inverse(identity) != identity
| inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))) = identity ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(identity)) )],[refute_0_1357,refute_0_1358]) ).
cnf(refute_0_1360,plain,
inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_1352,refute_0_1359]) ).
cnf(refute_0_1361,plain,
greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) = greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))))]]) ).
cnf(refute_0_1362,plain,
( greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) != greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))))
| inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))) != identity
| greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) = greatest_lower_bound(inverse(X_197),identity) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1363,plain,
( inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))) != identity
| greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) = greatest_lower_bound(inverse(X_197),identity) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))))) )],[refute_0_1361,refute_0_1362]) ).
cnf(refute_0_1364,plain,
greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) = greatest_lower_bound(inverse(X_197),identity),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),identity) )],[refute_0_1360,refute_0_1363]) ).
cnf(refute_0_1365,plain,
( greatest_lower_bound(inverse(X_197),identity) != greatest_lower_bound(identity,inverse(X_197))
| greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) != greatest_lower_bound(inverse(X_197),identity)
| greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) = greatest_lower_bound(identity,inverse(X_197)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))))),bind(Y0,$fot(greatest_lower_bound(inverse(X_197),identity))),bind(Z0,$fot(greatest_lower_bound(identity,inverse(X_197))))]]) ).
cnf(refute_0_1366,plain,
( greatest_lower_bound(inverse(X_197),identity) != greatest_lower_bound(identity,inverse(X_197))
| greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) = greatest_lower_bound(identity,inverse(X_197)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),greatest_lower_bound(inverse(X_197),identity)) )],[refute_0_1364,refute_0_1365]) ).
cnf(refute_0_1367,plain,
greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) = greatest_lower_bound(identity,inverse(X_197)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_197),identity),greatest_lower_bound(identity,inverse(X_197))) )],[refute_0_1345,refute_0_1366]) ).
cnf(refute_0_1368,plain,
multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)) = multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)))]]) ).
cnf(refute_0_1369,plain,
( multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)) != multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197))
| greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) != greatest_lower_bound(identity,inverse(X_197))
| multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)) = multiply(greatest_lower_bound(identity,inverse(X_197)),least_upper_bound(identity,X_197)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)),multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197))) ),[1,0],$fot(greatest_lower_bound(identity,inverse(X_197)))]]) ).
cnf(refute_0_1370,plain,
( greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))) != greatest_lower_bound(identity,inverse(X_197))
| multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)) = multiply(greatest_lower_bound(identity,inverse(X_197)),least_upper_bound(identity,X_197)) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)),multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197))) )],[refute_0_1368,refute_0_1369]) ).
cnf(refute_0_1371,plain,
multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)) = multiply(greatest_lower_bound(identity,inverse(X_197)),least_upper_bound(identity,X_197)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),greatest_lower_bound(identity,inverse(X_197))) )],[refute_0_1367,refute_0_1370]) ).
cnf(refute_0_1372,plain,
( multiply(greatest_lower_bound(identity,inverse(X_197)),least_upper_bound(identity,X_197)) != multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))
| multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)) != multiply(greatest_lower_bound(identity,inverse(X_197)),least_upper_bound(identity,X_197))
| multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)) = multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)))),bind(Y0,$fot(multiply(greatest_lower_bound(identity,inverse(X_197)),least_upper_bound(identity,X_197)))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))))]]) ).
cnf(refute_0_1373,plain,
( multiply(greatest_lower_bound(identity,inverse(X_197)),least_upper_bound(identity,X_197)) != multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))
| multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)) = multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)),multiply(greatest_lower_bound(identity,inverse(X_197)),least_upper_bound(identity,X_197))) )],[refute_0_1371,refute_0_1372]) ).
cnf(refute_0_1374,plain,
multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)) = multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,inverse(X_197)),least_upper_bound(identity,X_197)),multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))) )],[refute_0_1344,refute_0_1373]) ).
cnf(refute_0_1375,plain,
multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(X_197,identity))),
inference(subst,[],[refute_0_1336:[bind(X_52,$fot(X_197)),bind(X_92,$fot(X_198))]]) ).
cnf(refute_0_1376,plain,
least_upper_bound(identity,X_197) = least_upper_bound(X_197,identity),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_197))]]) ).
cnf(refute_0_1377,plain,
( least_upper_bound(identity,X_197) != least_upper_bound(X_197,identity)
| least_upper_bound(X_197,identity) = least_upper_bound(identity,X_197) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(identity,X_197))),bind(Y0,$fot(least_upper_bound(X_197,identity)))]]) ).
cnf(refute_0_1378,plain,
least_upper_bound(X_197,identity) = least_upper_bound(identity,X_197),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_197),least_upper_bound(X_197,identity)) )],[refute_0_1376,refute_0_1377]) ).
cnf(refute_0_1379,plain,
( multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(X_197,identity)))
| least_upper_bound(X_197,identity) != least_upper_bound(identity,X_197)
| multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(identity,X_197))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(X_197,identity)))) ),[1,1,1],$fot(least_upper_bound(identity,X_197))]]) ).
cnf(refute_0_1380,plain,
( multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(X_197,identity)))
| multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(identity,X_197))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_197,identity),least_upper_bound(identity,X_197)) )],[refute_0_1378,refute_0_1379]) ).
cnf(refute_0_1381,plain,
multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(identity,X_197))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(X_197,identity)))) )],[refute_0_1375,refute_0_1380]) ).
cnf(refute_0_1382,plain,
multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)) = greatest_lower_bound(multiply(inverse(X_105),least_upper_bound(identity,X_105)),multiply(Z,least_upper_bound(identity,X_105))),
inference(subst,[],[monotony_glb2:[bind(X,$fot(least_upper_bound(identity,X_105))),bind(Y,$fot(inverse(X_105)))]]) ).
cnf(refute_0_1383,plain,
multiply(inverse(X_105),least_upper_bound(identity,X_105)) = least_upper_bound(identity,inverse(X_105)),
inference(subst,[],[refute_0_600:[bind(X_59,$fot(X_105))]]) ).
cnf(refute_0_1384,plain,
( multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)) != greatest_lower_bound(multiply(inverse(X_105),least_upper_bound(identity,X_105)),multiply(Z,least_upper_bound(identity,X_105)))
| multiply(inverse(X_105),least_upper_bound(identity,X_105)) != least_upper_bound(identity,inverse(X_105))
| multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_105)),multiply(Z,least_upper_bound(identity,X_105))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)),greatest_lower_bound(multiply(inverse(X_105),least_upper_bound(identity,X_105)),multiply(Z,least_upper_bound(identity,X_105)))) ),[1,0],$fot(least_upper_bound(identity,inverse(X_105)))]]) ).
cnf(refute_0_1385,plain,
( multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)) != greatest_lower_bound(multiply(inverse(X_105),least_upper_bound(identity,X_105)),multiply(Z,least_upper_bound(identity,X_105)))
| multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_105)),multiply(Z,least_upper_bound(identity,X_105))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_105),least_upper_bound(identity,X_105)),least_upper_bound(identity,inverse(X_105))) )],[refute_0_1383,refute_0_1384]) ).
cnf(refute_0_1386,plain,
multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)) = greatest_lower_bound(least_upper_bound(identity,inverse(X_105)),multiply(Z,least_upper_bound(identity,X_105))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)),greatest_lower_bound(multiply(inverse(X_105),least_upper_bound(identity,X_105)),multiply(Z,least_upper_bound(identity,X_105)))) )],[refute_0_1382,refute_0_1385]) ).
cnf(refute_0_1387,plain,
( multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_105)),multiply(Z,least_upper_bound(identity,X_105)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_105)),multiply(Z,least_upper_bound(identity,X_105))) = multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_105)),multiply(Z,least_upper_bound(identity,X_105)))))]]) ).
cnf(refute_0_1388,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_105)),multiply(Z,least_upper_bound(identity,X_105))) = multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_105),Z),least_upper_bound(identity,X_105)),greatest_lower_bound(least_upper_bound(identity,inverse(X_105)),multiply(Z,least_upper_bound(identity,X_105)))) )],[refute_0_1386,refute_0_1387]) ).
cnf(refute_0_1389,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(identity,X_197))) = multiply(greatest_lower_bound(inverse(X_197),X_198),least_upper_bound(identity,X_197)),
inference(subst,[],[refute_0_1388:[bind(Z,$fot(X_198)),bind(X_105,$fot(X_197))]]) ).
cnf(refute_0_1390,plain,
( multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(identity,X_197)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(identity,X_197))) != multiply(greatest_lower_bound(inverse(X_197),X_198),least_upper_bound(identity,X_197))
| multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)) = multiply(greatest_lower_bound(inverse(X_197),X_198),least_upper_bound(identity,X_197)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)),multiply(greatest_lower_bound(inverse(X_197),X_198),least_upper_bound(identity,X_197))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(identity,X_197))))]]) ).
cnf(refute_0_1391,plain,
( multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(identity,X_197)))
| multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)) = multiply(greatest_lower_bound(inverse(X_197),X_198),least_upper_bound(identity,X_197)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(identity,X_197))),multiply(greatest_lower_bound(inverse(X_197),X_198),least_upper_bound(identity,X_197))) )],[refute_0_1389,refute_0_1390]) ).
cnf(refute_0_1392,plain,
multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)) = multiply(greatest_lower_bound(inverse(X_197),X_198),least_upper_bound(identity,X_197)),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(X_198,inverse(X_197)),least_upper_bound(X_197,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),multiply(X_198,least_upper_bound(identity,X_197)))) )],[refute_0_1381,refute_0_1391]) ).
cnf(refute_0_1393,plain,
multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) = multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)),
inference(subst,[],[refute_0_1392:[bind(X_198,$fot(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))))]]) ).
cnf(refute_0_1394,plain,
( multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)) != multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))
| multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) != multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197))
| multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) = multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)))),bind(Y0,$fot(multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)))),bind(Z0,$fot(multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))))]]) ).
cnf(refute_0_1395,plain,
( multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)) != multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))
| multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) = multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)),multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197))) )],[refute_0_1393,refute_0_1394]) ).
cnf(refute_0_1396,plain,
multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) = multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(X_197),inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity)))),least_upper_bound(identity,X_197)),multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))) )],[refute_0_1374,refute_0_1395]) ).
cnf(refute_0_1397,plain,
( multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) != multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))
| multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))
| multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))) ),[0],$fot(multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))))]]) ).
cnf(refute_0_1398,plain,
( multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))
| multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)),multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197)))) )],[refute_0_1396,refute_0_1397]) ).
cnf(refute_0_1399,plain,
( multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88))) != greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88)))
| greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88))) = multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88)))))]]) ).
cnf(refute_0_1400,plain,
greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88))) = multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_88),least_upper_bound(identity,inverse(X_88))),greatest_lower_bound(least_upper_bound(X_88,identity),least_upper_bound(identity,inverse(X_88)))) )],[refute_0_1235,refute_0_1399]) ).
cnf(refute_0_1401,plain,
greatest_lower_bound(least_upper_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))),
inference(subst,[],[refute_0_1400:[bind(X_88,$fot(X_197))]]) ).
cnf(refute_0_1402,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)) = greatest_lower_bound(least_upper_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))),
inference(subst,[],[refute_0_38:[bind(X,$fot(least_upper_bound(X_197,identity))),bind(Y,$fot(least_upper_bound(identity,inverse(X_197))))]]) ).
cnf(refute_0_1403,plain,
( greatest_lower_bound(least_upper_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)) != greatest_lower_bound(least_upper_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))))]]) ).
cnf(refute_0_1404,plain,
( greatest_lower_bound(least_upper_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)),greatest_lower_bound(least_upper_bound(X_197,identity),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1402,refute_0_1403]) ).
cnf(refute_0_1405,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(X_197,identity),least_upper_bound(identity,inverse(X_197))),multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1401,refute_0_1404]) ).
cnf(refute_0_1406,plain,
inverse(inverse(least_upper_bound(X_197,identity))) = least_upper_bound(X_197,identity),
inference(subst,[],[refute_0_737:[bind(X_30,$fot(least_upper_bound(X_197,identity)))]]) ).
cnf(refute_0_1407,plain,
greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),multiply(inverse(least_upper_bound(X_58,identity)),least_upper_bound(X_58,identity))) = inverse(least_upper_bound(X_58,identity)),
inference(subst,[],[refute_0_400:[bind(X,$fot(inverse(least_upper_bound(X_58,identity)))),bind(X_52,$fot(X_58))]]) ).
cnf(refute_0_1408,plain,
multiply(inverse(least_upper_bound(X_58,identity)),least_upper_bound(X_58,identity)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(X_58,identity)))]]) ).
cnf(refute_0_1409,plain,
( multiply(inverse(least_upper_bound(X_58,identity)),least_upper_bound(X_58,identity)) != identity
| greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),multiply(inverse(least_upper_bound(X_58,identity)),least_upper_bound(X_58,identity))) != inverse(least_upper_bound(X_58,identity))
| greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),identity) = inverse(least_upper_bound(X_58,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),multiply(inverse(least_upper_bound(X_58,identity)),least_upper_bound(X_58,identity))),inverse(least_upper_bound(X_58,identity))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_1410,plain,
( greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),multiply(inverse(least_upper_bound(X_58,identity)),least_upper_bound(X_58,identity))) != inverse(least_upper_bound(X_58,identity))
| greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),identity) = inverse(least_upper_bound(X_58,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_58,identity)),least_upper_bound(X_58,identity)),identity) )],[refute_0_1408,refute_0_1409]) ).
cnf(refute_0_1411,plain,
greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),identity) = inverse(least_upper_bound(X_58,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),multiply(inverse(least_upper_bound(X_58,identity)),least_upper_bound(X_58,identity))),inverse(least_upper_bound(X_58,identity))) )],[refute_0_1407,refute_0_1410]) ).
cnf(refute_0_1412,plain,
greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(X_58,identity))),
inference(subst,[],[refute_0_38:[bind(X,$fot(identity)),bind(Y,$fot(inverse(least_upper_bound(X_58,identity))))]]) ).
cnf(refute_0_1413,plain,
( greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),identity) != greatest_lower_bound(identity,inverse(least_upper_bound(X_58,identity)))
| greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),identity) != inverse(least_upper_bound(X_58,identity))
| greatest_lower_bound(identity,inverse(least_upper_bound(X_58,identity))) = inverse(least_upper_bound(X_58,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),identity),inverse(least_upper_bound(X_58,identity))) ),[0],$fot(greatest_lower_bound(identity,inverse(least_upper_bound(X_58,identity))))]]) ).
cnf(refute_0_1414,plain,
( greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),identity) != inverse(least_upper_bound(X_58,identity))
| greatest_lower_bound(identity,inverse(least_upper_bound(X_58,identity))) = inverse(least_upper_bound(X_58,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),identity),greatest_lower_bound(identity,inverse(least_upper_bound(X_58,identity)))) )],[refute_0_1412,refute_0_1413]) ).
cnf(refute_0_1415,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X_58,identity))) = inverse(least_upper_bound(X_58,identity)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(least_upper_bound(X_58,identity)),identity),inverse(least_upper_bound(X_58,identity))) )],[refute_0_1411,refute_0_1414]) ).
cnf(refute_0_1416,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))) = inverse(least_upper_bound(X_197,identity)),
inference(subst,[],[refute_0_1415:[bind(X_58,$fot(X_197))]]) ).
cnf(refute_0_1417,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) = inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))]]) ).
cnf(refute_0_1418,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))) != inverse(least_upper_bound(X_197,identity))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) != inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) = inverse(inverse(least_upper_bound(X_197,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) ),[1,0],$fot(inverse(least_upper_bound(X_197,identity)))]]) ).
cnf(refute_0_1419,plain,
( greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))) != inverse(least_upper_bound(X_197,identity))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) = inverse(inverse(least_upper_bound(X_197,identity))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) )],[refute_0_1417,refute_0_1418]) ).
cnf(refute_0_1420,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) = inverse(inverse(least_upper_bound(X_197,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))),inverse(least_upper_bound(X_197,identity))) )],[refute_0_1416,refute_0_1419]) ).
cnf(refute_0_1421,plain,
( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) != inverse(inverse(least_upper_bound(X_197,identity)))
| inverse(inverse(least_upper_bound(X_197,identity))) != least_upper_bound(X_197,identity)
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) = least_upper_bound(X_197,identity) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(X_197,identity))))),bind(Z0,$fot(least_upper_bound(X_197,identity)))]]) ).
cnf(refute_0_1422,plain,
( inverse(inverse(least_upper_bound(X_197,identity))) != least_upper_bound(X_197,identity)
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) = least_upper_bound(X_197,identity) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))),inverse(inverse(least_upper_bound(X_197,identity)))) )],[refute_0_1420,refute_0_1421]) ).
cnf(refute_0_1423,plain,
inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) = least_upper_bound(X_197,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_197,identity))),least_upper_bound(X_197,identity)) )],[refute_0_1406,refute_0_1422]) ).
cnf(refute_0_1424,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))))]]) ).
cnf(refute_0_1425,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))
| inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) != least_upper_bound(X_197,identity)
| greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))),greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))) ),[1,1],$fot(least_upper_bound(X_197,identity))]]) ).
cnf(refute_0_1426,plain,
( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))) != least_upper_bound(X_197,identity)
| greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))),greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))) )],[refute_0_1424,refute_0_1425]) ).
cnf(refute_0_1427,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) = greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))),least_upper_bound(X_197,identity)) )],[refute_0_1423,refute_0_1426]) ).
cnf(refute_0_1428,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)))),bind(Z0,$fot(multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))))]]) ).
cnf(refute_0_1429,plain,
( greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))),greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity))) )],[refute_0_1427,refute_0_1428]) ).
cnf(refute_0_1430,plain,
greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),least_upper_bound(X_197,identity)),multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1405,refute_0_1429]) ).
cnf(refute_0_1431,plain,
( multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))
| greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))) != multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))
| multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))),multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) ),[0],$fot(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))))]]) ).
cnf(refute_0_1432,plain,
( multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))
| multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity))))),multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197)))) )],[refute_0_1430,refute_0_1431]) ).
cnf(refute_0_1433,plain,
( multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)) != greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))
| multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))),greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))) )],[refute_0_1398,refute_0_1432]) ).
cnf(refute_0_1434,plain,
multiply(least_upper_bound(identity,X_197),greatest_lower_bound(identity,inverse(X_197))) = multiply(greatest_lower_bound(identity,X_197),least_upper_bound(identity,inverse(X_197))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,least_upper_bound(X_197,identity))),inverse(X_197)),least_upper_bound(X_197,identity)),greatest_lower_bound(least_upper_bound(identity,inverse(X_197)),inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X_197,identity)))))) )],[refute_0_1343,refute_0_1433]) ).
cnf(refute_0_1435,plain,
multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))) = multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))),
inference(subst,[],[refute_0_1434:[bind(X_197,$fot(X_59))]]) ).
cnf(refute_0_1436,plain,
( multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))) != multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))
| multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))) != greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))
| multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))))]]) ).
cnf(refute_0_1437,plain,
( multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))) != greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))
| multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))),multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) )],[refute_0_1435,refute_0_1436]) ).
cnf(refute_0_1438,plain,
multiply(greatest_lower_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))) = greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,X_59),greatest_lower_bound(identity,inverse(X_59))),greatest_lower_bound(least_upper_bound(identity,X_59),least_upper_bound(identity,inverse(X_59)))) )],[refute_0_1328,refute_0_1437]) ).
cnf(refute_0_1439,plain,
multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))) = greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y))),
inference(subst,[],[refute_0_1438:[bind(X_59,$fot(Y))]]) ).
cnf(refute_0_1440,plain,
( multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))) != greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y)))
| greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y))) = multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))))),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y)))))]]) ).
cnf(refute_0_1441,plain,
greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y))) = multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))),greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) )],[refute_0_1439,refute_0_1440]) ).
cnf(refute_0_1442,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) != greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y)))
| greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y))) != multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) = greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y)))),greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y)))) ),[0,1],$fot(multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y))))]]) ).
cnf(refute_0_1443,plain,
( greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) != greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y)))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) = greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y))),multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) )],[refute_0_1441,refute_0_1442]) ).
cnf(refute_0_1444,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) = greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,Y),least_upper_bound(identity,inverse(Y)))),greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y)))) )],[refute_0_1271,refute_0_1443]) ).
cnf(refute_0_1445,plain,
greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y))) = identity,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(inverse(Y)))]]) ).
cnf(refute_0_1446,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) != greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y)))
| greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y))) != identity
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))),identity) ),[0],$fot(greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y))))]]) ).
cnf(refute_0_1447,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) != greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y)))
| greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y))),identity) )],[refute_0_1445,refute_0_1446]) ).
cnf(refute_0_1448,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,Y),least_upper_bound(identity,inverse(Y)))),greatest_lower_bound(identity,least_upper_bound(identity,inverse(Y)))) )],[refute_0_1444,refute_0_1447]) ).
cnf(refute_0_1449,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))) = identity,
inference(subst,[],[refute_0_1448:[bind(Y,$fot(X_442))]]) ).
cnf(refute_0_1450,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))) != identity
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))))) != multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)) = multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))))),multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))) ),[0,1,1],$fot(identity)]]) ).
cnf(refute_0_1451,plain,
( least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))))) != multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)) = multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))),identity) )],[refute_0_1449,refute_0_1450]) ).
cnf(refute_0_1452,plain,
least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)) = multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))))),multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))) )],[refute_0_1265,refute_0_1451]) ).
cnf(refute_0_1453,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X_36)) = identity,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(identity)),bind(Y,$fot(X_36))]]) ).
cnf(refute_0_1454,plain,
least_upper_bound(greatest_lower_bound(X_107,X_106),least_upper_bound(X_39,greatest_lower_bound(X_106,X_107))) = least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_106,X_107),greatest_lower_bound(X_107,X_106))),
inference(subst,[],[refute_0_454:[bind(X,$fot(greatest_lower_bound(X_107,X_106))),bind(X_40,$fot(greatest_lower_bound(X_106,X_107)))]]) ).
cnf(refute_0_1455,plain,
least_upper_bound(greatest_lower_bound(X_106,X_107),greatest_lower_bound(X_107,X_106)) = greatest_lower_bound(X_106,X_107),
inference(subst,[],[refute_0_695:[bind(X_18,$fot(X_106)),bind(X_9,$fot(X_107))]]) ).
cnf(refute_0_1456,plain,
( least_upper_bound(greatest_lower_bound(X_106,X_107),greatest_lower_bound(X_107,X_106)) != greatest_lower_bound(X_106,X_107)
| least_upper_bound(greatest_lower_bound(X_107,X_106),least_upper_bound(X_39,greatest_lower_bound(X_106,X_107))) != least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_106,X_107),greatest_lower_bound(X_107,X_106)))
| least_upper_bound(greatest_lower_bound(X_107,X_106),least_upper_bound(X_39,greatest_lower_bound(X_106,X_107))) = least_upper_bound(X_39,greatest_lower_bound(X_106,X_107)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_107,X_106),least_upper_bound(X_39,greatest_lower_bound(X_106,X_107))),least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_106,X_107),greatest_lower_bound(X_107,X_106)))) ),[1,1],$fot(greatest_lower_bound(X_106,X_107))]]) ).
cnf(refute_0_1457,plain,
( least_upper_bound(greatest_lower_bound(X_107,X_106),least_upper_bound(X_39,greatest_lower_bound(X_106,X_107))) != least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_106,X_107),greatest_lower_bound(X_107,X_106)))
| least_upper_bound(greatest_lower_bound(X_107,X_106),least_upper_bound(X_39,greatest_lower_bound(X_106,X_107))) = least_upper_bound(X_39,greatest_lower_bound(X_106,X_107)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_106,X_107),greatest_lower_bound(X_107,X_106)),greatest_lower_bound(X_106,X_107)) )],[refute_0_1455,refute_0_1456]) ).
cnf(refute_0_1458,plain,
least_upper_bound(greatest_lower_bound(X_107,X_106),least_upper_bound(X_39,greatest_lower_bound(X_106,X_107))) = least_upper_bound(X_39,greatest_lower_bound(X_106,X_107)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_107,X_106),least_upper_bound(X_39,greatest_lower_bound(X_106,X_107))),least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_106,X_107),greatest_lower_bound(X_107,X_106)))) )],[refute_0_1454,refute_0_1457]) ).
cnf(refute_0_1459,plain,
least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))) = least_upper_bound(X_346,greatest_lower_bound(X_344,X_345)),
inference(subst,[],[refute_0_1458:[bind(X_106,$fot(X_344)),bind(X_107,$fot(X_345)),bind(X_39,$fot(X_346))]]) ).
cnf(refute_0_1460,plain,
greatest_lower_bound(X_345,X_344) = greatest_lower_bound(X_344,X_345),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_345)),bind(Y,$fot(X_344))]]) ).
cnf(refute_0_1461,plain,
( greatest_lower_bound(X_345,X_344) != greatest_lower_bound(X_344,X_345)
| greatest_lower_bound(X_344,X_345) = greatest_lower_bound(X_345,X_344) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(greatest_lower_bound(X_345,X_344))),bind(Y0,$fot(greatest_lower_bound(X_344,X_345)))]]) ).
cnf(refute_0_1462,plain,
greatest_lower_bound(X_344,X_345) = greatest_lower_bound(X_345,X_344),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_345,X_344),greatest_lower_bound(X_344,X_345)) )],[refute_0_1460,refute_0_1461]) ).
cnf(refute_0_1463,plain,
( greatest_lower_bound(X_344,X_345) != greatest_lower_bound(X_345,X_344)
| least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))) != least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))
| least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_345,X_344))) = least_upper_bound(X_346,greatest_lower_bound(X_344,X_345)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))),least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))) ),[0,1,1],$fot(greatest_lower_bound(X_345,X_344))]]) ).
cnf(refute_0_1464,plain,
( least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))) != least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))
| least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_345,X_344))) = least_upper_bound(X_346,greatest_lower_bound(X_344,X_345)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_344,X_345),greatest_lower_bound(X_345,X_344)) )],[refute_0_1462,refute_0_1463]) ).
cnf(refute_0_1465,plain,
least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_345,X_344))) = least_upper_bound(X_346,greatest_lower_bound(X_344,X_345)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))),least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))) )],[refute_0_1459,refute_0_1464]) ).
cnf(refute_0_1466,plain,
least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_345,X_344))) = least_upper_bound(greatest_lower_bound(X_345,X_344),X_346),
inference(subst,[],[refute_0_387:[bind(X_13,$fot(X_346)),bind(X_9,$fot(greatest_lower_bound(X_345,X_344)))]]) ).
cnf(refute_0_1467,plain,
( least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_345,X_344))) != least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))
| least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_345,X_344))) != least_upper_bound(greatest_lower_bound(X_345,X_344),X_346)
| least_upper_bound(greatest_lower_bound(X_345,X_344),X_346) = least_upper_bound(X_346,greatest_lower_bound(X_344,X_345)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_345,X_344))),least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))) ),[0],$fot(least_upper_bound(greatest_lower_bound(X_345,X_344),X_346))]]) ).
cnf(refute_0_1468,plain,
( least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_345,X_344))) != least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))
| least_upper_bound(greatest_lower_bound(X_345,X_344),X_346) = least_upper_bound(X_346,greatest_lower_bound(X_344,X_345)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_345,X_344))),least_upper_bound(greatest_lower_bound(X_345,X_344),X_346)) )],[refute_0_1466,refute_0_1467]) ).
cnf(refute_0_1469,plain,
least_upper_bound(greatest_lower_bound(X_345,X_344),X_346) = least_upper_bound(X_346,greatest_lower_bound(X_344,X_345)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_345,X_344),least_upper_bound(X_346,greatest_lower_bound(X_345,X_344))),least_upper_bound(X_346,greatest_lower_bound(X_344,X_345))) )],[refute_0_1465,refute_0_1468]) ).
cnf(refute_0_1470,plain,
least_upper_bound(greatest_lower_bound(X_36,identity),identity) = least_upper_bound(identity,greatest_lower_bound(identity,X_36)),
inference(subst,[],[refute_0_1469:[bind(X_344,$fot(identity)),bind(X_345,$fot(X_36)),bind(X_346,$fot(identity))]]) ).
cnf(refute_0_1471,plain,
( least_upper_bound(greatest_lower_bound(X_36,identity),identity) != least_upper_bound(identity,greatest_lower_bound(identity,X_36))
| least_upper_bound(identity,greatest_lower_bound(identity,X_36)) != identity
| least_upper_bound(greatest_lower_bound(X_36,identity),identity) = identity ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(X_36,identity),identity))),bind(Y0,$fot(least_upper_bound(identity,greatest_lower_bound(identity,X_36)))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1472,plain,
( least_upper_bound(identity,greatest_lower_bound(identity,X_36)) != identity
| least_upper_bound(greatest_lower_bound(X_36,identity),identity) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,identity),identity),least_upper_bound(identity,greatest_lower_bound(identity,X_36))) )],[refute_0_1470,refute_0_1471]) ).
cnf(refute_0_1473,plain,
least_upper_bound(greatest_lower_bound(X_36,identity),identity) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,greatest_lower_bound(identity,X_36)),identity) )],[refute_0_1453,refute_0_1472]) ).
cnf(refute_0_1474,plain,
least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_9,X_39),X_41)) = least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_9,X_39)),X_41),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(greatest_lower_bound(X_9,X_39))),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_1475,plain,
least_upper_bound(X_39,greatest_lower_bound(X_9,X_39)) = X_39,
inference(subst,[],[refute_0_177:[bind(X_8,$fot(X_39))]]) ).
cnf(refute_0_1476,plain,
( least_upper_bound(X_39,greatest_lower_bound(X_9,X_39)) != X_39
| least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_9,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_9,X_39)),X_41)
| least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_9,X_39),X_41)) = least_upper_bound(X_39,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_9,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_9,X_39)),X_41)) ),[1,0],$fot(X_39)]]) ).
cnf(refute_0_1477,plain,
( least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_9,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_9,X_39)),X_41)
| least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_9,X_39),X_41)) = least_upper_bound(X_39,X_41) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,greatest_lower_bound(X_9,X_39)),X_39) )],[refute_0_1475,refute_0_1476]) ).
cnf(refute_0_1478,plain,
least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_9,X_39),X_41)) = least_upper_bound(X_39,X_41),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(greatest_lower_bound(X_9,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,greatest_lower_bound(X_9,X_39)),X_41)) )],[refute_0_1474,refute_0_1477]) ).
cnf(refute_0_1479,plain,
least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))),X_41)) = least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41),
inference(subst,[],[refute_0_1478:[bind(X_39,$fot(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))))),bind(X_9,$fot(identity))]]) ).
cnf(refute_0_1480,plain,
( greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))) != identity
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))),X_41)) != least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) = least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))),X_41)),least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_1481,plain,
( least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))),X_41)) != least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) = least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))),identity) )],[refute_0_1449,refute_0_1480]) ).
cnf(refute_0_1482,plain,
least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) = least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))),X_41)),least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)) )],[refute_0_1479,refute_0_1481]) ).
cnf(refute_0_1483,plain,
least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,least_upper_bound(X_44,greatest_lower_bound(X_44,Y))),
inference(subst,[],[refute_0_454:[bind(X,$fot(greatest_lower_bound(X_44,Y))),bind(X_39,$fot(X_43)),bind(X_40,$fot(X_44))]]) ).
cnf(refute_0_1484,plain,
least_upper_bound(X_44,greatest_lower_bound(X_44,Y)) = X_44,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_44))]]) ).
cnf(refute_0_1485,plain,
( least_upper_bound(X_44,greatest_lower_bound(X_44,Y)) != X_44
| least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)) != least_upper_bound(X_43,least_upper_bound(X_44,greatest_lower_bound(X_44,Y)))
| least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,X_44) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)),least_upper_bound(X_43,least_upper_bound(X_44,greatest_lower_bound(X_44,Y)))) ),[1,1],$fot(X_44)]]) ).
cnf(refute_0_1486,plain,
( least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)) != least_upper_bound(X_43,least_upper_bound(X_44,greatest_lower_bound(X_44,Y)))
| least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,X_44) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_44,greatest_lower_bound(X_44,Y)),X_44) )],[refute_0_1484,refute_0_1485]) ).
cnf(refute_0_1487,plain,
least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)) = least_upper_bound(X_43,X_44),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)),least_upper_bound(X_43,least_upper_bound(X_44,greatest_lower_bound(X_44,Y)))) )],[refute_0_1483,refute_0_1486]) ).
cnf(refute_0_1488,plain,
least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)) = least_upper_bound(X_44,least_upper_bound(X_43,greatest_lower_bound(X_44,Y))),
inference(subst,[],[refute_0_526:[bind(X_13,$fot(greatest_lower_bound(X_44,Y))),bind(X_42,$fot(X_44))]]) ).
cnf(refute_0_1489,plain,
( least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)) != least_upper_bound(X_43,X_44)
| least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)) != least_upper_bound(X_44,least_upper_bound(X_43,greatest_lower_bound(X_44,Y)))
| least_upper_bound(X_44,least_upper_bound(X_43,greatest_lower_bound(X_44,Y))) = least_upper_bound(X_43,X_44) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)),least_upper_bound(X_43,X_44)) ),[0],$fot(least_upper_bound(X_44,least_upper_bound(X_43,greatest_lower_bound(X_44,Y))))]]) ).
cnf(refute_0_1490,plain,
( least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)) != least_upper_bound(X_43,X_44)
| least_upper_bound(X_44,least_upper_bound(X_43,greatest_lower_bound(X_44,Y))) = least_upper_bound(X_43,X_44) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)),least_upper_bound(X_44,least_upper_bound(X_43,greatest_lower_bound(X_44,Y)))) )],[refute_0_1488,refute_0_1489]) ).
cnf(refute_0_1491,plain,
least_upper_bound(X_44,least_upper_bound(X_43,greatest_lower_bound(X_44,Y))) = least_upper_bound(X_43,X_44),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_44,Y),least_upper_bound(X_43,X_44)),least_upper_bound(X_43,X_44)) )],[refute_0_1487,refute_0_1490]) ).
cnf(refute_0_1492,plain,
least_upper_bound(identity,least_upper_bound(X_41,greatest_lower_bound(identity,X_442))) = least_upper_bound(X_41,identity),
inference(subst,[],[refute_0_1491:[bind(Y,$fot(X_442)),bind(X_43,$fot(X_41)),bind(X_44,$fot(identity))]]) ).
cnf(refute_0_1493,plain,
least_upper_bound(X_190,least_upper_bound(greatest_lower_bound(X_190,X_189),least_upper_bound(X_39,X_40))) = least_upper_bound(X_190,least_upper_bound(X_39,X_40)),
inference(subst,[],[refute_0_785:[bind(Y,$fot(X_189)),bind(X_39,$fot(X_190)),bind(X_41,$fot(least_upper_bound(X_39,X_40)))]]) ).
cnf(refute_0_1494,plain,
least_upper_bound(greatest_lower_bound(X_190,X_189),least_upper_bound(X_39,X_40)) = least_upper_bound(X_39,least_upper_bound(X_40,greatest_lower_bound(X_190,X_189))),
inference(subst,[],[refute_0_454:[bind(X,$fot(greatest_lower_bound(X_190,X_189)))]]) ).
cnf(refute_0_1495,plain,
( least_upper_bound(X_190,least_upper_bound(greatest_lower_bound(X_190,X_189),least_upper_bound(X_39,X_40))) != least_upper_bound(X_190,least_upper_bound(X_39,X_40))
| least_upper_bound(greatest_lower_bound(X_190,X_189),least_upper_bound(X_39,X_40)) != least_upper_bound(X_39,least_upper_bound(X_40,greatest_lower_bound(X_190,X_189)))
| least_upper_bound(X_190,least_upper_bound(X_39,least_upper_bound(X_40,greatest_lower_bound(X_190,X_189)))) = least_upper_bound(X_190,least_upper_bound(X_39,X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_190,least_upper_bound(greatest_lower_bound(X_190,X_189),least_upper_bound(X_39,X_40))),least_upper_bound(X_190,least_upper_bound(X_39,X_40))) ),[0,1],$fot(least_upper_bound(X_39,least_upper_bound(X_40,greatest_lower_bound(X_190,X_189))))]]) ).
cnf(refute_0_1496,plain,
( least_upper_bound(X_190,least_upper_bound(greatest_lower_bound(X_190,X_189),least_upper_bound(X_39,X_40))) != least_upper_bound(X_190,least_upper_bound(X_39,X_40))
| least_upper_bound(X_190,least_upper_bound(X_39,least_upper_bound(X_40,greatest_lower_bound(X_190,X_189)))) = least_upper_bound(X_190,least_upper_bound(X_39,X_40)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_190,X_189),least_upper_bound(X_39,X_40)),least_upper_bound(X_39,least_upper_bound(X_40,greatest_lower_bound(X_190,X_189)))) )],[refute_0_1494,refute_0_1495]) ).
cnf(refute_0_1497,plain,
least_upper_bound(X_190,least_upper_bound(X_39,least_upper_bound(X_40,greatest_lower_bound(X_190,X_189)))) = least_upper_bound(X_190,least_upper_bound(X_39,X_40)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_190,least_upper_bound(greatest_lower_bound(X_190,X_189),least_upper_bound(X_39,X_40))),least_upper_bound(X_190,least_upper_bound(X_39,X_40))) )],[refute_0_1493,refute_0_1496]) ).
cnf(refute_0_1498,plain,
least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))) = least_upper_bound(identity,least_upper_bound(X_41,greatest_lower_bound(identity,X_442))),
inference(subst,[],[refute_0_1497:[bind(X_189,$fot(inverse(X_442))),bind(X_190,$fot(identity)),bind(X_39,$fot(X_41)),bind(X_40,$fot(greatest_lower_bound(identity,X_442)))]]) ).
cnf(refute_0_1499,plain,
( least_upper_bound(identity,least_upper_bound(X_41,greatest_lower_bound(identity,X_442))) != least_upper_bound(X_41,identity)
| least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))) != least_upper_bound(identity,least_upper_bound(X_41,greatest_lower_bound(identity,X_442)))
| least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))) = least_upper_bound(X_41,identity) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_41,greatest_lower_bound(identity,X_442))))),bind(Z0,$fot(least_upper_bound(X_41,identity)))]]) ).
cnf(refute_0_1500,plain,
( least_upper_bound(identity,least_upper_bound(X_41,greatest_lower_bound(identity,X_442))) != least_upper_bound(X_41,identity)
| least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))) = least_upper_bound(X_41,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))),least_upper_bound(identity,least_upper_bound(X_41,greatest_lower_bound(identity,X_442)))) )],[refute_0_1498,refute_0_1499]) ).
cnf(refute_0_1501,plain,
least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))) = least_upper_bound(X_41,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_41,greatest_lower_bound(identity,X_442))),least_upper_bound(X_41,identity)) )],[refute_0_1492,refute_0_1500]) ).
cnf(refute_0_1502,plain,
multiply(least_upper_bound(inverse(X_84),X_86),X_84) = least_upper_bound(multiply(inverse(X_84),X_84),multiply(X_86,X_84)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_84)),bind(Y,$fot(inverse(X_84))),bind(Z,$fot(X_86))]]) ).
cnf(refute_0_1503,plain,
multiply(inverse(X_84),X_84) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_84))]]) ).
cnf(refute_0_1504,plain,
( multiply(inverse(X_84),X_84) != identity
| multiply(least_upper_bound(inverse(X_84),X_86),X_84) != least_upper_bound(multiply(inverse(X_84),X_84),multiply(X_86,X_84))
| multiply(least_upper_bound(inverse(X_84),X_86),X_84) = least_upper_bound(identity,multiply(X_86,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_84),X_86),X_84),least_upper_bound(multiply(inverse(X_84),X_84),multiply(X_86,X_84))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_1505,plain,
( multiply(least_upper_bound(inverse(X_84),X_86),X_84) != least_upper_bound(multiply(inverse(X_84),X_84),multiply(X_86,X_84))
| multiply(least_upper_bound(inverse(X_84),X_86),X_84) = least_upper_bound(identity,multiply(X_86,X_84)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_84),X_84),identity) )],[refute_0_1503,refute_0_1504]) ).
cnf(refute_0_1506,plain,
multiply(least_upper_bound(inverse(X_84),X_86),X_84) = least_upper_bound(identity,multiply(X_86,X_84)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_84),X_86),X_84),least_upper_bound(multiply(inverse(X_84),X_84),multiply(X_86,X_84))) )],[refute_0_1502,refute_0_1505]) ).
cnf(refute_0_1507,plain,
multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) = least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409)),
inference(subst,[],[refute_0_1506:[bind(X_84,$fot(X_409)),bind(X_86,$fot(least_upper_bound(identity,multiply(X_277,inverse(X_409)))))]]) ).
cnf(refute_0_1508,plain,
multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) = least_upper_bound(multiply(X_85,multiply(X_25,X_26)),multiply(inverse(X_25),multiply(X_25,X_26))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(multiply(X_25,X_26))),bind(Y,$fot(X_85)),bind(Z,$fot(inverse(X_25)))]]) ).
cnf(refute_0_1509,plain,
( multiply(inverse(X_25),multiply(X_25,X_26)) != X_26
| multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) != least_upper_bound(multiply(X_85,multiply(X_25,X_26)),multiply(inverse(X_25),multiply(X_25,X_26)))
| multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) = least_upper_bound(multiply(X_85,multiply(X_25,X_26)),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)),least_upper_bound(multiply(X_85,multiply(X_25,X_26)),multiply(inverse(X_25),multiply(X_25,X_26)))) ),[1,1],$fot(X_26)]]) ).
cnf(refute_0_1510,plain,
( multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) != least_upper_bound(multiply(X_85,multiply(X_25,X_26)),multiply(inverse(X_25),multiply(X_25,X_26)))
| multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) = least_upper_bound(multiply(X_85,multiply(X_25,X_26)),X_26) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),multiply(X_25,X_26)),X_26) )],[refute_0_73,refute_0_1509]) ).
cnf(refute_0_1511,plain,
multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) = least_upper_bound(multiply(X_85,multiply(X_25,X_26)),X_26),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)),least_upper_bound(multiply(X_85,multiply(X_25,X_26)),multiply(inverse(X_25),multiply(X_25,X_26)))) )],[refute_0_1508,refute_0_1510]) ).
cnf(refute_0_1512,plain,
least_upper_bound(multiply(X_85,multiply(X_25,X_26)),X_26) = least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26))),
inference(subst,[],[refute_0_159:[bind(X,$fot(X_26)),bind(Y,$fot(multiply(X_85,multiply(X_25,X_26))))]]) ).
cnf(refute_0_1513,plain,
( multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) != least_upper_bound(multiply(X_85,multiply(X_25,X_26)),X_26)
| least_upper_bound(multiply(X_85,multiply(X_25,X_26)),X_26) != least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26)))
| multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) = least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)),least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26)))) ),[0],$fot(least_upper_bound(multiply(X_85,multiply(X_25,X_26)),X_26))]]) ).
cnf(refute_0_1514,plain,
( multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) != least_upper_bound(multiply(X_85,multiply(X_25,X_26)),X_26)
| multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) = least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_85,multiply(X_25,X_26)),X_26),least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26)))) )],[refute_0_1512,refute_0_1513]) ).
cnf(refute_0_1515,plain,
multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) = least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)),least_upper_bound(multiply(X_85,multiply(X_25,X_26)),X_26)) )],[refute_0_1511,refute_0_1514]) ).
cnf(refute_0_1516,plain,
multiply(least_upper_bound(multiply(X,Y),identity),X_87) = least_upper_bound(X_87,multiply(multiply(X,Y),X_87)),
inference(subst,[],[refute_0_754:[bind(X_84,$fot(X_87)),bind(X_85,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_1517,plain,
multiply(multiply(X,Y),X_87) = multiply(X,multiply(Y,X_87)),
inference(subst,[],[associativity:[bind(Z,$fot(X_87))]]) ).
cnf(refute_0_1518,plain,
( multiply(multiply(X,Y),X_87) != multiply(X,multiply(Y,X_87))
| multiply(least_upper_bound(multiply(X,Y),identity),X_87) != least_upper_bound(X_87,multiply(multiply(X,Y),X_87))
| multiply(least_upper_bound(multiply(X,Y),identity),X_87) = least_upper_bound(X_87,multiply(X,multiply(Y,X_87))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(multiply(X,Y),identity),X_87),least_upper_bound(X_87,multiply(multiply(X,Y),X_87))) ),[1,1],$fot(multiply(X,multiply(Y,X_87)))]]) ).
cnf(refute_0_1519,plain,
( multiply(least_upper_bound(multiply(X,Y),identity),X_87) != least_upper_bound(X_87,multiply(multiply(X,Y),X_87))
| multiply(least_upper_bound(multiply(X,Y),identity),X_87) = least_upper_bound(X_87,multiply(X,multiply(Y,X_87))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X,Y),X_87),multiply(X,multiply(Y,X_87))) )],[refute_0_1517,refute_0_1518]) ).
cnf(refute_0_1520,plain,
multiply(least_upper_bound(multiply(X,Y),identity),X_87) = least_upper_bound(X_87,multiply(X,multiply(Y,X_87))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(multiply(X,Y),identity),X_87),least_upper_bound(X_87,multiply(multiply(X,Y),X_87))) )],[refute_0_1516,refute_0_1519]) ).
cnf(refute_0_1521,plain,
multiply(least_upper_bound(multiply(X,Y),identity),X_87) = multiply(least_upper_bound(identity,multiply(X,Y)),X_87),
inference(subst,[],[refute_0_972:[bind(X_15,$fot(X_87)),bind(X_88,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_1522,plain,
( multiply(least_upper_bound(multiply(X,Y),identity),X_87) != multiply(least_upper_bound(identity,multiply(X,Y)),X_87)
| multiply(least_upper_bound(multiply(X,Y),identity),X_87) != least_upper_bound(X_87,multiply(X,multiply(Y,X_87)))
| multiply(least_upper_bound(identity,multiply(X,Y)),X_87) = least_upper_bound(X_87,multiply(X,multiply(Y,X_87))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(multiply(X,Y),identity),X_87),least_upper_bound(X_87,multiply(X,multiply(Y,X_87)))) ),[0],$fot(multiply(least_upper_bound(identity,multiply(X,Y)),X_87))]]) ).
cnf(refute_0_1523,plain,
( multiply(least_upper_bound(multiply(X,Y),identity),X_87) != least_upper_bound(X_87,multiply(X,multiply(Y,X_87)))
| multiply(least_upper_bound(identity,multiply(X,Y)),X_87) = least_upper_bound(X_87,multiply(X,multiply(Y,X_87))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(multiply(X,Y),identity),X_87),multiply(least_upper_bound(identity,multiply(X,Y)),X_87)) )],[refute_0_1521,refute_0_1522]) ).
cnf(refute_0_1524,plain,
multiply(least_upper_bound(identity,multiply(X,Y)),X_87) = least_upper_bound(X_87,multiply(X,multiply(Y,X_87))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(multiply(X,Y),identity),X_87),least_upper_bound(X_87,multiply(X,multiply(Y,X_87)))) )],[refute_0_1520,refute_0_1523]) ).
cnf(refute_0_1525,plain,
( multiply(least_upper_bound(identity,multiply(X,Y)),X_87) != least_upper_bound(X_87,multiply(X,multiply(Y,X_87)))
| least_upper_bound(X_87,multiply(X,multiply(Y,X_87))) = multiply(least_upper_bound(identity,multiply(X,Y)),X_87) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(least_upper_bound(identity,multiply(X,Y)),X_87))),bind(Y0,$fot(least_upper_bound(X_87,multiply(X,multiply(Y,X_87)))))]]) ).
cnf(refute_0_1526,plain,
least_upper_bound(X_87,multiply(X,multiply(Y,X_87))) = multiply(least_upper_bound(identity,multiply(X,Y)),X_87),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X,Y)),X_87),least_upper_bound(X_87,multiply(X,multiply(Y,X_87)))) )],[refute_0_1524,refute_0_1525]) ).
cnf(refute_0_1527,plain,
least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26))) = multiply(least_upper_bound(identity,multiply(X_85,X_25)),X_26),
inference(subst,[],[refute_0_1526:[bind(X,$fot(X_85)),bind(Y,$fot(X_25)),bind(X_87,$fot(X_26))]]) ).
cnf(refute_0_1528,plain,
( multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) != least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26)))
| least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26))) != multiply(least_upper_bound(identity,multiply(X_85,X_25)),X_26)
| multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) = multiply(least_upper_bound(identity,multiply(X_85,X_25)),X_26) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)),multiply(least_upper_bound(identity,multiply(X_85,X_25)),X_26)) ),[0],$fot(least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26))))]]) ).
cnf(refute_0_1529,plain,
( multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) != least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26)))
| multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) = multiply(least_upper_bound(identity,multiply(X_85,X_25)),X_26) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26))),multiply(least_upper_bound(identity,multiply(X_85,X_25)),X_26)) )],[refute_0_1527,refute_0_1528]) ).
cnf(refute_0_1530,plain,
multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)) = multiply(least_upper_bound(identity,multiply(X_85,X_25)),X_26),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_85,inverse(X_25)),multiply(X_25,X_26)),least_upper_bound(X_26,multiply(X_85,multiply(X_25,X_26)))) )],[refute_0_1515,refute_0_1529]) ).
cnf(refute_0_1531,plain,
multiply(least_upper_bound(X_277,inverse(inverse(X_276))),multiply(inverse(X_276),X_276)) = multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276),
inference(subst,[],[refute_0_1530:[bind(X_25,$fot(inverse(X_276))),bind(X_26,$fot(X_276)),bind(X_85,$fot(X_277))]]) ).
cnf(refute_0_1532,plain,
multiply(inverse(X_276),X_276) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_276))]]) ).
cnf(refute_0_1533,plain,
( multiply(inverse(X_276),X_276) != identity
| multiply(least_upper_bound(X_277,inverse(inverse(X_276))),multiply(inverse(X_276),X_276)) != multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276)
| multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity) = multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_277,inverse(inverse(X_276))),multiply(inverse(X_276),X_276)),multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276)) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_1534,plain,
( multiply(least_upper_bound(X_277,inverse(inverse(X_276))),multiply(inverse(X_276),X_276)) != multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276)
| multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity) = multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_276),X_276),identity) )],[refute_0_1532,refute_0_1533]) ).
cnf(refute_0_1535,plain,
multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity) = multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_277,inverse(inverse(X_276))),multiply(inverse(X_276),X_276)),multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276)) )],[refute_0_1531,refute_0_1534]) ).
cnf(refute_0_1536,plain,
inverse(inverse(X_276)) = X_276,
inference(subst,[],[refute_0_737:[bind(X_30,$fot(X_276))]]) ).
cnf(refute_0_1537,plain,
least_upper_bound(X_277,inverse(inverse(X_276))) = least_upper_bound(X_277,inverse(inverse(X_276))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_277,inverse(inverse(X_276))))]]) ).
cnf(refute_0_1538,plain,
( inverse(inverse(X_276)) != X_276
| least_upper_bound(X_277,inverse(inverse(X_276))) != least_upper_bound(X_277,inverse(inverse(X_276)))
| least_upper_bound(X_277,inverse(inverse(X_276))) = least_upper_bound(X_277,X_276) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_277,inverse(inverse(X_276))),least_upper_bound(X_277,inverse(inverse(X_276)))) ),[1,1],$fot(X_276)]]) ).
cnf(refute_0_1539,plain,
( inverse(inverse(X_276)) != X_276
| least_upper_bound(X_277,inverse(inverse(X_276))) = least_upper_bound(X_277,X_276) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_277,inverse(inverse(X_276))),least_upper_bound(X_277,inverse(inverse(X_276)))) )],[refute_0_1537,refute_0_1538]) ).
cnf(refute_0_1540,plain,
least_upper_bound(X_277,inverse(inverse(X_276))) = least_upper_bound(X_277,X_276),
inference(resolve,[$cnf( $equal(inverse(inverse(X_276)),X_276) )],[refute_0_1536,refute_0_1539]) ).
cnf(refute_0_1541,plain,
multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity) = least_upper_bound(X_277,inverse(inverse(X_276))),
inference(subst,[],[refute_0_62:[bind(X_28,$fot(least_upper_bound(X_277,inverse(inverse(X_276)))))]]) ).
cnf(refute_0_1542,plain,
( multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity) != least_upper_bound(X_277,inverse(inverse(X_276)))
| least_upper_bound(X_277,inverse(inverse(X_276))) != least_upper_bound(X_277,X_276)
| multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity) = least_upper_bound(X_277,X_276) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity))),bind(Y0,$fot(least_upper_bound(X_277,inverse(inverse(X_276))))),bind(Z0,$fot(least_upper_bound(X_277,X_276)))]]) ).
cnf(refute_0_1543,plain,
( least_upper_bound(X_277,inverse(inverse(X_276))) != least_upper_bound(X_277,X_276)
| multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity) = least_upper_bound(X_277,X_276) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity),least_upper_bound(X_277,inverse(inverse(X_276)))) )],[refute_0_1541,refute_0_1542]) ).
cnf(refute_0_1544,plain,
multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity) = least_upper_bound(X_277,X_276),
inference(resolve,[$cnf( $equal(least_upper_bound(X_277,inverse(inverse(X_276))),least_upper_bound(X_277,X_276)) )],[refute_0_1540,refute_0_1543]) ).
cnf(refute_0_1545,plain,
( multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity) != multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276)
| multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity) != least_upper_bound(X_277,X_276)
| least_upper_bound(X_277,X_276) = multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity),multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276)) ),[0],$fot(least_upper_bound(X_277,X_276))]]) ).
cnf(refute_0_1546,plain,
( multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity) != multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276)
| least_upper_bound(X_277,X_276) = multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity),least_upper_bound(X_277,X_276)) )],[refute_0_1544,refute_0_1545]) ).
cnf(refute_0_1547,plain,
least_upper_bound(X_277,X_276) = multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_277,inverse(inverse(X_276))),identity),multiply(least_upper_bound(identity,multiply(X_277,inverse(X_276))),X_276)) )],[refute_0_1535,refute_0_1546]) ).
cnf(refute_0_1548,plain,
least_upper_bound(X_277,X_409) = multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409),
inference(subst,[],[refute_0_1547:[bind(X_276,$fot(X_409))]]) ).
cnf(refute_0_1549,plain,
( least_upper_bound(X_277,X_409) != multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409)
| multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409) = least_upper_bound(X_277,X_409) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_277,X_409))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409)))]]) ).
cnf(refute_0_1550,plain,
multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409) = least_upper_bound(X_277,X_409),
inference(resolve,[$cnf( $equal(least_upper_bound(X_277,X_409),multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409)) )],[refute_0_1548,refute_0_1549]) ).
cnf(refute_0_1551,plain,
( multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409) != least_upper_bound(X_277,X_409)
| multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) != least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409))
| multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) = least_upper_bound(identity,least_upper_bound(X_277,X_409)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409),least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409))) ),[1,1],$fot(least_upper_bound(X_277,X_409))]]) ).
cnf(refute_0_1552,plain,
( multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) != least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409))
| multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) = least_upper_bound(identity,least_upper_bound(X_277,X_409)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409),least_upper_bound(X_277,X_409)) )],[refute_0_1550,refute_0_1551]) ).
cnf(refute_0_1553,plain,
multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) = least_upper_bound(identity,least_upper_bound(X_277,X_409)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409),least_upper_bound(identity,multiply(least_upper_bound(identity,multiply(X_277,inverse(X_409))),X_409))) )],[refute_0_1507,refute_0_1552]) ).
cnf(refute_0_1554,plain,
multiply(inverse(X_409),X_409) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_409))]]) ).
cnf(refute_0_1555,plain,
least_upper_bound(X_277,multiply(inverse(X_409),X_409)) = least_upper_bound(X_277,multiply(inverse(X_409),X_409)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_277,multiply(inverse(X_409),X_409)))]]) ).
cnf(refute_0_1556,plain,
( multiply(inverse(X_409),X_409) != identity
| least_upper_bound(X_277,multiply(inverse(X_409),X_409)) != least_upper_bound(X_277,multiply(inverse(X_409),X_409))
| least_upper_bound(X_277,multiply(inverse(X_409),X_409)) = least_upper_bound(X_277,identity) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_277,multiply(inverse(X_409),X_409)),least_upper_bound(X_277,multiply(inverse(X_409),X_409))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1557,plain,
( multiply(inverse(X_409),X_409) != identity
| least_upper_bound(X_277,multiply(inverse(X_409),X_409)) = least_upper_bound(X_277,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_277,multiply(inverse(X_409),X_409)),least_upper_bound(X_277,multiply(inverse(X_409),X_409))) )],[refute_0_1555,refute_0_1556]) ).
cnf(refute_0_1558,plain,
least_upper_bound(X_277,multiply(inverse(X_409),X_409)) = least_upper_bound(X_277,identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_409),X_409),identity) )],[refute_0_1554,refute_0_1557]) ).
cnf(refute_0_1559,plain,
least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))) = least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))))]]) ).
cnf(refute_0_1560,plain,
( least_upper_bound(X_277,multiply(inverse(X_409),X_409)) != least_upper_bound(X_277,identity)
| least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))) != least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409)))
| least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))) = least_upper_bound(X_409,least_upper_bound(X_277,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))),least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409)))) ),[1,1],$fot(least_upper_bound(X_277,identity))]]) ).
cnf(refute_0_1561,plain,
( least_upper_bound(X_277,multiply(inverse(X_409),X_409)) != least_upper_bound(X_277,identity)
| least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))) = least_upper_bound(X_409,least_upper_bound(X_277,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))),least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409)))) )],[refute_0_1559,refute_0_1560]) ).
cnf(refute_0_1562,plain,
least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))) = least_upper_bound(X_409,least_upper_bound(X_277,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_277,multiply(inverse(X_409),X_409)),least_upper_bound(X_277,identity)) )],[refute_0_1558,refute_0_1561]) ).
cnf(refute_0_1563,plain,
multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X) = least_upper_bound(multiply(Y,X),multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X)),
inference(subst,[],[monotony_lub2:[bind(Z,$fot(least_upper_bound(identity,multiply(X_279,inverse(X)))))]]) ).
cnf(refute_0_1564,plain,
least_upper_bound(X_279,X) = multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X),
inference(subst,[],[refute_0_1547:[bind(X_276,$fot(X)),bind(X_277,$fot(X_279))]]) ).
cnf(refute_0_1565,plain,
( least_upper_bound(X_279,X) != multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X)
| multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X) = least_upper_bound(X_279,X) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_279,X))),bind(Y0,$fot(multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X)))]]) ).
cnf(refute_0_1566,plain,
multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X) = least_upper_bound(X_279,X),
inference(resolve,[$cnf( $equal(least_upper_bound(X_279,X),multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X)) )],[refute_0_1564,refute_0_1565]) ).
cnf(refute_0_1567,plain,
( multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X))
| multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X) != least_upper_bound(X_279,X)
| multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X) = least_upper_bound(multiply(Y,X),least_upper_bound(X_279,X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X))) ),[1,1],$fot(least_upper_bound(X_279,X))]]) ).
cnf(refute_0_1568,plain,
( multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X) != least_upper_bound(multiply(Y,X),multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X))
| multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X) = least_upper_bound(multiply(Y,X),least_upper_bound(X_279,X)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X),least_upper_bound(X_279,X)) )],[refute_0_1566,refute_0_1567]) ).
cnf(refute_0_1569,plain,
multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X) = least_upper_bound(multiply(Y,X),least_upper_bound(X_279,X)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X),least_upper_bound(multiply(Y,X),multiply(least_upper_bound(identity,multiply(X_279,inverse(X))),X))) )],[refute_0_1563,refute_0_1568]) ).
cnf(refute_0_1570,plain,
least_upper_bound(least_upper_bound(X_222,X_220),Y) = least_upper_bound(Y,least_upper_bound(X_222,X_220)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(least_upper_bound(X_222,X_220)))]]) ).
cnf(refute_0_1571,plain,
least_upper_bound(least_upper_bound(X_126,X_127),Y) = least_upper_bound(Y,least_upper_bound(X_126,X_127)),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(least_upper_bound(X_126,X_127)))]]) ).
cnf(refute_0_1572,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) = least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_13,X_39)),X_41),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(least_upper_bound(X_13,X_39))),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_1573,plain,
least_upper_bound(X_39,least_upper_bound(X_13,X_39)) = least_upper_bound(X_39,X_13),
inference(subst,[],[refute_0_387:[bind(X_9,$fot(X_39))]]) ).
cnf(refute_0_1574,plain,
( least_upper_bound(X_39,least_upper_bound(X_13,X_39)) != least_upper_bound(X_39,X_13)
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_13,X_39)),X_41)
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) = least_upper_bound(least_upper_bound(X_39,X_13),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_13,X_39)),X_41)) ),[1,0],$fot(least_upper_bound(X_39,X_13))]]) ).
cnf(refute_0_1575,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_13,X_39)),X_41)
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) = least_upper_bound(least_upper_bound(X_39,X_13),X_41) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_13,X_39)),least_upper_bound(X_39,X_13)) )],[refute_0_1573,refute_0_1574]) ).
cnf(refute_0_1576,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) = least_upper_bound(least_upper_bound(X_39,X_13),X_41),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_13,X_39)),X_41)) )],[refute_0_1572,refute_0_1575]) ).
cnf(refute_0_1577,plain,
least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_39,X_41))) = least_upper_bound(X_13,least_upper_bound(X_39,X_41)),
inference(subst,[],[refute_0_512:[bind(X_13,$fot(X_41)),bind(X_39,$fot(X_13)),bind(X_40,$fot(X_39))]]) ).
cnf(refute_0_1578,plain,
least_upper_bound(least_upper_bound(X_13,X_39),X_41) = least_upper_bound(X_13,least_upper_bound(X_39,X_41)),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_13)),bind(Y,$fot(X_39)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_1579,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) = least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)))]]) ).
cnf(refute_0_1580,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) != least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41))
| least_upper_bound(least_upper_bound(X_13,X_39),X_41) != least_upper_bound(X_13,least_upper_bound(X_39,X_41))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) = least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_39,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)),least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41))) ),[1,1],$fot(least_upper_bound(X_13,least_upper_bound(X_39,X_41)))]]) ).
cnf(refute_0_1581,plain,
( least_upper_bound(least_upper_bound(X_13,X_39),X_41) != least_upper_bound(X_13,least_upper_bound(X_39,X_41))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) = least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_39,X_41))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)),least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41))) )],[refute_0_1579,refute_0_1580]) ).
cnf(refute_0_1582,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) = least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_39,X_41))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,X_39),X_41),least_upper_bound(X_13,least_upper_bound(X_39,X_41))) )],[refute_0_1578,refute_0_1581]) ).
cnf(refute_0_1583,plain,
( least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_39,X_41))) != least_upper_bound(X_13,least_upper_bound(X_39,X_41))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) != least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_39,X_41)))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) = least_upper_bound(X_13,least_upper_bound(X_39,X_41)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)))),bind(Y0,$fot(least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_39,X_41))))),bind(Z0,$fot(least_upper_bound(X_13,least_upper_bound(X_39,X_41))))]]) ).
cnf(refute_0_1584,plain,
( least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_39,X_41))) != least_upper_bound(X_13,least_upper_bound(X_39,X_41))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) = least_upper_bound(X_13,least_upper_bound(X_39,X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)),least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_39,X_41)))) )],[refute_0_1582,refute_0_1583]) ).
cnf(refute_0_1585,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) = least_upper_bound(X_13,least_upper_bound(X_39,X_41)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_39,X_41))),least_upper_bound(X_13,least_upper_bound(X_39,X_41))) )],[refute_0_1577,refute_0_1584]) ).
cnf(refute_0_1586,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) != least_upper_bound(X_13,least_upper_bound(X_39,X_41))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,X_13),X_41)
| least_upper_bound(X_13,least_upper_bound(X_39,X_41)) = least_upper_bound(least_upper_bound(X_39,X_13),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,X_13),X_41)) ),[0],$fot(least_upper_bound(X_13,least_upper_bound(X_39,X_41)))]]) ).
cnf(refute_0_1587,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,X_13),X_41)
| least_upper_bound(X_13,least_upper_bound(X_39,X_41)) = least_upper_bound(least_upper_bound(X_39,X_13),X_41) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)),least_upper_bound(X_13,least_upper_bound(X_39,X_41))) )],[refute_0_1585,refute_0_1586]) ).
cnf(refute_0_1588,plain,
least_upper_bound(least_upper_bound(X_39,X_13),X_41) = least_upper_bound(X_39,least_upper_bound(X_13,X_41)),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_39)),bind(Y,$fot(X_13)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_1589,plain,
( least_upper_bound(X_13,least_upper_bound(X_39,X_41)) != least_upper_bound(least_upper_bound(X_39,X_13),X_41)
| least_upper_bound(least_upper_bound(X_39,X_13),X_41) != least_upper_bound(X_39,least_upper_bound(X_13,X_41))
| least_upper_bound(X_13,least_upper_bound(X_39,X_41)) = least_upper_bound(X_39,least_upper_bound(X_13,X_41)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_13,least_upper_bound(X_39,X_41)),least_upper_bound(X_39,least_upper_bound(X_13,X_41))) ),[0],$fot(least_upper_bound(least_upper_bound(X_39,X_13),X_41))]]) ).
cnf(refute_0_1590,plain,
( least_upper_bound(X_13,least_upper_bound(X_39,X_41)) != least_upper_bound(least_upper_bound(X_39,X_13),X_41)
| least_upper_bound(X_13,least_upper_bound(X_39,X_41)) = least_upper_bound(X_39,least_upper_bound(X_13,X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_13),X_41),least_upper_bound(X_39,least_upper_bound(X_13,X_41))) )],[refute_0_1588,refute_0_1589]) ).
cnf(refute_0_1591,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)) != least_upper_bound(least_upper_bound(X_39,X_13),X_41)
| least_upper_bound(X_13,least_upper_bound(X_39,X_41)) = least_upper_bound(X_39,least_upper_bound(X_13,X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(X_39,X_41)),least_upper_bound(least_upper_bound(X_39,X_13),X_41)) )],[refute_0_1587,refute_0_1590]) ).
cnf(refute_0_1592,plain,
least_upper_bound(X_13,least_upper_bound(X_39,X_41)) = least_upper_bound(X_39,least_upper_bound(X_13,X_41)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_13,X_39),X_41)),least_upper_bound(least_upper_bound(X_39,X_13),X_41)) )],[refute_0_1576,refute_0_1591]) ).
cnf(refute_0_1593,plain,
least_upper_bound(Y,least_upper_bound(X_126,X_127)) = least_upper_bound(X_126,least_upper_bound(Y,X_127)),
inference(subst,[],[refute_0_1592:[bind(X_13,$fot(Y)),bind(X_39,$fot(X_126)),bind(X_41,$fot(X_127))]]) ).
cnf(refute_0_1594,plain,
( least_upper_bound(Y,least_upper_bound(X_126,X_127)) != least_upper_bound(X_126,least_upper_bound(Y,X_127))
| least_upper_bound(least_upper_bound(X_126,X_127),Y) != least_upper_bound(Y,least_upper_bound(X_126,X_127))
| least_upper_bound(least_upper_bound(X_126,X_127),Y) = least_upper_bound(X_126,least_upper_bound(Y,X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_126,X_127),Y),least_upper_bound(Y,least_upper_bound(X_126,X_127))) ),[1],$fot(least_upper_bound(X_126,least_upper_bound(Y,X_127)))]]) ).
cnf(refute_0_1595,plain,
( least_upper_bound(least_upper_bound(X_126,X_127),Y) != least_upper_bound(Y,least_upper_bound(X_126,X_127))
| least_upper_bound(least_upper_bound(X_126,X_127),Y) = least_upper_bound(X_126,least_upper_bound(Y,X_127)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_126,X_127)),least_upper_bound(X_126,least_upper_bound(Y,X_127))) )],[refute_0_1593,refute_0_1594]) ).
cnf(refute_0_1596,plain,
least_upper_bound(least_upper_bound(X_126,X_127),Y) = least_upper_bound(X_126,least_upper_bound(Y,X_127)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_126,X_127),Y),least_upper_bound(Y,least_upper_bound(X_126,X_127))) )],[refute_0_1571,refute_0_1595]) ).
cnf(refute_0_1597,plain,
least_upper_bound(least_upper_bound(X_126,X_127),Y) = least_upper_bound(X_126,least_upper_bound(X_127,Y)),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_126)),bind(Y,$fot(X_127)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1598,plain,
( least_upper_bound(least_upper_bound(X_126,X_127),Y) != least_upper_bound(X_126,least_upper_bound(Y,X_127))
| least_upper_bound(least_upper_bound(X_126,X_127),Y) != least_upper_bound(X_126,least_upper_bound(X_127,Y))
| least_upper_bound(X_126,least_upper_bound(X_127,Y)) = least_upper_bound(X_126,least_upper_bound(Y,X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_126,X_127),Y),least_upper_bound(X_126,least_upper_bound(Y,X_127))) ),[0],$fot(least_upper_bound(X_126,least_upper_bound(X_127,Y)))]]) ).
cnf(refute_0_1599,plain,
( least_upper_bound(least_upper_bound(X_126,X_127),Y) != least_upper_bound(X_126,least_upper_bound(Y,X_127))
| least_upper_bound(X_126,least_upper_bound(X_127,Y)) = least_upper_bound(X_126,least_upper_bound(Y,X_127)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_126,X_127),Y),least_upper_bound(X_126,least_upper_bound(X_127,Y))) )],[refute_0_1597,refute_0_1598]) ).
cnf(refute_0_1600,plain,
least_upper_bound(X_126,least_upper_bound(X_127,Y)) = least_upper_bound(X_126,least_upper_bound(Y,X_127)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_126,X_127),Y),least_upper_bound(X_126,least_upper_bound(Y,X_127))) )],[refute_0_1596,refute_0_1599]) ).
cnf(refute_0_1601,plain,
least_upper_bound(Y,least_upper_bound(X_222,X_220)) = least_upper_bound(Y,least_upper_bound(X_220,X_222)),
inference(subst,[],[refute_0_1600:[bind(Y,$fot(X_220)),bind(X_126,$fot(Y)),bind(X_127,$fot(X_222))]]) ).
cnf(refute_0_1602,plain,
( least_upper_bound(Y,least_upper_bound(X_222,X_220)) != least_upper_bound(Y,least_upper_bound(X_220,X_222))
| least_upper_bound(least_upper_bound(X_222,X_220),Y) != least_upper_bound(Y,least_upper_bound(X_222,X_220))
| least_upper_bound(least_upper_bound(X_222,X_220),Y) = least_upper_bound(Y,least_upper_bound(X_220,X_222)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_222,X_220),Y),least_upper_bound(Y,least_upper_bound(X_222,X_220))) ),[1],$fot(least_upper_bound(Y,least_upper_bound(X_220,X_222)))]]) ).
cnf(refute_0_1603,plain,
( least_upper_bound(least_upper_bound(X_222,X_220),Y) != least_upper_bound(Y,least_upper_bound(X_222,X_220))
| least_upper_bound(least_upper_bound(X_222,X_220),Y) = least_upper_bound(Y,least_upper_bound(X_220,X_222)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_222,X_220)),least_upper_bound(Y,least_upper_bound(X_220,X_222))) )],[refute_0_1601,refute_0_1602]) ).
cnf(refute_0_1604,plain,
least_upper_bound(least_upper_bound(X_222,X_220),Y) = least_upper_bound(Y,least_upper_bound(X_220,X_222)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_222,X_220),Y),least_upper_bound(Y,least_upper_bound(X_222,X_220))) )],[refute_0_1570,refute_0_1603]) ).
cnf(refute_0_1605,plain,
least_upper_bound(least_upper_bound(X_222,X_220),Y) = least_upper_bound(X_222,least_upper_bound(X_220,Y)),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_222)),bind(Y,$fot(X_220)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_1606,plain,
( least_upper_bound(least_upper_bound(X_222,X_220),Y) != least_upper_bound(Y,least_upper_bound(X_220,X_222))
| least_upper_bound(least_upper_bound(X_222,X_220),Y) != least_upper_bound(X_222,least_upper_bound(X_220,Y))
| least_upper_bound(X_222,least_upper_bound(X_220,Y)) = least_upper_bound(Y,least_upper_bound(X_220,X_222)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_222,X_220),Y),least_upper_bound(Y,least_upper_bound(X_220,X_222))) ),[0],$fot(least_upper_bound(X_222,least_upper_bound(X_220,Y)))]]) ).
cnf(refute_0_1607,plain,
( least_upper_bound(least_upper_bound(X_222,X_220),Y) != least_upper_bound(Y,least_upper_bound(X_220,X_222))
| least_upper_bound(X_222,least_upper_bound(X_220,Y)) = least_upper_bound(Y,least_upper_bound(X_220,X_222)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_222,X_220),Y),least_upper_bound(X_222,least_upper_bound(X_220,Y))) )],[refute_0_1605,refute_0_1606]) ).
cnf(refute_0_1608,plain,
least_upper_bound(X_222,least_upper_bound(X_220,Y)) = least_upper_bound(Y,least_upper_bound(X_220,X_222)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_222,X_220),Y),least_upper_bound(Y,least_upper_bound(X_220,X_222))) )],[refute_0_1604,refute_0_1607]) ).
cnf(refute_0_1609,plain,
( least_upper_bound(X_222,least_upper_bound(X_220,Y)) != least_upper_bound(Y,least_upper_bound(X_220,X_222))
| least_upper_bound(Y,least_upper_bound(X_220,X_222)) = least_upper_bound(X_222,least_upper_bound(X_220,Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_222,least_upper_bound(X_220,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_220,X_222))))]]) ).
cnf(refute_0_1610,plain,
least_upper_bound(Y,least_upper_bound(X_220,X_222)) = least_upper_bound(X_222,least_upper_bound(X_220,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_222,least_upper_bound(X_220,Y)),least_upper_bound(Y,least_upper_bound(X_220,X_222))) )],[refute_0_1608,refute_0_1609]) ).
cnf(refute_0_1611,plain,
least_upper_bound(multiply(Y,X),least_upper_bound(X_279,X)) = least_upper_bound(X,least_upper_bound(X_279,multiply(Y,X))),
inference(subst,[],[refute_0_1610:[bind(Y,$fot(multiply(Y,X))),bind(X_220,$fot(X_279)),bind(X_222,$fot(X))]]) ).
cnf(refute_0_1612,plain,
( multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X) != least_upper_bound(multiply(Y,X),least_upper_bound(X_279,X))
| least_upper_bound(multiply(Y,X),least_upper_bound(X_279,X)) != least_upper_bound(X,least_upper_bound(X_279,multiply(Y,X)))
| multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X) = least_upper_bound(X,least_upper_bound(X_279,multiply(Y,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X),least_upper_bound(X,least_upper_bound(X_279,multiply(Y,X)))) ),[0],$fot(least_upper_bound(multiply(Y,X),least_upper_bound(X_279,X)))]]) ).
cnf(refute_0_1613,plain,
( multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X) != least_upper_bound(multiply(Y,X),least_upper_bound(X_279,X))
| multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X) = least_upper_bound(X,least_upper_bound(X_279,multiply(Y,X))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,X),least_upper_bound(X_279,X)),least_upper_bound(X,least_upper_bound(X_279,multiply(Y,X)))) )],[refute_0_1611,refute_0_1612]) ).
cnf(refute_0_1614,plain,
multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X) = least_upper_bound(X,least_upper_bound(X_279,multiply(Y,X))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(identity,multiply(X_279,inverse(X)))),X),least_upper_bound(multiply(Y,X),least_upper_bound(X_279,X))) )],[refute_0_1569,refute_0_1613]) ).
cnf(refute_0_1615,plain,
multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) = least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))),
inference(subst,[],[refute_0_1614:[bind(X,$fot(X_409)),bind(Y,$fot(inverse(X_409))),bind(X_279,$fot(X_277))]]) ).
cnf(refute_0_1616,plain,
( multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) != least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409)))
| least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))) != least_upper_bound(X_409,least_upper_bound(X_277,identity))
| multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) = least_upper_bound(X_409,least_upper_bound(X_277,identity)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409))),bind(Y0,$fot(least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))))),bind(Z0,$fot(least_upper_bound(X_409,least_upper_bound(X_277,identity))))]]) ).
cnf(refute_0_1617,plain,
( least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))) != least_upper_bound(X_409,least_upper_bound(X_277,identity))
| multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) = least_upper_bound(X_409,least_upper_bound(X_277,identity)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409),least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409)))) )],[refute_0_1615,refute_0_1616]) ).
cnf(refute_0_1618,plain,
multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) = least_upper_bound(X_409,least_upper_bound(X_277,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_409,least_upper_bound(X_277,multiply(inverse(X_409),X_409))),least_upper_bound(X_409,least_upper_bound(X_277,identity))) )],[refute_0_1562,refute_0_1617]) ).
cnf(refute_0_1619,plain,
( multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) != least_upper_bound(X_409,least_upper_bound(X_277,identity))
| multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) != least_upper_bound(identity,least_upper_bound(X_277,X_409))
| least_upper_bound(X_409,least_upper_bound(X_277,identity)) = least_upper_bound(identity,least_upper_bound(X_277,X_409)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409),least_upper_bound(identity,least_upper_bound(X_277,X_409))) ),[0],$fot(least_upper_bound(X_409,least_upper_bound(X_277,identity)))]]) ).
cnf(refute_0_1620,plain,
( multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409) != least_upper_bound(identity,least_upper_bound(X_277,X_409))
| least_upper_bound(X_409,least_upper_bound(X_277,identity)) = least_upper_bound(identity,least_upper_bound(X_277,X_409)) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409),least_upper_bound(X_409,least_upper_bound(X_277,identity))) )],[refute_0_1618,refute_0_1619]) ).
cnf(refute_0_1621,plain,
least_upper_bound(X_409,least_upper_bound(X_277,identity)) = least_upper_bound(identity,least_upper_bound(X_277,X_409)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_409),least_upper_bound(identity,multiply(X_277,inverse(X_409)))),X_409),least_upper_bound(identity,least_upper_bound(X_277,X_409))) )],[refute_0_1553,refute_0_1620]) ).
cnf(refute_0_1622,plain,
least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)) = least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127))),
inference(subst,[],[refute_0_1621:[bind(X_277,$fot(X_411)),bind(X_409,$fot(least_upper_bound(Y,X_127)))]]) ).
cnf(refute_0_1623,plain,
least_upper_bound(X_411,least_upper_bound(X_127,Y)) = least_upper_bound(X_411,least_upper_bound(Y,X_127)),
inference(subst,[],[refute_0_1600:[bind(X_126,$fot(X_411))]]) ).
cnf(refute_0_1624,plain,
( least_upper_bound(X_411,least_upper_bound(X_127,Y)) != least_upper_bound(X_411,least_upper_bound(Y,X_127))
| least_upper_bound(X_411,least_upper_bound(Y,X_127)) = least_upper_bound(X_411,least_upper_bound(X_127,Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_411,least_upper_bound(X_127,Y)))),bind(Y0,$fot(least_upper_bound(X_411,least_upper_bound(Y,X_127))))]]) ).
cnf(refute_0_1625,plain,
least_upper_bound(X_411,least_upper_bound(Y,X_127)) = least_upper_bound(X_411,least_upper_bound(X_127,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_411,least_upper_bound(X_127,Y)),least_upper_bound(X_411,least_upper_bound(Y,X_127))) )],[refute_0_1623,refute_0_1624]) ).
cnf(refute_0_1626,plain,
( least_upper_bound(X_411,least_upper_bound(Y,X_127)) != least_upper_bound(X_411,least_upper_bound(X_127,Y))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)) != least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127)))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)) = least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)),least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127)))) ),[1,1],$fot(least_upper_bound(X_411,least_upper_bound(X_127,Y)))]]) ).
cnf(refute_0_1627,plain,
( least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)) != least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127)))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)) = least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_411,least_upper_bound(Y,X_127)),least_upper_bound(X_411,least_upper_bound(X_127,Y))) )],[refute_0_1625,refute_0_1626]) ).
cnf(refute_0_1628,plain,
least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)) = least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)),least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127)))) )],[refute_0_1622,refute_0_1627]) ).
cnf(refute_0_1629,plain,
( least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)) != least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127)))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)) != least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y)))
| least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127))) = least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)),least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127))))]]) ).
cnf(refute_0_1630,plain,
( least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)) != least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y)))
| least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127))) = least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)),least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127)))) )],[refute_0_1622,refute_0_1629]) ).
cnf(refute_0_1631,plain,
least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127))) = least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_411,identity)),least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y)))) )],[refute_0_1628,refute_0_1630]) ).
cnf(refute_0_1632,plain,
( least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127))) != least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y)))
| least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y))) = least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y)))))]]) ).
cnf(refute_0_1633,plain,
least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y))) = least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127))),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(Y,X_127))),least_upper_bound(identity,least_upper_bound(X_411,least_upper_bound(X_127,Y)))) )],[refute_0_1631,refute_0_1632]) ).
cnf(refute_0_1634,plain,
least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))) = least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))),
inference(subst,[],[refute_0_1633:[bind(Y,$fot(greatest_lower_bound(identity,X_442))),bind(X_127,$fot(greatest_lower_bound(identity,inverse(X_442)))),bind(X_411,$fot(X_41))]]) ).
cnf(refute_0_1635,plain,
( least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))) != least_upper_bound(X_41,identity)
| least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))) != least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442)))))
| least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))) = least_upper_bound(X_41,identity) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))))),bind(Z0,$fot(least_upper_bound(X_41,identity)))]]) ).
cnf(refute_0_1636,plain,
( least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))) != least_upper_bound(X_41,identity)
| least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))) = least_upper_bound(X_41,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))),least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442)))))) )],[refute_0_1634,refute_0_1635]) ).
cnf(refute_0_1637,plain,
least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))) = least_upper_bound(X_41,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,X_442),greatest_lower_bound(identity,inverse(X_442))))),least_upper_bound(X_41,identity)) )],[refute_0_1501,refute_0_1636]) ).
cnf(refute_0_1638,plain,
least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(identity,least_upper_bound(X_411,X_412)))) = least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity)),
inference(subst,[],[refute_0_582:[bind(X_40,$fot(identity)),bind(X_9,$fot(least_upper_bound(X_411,X_412)))]]) ).
cnf(refute_0_1639,plain,
least_upper_bound(X_412,least_upper_bound(X_411,identity)) = least_upper_bound(identity,least_upper_bound(X_411,X_412)),
inference(subst,[],[refute_0_1621:[bind(X_277,$fot(X_411)),bind(X_409,$fot(X_412))]]) ).
cnf(refute_0_1640,plain,
( least_upper_bound(X_412,least_upper_bound(X_411,identity)) != least_upper_bound(identity,least_upper_bound(X_411,X_412))
| least_upper_bound(identity,least_upper_bound(X_411,X_412)) = least_upper_bound(X_412,least_upper_bound(X_411,identity)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_412,least_upper_bound(X_411,identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_411,X_412))))]]) ).
cnf(refute_0_1641,plain,
least_upper_bound(identity,least_upper_bound(X_411,X_412)) = least_upper_bound(X_412,least_upper_bound(X_411,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_412,least_upper_bound(X_411,identity)),least_upper_bound(identity,least_upper_bound(X_411,X_412))) )],[refute_0_1639,refute_0_1640]) ).
cnf(refute_0_1642,plain,
( least_upper_bound(identity,least_upper_bound(X_411,X_412)) != least_upper_bound(X_412,least_upper_bound(X_411,identity))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(identity,least_upper_bound(X_411,X_412)))) != least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) = least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(identity,least_upper_bound(X_411,X_412)))),least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))) ),[0,1,1],$fot(least_upper_bound(X_412,least_upper_bound(X_411,identity)))]]) ).
cnf(refute_0_1643,plain,
( least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(identity,least_upper_bound(X_411,X_412)))) != least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) = least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_411,X_412)),least_upper_bound(X_412,least_upper_bound(X_411,identity))) )],[refute_0_1641,refute_0_1642]) ).
cnf(refute_0_1644,plain,
least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) = least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(identity,least_upper_bound(X_411,X_412)))),least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))) )],[refute_0_1638,refute_0_1643]) ).
cnf(refute_0_1645,plain,
least_upper_bound(X_412,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))),
inference(subst,[],[refute_0_416:[bind(X_14,$fot(least_upper_bound(X_411,least_upper_bound(identity,X_39)))),bind(X_15,$fot(X_412))]]) ).
cnf(refute_0_1646,plain,
least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))),
inference(subst,[],[refute_0_512:[bind(X_13,$fot(least_upper_bound(identity,X_39))),bind(X_39,$fot(X_412)),bind(X_40,$fot(X_411))]]) ).
cnf(refute_0_1647,plain,
least_upper_bound(least_upper_bound(X_411,identity),X_39) = least_upper_bound(X_411,least_upper_bound(identity,X_39)),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_411)),bind(Y,$fot(identity)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_1648,plain,
least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)) = least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)))]]) ).
cnf(refute_0_1649,plain,
( least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)) != least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))
| least_upper_bound(least_upper_bound(X_411,identity),X_39) != least_upper_bound(X_411,least_upper_bound(identity,X_39))
| least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)),least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) ),[1,1],$fot(least_upper_bound(X_411,least_upper_bound(identity,X_39)))]]) ).
cnf(refute_0_1650,plain,
( least_upper_bound(least_upper_bound(X_411,identity),X_39) != least_upper_bound(X_411,least_upper_bound(identity,X_39))
| least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)),least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) )],[refute_0_1648,refute_0_1649]) ).
cnf(refute_0_1651,plain,
least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_411,identity),X_39),least_upper_bound(X_411,least_upper_bound(identity,X_39))) )],[refute_0_1647,refute_0_1650]) ).
cnf(refute_0_1652,plain,
least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))))]]) ).
cnf(refute_0_1653,plain,
( least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) != least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)))
| least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))),least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)))) ),[1,1],$fot(least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))))]]) ).
cnf(refute_0_1654,plain,
( least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))),least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)))) )],[refute_0_1652,refute_0_1653]) ).
cnf(refute_0_1655,plain,
least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)),least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) )],[refute_0_1651,refute_0_1654]) ).
cnf(refute_0_1656,plain,
( least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) != least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))))
| least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))))),bind(Y0,$fot(least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))))),bind(Z0,$fot(least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))))]]) ).
cnf(refute_0_1657,plain,
( least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))),least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))))) )],[refute_0_1655,refute_0_1656]) ).
cnf(refute_0_1658,plain,
least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))),least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) )],[refute_0_1646,refute_0_1657]) ).
cnf(refute_0_1659,plain,
least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)) = least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_411)),bind(Y,$fot(X_412)),bind(Z,$fot(least_upper_bound(least_upper_bound(X_411,identity),X_39)))]]) ).
cnf(refute_0_1660,plain,
( least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)) != least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)))),bind(Y0,$fot(least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))))),bind(Z0,$fot(least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))))]]) ).
cnf(refute_0_1661,plain,
( least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)),least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39)))) )],[refute_0_1659,refute_0_1660]) ).
cnf(refute_0_1662,plain,
least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_411,least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,identity),X_39))),least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) )],[refute_0_1658,refute_0_1661]) ).
cnf(refute_0_1663,plain,
least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))),
introduced(tautology,[refl,[$fot(least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))))]]) ).
cnf(refute_0_1664,plain,
( least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))) != least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_412,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))),least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)))) ),[1,1],$fot(least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))))]]) ).
cnf(refute_0_1665,plain,
( least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_412,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))),least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)))) )],[refute_0_1663,refute_0_1664]) ).
cnf(refute_0_1666,plain,
least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_412,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)),least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) )],[refute_0_1662,refute_0_1665]) ).
cnf(refute_0_1667,plain,
( least_upper_bound(X_412,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))) != least_upper_bound(X_412,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))))
| least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))))),bind(Y0,$fot(least_upper_bound(X_412,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))))),bind(Z0,$fot(least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))))]]) ).
cnf(refute_0_1668,plain,
( least_upper_bound(X_412,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))),least_upper_bound(X_412,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))))) )],[refute_0_1666,refute_0_1667]) ).
cnf(refute_0_1669,plain,
least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_412,least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))),least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) )],[refute_0_1645,refute_0_1668]) ).
cnf(refute_0_1670,plain,
least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(Y,X_127)))) = least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322)),
inference(subst,[],[refute_0_582:[bind(X_39,$fot(X_321)),bind(X_40,$fot(X_322)),bind(X_9,$fot(least_upper_bound(Y,X_127)))]]) ).
cnf(refute_0_1671,plain,
least_upper_bound(X_322,least_upper_bound(X_127,Y)) = least_upper_bound(X_322,least_upper_bound(Y,X_127)),
inference(subst,[],[refute_0_1600:[bind(X_126,$fot(X_322))]]) ).
cnf(refute_0_1672,plain,
( least_upper_bound(X_322,least_upper_bound(X_127,Y)) != least_upper_bound(X_322,least_upper_bound(Y,X_127))
| least_upper_bound(X_322,least_upper_bound(Y,X_127)) = least_upper_bound(X_322,least_upper_bound(X_127,Y)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_322,least_upper_bound(X_127,Y)))),bind(Y0,$fot(least_upper_bound(X_322,least_upper_bound(Y,X_127))))]]) ).
cnf(refute_0_1673,plain,
least_upper_bound(X_322,least_upper_bound(Y,X_127)) = least_upper_bound(X_322,least_upper_bound(X_127,Y)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_322,least_upper_bound(X_127,Y)),least_upper_bound(X_322,least_upper_bound(Y,X_127))) )],[refute_0_1671,refute_0_1672]) ).
cnf(refute_0_1674,plain,
( least_upper_bound(X_322,least_upper_bound(Y,X_127)) != least_upper_bound(X_322,least_upper_bound(X_127,Y))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(Y,X_127)))) != least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) = least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(Y,X_127)))),least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))) ),[0,1,1],$fot(least_upper_bound(X_322,least_upper_bound(X_127,Y)))]]) ).
cnf(refute_0_1675,plain,
( least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(Y,X_127)))) != least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) = least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_322,least_upper_bound(Y,X_127)),least_upper_bound(X_322,least_upper_bound(X_127,Y))) )],[refute_0_1673,refute_0_1674]) ).
cnf(refute_0_1676,plain,
least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) = least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322)),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(Y,X_127)))),least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))) )],[refute_0_1670,refute_0_1675]) ).
cnf(refute_0_1677,plain,
least_upper_bound(X_13,least_upper_bound(X_39,least_upper_bound(X_321,least_upper_bound(X_322,X_13)))) = least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_321,least_upper_bound(X_322,X_13)))),
inference(subst,[],[refute_0_1592:[bind(X_41,$fot(least_upper_bound(X_321,least_upper_bound(X_322,X_13))))]]) ).
cnf(refute_0_1678,plain,
least_upper_bound(X_13,least_upper_bound(X_321,least_upper_bound(X_322,X_13))) = least_upper_bound(X_13,least_upper_bound(X_321,X_322)),
inference(subst,[],[refute_0_582:[bind(X_39,$fot(X_321)),bind(X_40,$fot(X_322)),bind(X_9,$fot(X_13))]]) ).
cnf(refute_0_1679,plain,
( least_upper_bound(X_13,least_upper_bound(X_321,least_upper_bound(X_322,X_13))) != least_upper_bound(X_13,least_upper_bound(X_321,X_322))
| least_upper_bound(X_13,least_upper_bound(X_39,least_upper_bound(X_321,least_upper_bound(X_322,X_13)))) != least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_321,least_upper_bound(X_322,X_13))))
| least_upper_bound(X_13,least_upper_bound(X_39,least_upper_bound(X_321,least_upper_bound(X_322,X_13)))) = least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_321,X_322))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(X_39,least_upper_bound(X_321,least_upper_bound(X_322,X_13)))),least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_321,least_upper_bound(X_322,X_13))))) ),[1,1],$fot(least_upper_bound(X_13,least_upper_bound(X_321,X_322)))]]) ).
cnf(refute_0_1680,plain,
( least_upper_bound(X_13,least_upper_bound(X_39,least_upper_bound(X_321,least_upper_bound(X_322,X_13)))) != least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_321,least_upper_bound(X_322,X_13))))
| least_upper_bound(X_13,least_upper_bound(X_39,least_upper_bound(X_321,least_upper_bound(X_322,X_13)))) = least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_321,X_322))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(X_321,least_upper_bound(X_322,X_13))),least_upper_bound(X_13,least_upper_bound(X_321,X_322))) )],[refute_0_1678,refute_0_1679]) ).
cnf(refute_0_1681,plain,
least_upper_bound(X_13,least_upper_bound(X_39,least_upper_bound(X_321,least_upper_bound(X_322,X_13)))) = least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_321,X_322))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_13,least_upper_bound(X_39,least_upper_bound(X_321,least_upper_bound(X_322,X_13)))),least_upper_bound(X_39,least_upper_bound(X_13,least_upper_bound(X_321,least_upper_bound(X_322,X_13))))) )],[refute_0_1677,refute_0_1680]) ).
cnf(refute_0_1682,plain,
least_upper_bound(Y,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) = least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))),
inference(subst,[],[refute_0_1681:[bind(X_13,$fot(Y)),bind(X_321,$fot(X_322)),bind(X_322,$fot(X_127)),bind(X_39,$fot(X_321))]]) ).
cnf(refute_0_1683,plain,
least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(greatest_lower_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,X_310))),X_309)) = least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309),
inference(subst,[],[refute_0_1478:[bind(X_39,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_310)))),bind(X_41,$fot(X_309)),bind(X_9,$fot(X_310))]]) ).
cnf(refute_0_1684,plain,
greatest_lower_bound(X_12,least_upper_bound(least_upper_bound(X_39,X_40),X_12)) = X_12,
inference(subst,[],[refute_0_136:[bind(X_13,$fot(least_upper_bound(X_39,X_40)))]]) ).
cnf(refute_0_1685,plain,
least_upper_bound(X_39,least_upper_bound(X_40,X_12)) = least_upper_bound(least_upper_bound(X_39,X_40),X_12),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_1686,plain,
( least_upper_bound(X_39,least_upper_bound(X_40,X_12)) != least_upper_bound(least_upper_bound(X_39,X_40),X_12)
| least_upper_bound(least_upper_bound(X_39,X_40),X_12) = least_upper_bound(X_39,least_upper_bound(X_40,X_12)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_12)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_39,X_40),X_12)))]]) ).
cnf(refute_0_1687,plain,
least_upper_bound(least_upper_bound(X_39,X_40),X_12) = least_upper_bound(X_39,least_upper_bound(X_40,X_12)),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(X_40,X_12)),least_upper_bound(least_upper_bound(X_39,X_40),X_12)) )],[refute_0_1685,refute_0_1686]) ).
cnf(refute_0_1688,plain,
( greatest_lower_bound(X_12,least_upper_bound(least_upper_bound(X_39,X_40),X_12)) != X_12
| least_upper_bound(least_upper_bound(X_39,X_40),X_12) != least_upper_bound(X_39,least_upper_bound(X_40,X_12))
| greatest_lower_bound(X_12,least_upper_bound(X_39,least_upper_bound(X_40,X_12))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(least_upper_bound(X_39,X_40),X_12)),X_12) ),[0,1],$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_12)))]]) ).
cnf(refute_0_1689,plain,
( greatest_lower_bound(X_12,least_upper_bound(least_upper_bound(X_39,X_40),X_12)) != X_12
| greatest_lower_bound(X_12,least_upper_bound(X_39,least_upper_bound(X_40,X_12))) = X_12 ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,X_40),X_12),least_upper_bound(X_39,least_upper_bound(X_40,X_12))) )],[refute_0_1687,refute_0_1688]) ).
cnf(refute_0_1690,plain,
greatest_lower_bound(X_12,least_upper_bound(X_39,least_upper_bound(X_40,X_12))) = X_12,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_12,least_upper_bound(least_upper_bound(X_39,X_40),X_12)),X_12) )],[refute_0_1684,refute_0_1689]) ).
cnf(refute_0_1691,plain,
greatest_lower_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,X_310))) = X_310,
inference(subst,[],[refute_0_1690:[bind(X_12,$fot(X_310))]]) ).
cnf(refute_0_1692,plain,
( greatest_lower_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,X_310))) != X_310
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(greatest_lower_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,X_310))),X_309)) != least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) = least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(greatest_lower_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,X_310))),X_309)),least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) ),[0,1,0],$fot(X_310)]]) ).
cnf(refute_0_1693,plain,
( least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(greatest_lower_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,X_310))),X_309)) != least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) = least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,X_310))),X_310) )],[refute_0_1691,refute_0_1692]) ).
cnf(refute_0_1694,plain,
least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) = least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(greatest_lower_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,X_310))),X_309)),least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) )],[refute_0_1683,refute_0_1693]) ).
cnf(refute_0_1695,plain,
least_upper_bound(least_upper_bound(X_40,X_310),X_309) = least_upper_bound(X_40,least_upper_bound(X_310,X_309)),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_40)),bind(Y,$fot(X_310)),bind(Z,$fot(X_309))]]) ).
cnf(refute_0_1696,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)) = least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)))]]) ).
cnf(refute_0_1697,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)) != least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309))
| least_upper_bound(least_upper_bound(X_40,X_310),X_309) != least_upper_bound(X_40,least_upper_bound(X_310,X_309))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)),least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309))) ),[1,1],$fot(least_upper_bound(X_40,least_upper_bound(X_310,X_309)))]]) ).
cnf(refute_0_1698,plain,
( least_upper_bound(least_upper_bound(X_40,X_310),X_309) != least_upper_bound(X_40,least_upper_bound(X_310,X_309))
| least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)),least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309))) )],[refute_0_1696,refute_0_1697]) ).
cnf(refute_0_1699,plain,
least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_40,X_310),X_309),least_upper_bound(X_40,least_upper_bound(X_310,X_309))) )],[refute_0_1695,refute_0_1698]) ).
cnf(refute_0_1700,plain,
least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) = least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)),
inference(subst,[],[refute_0_383:[bind(X,$fot(X_39)),bind(Y,$fot(least_upper_bound(X_40,X_310))),bind(Z,$fot(X_309))]]) ).
cnf(refute_0_1701,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)) != least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) != least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309))
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309))),bind(Y0,$fot(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)))),bind(Z0,$fot(least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))))]]) ).
cnf(refute_0_1702,plain,
( least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)) != least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309),least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309))) )],[refute_0_1700,refute_0_1701]) ).
cnf(refute_0_1703,plain,
least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_39,least_upper_bound(least_upper_bound(X_40,X_310),X_309)),least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) )],[refute_0_1699,refute_0_1702]) ).
cnf(refute_0_1704,plain,
least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) = least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)),
introduced(tautology,[refl,[$fot(least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)))]]) ).
cnf(refute_0_1705,plain,
( least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) != least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309))
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) != least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))
| least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) = least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)),least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309))) ),[1,1],$fot(least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))))]]) ).
cnf(refute_0_1706,plain,
( least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) != least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))
| least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) = least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)),least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309))) )],[refute_0_1704,refute_0_1705]) ).
cnf(refute_0_1707,plain,
least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) = least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309),least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) )],[refute_0_1703,refute_0_1706]) ).
cnf(refute_0_1708,plain,
least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) = least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)),
inference(subst,[],[refute_0_592:[bind(X_13,$fot(X_309)),bind(X_43,$fot(least_upper_bound(X_39,least_upper_bound(X_40,X_310)))),bind(X_44,$fot(X_310))]]) ).
cnf(refute_0_1709,plain,
( least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) != least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))))
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) != least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309))
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) = least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)))),bind(Y0,$fot(least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)))),bind(Z0,$fot(least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))))))]]) ).
cnf(refute_0_1710,plain,
( least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) != least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))))
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) = least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)),least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309))) )],[refute_0_1708,refute_0_1709]) ).
cnf(refute_0_1711,plain,
least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) = least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_310,least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)),least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))))) )],[refute_0_1707,refute_0_1710]) ).
cnf(refute_0_1712,plain,
( least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) != least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))))
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) != least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)
| least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) = least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)),least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) ),[0],$fot(least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))))]]) ).
cnf(refute_0_1713,plain,
( least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) != least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)
| least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) = least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)),least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))))) )],[refute_0_1711,refute_0_1712]) ).
cnf(refute_0_1714,plain,
( least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) != least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)
| least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309) != least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))
| least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))),least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309))]]) ).
cnf(refute_0_1715,plain,
( least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) != least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)
| least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309),least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) )],[refute_0_1703,refute_0_1714]) ).
cnf(refute_0_1716,plain,
( least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)) != least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)
| least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))),least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) )],[refute_0_1713,refute_0_1715]) ).
cnf(refute_0_1717,plain,
least_upper_bound(X_310,least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309)))) = least_upper_bound(X_39,least_upper_bound(X_40,least_upper_bound(X_310,X_309))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),least_upper_bound(X_310,X_309)),least_upper_bound(least_upper_bound(X_39,least_upper_bound(X_40,X_310)),X_309)) )],[refute_0_1694,refute_0_1716]) ).
cnf(refute_0_1718,plain,
least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) = least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))),
inference(subst,[],[refute_0_1717:[bind(X_309,$fot(Y)),bind(X_310,$fot(X_127)),bind(X_39,$fot(X_321)),bind(X_40,$fot(X_322))]]) ).
cnf(refute_0_1719,plain,
least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) = least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))),
introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))))]]) ).
cnf(refute_0_1720,plain,
( least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) != least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))))
| least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) != least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))
| least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) = least_upper_bound(Y,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))),least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))))) ),[1,1],$fot(least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))]]) ).
cnf(refute_0_1721,plain,
( least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) != least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))
| least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) = least_upper_bound(Y,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))),least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))))) )],[refute_0_1719,refute_0_1720]) ).
cnf(refute_0_1722,plain,
least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) = least_upper_bound(Y,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) )],[refute_0_1718,refute_0_1721]) ).
cnf(refute_0_1723,plain,
( least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) != least_upper_bound(Y,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))
| least_upper_bound(Y,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) != least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127)))
| least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) = least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))))),bind(Z0,$fot(least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127)))))]]) ).
cnf(refute_0_1724,plain,
( least_upper_bound(Y,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) != least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127)))
| least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) = least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))),least_upper_bound(Y,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) )],[refute_0_1722,refute_0_1723]) ).
cnf(refute_0_1725,plain,
least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) = least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))),least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127)))) )],[refute_0_1682,refute_0_1724]) ).
cnf(refute_0_1726,plain,
least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) = least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))),
inference(subst,[],[refute_0_383:[bind(X,$fot(Y)),bind(Y,$fot(X_127)),bind(Z,$fot(least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))))]]) ).
cnf(refute_0_1727,plain,
( least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) != least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127)))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) != least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) = least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))))),bind(Z0,$fot(least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127)))))]]) ).
cnf(refute_0_1728,plain,
( least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))) != least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127)))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) = least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))),least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))))) )],[refute_0_1726,refute_0_1727]) ).
cnf(refute_0_1729,plain,
least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) = least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))),
inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y))))),least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127)))) )],[refute_0_1725,refute_0_1728]) ).
cnf(refute_0_1730,plain,
( least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) != least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127)))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) != least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))
| least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) = least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))),least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))) ),[0],$fot(least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))))]]) ).
cnf(refute_0_1731,plain,
( least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) != least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))
| least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) = least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))),least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127)))) )],[refute_0_1729,refute_0_1730]) ).
cnf(refute_0_1732,plain,
least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322)) = least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322))),
inference(subst,[],[refute_0_383:[bind(X,$fot(Y)),bind(Y,$fot(X_127)),bind(Z,$fot(least_upper_bound(X_321,X_322)))]]) ).
cnf(refute_0_1733,plain,
( least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) != least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))
| least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322)) != least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322)))
| least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) = least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))),least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322)))) ),[0],$fot(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322)))]]) ).
cnf(refute_0_1734,plain,
( least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) != least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))
| least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) = least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322)),least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322)))) )],[refute_0_1732,refute_0_1733]) ).
cnf(refute_0_1735,plain,
( least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))) != least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))
| least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) = least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))),least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))) )],[refute_0_1731,refute_0_1734]) ).
cnf(refute_0_1736,plain,
least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) = least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,least_upper_bound(X_322,least_upper_bound(X_127,Y)))),least_upper_bound(least_upper_bound(Y,X_127),least_upper_bound(X_321,X_322))) )],[refute_0_1676,refute_0_1735]) ).
cnf(refute_0_1737,plain,
( least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) != least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322)))
| least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322))) = least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322)))))]]) ).
cnf(refute_0_1738,plain,
least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322))) = least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_321,least_upper_bound(Y,least_upper_bound(X_322,X_127))),least_upper_bound(Y,least_upper_bound(X_127,least_upper_bound(X_321,X_322)))) )],[refute_0_1736,refute_0_1737]) ).
cnf(refute_0_1739,plain,
least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) = least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))),
inference(subst,[],[refute_0_1738:[bind(Y,$fot(least_upper_bound(X_411,X_412))),bind(X_127,$fot(X_39)),bind(X_321,$fot(X_412)),bind(X_322,$fot(least_upper_bound(X_411,identity)))]]) ).
cnf(refute_0_1740,plain,
( least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) != least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))))),bind(Y0,$fot(least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))))),bind(Z0,$fot(least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))))]]) ).
cnf(refute_0_1741,plain,
( least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))),least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39)))) )],[refute_0_1739,refute_0_1740]) ).
cnf(refute_0_1742,plain,
least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) = least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_412,least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(least_upper_bound(X_411,identity),X_39))),least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) )],[refute_0_1669,refute_0_1741]) ).
cnf(refute_0_1743,plain,
( least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) != least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) != least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))
| least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) = least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))),least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))) ),[0],$fot(least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))))]]) ).
cnf(refute_0_1744,plain,
( least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) != least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))
| least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) = least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))),least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39)))) )],[refute_0_1742,refute_0_1743]) ).
cnf(refute_0_1745,plain,
least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity)) = least_upper_bound(identity,least_upper_bound(X_39,least_upper_bound(X_411,X_412))),
inference(subst,[],[refute_0_1621:[bind(X_277,$fot(X_39)),bind(X_409,$fot(least_upper_bound(X_411,X_412)))]]) ).
cnf(refute_0_1746,plain,
( least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) != least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))
| least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity)) != least_upper_bound(identity,least_upper_bound(X_39,least_upper_bound(X_411,X_412)))
| least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) = least_upper_bound(identity,least_upper_bound(X_39,least_upper_bound(X_411,X_412))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))),least_upper_bound(identity,least_upper_bound(X_39,least_upper_bound(X_411,X_412)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity)))]]) ).
cnf(refute_0_1747,plain,
( least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) != least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))
| least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) = least_upper_bound(identity,least_upper_bound(X_39,least_upper_bound(X_411,X_412))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity)),least_upper_bound(identity,least_upper_bound(X_39,least_upper_bound(X_411,X_412)))) )],[refute_0_1745,refute_0_1746]) ).
cnf(refute_0_1748,plain,
( least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))) != least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))
| least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) = least_upper_bound(identity,least_upper_bound(X_39,least_upper_bound(X_411,X_412))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))),least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))) )],[refute_0_1744,refute_0_1747]) ).
cnf(refute_0_1749,plain,
least_upper_bound(X_412,least_upper_bound(X_411,least_upper_bound(identity,X_39))) = least_upper_bound(identity,least_upper_bound(X_39,least_upper_bound(X_411,X_412))),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,least_upper_bound(X_412,least_upper_bound(X_411,identity)))),least_upper_bound(least_upper_bound(X_411,X_412),least_upper_bound(X_39,identity))) )],[refute_0_1644,refute_0_1748]) ).
cnf(refute_0_1750,plain,
least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))) = least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))),
inference(subst,[],[refute_0_1749:[bind(X_39,$fot(X_41)),bind(X_411,$fot(greatest_lower_bound(identity,inverse(X_442)))),bind(X_412,$fot(greatest_lower_bound(identity,X_442)))]]) ).
cnf(refute_0_1751,plain,
( least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))) != least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442))))
| least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))) != least_upper_bound(X_41,identity)
| least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))) = least_upper_bound(X_41,identity) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))))),bind(Z0,$fot(least_upper_bound(X_41,identity)))]]) ).
cnf(refute_0_1752,plain,
( least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))) != least_upper_bound(X_41,identity)
| least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))) = least_upper_bound(X_41,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))),least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442))))) )],[refute_0_1750,refute_0_1751]) ).
cnf(refute_0_1753,plain,
least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))) = least_upper_bound(X_41,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_41,least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(identity,X_442)))),least_upper_bound(X_41,identity)) )],[refute_0_1637,refute_0_1752]) ).
cnf(refute_0_1754,plain,
least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)) = least_upper_bound(least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288))),Z),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(greatest_lower_bound(identity,X_288))),bind(Y,$fot(greatest_lower_bound(identity,inverse(X_288))))]]) ).
cnf(refute_0_1755,plain,
multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)) = multiply(greatest_lower_bound(identity,X_80),least_upper_bound(identity,inverse(X_80))),
inference(subst,[],[refute_0_1227:[bind(X_132,$fot(X_80))]]) ).
cnf(refute_0_1756,plain,
( multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)) != multiply(greatest_lower_bound(identity,X_80),least_upper_bound(identity,inverse(X_80)))
| multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)) != least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80)))
| multiply(greatest_lower_bound(identity,X_80),least_upper_bound(identity,inverse(X_80))) = least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)),least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80)))) ),[0],$fot(multiply(greatest_lower_bound(identity,X_80),least_upper_bound(identity,inverse(X_80))))]]) ).
cnf(refute_0_1757,plain,
( multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)) != least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80)))
| multiply(greatest_lower_bound(identity,X_80),least_upper_bound(identity,inverse(X_80))) = least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)),multiply(greatest_lower_bound(identity,X_80),least_upper_bound(identity,inverse(X_80)))) )],[refute_0_1755,refute_0_1756]) ).
cnf(refute_0_1758,plain,
multiply(greatest_lower_bound(identity,X_80),least_upper_bound(identity,inverse(X_80))) = least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,inverse(X_80)),greatest_lower_bound(identity,X_80)),least_upper_bound(greatest_lower_bound(identity,X_80),greatest_lower_bound(identity,inverse(X_80)))) )],[refute_0_1218,refute_0_1757]) ).
cnf(refute_0_1759,plain,
multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))) = least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288))),
inference(subst,[],[refute_0_1758:[bind(X_80,$fot(X_288))]]) ).
cnf(refute_0_1760,plain,
( multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))) != least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288)))
| least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288))) = multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288)))))]]) ).
cnf(refute_0_1761,plain,
least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288))) = multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))),least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288)))) )],[refute_0_1759,refute_0_1760]) ).
cnf(refute_0_1762,plain,
( least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288))) != multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288)))
| least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)) != least_upper_bound(least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288))),Z)
| least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)) = least_upper_bound(multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))),Z) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)),least_upper_bound(least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288))),Z)) ),[1,0],$fot(multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))))]]) ).
cnf(refute_0_1763,plain,
( least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)) != least_upper_bound(least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288))),Z)
| least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)) = least_upper_bound(multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))),Z) ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288))),multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288)))) )],[refute_0_1761,refute_0_1762]) ).
cnf(refute_0_1764,plain,
least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)) = least_upper_bound(multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))),Z),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)),least_upper_bound(least_upper_bound(greatest_lower_bound(identity,X_288),greatest_lower_bound(identity,inverse(X_288))),Z)) )],[refute_0_1754,refute_0_1763]) ).
cnf(refute_0_1765,plain,
( least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)) != least_upper_bound(multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))),Z)
| least_upper_bound(multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))),Z) = least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)))),bind(Y0,$fot(least_upper_bound(multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))),Z)))]]) ).
cnf(refute_0_1766,plain,
least_upper_bound(multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))),Z) = least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_288),least_upper_bound(greatest_lower_bound(identity,inverse(X_288)),Z)),least_upper_bound(multiply(greatest_lower_bound(identity,X_288),least_upper_bound(identity,inverse(X_288))),Z)) )],[refute_0_1764,refute_0_1765]) ).
cnf(refute_0_1767,plain,
least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) = least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))),
inference(subst,[],[refute_0_1766:[bind(Z,$fot(least_upper_bound(identity,X_41))),bind(X_288,$fot(X_442))]]) ).
cnf(refute_0_1768,plain,
( least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) != least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41)))
| least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))) != least_upper_bound(X_41,identity)
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) = least_upper_bound(X_41,identity) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))))),bind(Z0,$fot(least_upper_bound(X_41,identity)))]]) ).
cnf(refute_0_1769,plain,
( least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))) != least_upper_bound(X_41,identity)
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) = least_upper_bound(X_41,identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)),least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41)))) )],[refute_0_1767,refute_0_1768]) ).
cnf(refute_0_1770,plain,
least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) = least_upper_bound(X_41,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),least_upper_bound(identity,X_41))),least_upper_bound(X_41,identity)) )],[refute_0_1753,refute_0_1769]) ).
cnf(refute_0_1771,plain,
( least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) != least_upper_bound(X_41,identity)
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) != least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)
| least_upper_bound(X_41,identity) = least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)),least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)) ),[0],$fot(least_upper_bound(X_41,identity))]]) ).
cnf(refute_0_1772,plain,
( least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) != least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)
| least_upper_bound(X_41,identity) = least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)),least_upper_bound(X_41,identity)) )],[refute_0_1770,refute_0_1771]) ).
cnf(refute_0_1773,plain,
least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41) = least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41)),
inference(subst,[],[refute_0_1766:[bind(Z,$fot(X_41)),bind(X_288,$fot(X_442))]]) ).
cnf(refute_0_1774,plain,
( least_upper_bound(X_41,identity) != least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41) != least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41))
| least_upper_bound(X_41,identity) = least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_41,identity),least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41))) ),[0],$fot(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41))]]) ).
cnf(refute_0_1775,plain,
( least_upper_bound(X_41,identity) != least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)
| least_upper_bound(X_41,identity) = least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41),least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41))) )],[refute_0_1773,refute_0_1774]) ).
cnf(refute_0_1776,plain,
( least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)) != least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)
| least_upper_bound(X_41,identity) = least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,identity),least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)) )],[refute_0_1772,refute_0_1775]) ).
cnf(refute_0_1777,plain,
least_upper_bound(X_41,identity) = least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41)),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),least_upper_bound(identity,X_41)),least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),X_41)) )],[refute_0_1482,refute_0_1776]) ).
cnf(refute_0_1778,plain,
( least_upper_bound(X_41,identity) != least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41))
| least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41)) = least_upper_bound(X_41,identity) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(least_upper_bound(X_41,identity))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41))))]]) ).
cnf(refute_0_1779,plain,
least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41)) = least_upper_bound(X_41,identity),
inference(resolve,[$cnf( $equal(least_upper_bound(X_41,identity),least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),X_41))) )],[refute_0_1777,refute_0_1778]) ).
cnf(refute_0_1780,plain,
least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))) = least_upper_bound(greatest_lower_bound(X_36,identity),identity),
inference(subst,[],[refute_0_1779:[bind(X_41,$fot(greatest_lower_bound(X_36,identity)))]]) ).
cnf(refute_0_1781,plain,
( least_upper_bound(greatest_lower_bound(X_36,identity),identity) != identity
| least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))) != least_upper_bound(greatest_lower_bound(X_36,identity),identity)
| least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))) = identity ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(X_36,identity),identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1782,plain,
( least_upper_bound(greatest_lower_bound(X_36,identity),identity) != identity
| least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))),least_upper_bound(greatest_lower_bound(X_36,identity),identity)) )],[refute_0_1780,refute_0_1781]) ).
cnf(refute_0_1783,plain,
least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(X_36,identity),identity),identity) )],[refute_0_1473,refute_0_1782]) ).
cnf(refute_0_1784,plain,
least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)) = least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))),
inference(subst,[],[refute_0_1766:[bind(Z,$fot(greatest_lower_bound(X_36,identity))),bind(X_288,$fot(X_442))]]) ).
cnf(refute_0_1785,plain,
( least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)) != least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity)))
| least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))) != identity
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)) = identity ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)))),bind(Y0,$fot(least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_1786,plain,
( least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))) != identity
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)) = identity ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)),least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity)))) )],[refute_0_1784,refute_0_1785]) ).
cnf(refute_0_1787,plain,
least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)) = identity,
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(identity,X_442),least_upper_bound(greatest_lower_bound(identity,inverse(X_442)),greatest_lower_bound(X_36,identity))),identity) )],[refute_0_1783,refute_0_1786]) ).
cnf(refute_0_1788,plain,
( least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)) != multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))
| least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)) != identity
| identity = multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)),multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_1789,plain,
( least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)) != multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))
| identity = multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)),identity) )],[refute_0_1787,refute_0_1788]) ).
cnf(refute_0_1790,plain,
identity = multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))),greatest_lower_bound(X_36,identity)),multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))) )],[refute_0_1452,refute_0_1789]) ).
cnf(refute_0_1791,plain,
( identity != multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))
| multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))) = identity ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))))]]) ).
cnf(refute_0_1792,plain,
multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442))) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(greatest_lower_bound(identity,X_442),least_upper_bound(identity,inverse(X_442)))) )],[refute_0_1790,refute_0_1791]) ).
cnf(refute_0_1793,plain,
multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))) = identity,
inference(subst,[],[refute_0_1792:[bind(X_442,$fot(X_223))]]) ).
cnf(refute_0_1794,plain,
multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))),
introduced(tautology,[refl,[$fot(multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))))]]) ).
cnf(refute_0_1795,plain,
( multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))) != identity
| multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) != multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))))
| multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = multiply(inverse(least_upper_bound(X_223,identity)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))),multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_1796,plain,
( multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))) != identity
| multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = multiply(inverse(least_upper_bound(X_223,identity)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))),multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))))) )],[refute_0_1794,refute_0_1795]) ).
cnf(refute_0_1797,plain,
multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = multiply(inverse(least_upper_bound(X_223,identity)),identity),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223))),identity) )],[refute_0_1793,refute_0_1796]) ).
cnf(refute_0_1798,plain,
( multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) != multiply(inverse(least_upper_bound(X_223,identity)),identity)
| multiply(inverse(least_upper_bound(X_223,identity)),identity) != inverse(least_upper_bound(X_223,identity))
| multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = inverse(least_upper_bound(X_223,identity)) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))))),bind(Y0,$fot(multiply(inverse(least_upper_bound(X_223,identity)),identity))),bind(Z0,$fot(inverse(least_upper_bound(X_223,identity))))]]) ).
cnf(refute_0_1799,plain,
( multiply(inverse(least_upper_bound(X_223,identity)),identity) != inverse(least_upper_bound(X_223,identity))
| multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = inverse(least_upper_bound(X_223,identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))),multiply(inverse(least_upper_bound(X_223,identity)),identity)) )],[refute_0_1797,refute_0_1798]) ).
cnf(refute_0_1800,plain,
multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) = inverse(least_upper_bound(X_223,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_223,identity)),identity),inverse(least_upper_bound(X_223,identity))) )],[refute_0_1257,refute_0_1799]) ).
cnf(refute_0_1801,plain,
( multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) != greatest_lower_bound(identity,inverse(X_223))
| multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) != inverse(least_upper_bound(X_223,identity))
| inverse(least_upper_bound(X_223,identity)) = greatest_lower_bound(identity,inverse(X_223)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))),greatest_lower_bound(identity,inverse(X_223))) ),[0],$fot(inverse(least_upper_bound(X_223,identity)))]]) ).
cnf(refute_0_1802,plain,
( multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))) != greatest_lower_bound(identity,inverse(X_223))
| inverse(least_upper_bound(X_223,identity)) = greatest_lower_bound(identity,inverse(X_223)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))),inverse(least_upper_bound(X_223,identity))) )],[refute_0_1800,refute_0_1801]) ).
cnf(refute_0_1803,plain,
inverse(least_upper_bound(X_223,identity)) = greatest_lower_bound(identity,inverse(X_223)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_223,identity)),multiply(greatest_lower_bound(identity,X_223),least_upper_bound(identity,inverse(X_223)))),greatest_lower_bound(identity,inverse(X_223))) )],[refute_0_1256,refute_0_1802]) ).
cnf(refute_0_1804,plain,
( inverse(least_upper_bound(X_223,identity)) != greatest_lower_bound(identity,inverse(X_223))
| greatest_lower_bound(identity,inverse(X_223)) = inverse(least_upper_bound(X_223,identity)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(inverse(least_upper_bound(X_223,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_223))))]]) ).
cnf(refute_0_1805,plain,
greatest_lower_bound(identity,inverse(X_223)) = inverse(least_upper_bound(X_223,identity)),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_223,identity)),greatest_lower_bound(identity,inverse(X_223))) )],[refute_0_1803,refute_0_1804]) ).
cnf(refute_0_1806,plain,
greatest_lower_bound(identity,inverse(X_73)) = inverse(least_upper_bound(X_73,identity)),
inference(subst,[],[refute_0_1805:[bind(X_223,$fot(X_73))]]) ).
cnf(refute_0_1807,plain,
inverse(greatest_lower_bound(identity,inverse(X_73))) = inverse(greatest_lower_bound(identity,inverse(X_73))),
introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(identity,inverse(X_73))))]]) ).
cnf(refute_0_1808,plain,
( greatest_lower_bound(identity,inverse(X_73)) != inverse(least_upper_bound(X_73,identity))
| inverse(greatest_lower_bound(identity,inverse(X_73))) != inverse(greatest_lower_bound(identity,inverse(X_73)))
| inverse(greatest_lower_bound(identity,inverse(X_73))) = inverse(inverse(least_upper_bound(X_73,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_73))),inverse(greatest_lower_bound(identity,inverse(X_73)))) ),[1,0],$fot(inverse(least_upper_bound(X_73,identity)))]]) ).
cnf(refute_0_1809,plain,
( greatest_lower_bound(identity,inverse(X_73)) != inverse(least_upper_bound(X_73,identity))
| inverse(greatest_lower_bound(identity,inverse(X_73))) = inverse(inverse(least_upper_bound(X_73,identity))) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_73))),inverse(greatest_lower_bound(identity,inverse(X_73)))) )],[refute_0_1807,refute_0_1808]) ).
cnf(refute_0_1810,plain,
inverse(greatest_lower_bound(identity,inverse(X_73))) = inverse(inverse(least_upper_bound(X_73,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_73)),inverse(least_upper_bound(X_73,identity))) )],[refute_0_1806,refute_0_1809]) ).
cnf(refute_0_1811,plain,
( inverse(greatest_lower_bound(identity,inverse(X_73))) != inverse(inverse(least_upper_bound(X_73,identity)))
| inverse(inverse(least_upper_bound(X_73,identity))) != least_upper_bound(X_73,identity)
| inverse(greatest_lower_bound(identity,inverse(X_73))) = least_upper_bound(X_73,identity) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X_73))))),bind(Y0,$fot(inverse(inverse(least_upper_bound(X_73,identity))))),bind(Z0,$fot(least_upper_bound(X_73,identity)))]]) ).
cnf(refute_0_1812,plain,
( inverse(inverse(least_upper_bound(X_73,identity))) != least_upper_bound(X_73,identity)
| inverse(greatest_lower_bound(identity,inverse(X_73))) = least_upper_bound(X_73,identity) ),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_73))),inverse(inverse(least_upper_bound(X_73,identity)))) )],[refute_0_1810,refute_0_1811]) ).
cnf(refute_0_1813,plain,
inverse(greatest_lower_bound(identity,inverse(X_73))) = least_upper_bound(X_73,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_73,identity))),least_upper_bound(X_73,identity)) )],[refute_0_738,refute_0_1812]) ).
cnf(refute_0_1814,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))),
introduced(tautology,[refl,[$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))))]]) ).
cnf(refute_0_1815,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73))))
| inverse(greatest_lower_bound(identity,inverse(X_73))) != least_upper_bound(X_73,identity)
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),least_upper_bound(X_73,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73))))) ),[1,1],$fot(least_upper_bound(X_73,identity))]]) ).
cnf(refute_0_1816,plain,
( inverse(greatest_lower_bound(identity,inverse(X_73))) != least_upper_bound(X_73,identity)
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),least_upper_bound(X_73,identity)) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73))))) )],[refute_0_1814,refute_0_1815]) ).
cnf(refute_0_1817,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),least_upper_bound(X_73,identity)),
inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X_73))),least_upper_bound(X_73,identity)) )],[refute_0_1813,refute_0_1816]) ).
cnf(refute_0_1818,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),least_upper_bound(X_73,identity))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),least_upper_bound(X_73,identity)) != greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity)))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) = greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity))) ),
inference(subst,[],[refute_0_116:[bind(X0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))))),bind(Y0,$fot(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),least_upper_bound(X_73,identity)))),bind(Z0,$fot(greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity)))))]]) ).
cnf(refute_0_1819,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),least_upper_bound(X_73,identity)) != greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity)))
| greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) = greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))),greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),least_upper_bound(X_73,identity))) )],[refute_0_1817,refute_0_1818]) ).
cnf(refute_0_1820,plain,
greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) = greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity))),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),least_upper_bound(X_73,identity)),greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity)))) )],[refute_0_726,refute_0_1819]) ).
cnf(refute_0_1821,plain,
( greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))) != greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity)))
| identity != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73))))
| identity = greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73))))) ),[1],$fot(greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity))))]]) ).
cnf(refute_0_1822,plain,
( identity != greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73))))
| identity = greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity))) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73)))),greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity)))) )],[refute_0_1820,refute_0_1821]) ).
cnf(refute_0_1823,plain,
identity = greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity))),
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(inverse(greatest_lower_bound(identity,X_73)),inverse(greatest_lower_bound(identity,inverse(X_73))))) )],[refute_0_189,refute_0_1822]) ).
cnf(refute_0_1824,plain,
( identity != greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity)))
| greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity))) = identity ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(identity)),bind(Y0,$fot(greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity)))))]]) ).
cnf(refute_0_1825,plain,
greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity))) = identity,
inference(resolve,[$cnf( $equal(identity,greatest_lower_bound(least_upper_bound(X_73,identity),inverse(greatest_lower_bound(X_73,identity)))) )],[refute_0_1823,refute_0_1824]) ).
cnf(refute_0_1826,plain,
greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = identity,
inference(subst,[],[refute_0_1825:[bind(X_73,$fot(a))]]) ).
cnf(refute_0_1827,plain,
( greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != identity
| identity != identity
| greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),identity) ),[0],$fot(identity)]]) ).
cnf(refute_0_1828,plain,
( identity != identity
| greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),identity) )],[refute_0_1826,refute_0_1827]) ).
cnf(refute_0_1829,plain,
identity != identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),identity) )],[refute_0_1828,prove_p20]) ).
cnf(refute_0_1830,plain,
identity = identity,
introduced(tautology,[refl,[$fot(identity)]]) ).
cnf(refute_0_1831,plain,
$false,
inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_1830,refute_0_1829]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP183-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 12:55:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 28.43/28.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.43/28.69
% 28.43/28.69 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.74/28.92
%------------------------------------------------------------------------------